The document summarizes the development of effective cooling schemes for gas turbine blades based on computer simulation. It describes:
1) The development of mathematical models and numerical methods (BIEM and FDM) to accurately calculate the temperature fields of turbine blades with complex cooling channel configurations, taking into account various heat transfer factors.
2) The application of boundary integral equation methods (BIEM) to solve the boundary value problems describing the temperature distributions, which involves discretizing the boundary into elements and setting up a system of linear algebraic equations relating the unknown boundary temperatures.
3) The extension of the techniques to model transient/non-steady state heat transfer problems by using a substitution to reduce the problem to a stationary boundary value problem.
Natural convection heat transfer flow visualization of perforated fin arrays ...eSAT Journals
Abstract
The present paper reports, the validation of results of modeling and simulation in CFD by experiment on the fluid flow and heat
transfer characteristics of a fin arrays with lateral circular perforation and its external dimensionally equivalent solid fin arrays
equipped on horizontal flat surface a problem of natural convection. The simulation is carried out using the fluid flow (CFX)
workbench of ANSYS 12.0. In this study, results shows that formation of the stagnant layer around the solid fin array which slowdowns
the heat dissipation rate. Increase in the fluid flow movement around the fin results increase in the heat dissipation rate. It can
be achieved by adding perforation to the fins. Natural convection is a buoyancy driven phenomenon; the state of the art of CFX was
used to carry the study of fluid flow separation and velocity field over a fin array. New designed perforated fins have an improvement
in average Nusselt number, over its external dimensionally equivalent solid fin arrays.
Keywords: CFD simulation, perforated fins, Natural convection, Heat sink, Nusselt number, Flow Visualization
Evaluating mathematical heat transfer effectiveness equations using cfd techn...aeijjournal
Mathematical heat transfer equations for finned double pipe heat exchangers based on experimental work carried out in the 1970s can be programmed in a spreadsheet for repetitive use. Thus avoiding CFD analysis which can be time consuming and costly. However, it is important that such mathematical equations be evaluated for their accuracy. This paper uses CFD methods in evaluating the accuracy of mathematical equations. Several models were created with varying; geometry, flue gas entry temperature,
and flow rates. The analysis should provide designers and manufacturers a judgment on the expected level
of accuracy when using mathematical modelling methodology. This paper simultaneously identifies best
practices in carrying out such CFD analysis
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes a study on assessing the thermal performance of semicircular fins under forced air convection and its application to air preheaters. The study finds that semicircular fins have greater thermal efficiency compared to circular fins of the same volume due to their larger surface area. Mathematical models are developed to analyze heat transfer in the fins and an air preheater. Various parameters like number of fins, pipe size, air velocity and temperature are examined. The results show that larger preheat can be achieved using semicircular fins, providing potential for higher energy efficiency.
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Publishing House
The document experimentally studies heat transfer augmentation through various dimpled surface geometries under natural convection. It tests aluminum and copper plates with square, circular, and triangular dimple shapes. It finds that heat transfer rate, coefficient, and Nusselt number all increase for dimpled surfaces compared to plain surfaces, and are highest for triangular dimples with the apex facing inlet air flow. Heat transfer generally increases more for aluminum with square and triangular base dimples, while copper performs better with circular and triangular apex dimples. The study concludes dimples enhance heat transfer under natural convection compared to plain surfaces.
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Journals
Abstract The prime objective of present work is to study experimentally the heat transfer augmentation through various geometries of dimpled surfaces in longitudinal and lateral directions. In this paper horizontal rectangular plates of copper and aluminum with different dimpled geometries (like square, circular and triangular) for in-line arrangements were studied in natural convection with steady laminar external flow condition. The various parameters considered for study are Nusselt number, heat transfer coefficient and heat transfer rate for a constant Prandtl number (0.7) and Grashof number (104-107).It has been found that the heat transfer coefficient and heat transfer rate increases for various dimpled surfaces as compared to plane surface. It has been also found that the heat transfer coefficient and heat transfer rate increases along longitudinal direction as compared to lateral direction. And it is seen that heat transfer rate is maximum for triangular shape dimple when the apex of triangle is faced towards inlet of air flow Finally it is concluded that heat transfer enhancement takes place along the dimpled surface
This document summarizes the numerical analysis of different parallel plate heat sink designs for electronic cooling applications. It discusses:
1) The simulation of a baseline heat sink case and a shielded heat sink within a chimney structure to compare heat transfer performance. The shielded case showed a 50% improvement in heat transfer.
2) The addition of a cross-cut modification to the heat sink, which was modeled using two turbulence models. This cross-cut design showed an average 17% increase in heat transfer compared to the shielded straight fin case.
3) The modeling of the cross-cut heat sink within a pumping system to induce forced convection. A pressure difference between the cross-cut and outlet was
This document summarizes a student project analyzing the effectiveness of different fin designs on a CPU heatsink. It includes the design of a base heatsink model with 30 fins and details simulations varying the number of fins, fin height, and rotation speed. The results show that increasing the number of fins from 30 to 50 lowers the maximum surface temperature by 5.4°C, while further increases do not impact temperature as much.
Natural convection heat transfer flow visualization of perforated fin arrays ...eSAT Journals
Abstract
The present paper reports, the validation of results of modeling and simulation in CFD by experiment on the fluid flow and heat
transfer characteristics of a fin arrays with lateral circular perforation and its external dimensionally equivalent solid fin arrays
equipped on horizontal flat surface a problem of natural convection. The simulation is carried out using the fluid flow (CFX)
workbench of ANSYS 12.0. In this study, results shows that formation of the stagnant layer around the solid fin array which slowdowns
the heat dissipation rate. Increase in the fluid flow movement around the fin results increase in the heat dissipation rate. It can
be achieved by adding perforation to the fins. Natural convection is a buoyancy driven phenomenon; the state of the art of CFX was
used to carry the study of fluid flow separation and velocity field over a fin array. New designed perforated fins have an improvement
in average Nusselt number, over its external dimensionally equivalent solid fin arrays.
Keywords: CFD simulation, perforated fins, Natural convection, Heat sink, Nusselt number, Flow Visualization
Evaluating mathematical heat transfer effectiveness equations using cfd techn...aeijjournal
Mathematical heat transfer equations for finned double pipe heat exchangers based on experimental work carried out in the 1970s can be programmed in a spreadsheet for repetitive use. Thus avoiding CFD analysis which can be time consuming and costly. However, it is important that such mathematical equations be evaluated for their accuracy. This paper uses CFD methods in evaluating the accuracy of mathematical equations. Several models were created with varying; geometry, flue gas entry temperature,
and flow rates. The analysis should provide designers and manufacturers a judgment on the expected level
of accuracy when using mathematical modelling methodology. This paper simultaneously identifies best
practices in carrying out such CFD analysis
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes a study on assessing the thermal performance of semicircular fins under forced air convection and its application to air preheaters. The study finds that semicircular fins have greater thermal efficiency compared to circular fins of the same volume due to their larger surface area. Mathematical models are developed to analyze heat transfer in the fins and an air preheater. Various parameters like number of fins, pipe size, air velocity and temperature are examined. The results show that larger preheat can be achieved using semicircular fins, providing potential for higher energy efficiency.
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Publishing House
The document experimentally studies heat transfer augmentation through various dimpled surface geometries under natural convection. It tests aluminum and copper plates with square, circular, and triangular dimple shapes. It finds that heat transfer rate, coefficient, and Nusselt number all increase for dimpled surfaces compared to plain surfaces, and are highest for triangular dimples with the apex facing inlet air flow. Heat transfer generally increases more for aluminum with square and triangular base dimples, while copper performs better with circular and triangular apex dimples. The study concludes dimples enhance heat transfer under natural convection compared to plain surfaces.
Heat transfer augmentation in different geometries of dimpled surface under n...eSAT Journals
Abstract The prime objective of present work is to study experimentally the heat transfer augmentation through various geometries of dimpled surfaces in longitudinal and lateral directions. In this paper horizontal rectangular plates of copper and aluminum with different dimpled geometries (like square, circular and triangular) for in-line arrangements were studied in natural convection with steady laminar external flow condition. The various parameters considered for study are Nusselt number, heat transfer coefficient and heat transfer rate for a constant Prandtl number (0.7) and Grashof number (104-107).It has been found that the heat transfer coefficient and heat transfer rate increases for various dimpled surfaces as compared to plane surface. It has been also found that the heat transfer coefficient and heat transfer rate increases along longitudinal direction as compared to lateral direction. And it is seen that heat transfer rate is maximum for triangular shape dimple when the apex of triangle is faced towards inlet of air flow Finally it is concluded that heat transfer enhancement takes place along the dimpled surface
This document summarizes the numerical analysis of different parallel plate heat sink designs for electronic cooling applications. It discusses:
1) The simulation of a baseline heat sink case and a shielded heat sink within a chimney structure to compare heat transfer performance. The shielded case showed a 50% improvement in heat transfer.
2) The addition of a cross-cut modification to the heat sink, which was modeled using two turbulence models. This cross-cut design showed an average 17% increase in heat transfer compared to the shielded straight fin case.
3) The modeling of the cross-cut heat sink within a pumping system to induce forced convection. A pressure difference between the cross-cut and outlet was
This document summarizes a student project analyzing the effectiveness of different fin designs on a CPU heatsink. It includes the design of a base heatsink model with 30 fins and details simulations varying the number of fins, fin height, and rotation speed. The results show that increasing the number of fins from 30 to 50 lowers the maximum surface temperature by 5.4°C, while further increases do not impact temperature as much.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
The document compares the thermal performance of flat plate fins and inline strip fins heat sinks. It presents Nusselt number correlations from literature to model the convective heat transfer from the fins. The correlations consider heat transfer from the fins but not the bare heat sink base. The study includes an estimate of heat transfer from the base, providing a more realistic thermal resistance calculation. Results show inline strip fins have higher heat transfer coefficients that compensate for their reduced area, yielding lower thermal resistances than plate fins. Considering heat transfer from the base provides an even lower thermal resistance for both heat sink designs.
Numerical Analysis of Inverted Notched Fin Array Using Natural ConvectionIOSR Journals
Abstract:Geometry and orientation plays an important role in natural convection heat transfer. For
horizontal rectangular fin array a chimney flow pattern is developed due to density difference. This flow
pattern creates a stagnant zone near central bottom region. That portion does not contribute much towards
heat dissipation. This area is removed from fins and they became inverted notched fins. This modified geometry
reduces material cost, material weight without hampering heat transfer rate. Numerical models are prepaid to
investigate heat transfer characteristics in plane fins and inverted notched fins. This investigation is also
extended over different types of notches and their effectiveness comparison. Fin spacing, fin height, fin length,
heater input, percentage of area removed in the form of inverted notch are the parameters under
consideration. This analysis is done numerically using CFD package (Fluent). It is found that the heat transfer
coefficient of inverted notch fin array is 25% to 35% higher as compared with normal fin array. Also we found
that the triangular shape notch gives better result than trapezoidal and rectangular shape notch.
Key words: Inverted Notched Fin, Chimney Flow, Natural Convection, Heat transfer coefficient enhancement
EXPERIMENTAL STUDY OF HEAT TRANSFER FROM PLATE FIN ARRAY IN MIXED CONVECTION ...ijiert bestjournal
The document presents an experimental study on mixed convection heat transfer from plate fin arrays. Experiments were conducted on 9 plate fins attached to a 150mm by 150mm aluminum base plate. Temperature measurements were taken at varying fan velocities and input powers to determine heat transfer coefficients and relationships between parameters like Nusselt number, Reynolds number, and Grashof number. Key findings included that plate fins provided better heat transfer performance than solid pins, and the dimensionless parameter Gr/Re2 could be used to identify the mixed convection heat transfer region.
Cfd Simulation and Experimentalverification of Air Flow through Heated PipeIOSR Journals
The aim of this work is to validate the Dittus-Boelter equation by experimental,correlation and Simulation method. It used to find the value of heat transfer coefficient ‘h’ for turbulent flow in many fluid transfer systems. This work discusses how the Dittus-Boelter equation is applied to the problem of circular pipe. In CFD simulation ICEM CFD for modeling and CFX13 for analysis are used. Results of CFD simulation will be obtained by CFD-POST. Here heat transfer coefficient value is compared by correlations,experiment and CFD simulations, finally the aim of this work is to validate Dittus-Boelter equation.
IRJET-Enhancing the Performance of Hybrid Microgrid using non Isolated Single...IRJET Journal
This document analyzes heat transfer in a light passenger car radiator with various geometrical configurations using computational fluid dynamics (CFD). It studies a staggered fin-and-tube radiator with circular and oval tubes. The radiator is modeled and analyzed in FLUENT to obtain velocity, temperature, and pressure contours. Oval tubes are found to improve heat transfer compared to circular tubes. Specifically, oval tube configurations reduce temperature differences between the tubes and air, indicating more efficient heat absorption. While circular tubes show higher temperatures, oval tube designs enhance convection and lower outlet temperatures. In conclusion, varying the tube shape geometrically through oval designs improves the radiator's thermal performance.
Computational Analysis of Heat sink or Extended SurfaceIRJET Journal
This document summarizes a study on the computational analysis of heat sinks using finite element analysis. Heat sinks with different fin configurations were modeled and analyzed using ANSYS Fluent software to evaluate heat transfer characteristics. The results were validated by comparing with previous studies and analytical solutions. Key findings include that increasing the number of fins and base-to-ambient temperature difference leads to higher convective heat transfer. An optimum fin spacing was identified that balances heat transfer and pressure drop, and this agreed with results from other studies. In conclusion, finite element analysis was found to be an effective method for evaluating heat transfer in heat sinks with different parameters.
Validation of Results of Analytical Calculation of Steady State Heat Transfer...IRJET Journal
The document summarizes the analytical calculation and ANSYS simulation of steady state heat transfer in a nuclear fuel element. It presents the analytical solution to the heat conduction equations and plots the temperature profile. The simulation results for temperature, heat flux, and thermal gradient contours along with their corresponding graphs are also presented. Comparison shows that the analytical and simulation results match, validating the analytical model. Observation of boundary effects on axial thermal properties is also noted.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document summarizes an experimental study on jet impingement cooling of a ribbed surface with holes. The researchers varied parameters like heat flux, nozzle-to-plate distance ratio (H/d ratio), and Reynolds number. They measured temperatures at different locations and calculated heat transfer coefficients and Nusselt numbers. Key findings include that heat transfer increased with decreasing H/d ratio and increasing heat flux. Nusselt numbers generally increased with Reynolds number and heat flux. The presence of holes and enclosure affected flow patterns and temperature readings.
International Journal of Engineering Research and Applications (IJERA) aims to cover the latest outstanding developments in the field of all Engineering Technologies & science.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
This document summarizes a study that uses computational fluid dynamics (CFD) to analyze the flow and heat transfer characteristics of different elliptical pin fin heat sink configurations. The study aims to examine the effects of elliptical pin fin design parameters on heat sink performance. CFD simulations are conducted using ANSYS Fluent software to compute the thermal resistance, heat transfer coefficient, and surface Nusselt number of plate fin and elliptical pin fin heat sinks. Results show that the elliptical pin fin heat sink has better heat transfer performance than the plate fin heat sink. Simulation results for thermal resistance and pressure drop are validated against experimental data from previous studies.
Analysis of Coiled-Tube Heat Exchangers to Improve Heat Transfer Rate With Sp...IJMER
Steady heat transfer enhancement has been studied in helically coiled-tube heat exchangers. The outer side of the wall of the heat exchanger contains a helical corrugation which makes a helical rib on the inner side of the tube wall to induce additional swirling motion of fluid particles. Numerical calculations have been carried out to examine different geometrical parameters and the impact of flow and thermal boundary conditions for the heat transfer rate in laminar and transitional flow regimes. Calculated results have been compared to existing empirical formula and experimental tests to investigate the validity of the numerical results in case of common helical tube heat exchanger and additionally results of the numerical computation of corrugated straight tubes for laminar and transition flow have been validated with experimental tests available in the literature. Comparison of the flow and temperature fields in case of common helical tube and the coil with spirally corrugated wall configuration are discussed. Heat exchanger coils with helically corrugated wall configuration show 80–100% increase for the inner side heat transfer rate due to the additionally developed swirling motion while the relative pressure drop is 10–600% larger compared to the common helically coiled heat exchangers. New empirical Co-relation has been proposed for the fully developed inner side heat transfer prediction in case of helically corrugated wall configuration.
Experimental Investigation of Natural Convection Heat Transfer Enhancement fr...IRJET Journal
This document describes an experimental investigation of natural convection heat transfer from rectangular fin arrays with combinations of V-notches and perforations. Four fin array configurations were tested: one without notches or perforations (un-notched), and three with different combinations of V-notches and perforations removing different percentages of the fin area. The fin arrays were heated to different temperatures and the resulting heat transfer coefficients were measured and compared. The results showed that the combination of V-notches and perforations both increased the surface area and the turbulence near the fins, allowing more air contact and higher heat transfer coefficients compared to the un-notched fins. Among the configurations tested, the fin array with 20% of its area removed
This document discusses cold-junction corrections that must be applied when thermocouples are calibrated with the cold junction at a standard reference temperature like 0°C, but are then used with the cold junction at the temperature of the room. It presents three forms for the cold-junction correction and evaluates their accuracy. The preferred Form III correction multiplies the cold-junction temperature by the ratio of the mean slope of the calibration curve from 0°C to the cold-junction temperature, and the slope at the observed temperature. For typical thermocouples, this correction is accurate to within the precision of pyrometric measurements if the cold junction is below 50°C.
JIMEC Thermal modeling and Simulation of HX Conference PaperAhmed Sohail Izhar
1) The document describes a thermal modeling and simulation of an industrial shell and tube heat exchanger used to cool raw natural gas.
2) A thermal model was developed using the effectiveness-NTU method to determine the required heat transfer area and estimate the tube-side and shell-side heat transfer coefficients.
3) The results of the model showed that a heat transfer area of about 1132 m2 is required to provide a thermal duty of 1.4 MW, with tube-side and shell-side heat transfer coefficients of 950 W/m2K and 495 W/m2K respectively.
A practical approach to design and optimization of single phase liquid to liq...iaemedu
The document describes the design and optimization of a shell and tube heat exchanger. It presents a method based on Tinker's approach that incorporates modifications from Kern and Kakac. A 17-step thermal design procedure is outlined that involves sizing the heat exchanger dimensions and components through an iterative process to meet a specified heat load. A computer program was developed to automate the calculations and optimize the design in a more efficient manner than manual calculations. The program allows the user to input parameters and obtain an optimized design solution.
This document describes mathematical models for simulating the temperature fields of gas turbine blades during convective cooling. It presents boundary integral equation methods (BIEM) and finite difference methods (FDM) for calculating the stationary and quasi-stationary temperature distribution on a blade profile with radial cooling channels. The BIEM approach formulates the problem as a system of boundary integral equations involving temperature values and heat transfer coefficients on the blade surface and cooling channel boundaries. Numerical methods are developed to solve these equations, including discrete logarithmic potential operators and non-uniform surface discretizations. The reliability of the proposed methods is confirmed through computational and experimental analysis of heat transfer for a gas turbine nozzle blade.
This document summarizes a study on modeling and simulating gas turbine cooled blades. It develops mathematical models and numerical methods to calculate the stationary and quasi-stationary temperature fields of a blade profile part with convective cooling. It considers the heat conduction equation and boundary conditions for the problem. It then outlines the following key points:
1) It uses the Boundary Integral Equation Method (BIEM) and Finite Difference Method (FDM) combination to solve the temperature field calculation problem.
2) It develops effective quadrature processes to evaluate singular integral operators in the boundary integral equations.
3) It extends the modeling technique to cases with blade inserts and for quasi-stationary temperature calculations.
4) It
New technologies-for-modeling-of-gas-turbine-cooled-bladesCemal Ardil
The document describes new technologies for modeling gas turbine cooled blades, including:
1) Developing mathematical models and numerical methods using the boundary integral equation method (BIEM) and finite difference method (FDM) to calculate the stationary and quasi-stationary temperature field of a blade profile with convective cooling.
2) Using splines, smooth interpolation, and neural networks for visualization of blade profiles.
3) Validating the designed methods through computational and experimental investigations of heat and hydraulic characteristics of a gas turbine nozzle blade.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
The document compares the thermal performance of flat plate fins and inline strip fins heat sinks. It presents Nusselt number correlations from literature to model the convective heat transfer from the fins. The correlations consider heat transfer from the fins but not the bare heat sink base. The study includes an estimate of heat transfer from the base, providing a more realistic thermal resistance calculation. Results show inline strip fins have higher heat transfer coefficients that compensate for their reduced area, yielding lower thermal resistances than plate fins. Considering heat transfer from the base provides an even lower thermal resistance for both heat sink designs.
Numerical Analysis of Inverted Notched Fin Array Using Natural ConvectionIOSR Journals
Abstract:Geometry and orientation plays an important role in natural convection heat transfer. For
horizontal rectangular fin array a chimney flow pattern is developed due to density difference. This flow
pattern creates a stagnant zone near central bottom region. That portion does not contribute much towards
heat dissipation. This area is removed from fins and they became inverted notched fins. This modified geometry
reduces material cost, material weight without hampering heat transfer rate. Numerical models are prepaid to
investigate heat transfer characteristics in plane fins and inverted notched fins. This investigation is also
extended over different types of notches and their effectiveness comparison. Fin spacing, fin height, fin length,
heater input, percentage of area removed in the form of inverted notch are the parameters under
consideration. This analysis is done numerically using CFD package (Fluent). It is found that the heat transfer
coefficient of inverted notch fin array is 25% to 35% higher as compared with normal fin array. Also we found
that the triangular shape notch gives better result than trapezoidal and rectangular shape notch.
Key words: Inverted Notched Fin, Chimney Flow, Natural Convection, Heat transfer coefficient enhancement
EXPERIMENTAL STUDY OF HEAT TRANSFER FROM PLATE FIN ARRAY IN MIXED CONVECTION ...ijiert bestjournal
The document presents an experimental study on mixed convection heat transfer from plate fin arrays. Experiments were conducted on 9 plate fins attached to a 150mm by 150mm aluminum base plate. Temperature measurements were taken at varying fan velocities and input powers to determine heat transfer coefficients and relationships between parameters like Nusselt number, Reynolds number, and Grashof number. Key findings included that plate fins provided better heat transfer performance than solid pins, and the dimensionless parameter Gr/Re2 could be used to identify the mixed convection heat transfer region.
Cfd Simulation and Experimentalverification of Air Flow through Heated PipeIOSR Journals
The aim of this work is to validate the Dittus-Boelter equation by experimental,correlation and Simulation method. It used to find the value of heat transfer coefficient ‘h’ for turbulent flow in many fluid transfer systems. This work discusses how the Dittus-Boelter equation is applied to the problem of circular pipe. In CFD simulation ICEM CFD for modeling and CFX13 for analysis are used. Results of CFD simulation will be obtained by CFD-POST. Here heat transfer coefficient value is compared by correlations,experiment and CFD simulations, finally the aim of this work is to validate Dittus-Boelter equation.
IRJET-Enhancing the Performance of Hybrid Microgrid using non Isolated Single...IRJET Journal
This document analyzes heat transfer in a light passenger car radiator with various geometrical configurations using computational fluid dynamics (CFD). It studies a staggered fin-and-tube radiator with circular and oval tubes. The radiator is modeled and analyzed in FLUENT to obtain velocity, temperature, and pressure contours. Oval tubes are found to improve heat transfer compared to circular tubes. Specifically, oval tube configurations reduce temperature differences between the tubes and air, indicating more efficient heat absorption. While circular tubes show higher temperatures, oval tube designs enhance convection and lower outlet temperatures. In conclusion, varying the tube shape geometrically through oval designs improves the radiator's thermal performance.
Computational Analysis of Heat sink or Extended SurfaceIRJET Journal
This document summarizes a study on the computational analysis of heat sinks using finite element analysis. Heat sinks with different fin configurations were modeled and analyzed using ANSYS Fluent software to evaluate heat transfer characteristics. The results were validated by comparing with previous studies and analytical solutions. Key findings include that increasing the number of fins and base-to-ambient temperature difference leads to higher convective heat transfer. An optimum fin spacing was identified that balances heat transfer and pressure drop, and this agreed with results from other studies. In conclusion, finite element analysis was found to be an effective method for evaluating heat transfer in heat sinks with different parameters.
Validation of Results of Analytical Calculation of Steady State Heat Transfer...IRJET Journal
The document summarizes the analytical calculation and ANSYS simulation of steady state heat transfer in a nuclear fuel element. It presents the analytical solution to the heat conduction equations and plots the temperature profile. The simulation results for temperature, heat flux, and thermal gradient contours along with their corresponding graphs are also presented. Comparison shows that the analytical and simulation results match, validating the analytical model. Observation of boundary effects on axial thermal properties is also noted.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document summarizes an experimental study on jet impingement cooling of a ribbed surface with holes. The researchers varied parameters like heat flux, nozzle-to-plate distance ratio (H/d ratio), and Reynolds number. They measured temperatures at different locations and calculated heat transfer coefficients and Nusselt numbers. Key findings include that heat transfer increased with decreasing H/d ratio and increasing heat flux. Nusselt numbers generally increased with Reynolds number and heat flux. The presence of holes and enclosure affected flow patterns and temperature readings.
International Journal of Engineering Research and Applications (IJERA) aims to cover the latest outstanding developments in the field of all Engineering Technologies & science.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
This document summarizes a study that uses computational fluid dynamics (CFD) to analyze the flow and heat transfer characteristics of different elliptical pin fin heat sink configurations. The study aims to examine the effects of elliptical pin fin design parameters on heat sink performance. CFD simulations are conducted using ANSYS Fluent software to compute the thermal resistance, heat transfer coefficient, and surface Nusselt number of plate fin and elliptical pin fin heat sinks. Results show that the elliptical pin fin heat sink has better heat transfer performance than the plate fin heat sink. Simulation results for thermal resistance and pressure drop are validated against experimental data from previous studies.
Analysis of Coiled-Tube Heat Exchangers to Improve Heat Transfer Rate With Sp...IJMER
Steady heat transfer enhancement has been studied in helically coiled-tube heat exchangers. The outer side of the wall of the heat exchanger contains a helical corrugation which makes a helical rib on the inner side of the tube wall to induce additional swirling motion of fluid particles. Numerical calculations have been carried out to examine different geometrical parameters and the impact of flow and thermal boundary conditions for the heat transfer rate in laminar and transitional flow regimes. Calculated results have been compared to existing empirical formula and experimental tests to investigate the validity of the numerical results in case of common helical tube heat exchanger and additionally results of the numerical computation of corrugated straight tubes for laminar and transition flow have been validated with experimental tests available in the literature. Comparison of the flow and temperature fields in case of common helical tube and the coil with spirally corrugated wall configuration are discussed. Heat exchanger coils with helically corrugated wall configuration show 80–100% increase for the inner side heat transfer rate due to the additionally developed swirling motion while the relative pressure drop is 10–600% larger compared to the common helically coiled heat exchangers. New empirical Co-relation has been proposed for the fully developed inner side heat transfer prediction in case of helically corrugated wall configuration.
Experimental Investigation of Natural Convection Heat Transfer Enhancement fr...IRJET Journal
This document describes an experimental investigation of natural convection heat transfer from rectangular fin arrays with combinations of V-notches and perforations. Four fin array configurations were tested: one without notches or perforations (un-notched), and three with different combinations of V-notches and perforations removing different percentages of the fin area. The fin arrays were heated to different temperatures and the resulting heat transfer coefficients were measured and compared. The results showed that the combination of V-notches and perforations both increased the surface area and the turbulence near the fins, allowing more air contact and higher heat transfer coefficients compared to the un-notched fins. Among the configurations tested, the fin array with 20% of its area removed
This document discusses cold-junction corrections that must be applied when thermocouples are calibrated with the cold junction at a standard reference temperature like 0°C, but are then used with the cold junction at the temperature of the room. It presents three forms for the cold-junction correction and evaluates their accuracy. The preferred Form III correction multiplies the cold-junction temperature by the ratio of the mean slope of the calibration curve from 0°C to the cold-junction temperature, and the slope at the observed temperature. For typical thermocouples, this correction is accurate to within the precision of pyrometric measurements if the cold junction is below 50°C.
JIMEC Thermal modeling and Simulation of HX Conference PaperAhmed Sohail Izhar
1) The document describes a thermal modeling and simulation of an industrial shell and tube heat exchanger used to cool raw natural gas.
2) A thermal model was developed using the effectiveness-NTU method to determine the required heat transfer area and estimate the tube-side and shell-side heat transfer coefficients.
3) The results of the model showed that a heat transfer area of about 1132 m2 is required to provide a thermal duty of 1.4 MW, with tube-side and shell-side heat transfer coefficients of 950 W/m2K and 495 W/m2K respectively.
A practical approach to design and optimization of single phase liquid to liq...iaemedu
The document describes the design and optimization of a shell and tube heat exchanger. It presents a method based on Tinker's approach that incorporates modifications from Kern and Kakac. A 17-step thermal design procedure is outlined that involves sizing the heat exchanger dimensions and components through an iterative process to meet a specified heat load. A computer program was developed to automate the calculations and optimize the design in a more efficient manner than manual calculations. The program allows the user to input parameters and obtain an optimized design solution.
This document describes mathematical models for simulating the temperature fields of gas turbine blades during convective cooling. It presents boundary integral equation methods (BIEM) and finite difference methods (FDM) for calculating the stationary and quasi-stationary temperature distribution on a blade profile with radial cooling channels. The BIEM approach formulates the problem as a system of boundary integral equations involving temperature values and heat transfer coefficients on the blade surface and cooling channel boundaries. Numerical methods are developed to solve these equations, including discrete logarithmic potential operators and non-uniform surface discretizations. The reliability of the proposed methods is confirmed through computational and experimental analysis of heat transfer for a gas turbine nozzle blade.
This document summarizes a study on modeling and simulating gas turbine cooled blades. It develops mathematical models and numerical methods to calculate the stationary and quasi-stationary temperature fields of a blade profile part with convective cooling. It considers the heat conduction equation and boundary conditions for the problem. It then outlines the following key points:
1) It uses the Boundary Integral Equation Method (BIEM) and Finite Difference Method (FDM) combination to solve the temperature field calculation problem.
2) It develops effective quadrature processes to evaluate singular integral operators in the boundary integral equations.
3) It extends the modeling technique to cases with blade inserts and for quasi-stationary temperature calculations.
4) It
New technologies-for-modeling-of-gas-turbine-cooled-bladesCemal Ardil
The document describes new technologies for modeling gas turbine cooled blades, including:
1) Developing mathematical models and numerical methods using the boundary integral equation method (BIEM) and finite difference method (FDM) to calculate the stationary and quasi-stationary temperature field of a blade profile with convective cooling.
2) Using splines, smooth interpolation, and neural networks for visualization of blade profiles.
3) Validating the designed methods through computational and experimental investigations of heat and hydraulic characteristics of a gas turbine nozzle blade.
This document summarizes a research article about numerical modeling of gas turbine engines. The researchers developed mathematical models and numerical methods to calculate the stationary and quasi-stationary temperature fields of gas turbine blades with convective cooling. They combined the boundary integral equation method and finite difference method to solve this problem. The researchers proved the validity of these methods through theorems and estimates. They were able to visualize the temperature profiles using methods like least squares fitting with automatic interpolation, spline smoothing, and neural networks. The reliability of the numerical methods was confirmed through calculations and experimental tests of heat transfer characteristics on gas turbine nozzle blades.
This document discusses estimating the hottest spot temperature in power transformer windings using different cooling methods. It presents the mathematical formulation of the heat conduction equation for solving temperature distribution numerically using the finite element method. The selected model is a 32MVA transformer with two cooling methods: Non-Directed Oil-Forced (NDOF) cooling and Directed Oil-Forced (DOF) cooling. Equations are provided for calculating heat transfer coefficients, boundary conditions, and temperature gradients needed to solve the heat conduction equation.
1) During welding, the material experiences a thermal cycle where it is rapidly heated and more slowly cools. This temperature cycle influences the structure and properties of the material.
2) Analytical equations are presented to describe the temperature distribution and peak temperatures experienced during welding. These equations simplify the complex heat transfer process.
3) The shape and size of the weld pool impacts the solidified weld metal microstructure. Flow within the molten weld pool is driven by surface tension gradients and electromagnetic forces, influencing the weld pool shape.
Cfd simulation of telecommunications cabinetmahdi Mokrane
This document discusses simulations of cooling a telecommunications cabinet prototype using computational fluid dynamics (CFD). It presents the following key points:
1) A CFD model was created using GAMBIT meshing software to simulate air flow and heat transfer within a telecommunications cabinet measuring 0.65x0.65x0.30 m containing a heating element.
2) Simulations were run with and without ventilation openings, showing ventilation is needed to maintain safe temperature levels inside the closed cabinet.
3) Forced convection cooling via an air inlet and outlets was able to maintain air temperatures of 309-311K, an improvement of 8-10K over the natural convection scenario without openings.
This document analyzes heat transfer from a finned-tube heat exchanger. It begins with an introduction to heat exchangers and finned tubes, then presents the problem statement analyzing heat transfer from a pipe with annular fins exposed to glycol fluid. Calculations are shown for heat transfer with and without fins, finding a 16.81 kW rate with fins and 15.28 kW without. Simulation in ANSYS is used to verify the calculations, finding 18.93 kW with fins and 15.28 kW without. Mesh refinement could improve accuracy between simulated and theoretical values.
Thermal Stresses of a Semi-Infinite Rectangular Slab with Internal Heat Gener...IJLT EMAS
This paper is concerned with transient thermoelastic
problem in which we need to determine the temperature
distribution, displacement function and thermal stresses of a
semi- infinite rectangular slab when the boundary conditions are
known. Integral transform techniques are used to obtain the
solution of the problem.
Modeling and Simulation of Thermal Stress in Electrical Discharge Machining ...Mohan Kumar Pradhan
In this research the effect of input variables namely: discharge current, pulse
duration on thermal stresses has been investigated. A finite element modelling for
the EDM process and the effect of a single-pulse discharge has been presented and
results concerning the temperature distribution, the thermal stresses of AISI D2 steel
machined by EDM have been illustrated. It was found that the compressive thermal
stresses were developed beneath the crater and the tensile stresses were occur away
from the axis of symmetry however, the thermal stresses affects to a larger depth with
increasing pulse energy.
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
This document summarizes a study on assessing the thermal performance of semicircular fins under forced air convection and its application to air preheaters. The study finds that semicircular fins have greater thermal efficiency compared to circular fins of the same volume due to their larger surface area. Mathematical models are developed to analyze heat transfer in the fins and an air preheater. Various parameters like number of fins, pipe size, air velocity and temperature are examined. The results show that larger preheat can be achieved using semicircular fins, providing potential for higher energy efficiency.
The document compares three computational fluid dynamics (CFD) models - laminar, standard low-Reynolds k-ε, and V2F low-Reynolds k-ε models - in simulating a plate-fin heat sink with forced convection. Star CCM+ software is used to model the heat sink and apply a heat flux at the base. Simulations are run with each model and benchmarked against theoretical calculations for heat sink thermal resistance and pressure drop. The laminar model is found to yield results matching the turbulence models' accuracy in less time, making it deemed most suitable for the problem.
A Finite Element Thermo-Mechanical Stress Analysis of IC Engine PistonIRJET Journal
This document discusses a finite element analysis of thermal and mechanical stresses on an internal combustion engine piston. It begins with an introduction to pistons and the stresses they experience from high temperatures and pressures within the engine cylinder. It then describes a thermal analysis conducted using ANSYS software to model the piston's temperature distribution and calculate thermal stresses. The analysis applies thermal boundary conditions at different surfaces of the piston based on convection heat transfer calculations. The goal is to identify locations of maximum and minimum stress on the piston.
The document reports on an experimental and numerical study of heat transfer from a premixed methane/air slot flame impinging on a flat surface. Key findings include:
- A second peak in heat flux along the target surface was observed experimentally for the shortest nozzle-to-plate spacing and highest firing rate.
- Numerical simulations successfully predicted this second heat flux peak and found it corresponded to a second stagnation point caused by the confined flame geometry.
- The presence of this second stagnation point and peak could be controlled by adjusting the nozzle-to-plate spacing and firing rate.
Measuring the Thermal Conductivities of Low Heat Conducting Disk Samples by M...IJERA Editor
This article aims to establish an experimental procedure to measure heat transmission coefficients in low heat conductive materials. The newly developed model takes as starting point the application of Fourier’s law to a disk sample when a temperature gradient is established between its faces. The power of a heating element is determined as the heat transfer coefficient of the problem disk. Initially, a glass vessel containing water is placed in direct contact with the heating element; then, a problem plastic disk is placed between this element and the glass vessel, treating the set as a composite wall. Prior to the above the water equivalent of a calorimetric set (vessel + water + accessories) and the thermal conductivity of the vessel must be determined. The thermal conductivity of the problem plastic disk sample is obtained for temperatures ranging from 30 to 70° C. The results reveal the existence of some type of structural transition for the problem material.
This document discusses air transient cooling characteristics in the entry regions of ducts with non-circular cross sections. It presents correlations and equations to calculate the hydrodynamic and thermal entrance lengths for triangular, rectangular, circular and square ducts. It also provides equations for the local Nusselt number and convective heat transfer coefficient in the combined entry region where the flow is both thermally and hydrodynamically developing. The analysis considers the transient heat transfer in the duct entry regions using temperature-dependent air properties and numerical modeling. The results indicate that the triangular duct enhances heat transfer the most compared to the other cross section ducts.
THERMAL ANALYSIS OF WELDING IN T-JOINT PLATES USING FINITE ELEMENT ANALYSISIjorat1
This document summarizes a finite element analysis of thermal properties during welding of T-joint stainless steel plates. It describes:
1) Modeling the welded plates using 3D solid elements and applying a moving circular heat source to model the welding process.
2) Analyzing the model to determine temperature distributions and histories using properties of 304L stainless steel at different temperatures.
3) The analysis uses a Gaussian distributed heat source model and finite element method to simulate the complex 3-dimensional heat transfer during welding, providing more accurate temperature predictions than simplified point or line heat sources.
Development and theoretical analysis of mathematical expressions for change o...ijsrd.com
This paper introduces a novel technique and algorithm for theoretical study of entropy changes for exothermic reactions by mechanistic modelling and dynamic simulation; considering factors such as kinetics, reaction environment and flow patterns with an ultimate objective of minimization of energy loss and entropy generation in the system. It mainly focuses on exothermic reactors cooled by means of a constant inlet temperature utility fluid which flows along the external surface of the reactor vessel. Using basic concepts of heat and mass balances and definitions in thermodynamics, variation of related system variables with time is modelled and by simulation in MS-Excel, a polynomial fit is generated for sample problems in order to make the illustrations handier. Usages of the developed expressions for energy optimization are also commented upon.
One dim, steady-state, heat conduction_with_heat_generationtmuliya
This file contains slides on One-dimensional, steady-state heat conduction with heat generation.
The slides were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India, during Sept. – Dec. 2010.
It is hoped that these Slides will be useful to teachers, students, researchers and professionals working in this field.
Similar to Development of-effective-cooling-schemes-of-gas-turbine-blades-based-on-computer-simulation (20)
This document summarizes a research paper that proposes using a Real-Coded Genetic Algorithm to design Unified Power Flow Controller (UPFC) damping controllers. The goal is to damp low frequency oscillations in power systems. The paper models a single-machine infinite-bus power system installed with a UPFC. It linearizes the system equations and formulates the controller design as an optimization problem to minimize oscillations. Simulation results comparing the proposed RCGA approach to conventional tuning are presented to demonstrate its effectiveness and robustness in damping power system oscillations.
The main-principles-of-text-to-speech-synthesis-systemCemal Ardil
This document discusses text-to-speech synthesis systems. It provides background on the history and development of such systems over three generations from 1962 to the present. It describes some of the main challenges in developing speech synthesis for different languages. The document then focuses on specifics of the Azerbaijani language and outlines the approach used in the text-to-speech synthesis system developed by the authors, which combines concatenative synthesis and formant synthesis methods.
The feedback-control-for-distributed-systemsCemal Ardil
The document summarizes a study on feedback control synthesis for distributed systems. The study proposes a zone control approach, where the state space is partitioned into zones defined by observable points. Control actions are piecewise constant functions that only change when the system transitions between zones. An optimization problem is formulated to determine the optimal constant control value for each zone. Gradient formulas are derived to solve this using numerical optimization methods. The zone control approach was tested on heat exchanger process control problems and showed more robust performance than alternative methods.
System overflow blocking-transients-for-queues-with-batch-arrivals-using-a-fa...Cemal Ardil
This document summarizes a research paper that analyzes the transient behavior of the overflow probability in a queuing system with fixed-size batch arrivals. It introduces a set of polynomials that generalize Chebyshev polynomials and can be used to assess the transient behavior. The key findings are:
1≤k ≤ B
k≥B+1
which is just the generating function of the Chebyshev
polynomials of the second kind.
Furthermore, if we consider the special case when B = 1 in
(9), and make the substitution x → 2x, we obtain
k =0
0≤k ≤ B
Pk −1
λ
μ
Sonic localization-cues-for-classrooms-a-structural-model-proposalCemal Ardil
The document describes a proposed structural model for sonic localization cues in classrooms. It discusses two primary cues for localization - interaural time difference (ITD) and interaural level difference (ILD) created by sounds reaching each ear. While these cues provide azimuth information, they do not provide elevation information. Elevation information is provided by spectral filtering effects of the head, torso and outer ears (pinnae) known as the head related transfer function (HRTF). The proposed structural model aims to produce well-controlled horizontal and vertical localization cues through a signal processing model of the HRTF that mimics how sounds interact with the body. The effectiveness of the model is tested through synthesized spatial audio experiments with human subjects
This document summarizes a new method for designing robust fuzzy observers for nonlinear systems based on Takagi-Sugeno fuzzy models. The method uses linear matrix inequalities to design observers that minimize the H-norm of the closed loop system, providing a measure of robustness and disturbance attenuation. The observer design method is similar to existing parallel distributed compensation controller design methods, making it possible to adapt controller design techniques for observer design. The observer estimates system states and outputs based on measured outputs and system inputs while attenuating effects of disturbances and uncertainties.
This document discusses evaluating the response quality of heterogeneous question answering systems. It begins by noting the lack of standard evaluation metrics for systems that use natural language understanding and reasoning to answer questions, as opposed to just information retrieval. It proposes a "black-box" approach to evaluate response quality by observing system responses, developing a classification scheme to categorize responses, and assigning scores. As a demonstration, it applies this approach to evaluate three example systems (AnswerBus, START, and NaLURI) on a set of questions about cyberlaw.
The document describes two methods for reducing the order of linear time-invariant systems: Routh approximation and particle swarm optimization (PSO). Routh approximation determines the denominator of the reduced order model using a Routh array, while retaining time moments or Markov parameters to determine the numerator. PSO reduces order by minimizing the integral squared error between responses of the original and reduced models, adjusting numerator and denominator coefficients. The methods are illustrated on examples, with Routh approximation providing stability guarantees when applied to stable systems.
Real coded-genetic-algorithm-for-robust-power-system-stabilizer-designCemal Ardil
This document summarizes a research paper that uses a real-coded genetic algorithm to optimize the design of power system stabilizers. The algorithm is applied to both single-machine and multi-machine power systems. The goal is to minimize rotor speed deviations and improve stability under disturbances. Simulation results show the proposed controller provides effective damping of low frequency oscillations across different operating conditions.
This summary provides the key points about the document in 3 sentences:
The document presents a method for obtaining the exact probability of error for block codes using soft-decision decoding and the eigenstructure of the code correlation matrix. It shows that under a unitary transformation, the performance evaluation of a block code becomes a one-dimensional problem involving only the dominant eigenvalue and its corresponding eigenvector. Simulation results demonstrate good agreement with the analysis, validating the method for computing the bit error rate of block codes based on the properties of the code correlation matrix.
This document presents an optimal supplementary damping controller design for Thyristor Controlled Series Compensator (TCSC) using Real-Coded Genetic Algorithm (RCGA). TCSC is capable of improving power system stability by modulating reactance during disturbances. The document proposes using a multi-objective fitness function consisting of damping factors and real parts of eigenvalues to optimize the parameters of a TCSC-based supplementary damping controller using RCGA. Simulation results presented show the effectiveness of the proposed controller over a wide range of operating conditions and disturbances.
This document presents a method for generating optimal straight line trajectories in 3D space using an algorithm called the Bounded Deviation Algorithm (BDA). BDA approximates a straight line trajectory between two points by iteratively inserting knot points to minimize the deviation between the actual trajectory and the joint space trajectory. The document provides the mathematical formulation and simulation results of applying BDA to generate a straight line trajectory for a 5-axis articulated robot between two specified points.
On the-optimal-number-of-smart-dust-particlesCemal Ardil
This document discusses optimizing the number of smart dust particles used to generate weather maps. It addresses two main challenges: 1) how to match signals from smart dust particles to receivers given atmospheric constraints, and 2) what is the optimal number of particles needed to generate precise and cost-effective 3D maps. The document presents an algorithm to optimally match particles to receivers in O(n*m) time by framing it as a maximal bipartite graph matching problem. It also develops mathematics to prove a conjecture that the optimal number of particles is approximately 1/ε, where ε is the drift error.
On the-joint-optimization-of-performance-and-power-consumption-in-data-centersCemal Ardil
The document summarizes research on jointly optimizing performance and power consumption in data centers. It models the process of mapping tasks in a data center onto machines as a multi-objective problem to minimize both energy consumption and response time (makespan), subject to deadline and architectural constraints. It proposes using a simple goal programming technique that guarantees Pareto optimal solutions with good convergence. Simulation results show the technique achieves superior performance compared to other approaches and is competitive with optimal solutions for small-scale problems.
On the-approximate-solution-of-a-nonlinear-singular-integral-equationCemal Ardil
This document summarizes a study on finding approximate solutions to nonlinear singular integral equations. The study proves the existence and uniqueness of solutions to such equations defined on bounded regions of the complex plane. It then presents a method for finding approximate solutions using an iterative fixed-point principle approach. Nonlinear singular integral equations have many applications in fields like elasticity, fluid mechanics, and mathematical physics. The study contributes to improving methods for solving these important types of equations.
On problem-of-parameters-identification-of-dynamic-objectCemal Ardil
This document discusses methods for identifying parameters of dynamic objects described by systems of ordinary differential equations. Specifically, it addresses problems with multiple initial boundary conditions that are not shared across points.
The paper proposes a new "conditions shift" method to transfer the initial boundary conditions in a way that eliminates differential links and multipoint conditions. This reduces the parameter identification problem to solving either an algebraic system or a quadratic programming problem.
Two cases are considered: case A where the number of conditions equals the number of conditionally free parameters, resulting in a single parameter vector solution. Case B where additional conditions on the parameters are needed in the form of equalities or inequalities, resulting in an optimization problem to select optimal parameter values.
This document discusses using neuro-fuzzy networks to identify parameters for mathematical models of geofields. It proposes a new technique using fuzzy neural networks that can be applied even when data is limited and uncertain in the early stages of modeling. A numerical example is provided to demonstrate the identification of parameters for a regression equation model of a geofield using a fuzzy neural network structure. The network is trained on experimental fuzzy statistical data to determine values for the regression coefficients that satisfy the data. The technique is concluded to have advantages over traditional statistical methods as it can be applied regardless of the parameter distribution and is well-suited for cases with insufficient data in early modeling stages.
This document presents a new multivariate fuzzy time series forecasting method to predict car road accidents. The method uses four secondary factors (number killed, mortally wounded, died 30 days after accident, severely wounded, and lightly casualties) along with the main factor of total annual car accidents in Belgium from 1974 to 2004. The new method establishes fuzzy logical relationships between the factors to generate forecasts. Experimental results show the proposed method performs better than existing fuzzy time series forecasting approaches at predicting car accidents. Actuaries can use this kind of multivariate fuzzy time series analysis to help define insurance premiums and underwriting.
The document describes a multistage system for monitoring the technical condition of aircraft gas turbine engines. It proposes using soft computing methods like fuzzy logic and neural networks at early stages when data is limited or uncertain. At later stages, it uses statistical analysis methods like analyzing changes in skewness, kurtosis, and correlation coefficients of engine parameters. Fuzzy regression models are developed using these techniques to estimate engine condition. The system provides staged estimation of engine technical conditions from initial to later stages of operation.
Multi objective-optimization-with-fuzzy-based-ranking-for-tcsc-supplementary-...Cemal Ardil
This document summarizes a research paper that investigates using multi-objective optimization and genetic algorithms to design a thyristor controlled series compensator (TCSC) controller to improve both rotor angle stability and voltage stability in a power system. The researchers formulate the controller design as a multi-objective optimization problem with the objectives of improving oscillatory stability and voltage profile. A genetic algorithm is used to generate a Pareto set of optimal solutions. A fuzzy-based method is then employed to select the best compromise solution from the Pareto set. Simulation results demonstrate the effectiveness of the proposed approach.
20 Comprehensive Checklist of Designing and Developing a WebsitePixlogix Infotech
Dive into the world of Website Designing and Developing with Pixlogix! Looking to create a stunning online presence? Look no further! Our comprehensive checklist covers everything you need to know to craft a website that stands out. From user-friendly design to seamless functionality, we've got you covered. Don't miss out on this invaluable resource! Check out our checklist now at Pixlogix and start your journey towards a captivating online presence today.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfMalak Abu Hammad
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
A tale of scale & speed: How the US Navy is enabling software delivery from l...sonjaschweigert1
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Building RAG with self-deployed Milvus vector database and Snowpark Container...Zilliz
This talk will give hands-on advice on building RAG applications with an open-source Milvus database deployed as a docker container. We will also introduce the integration of Milvus with Snowpark Container Services.
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
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Mental Health: Maintaining balance and not feeling pressured by user demands.
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Development of-effective-cooling-schemes-of-gas-turbine-blades-based-on-computer-simulation
1. World Academy of Science, Engineering and Technology
International Journal of Mathematical, Computational Science and Engineering Vol:1 No:3, 2007
Development of Effective Cooling Schemes of Gas
Turbine Blades Based on Computer Simulation
1
. Pasayev, 2C. Askerov, 3R. Sadiqov, 4C. Ardil
1-4
Azerbaijan National Academy of Aviation
370057, Airport “Bina”, Baku, Azerbaijan
Phone: (99412) 97-26-00, 23-91; Fax:(99412) 97-28-29
e-mail :sadixov@mail.ru
Abstract: In contrast to existing of calculation of temperature
field of a profile part a blade with convective cooling which are not
taking into account multi connective in a broad sense of this term,
we develop mathematical models and highly effective combination
(BIEM AND FDM) numerical methods from the point of view of a
realization on the PC. The theoretical substantiation of these
methods is proved by the appropriate theorems.
Keywords: multi coherent systems, method of the boundary
integrated equations, singular operators, gas turbines
International Science Index 3, 2007 waset.org/publications/3293
1. INTRODUCTION
OR this purpose, were there developed converging
quadrature processes and the estimations of errors in the
terms of modules of a continuity .Ziqmound are
received. The offered technique of account of temperature
fields is applied to cooled gas turbine blades. For
visualization of structures is used peace-polynomial
smoothing with automatic joining: a method of the least
squares and smooth splines.
F
The repeated computing experiments with use BIEM on
account of temperature fields and workers blades with
various amount and arrangement of cooled channels having
a difficult configuration at stationary and quasi-stationer
modes, have shown increased reactive of the developed
algorithms and their high accuracy.
The development of modern air engineering is stipulated, in
main. development and refinement aviation gas turbine
engines (AGTE) creation of perfect designs of flights
vehicles (FV) with improved weight, strength, aerodynamic
and dynamic characteristics, decreasing of harmful effects
on an ecology of an environment (harmful lets, noise effects
etc.), increase of a reliability, survival, acceleration
characteristics, which conduct, as a whole, to increase of
efficiency FV and growth of safety of flights.
What concerns development and refinement AGTE, at the
present stage it is reached, in main assimilation of high
values of temperature of gas in front of the turbine (T ) at
simultaneous increase of a degree of recompression in the
compressor. The attempts of use of other means, such as
thickening of a thermal cycle, salvaging of a heat of exhaust
gases and other well recommending in other branches gasturbine engineering, in application to aircraft have not
justified. The activities on increase T are conducted in
several directions. The fist direction is a creation of new
metal alloys with the more improved heat resisting and
resisting properties. The second direction is a development
of ceramic, cermet and sintering of materials. At last, the
third direction is a cooling of hot parts of the turbine.
Therefore assimilation high T in AGTE at the present stage
in main is reached in refinement of systems and schemes of
cooling of hot details of turbines, and fist of all, nozzle and
working blades.
Especially it is necessary to underline, that with increase
of the requirement to accuracy of eventual results will
increase. From the experimental and operational data it is
known, what for of details of gas turbines the error
calculation of temperatures should be very small, no more
than 2-3%. In other words, at allowed (permissible) in
0
AGTE to temperature of metal Tlim (1100...1300 K ) ,
t0, intrinsic for heat resisting and heat resisting alloys on
nickel or cobalt to the basis with various alloying by dopes,
the absolute error of calculation of temperature should be in
limits (20-300K).
To achieve it is difficult. Especially in skew fields of the
difficult shape with various quantity and arrangement of
cooling channels have a difficult configuration, in multiply
connected areas with variables in time and or coordinates by
boundary conditions even separate problem solving of heat
conduction ramified hydraulic circuits and the definition of
the intense condition is business not simple. Despite of a
numbers of assumptions the solution of such problems
requires application modern and perfect mathematical
vehicle.
2. PROBLEM FORMULATION
In classical statement a differential heat conduction equation
circumscribing in common case non-stationary process of
distribution of a heat in many – dimensional area in there is
internal sources of the heat qv , under difficult boundary
conditions and relation of factors, included in an equation,
to required temperature coordinates and time (an equation
the Fourier-Kirchhoff) has a kind:
( CvT )
t
180
div( grad T) qv ,
(1)
2. where , C v and
-
World Academy of Science, Engineering and Technology
International Journal of Mathematical, Computational Science and Engineering Vol:1 No:3, 2007
3. PROBLEM SOLUTION
accordingly material’s density, thermal
capacity heat conduction, q v - internal source or drain of
heat, and T- required temperature.
By results of researches is established [2], that the
temperature condition of a profile part of a blade with radial
cooling channels can with a sufficient degree of accuracy
determined, as two-dimensional. Besides if to suppose a
constancy of physical properties, absence of internal sources
(drains) heat the temperature field under fixed conditions
will depend only on the shape of a skew field and from
distribution of temperature on a boundaries skew field. In
this case equation (1) will look like:
As of today for the solution of this boundary value problem
(2)-(4) most broad distributions have received four
numerical methods – methods of final differences (MFD),
finite element method (FEM) , probabilistic method ( or
method Monte-Carlo) and method of boundary integral
equations (BIEM) (or it discrete analog a method of
boundary element (BEM). Let’s consider application BIEM
for the solution of a problem (2)-(4).
3.1. The function T=T(x,y) , continuous with the derivatives
up to the second order satisfying to an equation of the
Laplace in considered area , including it an outline
M
2
International Science Index 3, 2007 waset.org/publications/3293
T
2
T
x2
T
y2
i
0
(2)
Grin for a researched potential function T=T(x,y) is the
ratio;
For allocation from a set of the possible solutions it is
necessary to supplement one, circumscribing a particular
temperature field given a differential equation by conditions
of uniqueness. In practice of problem solving temperature
fields, connected to determination in elements of gas
turbines washed by a flow of high – enthalpy gas more often
set boundary conditions of the third kind describing heat
exchange between a skew field and an environment because
of a hypothesis of a Newton- of the Riemann. In that case
these boundary conditions will be recorded as follows:
0
(T0
T
T 0)
0
n
i
n
(T i
Ti )
(x, y)
k
1, M (temperature of the chiller),
where M- quantity of outlines; T 0 -- temperature on an
i
at i
temperature on an
channels);
a blade (at i
0
0 , (outside outline of blade); T i -i
at
i 1, M (outline of cooling
- heat transfer factor from gas to a surface of
0)
i-
heat transfer factor of environment
from a blade to a cooling air at ( i 1, M ); -- thermal
conductivity of a material of a blade; n-external normally
on an outline of researched area.
( nR k )
ds
n
1
2
T 01
k1
k
nR
n
]ds
(5)
n
nR k ds
(6)
0
k2
T0
T 02
k
i
Ti
...
2 Tk
kn
T 0m
(7)
0
where n-quantity of sites of a partition of an outside outline
of a blade
( i on i 0) on small sections
0
S0 ( Si at i
environment at i
outline
( nR)
n
[
With allowance for of entered boundary conditions (2)-(3),
after a collecting terms of terms and input of new factors the
ratio (6) can be presented as a linear algebraic equation,
computed for the point R:
(4)
Characterizes quantity of a heats assigned by a convection
of the chiller, which is transmitted by heat conduction of a
material of a blade to a surface of cooling channels; where
T0 – temperature of environment at i=0; Ti – temperature of
1
2
Where R – variable at an integration of a distance between a
point K(x,y) and “running” on an outline k- point; T temperature on an outline . The value of temperature in
some k t0 a point lying on the boundary, is received as
limiting at approach of a point K(x,y) to the boundary
(3)
Characterizes quantity of heat transmitted convection from
gas to unit of a surface of a blade and assigned by heat
conduction in a skew field of a blade:
Ti
is harmonic. A corollary of the integral formula
i 0
0) , m-quantity of sites of a partition of
outside outlines of all cooling channels
small sections
i
(i 1, M ) on
Si .
Shall remark, that by unknowns in an equation (7) except a
unknown quantity of a true value Tk in a point to are also
mean on sections of a partition of outlines S 0 and S i of
temperature T 01 , T
02
,..., T 0 m and T i1 , T i 2 ,..., T im (total
number n+ ).
From a ratio (7) we shall receive required temperature for
any point, using the formula (5)
181
3. World Academy of Science, Engineering and Technology
International Journal of Mathematical, Computational Science and Engineering Vol:1 No:3, 2007
T(x, y)
...
1
[ k1T 01
2
T
km im
k 0T 0
cp
k 2T 02 ...
k
i
(8)
i
Tcpi ]
2
( nR k )
ds
n
k1
S01
.
.
( ))
nR( s, )d
n
(12)
( s) nR 1ds)
(T
01
1
For an evaluation of the singular integral operators
which are included in the discrete operators of a
logarithmic potential simple and double layer (10) are
investigated, their connection is shown and the
evaluations in term of modules of a continuity
(evaluation such as assessments are obtained A.
Zigmound).Theorem (main).
Let
( x)
.
0m
nR k ds
m
S0m
0n
nR k ds
n
S01
01
k ii
S01
.
nR k ds ...
1
R(s, ) ((x(s) x( ))2 ( y(s) y( ))2)1/ 2
nR k ds
1
( nR k )
ds
n
S0m
k 0
01
.
kn
nR k ds ...
Sn
im
nR k ds
m
Si1
Sim
M
i
by a
i 0
great many of a discrete point and integrals which are
included in an equations as logarithmic potentials,
calculated approximately was made, being substituted the
following ratios:
( nR k )
S
n
( nR k )
ds
n
And let the equation (10) have the solution f* C (the set of
continuous functions on ).Then
={1,2…} such that
0
N>N0 the discrete system, obtained by using the discrete
double layer potential operator (its properties has been
(N)
studied), has unique solution {f jk }, k
*
| f jk
(N)
f jk |
( )(
(9)
L/2
(x)
i
dx
L/2
dx
f
*
(
f*
)
N
(x)
L
li ; li
i 0
(x)
dx ),
ds)
; {
sequence of partitions of
N
1
T(x, y)
nR ds
(11)
-smooth closed Jordan curve; M-quantity of
i
i 0
cooled channels;
i
Let
0, d
-density of a logarithmic potential uniformly
N
,,
N
)
p.
where d-diameter , and the splitting
2
2
C
Then for all
continuous on )
and z
,(z
(C
- space of all functions
x iy )
i 0
distributed on
M
i
si .
S
I
i 0
f ( z)
,
M
Thus curve
i
is
those, that is satisfied condition
p
M
1
satisfies the condition 2
N N 1 --the
}N 1 -- the sequence of
positive numbers such that the pair (
M
dx
x
i
3.2. In difference from [4] we offer to decide the given
boundary value problem (2)-(4) as follows. We suppose that
distribution of temperature T(x,y) we locate as follows:
where
1, m j ; j 1, n;
where C( ) is constant, depending only on
M
S
(x)
0
x
N
S i
(where
f*
N
i
(x)
x
L/2
(10)
f*
f*
x
0
i
nR k S
(x)
N
N
nR k ds
x
0
In activities [2] the discretization of an antline Ã
International Science Index 3, 2007 waset.org/publications/3293
( (s)
where
where
S i
1
2
( s)
knT 0n
positively are oriented and are given
f
C
i 0
in a parametric kind:
x=x(s), y=y(s), s [0, L]
Using BIEM and expression (9) problem (2)-(4) we shall put
to the following system of boundary integral equations:
L
,
ln
f ( z)
( )
2d
ln
f
~
f ( z)
f ( z)
2d
f
f
( )
x
0
d
l
f
182
( x)
dx
x
d
f
( x)
( x)
x2
dx
2
C
l
( x)
;
Z
dx
4. World Academy of Science, Engineering and Technology
International Journal of Mathematical, Computational Science and Engineering Vol:1 No:3, 2007
where
L
f ( z k ,e 1 )
f ( z)
,
zm,e
( y k ,e
x)
z
( x k ,e
z k ,e
1
under boundary conditions III kinds from a leg of gas
and boundary conditions I kinds from a leg of a
cooling air
f ( z)
2
(z)
y k ,e )( x k ,e
1
f ( z k ,e )
x k ,e )( y k ,e
y)
2
Tv (x, y)
f ( z)
0
Ti 0
(15)
Were Ti 0 -unknown optimum temperature of a wall of
a blade from a leg of a cooling air.
L , f ( z ) -two parameter ( depending on
parameters)
and
quadrature formula for logarithmic double layer potential
~ - double layer logarithmic potential operator with C (
f ( z)
) – constant, dependent only from a curve
f
(x ) a
3.4. The developed technique for the numerical decision of a
stationary task heat conduction in cooled
can be
distributed also on cvazistasionare case.
Let's consider a third regional task for cvazilines of the
equation heat conduction
module of a continuity of functions f;
I
f (zk, j 1 )
f ( z)
,
zm ,e
ln
International Science Index 3, 2007 waset.org/publications/3293
I
1
zk, j
,
z
x
T
x
zk, j
1
i
f ( z ) - two parameter (depending on
and
parameters) quadrature formula for logarithmic potential
simple layer; f (z ) - simple layer logarithmic potential
y
(Tci
Ti)
( z)
k
0
(16)
(T )
Ti
n
0
(17)
For lines of a task (14) - (15) we shall take advantage of
substitution Kirkov
T
A
operator
z k ,e
T
y
(T )
2
(z)
zk, j
f (zk, j )
(T )
( )d
(18)
0
, z k ,e
x k ,e
z k ,e z k ,e
iy k ,e
z
{z k ,1 ,..., z k ,mk }, z k ,1
max z k , j
j 1, mk
1
Then the equation (14) is transformed to the following
equation Laplace:
2
zk ,2
...
zk , j
are developed effective from the point of view of
realization on computers the numerical methods basing on
again constructed, converging two-parametric quadratute
processes for the discrete operators logarithmic potential of
a double and of a simple layer (the regular errors are
appreciated and mathematically the methods quadratures for
the approximate solution Fredgolm I and II boundary
integral equation are proved –is made regularization on
Tihonov and the appropriate theorems are proved.
3.3. The given technique of calculation of a temperature
field of a blade can be applied and to blades with the plug –
in splash plate. By their consideration in addition to
boundary conditions III kinds adjoin also conditions of
interfaces between segments of a partition of an outline as
equalities
of
temperatures
and
heat
flows
Tv ( x, y )
Tv ( x, y )
n
Tv 1 ( x, y )
Tv 1 ( x, y )
n
(13)
2
y2
A
0
(19)
For preservation lines converging composed in a regional
condition (15) we shall accept in initial approximation
constant (T) = lc. Then from (16) we have
T=A/ c
(20)
And the regional condition (15) will be transformed as
follows:
i
(Tci
Ai /
c
)
Ai
n
0
(21)
So, the stationary task (17), (19) method of the boundary
integrated equations is decided. If the decision L (x, y) in a
point (x, y) of a linear third regional task (17), (19) for the
equation Laplace to substitute in (16) and after integration to
decide (solve) the appropriate algebraic equation, which
degree is higher unit than a degree of function (T), we
shall receive meaning of temperature T (x, y) in the same
point. Thus in radicals the algebraic equation of a degree
above fourth is decided
(14)
Where
- number of segments of a partition of an
outline of section of a blade; x,y- coordinates. At finding
of best values T(chiller), it is necessary to decide a return
problem of heat conduction. For it is necessary to find
at first solution of a direct problem of heat conduction
2
x
z k , mk
A
a0T4+ a1T3+ a2T2+ a3T+ a4=A,
(22)
That corresponds to the task (T) as the multimember of a
degree above by third. In result the temperature field will be
determined as a first approximation, as the boundary
condition (17) took into account constant meaning heat
conduction lc in convective thermal flows. According to it
183
5. World Academy of Science, Engineering and Technology
International Journal of Mathematical, Computational Science and Engineering Vol:1 No:3, 2007
(1)
(1)
we shall designate this decision T (accordingly A ). For
definition subsequent and (2) (accordingly T(2)) the function
and A( ) is displayed in a number Taylor a vicinity T(1)
and the linear members are left in it only. In result is
received a third regional task for the equation Laplace
is
concerning function And A(2). Temperature T(2)
determined by the decision of the equation (18).
International Science Index 3, 2007 waset.org/publications/3293
3.5. The repeated computing experiments with use
BIEM on calculation of temperature fields nozzle and
working blades with various quantity and arrangement
of cooling channels have a difficult configuration have
shown, that for practical calculations in the approach,
offered us, the discretization of areas of an integration
can be conducted with rather smaller quantity of
discrete points. Thus the reactivity of the developed
algorithms and accuracy of evaluations is increased. The
accuracy of calculation of
temperatures, required
consumption of a cooling air, heat flows, losses from
cooling margins of safety etc. essentially depends on
reliability
of
boundary
conditions, included
in
calculation, of heat exchange.
3.6. It is considered piece-polynomial smoothing of
structures cooled gas-turbine blades with automatic
conjecture: the method of the least squares, device spline
and smooth is used.
3.6.1. Let equation of sites of a structure cooled blades is
polynomial of the third order.
y(x)=a0+a1x+a2x2+a3x3
(23)
The equation of measurements of target coordinate has a
kind:
Zy=a0+a1x+a2x2+a3x3+
y
(24)
where Zy= z1y, z2y, …, zny T– Vector of measurements of
target coordinate, n-quantity(n-amount) of points in a
examined interval. For an estimation polynomial factors
(23) the method of the least squares of the following kind is
used
=(XTX)-1(XTZy)
D =(XTX)-1
(25)
2
(26)
where
1 x1 x12 x13
X=
2
3
1 x2 x2 x2
2
3
1 x3 x3 x3
- Structural matrix;
............
2
3
1 xn xn xn
Estimations of factors for the first site is received under the
formula (25). Beginning with second, the components of a
vector pay off on experimental data from this site, but in
view of parameters found on the previous site. Thus, each
subsequent site of a structure we shall choose with blocking.
Thus it is expedient to use the following linear connections
between the appreciated parameters of the previous site
N 1
and required
N
N-
of a site:
A N=V,
(27)
3
1 xe xe2 x e
2
A= 0 1 2 x e 3 x e
,
(28)
0 0 2 6 xe
a0 N
1
a1N 1 xe
a 2 N 1 xe2
V= a1N
1
a 2 N 1 xe
3a 3 N 1 xe2
2a 2 N
1
3
a3 N 1 xe
,
(29)
6a 3 N 1 x e
e=(N-1)(n-L); L- Number points of blocking.
The expressions (27)-(29) describe communications, which
provide joining of sites of interpolation on function, first and
second with derivative.
Taking into account accuracy of measurements, the task of
definition of unknown factors of model in this case can be
formulated as a task on conditional: minimization of the
square-law form (Zy-X )T 2I(Zy- )under a limiting
condition (27). Here I - individual matrix. For the decision
of such tasks usually use a method of uncertain multipliers
Lagrange. In result we shall write down the following
expressions for estimation a vector of factors at presence of
linear connections (27):
~T
D~
=
T
D
+(VT-
T
AT)[A(XTX)-1AT]-1A(XTX)-1
(XTX)-1AT[A(XTX)-1AT]-1A(XTX)-1
(30)
2
(31)
Substituting matrixes A,
and vectors Zy and V in
expressions (25), (26), (30) and (31), we receive an
estimation of a vector of factors for a site of a structure
cooled
with number N, and also
a
matrix of mistakes of estimations.
As a result of consecutive application of the described
procedure and use of experimental data we shall receive
peace-polynomial interpolation of a researched site with
automatic
.On the basis of the carried out
experimental researches is shown, that optimum overlapping
in most cases is the 50%-s' overlapping.
D -dispersion a matrix of mistakes;
= a0, a1, a2, a3
T
- Vector of estimated factors.
3.6.2. Besides peace-polynomial regression exist which
represent polynomial (low odd degrees - third, fifth),
continuity, subordinated to a condition, of function and
derivative (first and second in case of cubic spinal in
184
6. World Academy of Science, Engineering and Technology
International Journal of Mathematical, Computational Science and Engineering Vol:1 No:3, 2007
general(common) points of the next sites. If the equation of
a structure cooled gas-turbine blades is described cubic
spinal submitted in obvious polynomial a kind (23), the
factors 0, 1, 2, 3 determining j- spinal, i.e. line
connecting the points Zj=(xj, yj) and Zj+1=(xj+1, yj+1),
calculate as follows:
a0
zj;
a1
z 'j ;
a2
''
j
z /2
3( z j
a3
z 'j'' / 6
2( z j
(32)
z j )h
1
International Science Index 3, 2007 waset.org/publications/3293
2
j 1
z j 1 )h j 31
hj+1= zj+1-zj , j= 1, N
'
j
2z h
1
j 1
z 'j h j 21
z
'
j 1
a2
a3
(z j
h ;
z 'j 1 h j 21 ;
1
z j )h j 11 ;
1
(( z j
(( z j
2
2
[1] Pashaev A.M., Sadykhov R.A., Iskenderov M.G., Samedov A.S.,
Sadykhov A.H. (1997). The effeciency of potential theory method for
solving of the tasks of aircraft and rocket design. 10-th National Mechanic
Conference. Istanbul Technical University, Aeronautics and astronautics
faculty, Istanbul, Turkey, July, p.61-62. 1997.
[2] R.A. Sadigov, A.S. Samedov, (1998). Modelling of temperature fields
of elements of base turbines, scientists of a slip zTU, Baku, Vol.VI,
5,
p.234-239.
[3] Pashaev A.M., Sadykhov R.A., Samedov A.S. (1999). Highly effective
methods of calculation temperature fields of blades of gas turbines. V
International Symposium an Aeronautical Sciences “New Aviation
Technologies of the XXI century”, A collection of technical papers, section
N3, Zhukovsky, Russia, August 1999.
[4] L.N. Zisina-Mologen and etc., (1974). Heat Exchange in turbineengines. M.,
[5] G. Galicheiskiy, (1996). A thermal guard of blades, .:
I, 1996.
[6] A.M.Pashaev, R.A.Sadiqov, C.M.Hajiev, (2002). The BEM Application
in development of Effective Cooling Schemes of Gas Turbine Blades. 6th
Bienial Conference on Engineering Systems Design and Analysis, Istanbul,
Turkey, July, 8-11.
(33)
z j 1 )h j
z j 1 )h j
REFERENCES
1
j 1
3.6.3. Let's consider other way smooth
of a
structure cooled gas-turbine blades on the precisely
measured meaning of coordinates in final system of discrete
points distinct from method of spinal-function and also
effective from the point of view of realization on computers.
Let equation of sites of a structure cooled blades is
described by the multimember of the third order of a type
(23), then by taking advantage a method smooth supply (the
conditions smooth of function are carried out and first by
derivative) we shall define its factors
a0 z j ;
a1
calculated in tens interest. Therefore, the application of
perfect methods of calculation of temperature fields of
elements of gas turbines is one from actual problems of an
air engine building. The efficiency of these methods in the
total rends directs influence to operational manufacturability
and reliability of elements of designs, and also on
acceleration characteristics of the engine.
1
2
1
2
(z j
(z j
1
1
z j )h
z j )h
1
j 1
1
j 1
1
j 1
)h ;
)h j 21 ;
j= 1, N 1 S , S=1.
If it’s required to perform a condition of function smooth
first and second derivative, i.e. appropriate smooth of cubic
splines, we shall deal with the multimember of the fifth
degree (degree of the multimember is equal 2S + 1, i.e. S =
2).
The advantage of such approach (smooth supply) consists
that it is not necessary to decide system of the linear
algebraic equations, as in case of application spinal, though
the degree of the multimember is higher on 2.
4. CONCLUSIONS
In view of extreme complexity of appearances determining
regularities of heat exchange, value
0
with an adequate
accuracy purely theoretically to calcite usually it fails.
Therefore practically they prefer to determine from an
experimental data generalized because of the theory of a
similarity. As per the last years there were activities,
permitting to take into account influence to heat exchange of
an initial degree of a turbulence, angle of attack, mass forces
and radiation of gas, compressibility and acceleration of a
flow, temperature non-stationary at increase and drop of a
load etc.[5]. Between that, the recommendations, being
available in the literature, at the best allow to determine
cooling of an air i
factors
0 with accuracy +15%
with accuracy + 10%. The latter does not mean, certainly,
that the errors in definition of temperature of details also are
185