This document discusses a numerical study of supersonic flow in conical rocket nozzles using computational fluid dynamics (CFD). The study uses Gambit software to design nozzle geometries and Fluent software to simulate flows. Specifically, it analyzes the flow in a conical nozzle with a divergence angle of 7 degrees. The results show the variation in parameters like Mach number, pressure, temperature, and velocity across the nozzle. Mach number increases from subsonic to supersonic values, static pressure decreases, and total temperature remains nearly constant before increasing near the nozzle exit.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
This document outlines the contents of the course ME 6604 Gas Dynamics and Jet Propulsion. It contains 5 units:
1. Basic concepts and isentropic flows, including concepts of compressible flow, stagnation properties, and flow through nozzles and diffusers.
2. Flow through ducts, including Fanno flow with friction and Rayleigh flow with heat transfer.
3. Normal and oblique shocks, including governing equations and properties across shock waves.
4. Jet propulsion, including theories of jet propulsion and performance of ramjets, turbojets, turbofans and turboprops.
5. Space propulsion, including rocket propulsion principles, types of rocket
Unit1 principle concepts of fluid mechanicsMalaysia
This document discusses key concepts in fluid mechanics including temperature scales, pressure measurements, and fluid properties. It defines temperature scales like Celsius, Fahrenheit, Kelvin and Rankine and shows conversions between them using formulas. It describes different pressure terms like atmospheric pressure, gauge pressure, absolute pressure and vacuum. Atmospheric pressure is the pressure at sea level of about 101 kPa. Gauge pressure is measured relative to atmospheric pressure and can be positive or negative. Absolute pressure is the sum of gauge and atmospheric pressures. Vacuum refers to a perfect empty space with zero pressure. Formulas are provided to convert between these pressure terms and examples are given to demonstrate conversions and calculations.
Diffusers are extensively used in centrifugal
compressors, axial flow compressors, ram jets, combustion
chambers, inlet portions of jet engines and etc. A small change in
pressure recovery can increases the efficiency significantly.
Therefore diffusers are absolutely essential for good turbo
machinery performance. The geometric limitations in aircraft
applications where the diffusers need to be specially designed so
as to achieve maximum pressure recovery and avoiding flow
separation.
The study behind the investigation of flow separation in a planar
diffuser by varying the diffuser taper angle for axisymmetric
expansion. Numerical solution of 2D axisymmetric diffuser model
is validated for skin friction coefficient and pressure coefficient
along upper and bottom wall surfaces with the experimental
results of planar diffuser predicted by Vance Dippold and
Nicholas J. Georgiadis in NASA research center [2]
.
Further the diffuser taper angle is varied for other different
angles and results shows the effect of flow separation were it is
reduces i.e., for what angle and at which angle it is just avoided.
This document discusses pressure measurement. It defines pressure as the force exerted by a fluid per unit area. Absolute pressure is measured with respect to zero pressure, while gauge pressure is absolute pressure minus atmospheric pressure. Pascal's Law states that pressure is equally distributed in all directions in a static fluid. Hydrostatic law relates pressure, depth, and fluid density. Manometry uses hydrostatic law to measure pressure by relating the height of a fluid column to pressure. Common pressure measurement instruments include piezometers, manometers, and pressure transducers such as capsules, bellows, bourdon tubes, and LVDT transducers, which convert pressure into mechanical movement.
This document contains 73 comments on "Fluid Mechanics Fundamentals and Applications" by Yunus Cengel and Michael Boles. The comments note typos, provide suggestions to improve clarity or accuracy, and point out places where figures or explanations could be enhanced. Suggestions include rephrasing sentences for correctness, modifying figures, and adding mathematical definitions or explanations for concepts like the Leibnitz theorem before applying it. The goal of the comments is to refine the technical details and explanations provided in the textbook.
There are several types of pressure measurements. Absolute pressure is measured relative to a full vacuum and uses units like PSIA. Atmospheric pressure refers to pressure at sea level, about 14.7 PSIA. Barometric pressure measures atmospheric conditions using units like millibars. Compound pressure measures from full vacuum through atmospheric pressure to positive gauge pressure in PSIC. Differential pressure measures the difference between two pressures in PSID. Gauge pressure is measured relative to ambient atmospheric pressure in PSIG. Vacuum pressure refers to pressures below atmospheric measured in PSIV or inches of mercury.
This document contains solutions to problems from Chapter 3 of the textbook "Fluid Mechanics: Fundamentals and Applications" by Çengel & Cimbala. The chapter discusses pressure and fluid statics. The solutions cover topics such as absolute versus gauge pressure, pressure measurements using manometers and barometers, and pressure variations in fluids with depth. The document is the proprietary property of McGraw-Hill and is only to be used by authorized instructors for class preparation.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
This document outlines the contents of the course ME 6604 Gas Dynamics and Jet Propulsion. It contains 5 units:
1. Basic concepts and isentropic flows, including concepts of compressible flow, stagnation properties, and flow through nozzles and diffusers.
2. Flow through ducts, including Fanno flow with friction and Rayleigh flow with heat transfer.
3. Normal and oblique shocks, including governing equations and properties across shock waves.
4. Jet propulsion, including theories of jet propulsion and performance of ramjets, turbojets, turbofans and turboprops.
5. Space propulsion, including rocket propulsion principles, types of rocket
Unit1 principle concepts of fluid mechanicsMalaysia
This document discusses key concepts in fluid mechanics including temperature scales, pressure measurements, and fluid properties. It defines temperature scales like Celsius, Fahrenheit, Kelvin and Rankine and shows conversions between them using formulas. It describes different pressure terms like atmospheric pressure, gauge pressure, absolute pressure and vacuum. Atmospheric pressure is the pressure at sea level of about 101 kPa. Gauge pressure is measured relative to atmospheric pressure and can be positive or negative. Absolute pressure is the sum of gauge and atmospheric pressures. Vacuum refers to a perfect empty space with zero pressure. Formulas are provided to convert between these pressure terms and examples are given to demonstrate conversions and calculations.
Diffusers are extensively used in centrifugal
compressors, axial flow compressors, ram jets, combustion
chambers, inlet portions of jet engines and etc. A small change in
pressure recovery can increases the efficiency significantly.
Therefore diffusers are absolutely essential for good turbo
machinery performance. The geometric limitations in aircraft
applications where the diffusers need to be specially designed so
as to achieve maximum pressure recovery and avoiding flow
separation.
The study behind the investigation of flow separation in a planar
diffuser by varying the diffuser taper angle for axisymmetric
expansion. Numerical solution of 2D axisymmetric diffuser model
is validated for skin friction coefficient and pressure coefficient
along upper and bottom wall surfaces with the experimental
results of planar diffuser predicted by Vance Dippold and
Nicholas J. Georgiadis in NASA research center [2]
.
Further the diffuser taper angle is varied for other different
angles and results shows the effect of flow separation were it is
reduces i.e., for what angle and at which angle it is just avoided.
This document discusses pressure measurement. It defines pressure as the force exerted by a fluid per unit area. Absolute pressure is measured with respect to zero pressure, while gauge pressure is absolute pressure minus atmospheric pressure. Pascal's Law states that pressure is equally distributed in all directions in a static fluid. Hydrostatic law relates pressure, depth, and fluid density. Manometry uses hydrostatic law to measure pressure by relating the height of a fluid column to pressure. Common pressure measurement instruments include piezometers, manometers, and pressure transducers such as capsules, bellows, bourdon tubes, and LVDT transducers, which convert pressure into mechanical movement.
This document contains 73 comments on "Fluid Mechanics Fundamentals and Applications" by Yunus Cengel and Michael Boles. The comments note typos, provide suggestions to improve clarity or accuracy, and point out places where figures or explanations could be enhanced. Suggestions include rephrasing sentences for correctness, modifying figures, and adding mathematical definitions or explanations for concepts like the Leibnitz theorem before applying it. The goal of the comments is to refine the technical details and explanations provided in the textbook.
There are several types of pressure measurements. Absolute pressure is measured relative to a full vacuum and uses units like PSIA. Atmospheric pressure refers to pressure at sea level, about 14.7 PSIA. Barometric pressure measures atmospheric conditions using units like millibars. Compound pressure measures from full vacuum through atmospheric pressure to positive gauge pressure in PSIC. Differential pressure measures the difference between two pressures in PSID. Gauge pressure is measured relative to ambient atmospheric pressure in PSIG. Vacuum pressure refers to pressures below atmospheric measured in PSIV or inches of mercury.
This document contains solutions to problems from Chapter 3 of the textbook "Fluid Mechanics: Fundamentals and Applications" by Çengel & Cimbala. The chapter discusses pressure and fluid statics. The solutions cover topics such as absolute versus gauge pressure, pressure measurements using manometers and barometers, and pressure variations in fluids with depth. The document is the proprietary property of McGraw-Hill and is only to be used by authorized instructors for class preparation.
This document provides an overview of fluid statics and pressure measurements. It begins with defining key fluid properties like viscosity and continuum hypothesis. It then discusses pressure at a point using Pascal's law and basic equations for pressure fields. The hydrostatic condition of zero acceleration is examined, leading to equations for pressure variation in incompressible and compressible fluids. Standard atmospheric models and various pressure measurement techniques like manometers, barometers, and mechanical devices are also summarized. Example problems are provided to demonstrate applications of the fluid statics concepts.
This document provides a course plan for a class on Gas Dynamics and Jet Propulsion taught by Mr. R. Deepak at KIT-Kalaignar Karunanidhi Institute of Technology. The course covers 5 units: basic concepts and isentropic flows, flow through ducts, normal and oblique shocks, jet propulsion, and space propulsion. The course aims to help students understand compressible flow, shock waves, and jet and rocket propulsion. It includes learning objectives, outcomes, assignments, exams, reference materials and an evaluation plan following Anna University guidelines.
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
The document discusses steady flow processes and the steady flow energy equation. It provides the conditions that must be satisfied for a steady flow process, including constant mass flow rate, constant fluid properties over time, and uniform rates of work, heat, and energy transfer. It then derives the steady flow energy equation and discusses its various terms. Finally, it provides examples of applying the equation to boilers and condensers.
Pressure Handbook for Industrial Process Measurement and ControlMiller Energy, Inc.
Illustrated handbook provides clear explanation of pressure concepts and measurement. Various sensor technologies are explained and compared. Good quick reference.
The document provides information about pressure measurement devices. It discusses the barometer and how it is used to measure atmospheric pressure by measuring the height of a mercury column. It also discusses manometers, which are commonly used to measure small and moderate pressure differences by using different fluids in a U-tube configuration. Differential manometers can be used to measure pressure drops across sections in a flow system by connecting the legs of the manometer to the two points of interest.
This document discusses pressure measurements and different types of pressure gauges. It defines pressure as force per unit area and describes two types: static and dynamic. Static pressure refers to a constant force, while dynamic pressure varies. Common pressure units are then defined. Pressure gauges are classified as mechanical or electromechanical. Mechanical gauges include U-tube manometers, well manometers, and force summing devices like diaphragms, bellows, and Bourdon tubes which convert pressure into displacement.
The document summarizes an experiment investigating flow around a 90-degree bend in a rectangular duct. Pressure measurements were taken along the inner and outer curved walls and across a radial section of the bend. The measurements showed that pressure decreases around the inner wall and increases around the outer wall, as predicted by assuming a free vortex velocity distribution in the bend. The pressure distribution across the radial section also closely matched the calculated values. The loss coefficient for pressure loss around the bend was determined to be 0.15 based on the change in pressure coefficient from the inlet to outlet sections.
This document presents explicit analytical solutions for pressure across oblique shock and expansion waves in supersonic flow. It begins by introducing the need for explicit pressure-deflection solutions in solving aerodynamic problems. It then presents:
1) Exact explicit solutions for pressure coefficient and ratio across weak and strong oblique shock waves as functions of deflection angle.
2) Third-order accurate explicit unitary solutions for pressure coefficient and ratio across oblique shocks and expansions as functions of deflection angle.
3) Numerical validation showing good agreement of the new explicit solutions with exact solutions for a range of Mach numbers and deflection angles.
Using the convergent steam nozzle type in the entranceSaif al-din ali
This document discusses using a convergent steam nozzle in the entrance region of a steam turbine. It provides background on steam turbines and how they work, describing how steam is expanded through nozzles to convert heat energy to kinetic energy. It then discusses different types of steam nozzles, focusing on convergent nozzles, and how nozzle shape affects steam velocity and pressure distribution. A numerical simulation will be performed to analyze pressure and velocity within a simple convergent nozzle design.
Total pressure measurements are important for determining velocity fields. The total pressure is defined as the pressure obtained by isentropically decelerating the flow to rest. Several factors can influence total pressure measurements, including incidence, Reynolds number, Mach number, velocity gradients, proximity to walls, and flow unsteadiness. Different probe geometries are better suited for different flow conditions in order to obtain accurate total pressure readings.
This document provides objectives and information about pressure measurement techniques. It discusses piezometers, barometers, bourdon gauges, and several types of manometers. The key points are:
- Piezometers, barometers, bourdon gauges, and manometers can be used to measure pressure.
- Piezometers use the height of liquid in a tube to determine pressure. Barometers measure atmospheric pressure using the height of a mercury column.
- Bourdon gauges use the deflection of a curved tube to indicate pressure differences over 1 bar.
- Manometers like the simple and differential types utilize the relationship between pressure and liquid height to measure pressures.
Pressure is defined as force per unit area. It has various units like pascals and pounds per square inch. High pressure can result from a small contact area like spike heels. Atmospheric pressure is caused by air weight and varies with altitude. Vapor pressure depends on temperature and indicates evaporation rate. Differential pressure is the difference between two pressures. Overpressure refers to absolute pressure above atmosphere. Manometers like U-tubes measure pressure differences using fluid columns. Laminar flow has constant velocity while turbulent flow is irregular. Pressure gauges measure vessel interior pressure.
This document summarizes an experiment analyzing potential flow theory for fluid flowing around a cylinder. Potential flow theory assumes an inviscid fluid and cannot account for drag. The experiment measured pressure coefficients around a cylinder in a wind tunnel and compared the results to potential flow theory. As expected, the experimental results showed drag due to viscosity that the theory could not capture. The boundary layer separation point varied with Reynolds number, supporting that viscosity affects the flow behavior.
This document provides short questions and answers related to gas dynamics and jet propulsion for a 6th semester mechanical engineering course. It covers topics like basic concepts of compressible flow, stagnation properties, flow through nozzles and diffusers, and flow through ducts. The questions define key terms, derive important equations, and ask students to analyze example problems involving isentropic flow of air through nozzles and ducts. The document aims to test students' understanding of fundamental compressible flow concepts and their ability to apply equations of compressible flow to practical problems.
Unit - I BASIC CONCEPTS AND ISENTROPIC FLOW IN VARIABLE AREA DUCTSsureshkcet
This document discusses gas dynamics and jet propulsion. It covers fundamental concepts of compressible flow, including the energy and momentum equations. It also discusses isentropic flow through variable area ducts like nozzles and diffusers. The conservation of mass, momentum and energy are applied to one-dimensional, steady, inviscid flow. The flow is analyzed through a variable area duct and expressions are developed relating pressure, velocity, temperature and Mach number for a perfect gas. Frictional flow in a constant area duct is also analyzed.
The document discusses different methods for measuring the flow rate of fluids, including orifice meters, venturi meters, and pitot tubes. It explains the principles behind each method, involving Bernoulli's theorem and relating changes in pressure and velocity. For orifice and venturi meters, it provides equations to calculate flow velocity based on the pressure difference measured by an attached manometer. The document also discusses Reynolds number and its significance in determining laminar or turbulent flow.
This document outlines key concepts in gas dynamics and compressible flow. It defines gas dynamics as the branch of fluid dynamics concerned with compressible flow. Some main topics covered include the fundamental laws of thermodynamics, definitions of basic terms like system and state, and equations for the conservation of mass, momentum and energy. It also discusses different types of flow and processes like steady/unsteady, laminar/turbulent and adiabatic. Stagnation properties of gases are defined using equations relating stagnation temperature, pressure and density to static properties.
Simulation of flow past cylinder at moderate Reynolds numbersShahzaib Malik
This document summarizes a computational fluid dynamics study of flow past a cylinder at moderate Reynolds numbers from 1 to 150. The study used the Fluent software to simulate the flow and examine the effects on flow patterns and hydrodynamic forces. As the Reynolds number increased, the flow transitioned from attached to separated flow with the formation of a von Karman vortex street. The drag coefficient decreased with Reynolds number until Re=75 then slightly increased at Re=150 due to swirling flow. The lift coefficient was negligible at low Re but increased at Re=75 and 150 due to vortex shedding.
Lightning Talk #9: How UX and Data Storytelling Can Shape Policy by Mika Aldabaux singapore
How can we take UX and Data Storytelling out of the tech context and use them to change the way government behaves?
Showcasing the truth is the highest goal of data storytelling. Because the design of a chart can affect the interpretation of data in a major way, one must wield visual tools with care and deliberation. Using quantitative facts to evoke an emotional response is best achieved with the combination of UX and data storytelling.
This document provides an overview of fluid statics and pressure measurements. It begins with defining key fluid properties like viscosity and continuum hypothesis. It then discusses pressure at a point using Pascal's law and basic equations for pressure fields. The hydrostatic condition of zero acceleration is examined, leading to equations for pressure variation in incompressible and compressible fluids. Standard atmospheric models and various pressure measurement techniques like manometers, barometers, and mechanical devices are also summarized. Example problems are provided to demonstrate applications of the fluid statics concepts.
This document provides a course plan for a class on Gas Dynamics and Jet Propulsion taught by Mr. R. Deepak at KIT-Kalaignar Karunanidhi Institute of Technology. The course covers 5 units: basic concepts and isentropic flows, flow through ducts, normal and oblique shocks, jet propulsion, and space propulsion. The course aims to help students understand compressible flow, shock waves, and jet and rocket propulsion. It includes learning objectives, outcomes, assignments, exams, reference materials and an evaluation plan following Anna University guidelines.
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
The document discusses steady flow processes and the steady flow energy equation. It provides the conditions that must be satisfied for a steady flow process, including constant mass flow rate, constant fluid properties over time, and uniform rates of work, heat, and energy transfer. It then derives the steady flow energy equation and discusses its various terms. Finally, it provides examples of applying the equation to boilers and condensers.
Pressure Handbook for Industrial Process Measurement and ControlMiller Energy, Inc.
Illustrated handbook provides clear explanation of pressure concepts and measurement. Various sensor technologies are explained and compared. Good quick reference.
The document provides information about pressure measurement devices. It discusses the barometer and how it is used to measure atmospheric pressure by measuring the height of a mercury column. It also discusses manometers, which are commonly used to measure small and moderate pressure differences by using different fluids in a U-tube configuration. Differential manometers can be used to measure pressure drops across sections in a flow system by connecting the legs of the manometer to the two points of interest.
This document discusses pressure measurements and different types of pressure gauges. It defines pressure as force per unit area and describes two types: static and dynamic. Static pressure refers to a constant force, while dynamic pressure varies. Common pressure units are then defined. Pressure gauges are classified as mechanical or electromechanical. Mechanical gauges include U-tube manometers, well manometers, and force summing devices like diaphragms, bellows, and Bourdon tubes which convert pressure into displacement.
The document summarizes an experiment investigating flow around a 90-degree bend in a rectangular duct. Pressure measurements were taken along the inner and outer curved walls and across a radial section of the bend. The measurements showed that pressure decreases around the inner wall and increases around the outer wall, as predicted by assuming a free vortex velocity distribution in the bend. The pressure distribution across the radial section also closely matched the calculated values. The loss coefficient for pressure loss around the bend was determined to be 0.15 based on the change in pressure coefficient from the inlet to outlet sections.
This document presents explicit analytical solutions for pressure across oblique shock and expansion waves in supersonic flow. It begins by introducing the need for explicit pressure-deflection solutions in solving aerodynamic problems. It then presents:
1) Exact explicit solutions for pressure coefficient and ratio across weak and strong oblique shock waves as functions of deflection angle.
2) Third-order accurate explicit unitary solutions for pressure coefficient and ratio across oblique shocks and expansions as functions of deflection angle.
3) Numerical validation showing good agreement of the new explicit solutions with exact solutions for a range of Mach numbers and deflection angles.
Using the convergent steam nozzle type in the entranceSaif al-din ali
This document discusses using a convergent steam nozzle in the entrance region of a steam turbine. It provides background on steam turbines and how they work, describing how steam is expanded through nozzles to convert heat energy to kinetic energy. It then discusses different types of steam nozzles, focusing on convergent nozzles, and how nozzle shape affects steam velocity and pressure distribution. A numerical simulation will be performed to analyze pressure and velocity within a simple convergent nozzle design.
Total pressure measurements are important for determining velocity fields. The total pressure is defined as the pressure obtained by isentropically decelerating the flow to rest. Several factors can influence total pressure measurements, including incidence, Reynolds number, Mach number, velocity gradients, proximity to walls, and flow unsteadiness. Different probe geometries are better suited for different flow conditions in order to obtain accurate total pressure readings.
This document provides objectives and information about pressure measurement techniques. It discusses piezometers, barometers, bourdon gauges, and several types of manometers. The key points are:
- Piezometers, barometers, bourdon gauges, and manometers can be used to measure pressure.
- Piezometers use the height of liquid in a tube to determine pressure. Barometers measure atmospheric pressure using the height of a mercury column.
- Bourdon gauges use the deflection of a curved tube to indicate pressure differences over 1 bar.
- Manometers like the simple and differential types utilize the relationship between pressure and liquid height to measure pressures.
Pressure is defined as force per unit area. It has various units like pascals and pounds per square inch. High pressure can result from a small contact area like spike heels. Atmospheric pressure is caused by air weight and varies with altitude. Vapor pressure depends on temperature and indicates evaporation rate. Differential pressure is the difference between two pressures. Overpressure refers to absolute pressure above atmosphere. Manometers like U-tubes measure pressure differences using fluid columns. Laminar flow has constant velocity while turbulent flow is irregular. Pressure gauges measure vessel interior pressure.
This document summarizes an experiment analyzing potential flow theory for fluid flowing around a cylinder. Potential flow theory assumes an inviscid fluid and cannot account for drag. The experiment measured pressure coefficients around a cylinder in a wind tunnel and compared the results to potential flow theory. As expected, the experimental results showed drag due to viscosity that the theory could not capture. The boundary layer separation point varied with Reynolds number, supporting that viscosity affects the flow behavior.
This document provides short questions and answers related to gas dynamics and jet propulsion for a 6th semester mechanical engineering course. It covers topics like basic concepts of compressible flow, stagnation properties, flow through nozzles and diffusers, and flow through ducts. The questions define key terms, derive important equations, and ask students to analyze example problems involving isentropic flow of air through nozzles and ducts. The document aims to test students' understanding of fundamental compressible flow concepts and their ability to apply equations of compressible flow to practical problems.
Unit - I BASIC CONCEPTS AND ISENTROPIC FLOW IN VARIABLE AREA DUCTSsureshkcet
This document discusses gas dynamics and jet propulsion. It covers fundamental concepts of compressible flow, including the energy and momentum equations. It also discusses isentropic flow through variable area ducts like nozzles and diffusers. The conservation of mass, momentum and energy are applied to one-dimensional, steady, inviscid flow. The flow is analyzed through a variable area duct and expressions are developed relating pressure, velocity, temperature and Mach number for a perfect gas. Frictional flow in a constant area duct is also analyzed.
The document discusses different methods for measuring the flow rate of fluids, including orifice meters, venturi meters, and pitot tubes. It explains the principles behind each method, involving Bernoulli's theorem and relating changes in pressure and velocity. For orifice and venturi meters, it provides equations to calculate flow velocity based on the pressure difference measured by an attached manometer. The document also discusses Reynolds number and its significance in determining laminar or turbulent flow.
This document outlines key concepts in gas dynamics and compressible flow. It defines gas dynamics as the branch of fluid dynamics concerned with compressible flow. Some main topics covered include the fundamental laws of thermodynamics, definitions of basic terms like system and state, and equations for the conservation of mass, momentum and energy. It also discusses different types of flow and processes like steady/unsteady, laminar/turbulent and adiabatic. Stagnation properties of gases are defined using equations relating stagnation temperature, pressure and density to static properties.
Simulation of flow past cylinder at moderate Reynolds numbersShahzaib Malik
This document summarizes a computational fluid dynamics study of flow past a cylinder at moderate Reynolds numbers from 1 to 150. The study used the Fluent software to simulate the flow and examine the effects on flow patterns and hydrodynamic forces. As the Reynolds number increased, the flow transitioned from attached to separated flow with the formation of a von Karman vortex street. The drag coefficient decreased with Reynolds number until Re=75 then slightly increased at Re=150 due to swirling flow. The lift coefficient was negligible at low Re but increased at Re=75 and 150 due to vortex shedding.
Lightning Talk #9: How UX and Data Storytelling Can Shape Policy by Mika Aldabaux singapore
How can we take UX and Data Storytelling out of the tech context and use them to change the way government behaves?
Showcasing the truth is the highest goal of data storytelling. Because the design of a chart can affect the interpretation of data in a major way, one must wield visual tools with care and deliberation. Using quantitative facts to evoke an emotional response is best achieved with the combination of UX and data storytelling.
This document summarizes a study of CEO succession events among the largest 100 U.S. corporations between 2005-2015. The study analyzed executives who were passed over for the CEO role ("succession losers") and their subsequent careers. It found that 74% of passed over executives left their companies, with 30% eventually becoming CEOs elsewhere. However, companies led by succession losers saw average stock price declines of 13% over 3 years, compared to gains for companies whose CEO selections remained unchanged. The findings suggest that boards generally identify the most qualified CEO candidates, though differences between internal and external hires complicate comparisons.
The impact of innovation on travel and tourism industries (World Travel Marke...Brian Solis
From the impact of Pokemon Go on Silicon Valley to artificial intelligence, futurist Brian Solis talks to Mathew Parsons of World Travel Market about the future of travel, tourism and hospitality.
We’re all trying to find that idea or spark that will turn a good project into a great project. Creativity plays a huge role in the outcome of our work. Harnessing the power of collaboration and open source, we can make great strides towards excellence. Not just for designers, this talk can be applicable to many different roles – even development. In this talk, Seasoned Creative Director Sara Cannon is going to share some secrets about creative methodology, collaboration, and the strong role that open source can play in our work.
Reuters: Pictures of the Year 2016 (Part 2)maditabalnco
This document contains 20 photos from news events around the world between January and November 2016. The photos show international events like the US presidential election, the conflict in Ukraine, the migrant crisis in Europe, the Rio Olympics, and more. They also depict human interest stories and natural phenomena from various countries.
The Six Highest Performing B2B Blog Post FormatsBarry Feldman
If your B2B blogging goals include earning social media shares and backlinks to boost your search rankings, this infographic lists the size best approaches.
1) The document discusses the opportunity for technology to improve organizational efficiency and transition economies into a "smart and clean world."
2) It argues that aggregate efficiency has stalled at around 22% for 30 years due to limitations of the Second Industrial Revolution, but that digitizing transport, energy, and communication through technologies like blockchain can help manage resources and increase efficiency.
3) Technologies like precision agriculture, cloud computing, robotics, and autonomous vehicles may allow for "dematerialization" and do more with fewer physical resources through effects like reduced waste and need for transportation/logistics infrastructure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A comparatively analysis of plate type H.E. and helical type H.E. using ANOVA...IRJET Journal
This document compares plate type and helical type heat exchangers using ANOVA analysis. It first describes the design and operation of each type of heat exchanger. It then outlines the methodology used, including equations for heat transfer coefficients and an overview of ANOVA analysis. The results section describes the design of each heat exchanger in CATIA software and presents graphs comparing their pressure drops and R2 regression factors. Finally, it concludes the plate heat exchanger offers advantages in terms of space, heat transfer efficiency, turbulence, flexibility and lifespan.
Numerical simulation and optimization of high performance supersonic nozzle a...eSAT Journals
Abstract The Principle purpose of a nozzle is to accelerate the flow to higher exit velocities. The fluid acceleration is based on the design criteria and characteristics. To achieve good performance characteristics with minimum energy losses a nozzle must satisfy all the design requirements at all operating conditions. This is possible only when the nozzle theory is assumed to be isentropic irrespective of the changes in pressure, temperature and density which is generally caused due to formation of a Shock Wave. The thesis focuses on the design, development and optimization of a Supersonic Convergent-Divergent Nozzle where the analytical results are validated using theory calculations. The simulation work is carried out for CD Nozzles with different angles of divergence keeping the other inputs fixed. The objective of the proposed thesis is to show the best Expansion ratio, Nozzle Pressure ratio (NPR) and Nozzle Area Ratio(NAR) where the thrust obtained by the supersonic nozzle is maximum. The simulation is then repeated for expansion gas the results of which are later compared with standard air to show which possesses better performance characteristics. The Nozzle design chosen is based upon existing literature studies. Key Words: CD Nozzle, Expansion Ratio, Nozzle Pressure Ratio (NPR), Nozzle Area Ratio(NAR),Divergence Angle etc…
Estimation of Heat Flux on A Launch Vehicle Fin at Hypersonic Mach Numbers --...Abhishek Jain
1. The document evaluates heat flux on a launch vehicle fin at hypersonic Mach numbers using computational fluid dynamics (CFD) simulations from Mach 1.5 to 8.
2. Key areas of interest on the vehicle include the nose, fins, and cylindrical region between fins which experience very high heat transfer fluxes. Accurately estimating these fluxes can help designers choose appropriate materials.
3. Validation studies showed the CFD code could accurately predict shock properties and heat fluxes on axisymmetric shapes to within 3-5% of experimental data. Simulations of the actual vehicle geometry found maximum heat fluxes on the nose and fin tips rather than stagnation points, with values varying along the fin.
Investigation on Divergent Exit Curvature Effect on Nozzle Pressure Ratio of ...IJERA Editor
The objective of this project work is to computationally analyze shock waves in the Convergent Divergent (CD) Nozzle. The commercial CFD code Fluent is employed to analyze the compressible flow through the nozzle. The analysis is about NPR (Nozzle Pressure Ratio) i.e., the ratio between exit pressure of the nozzle to ambient pressure. The various models of CD Nozzle are designed and the results are compared. The flow characteristic of shockwave for various design of CD Nozzle is also discussed. The purpose of this project is to investigate supersonic C-D nozzle flow for increasing NPR (Nozzle pressure ratio) through CFD. The imperfect matching between the pressures and ambient pressure and exit pressure leads to the formation of a complicated shock wave structure. Supersonic nozzle flow separation occurs in CD nozzles at NPR values far above their design value that results in shock formation inside the nozzle. The one-dimensional analysis approximations are not accurate, in reality the flow detaches from the wall and forms a separation region, subsequently the flow downstream becomes non-uniform and unstable. Shock wave affects flow performance of nozzle from NPR value 1.63 for existing geometrical conditions of nozzle. Problem of using this nozzle above 1.63NPR is shock wave at downstream of throat. After shock wave, static pressure increases further downstream of flow. It leads to flow separation and back pressure effects. Back pressure makes nozzle chocked. To investigate this problem, geometry of divergent portion is introduced and analysed through CFD. This is expected in resulting of reduction of flow separation and back pressure effect as well as increase in nozzle working NPR.
Investigation on Divergent Exit Curvature Effect on Nozzle Pressure Ratio of ...IJERA Editor
The objective of this project work is to computationally analyze shock waves in the Convergent Divergent (CD) Nozzle. The commercial CFD code Fluent is employed to analyze the compressible flow through the nozzle. The analysis is about NPR (Nozzle Pressure Ratio) i.e., the ratio between exit pressure of the nozzle to ambient pressure. The various models of CD Nozzle are designed and the results are compared. The flow characteristic of shockwave for various design of CD Nozzle is also discussed. The purpose of this project is to investigate supersonic C-D nozzle flow for increasing NPR (Nozzle pressure ratio) through CFD. The imperfect matching between the pressures and ambient pressure and exit pressure leads to the formation of a complicated shock wave structure. Supersonic nozzle flow separation occurs in CD nozzles at NPR values far above their design value that results in shock formation inside the nozzle. The one-dimensional analysis approximations are not accurate, in reality the flow detaches from the wall and forms a separation region, subsequently the flow downstream becomes non-uniform and unstable. Shock wave affects flow performance of nozzle from NPR value 1.63 for existing geometrical conditions of nozzle. Problem of using this nozzle above 1.63NPR is shock wave at downstream of throat. After shock wave, static pressure increases further downstream of flow. It leads to flow separation and back pressure effects. Back pressure makes nozzle chocked. To investigate this problem, geometry of divergent portion is introduced and analysed through CFD. This is expected in resulting of reduction of flow separation and back pressure effect as well as increase in nozzle working NPR.
Flow Inside a Pipe with Fluent Modelling Andi Firdaus
This document describes a numerical simulation of laminar and turbulent flow inside a pipe using Fluent software. The simulation models water flow inside a 1m diameter pipe that is 20m long. Two models are considered: laminar flow at a Reynolds number of 300 and turbulent flow at 8500. Theoretical equations for laminar and turbulent velocity profiles, entrance length, and Reynolds number correlations are presented. The numerical simulation sets up the models with appropriate boundary and material properties to solve the steady-state Navier-Stokes equations and compare results to experimental data.
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.
Numerical simulations have been undertaken
for the benchmark problem in a Square cavity by using
computational fluid dynamics software. This work aims at
discussing the fundamental numerical and computational
fluid dynamic aspects which can lead to the definition of
the following meshing methods and turbulence models.
The meshes used for the simulation are hexahedral,
hexahedral cell with near wall refinement, tetrahedral
grid, polyhedral, tetrahedral with near wall refinement
and polyhedral mesh with prism layer cells based the near
wall thickness of Y+ less than one. The turbulence models
used for the simulation work are AKN K-Epsilon Low-Re,
Realizable K-Epsilon, Realizable K-Epsilon Two-Layer,
standard K-Epsilon, standard K-Epsilon Low-Re,
Standard K-Epsilon Two-Layer, V2F K-Epsilon,
SST(Menter) K-Omega, and Standard(Wilcox) K-Omega.
From these meshes and turbulence models, we will
conclude the suitable mesh and turbulence for the
recirculation flow by the grid independent test. These
analytical values of results are compared with reference
data which gives an optimization of experimental work.
Unsteady simulation was ran for all the Grid Independent
mesh with the SST k omega model with the time step of
0.01 sec for 40 seconds. The flow nature is studied with
and without the temperature for Reynolds number, 1000
and 10000.
Effect of Geometry on Variation of Heat Flux and Drag for Launch Vehicle -- Z...Abhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
The research paper aims at studying the variation of the geometry of the launch vehicle nose and its effect on heat flux. CFDExpert software is first validated on NASA's hyperballistic model and then used on proposed geometries. Various nose radius and blending shapes are studied for effect on drag and heat flux. Cone ogive shape is found to decrease heat flux with an insignificant increase in drag. Authors Abhishek Jain (Zeus Numerix), Rohan Kedar and Prof V Kalamkar (SPCOE).
IRJET - Characteristics of 90°/90° S-Shaped Diffusing Duct using SST K-O Turb...IRJET Journal
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Comparision of flow analysis through a different geometry of flowmeters using...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IRJET- A Research Paper on Analysis of De-Laval Nozzle on Ansys WorkbenchIRJET Journal
This document discusses research analyzing the effects of changing throat diameter in a convergent-divergent (De Laval) nozzle using computational fluid dynamics (CFD) software. The study models different nozzle designs varying in throat diameter and material using ANSYS Workbench to compute gas flow. Previous research examining nozzle performance when modifying parameters like mesh quality and throat size are summarized. The document outlines the components and functioning of a De Laval nozzle, and explores its applications in rockets and engines.
Computational Estimation of Flow through the C-D Supersonic Nozzle and Impuls...IJMTST Journal
In this paper, CFD analysis of flow within, Convergent – Divergent rectangular super sonic nozzle and super sonic impulse turbine with partial admission have been performed. The analysis has been performed according to shape of a super sonic nozzle and length of axial clearance and the objective is to investigate the effect of nozzle-rotor interaction on turbine’s performance. It is found that nozzle-rotor interaction losses are largely dependent on axial clearance, which affects the flow within nozzle and the extent of flow expansion. Therefore selecting appropriate length of axial clearance can decrease nozzle-rotor interaction losses. The work is carried in two stages:1) Modeling and analysis of flow for rectangular convergent divergent super sonic nozzle. 2) Prediction of optimal axial gap between the nozzle and rotor blades by allowing the above nozzle flow. In the present work, using a finite volume commercial code, ANSYS FLUENT 14.5, carries out flow through the convergent divergent nozzle study. The nozzle geometry is modeled and grid is generated using ANSYS14.5 Software. Computational results are in good agreement with the experimental ones.
IRJET - CFD Analysis of Hot and Cold Steam Flow in an ElbowIRJET Journal
This document presents a computational fluid dynamics (CFD) analysis of hot and cold steam flow through an elbow pipe using ANSYS software. The study aims to analyze pressure, velocity, temperature and mass transfer distribution for both laminar and turbulent flow conditions. A venturi pipe is used as the hot inlet to aid mixing. Meshing and simulations are performed and results are presented for velocity, temperature, pressure and viscosity at different points within the elbow. The results provide insight into flow patterns that can be used as a reference for elbow pipe design.
Numerical Investigation of Heat Transfer from Two Different Cylinders in Tand...IJERA Editor
A two dimensional technique has been studied numerically to predict the heat transfer from two different cylinders
in tandem arrangement (one is circular and the other is elliptical) using finite element technique with RNG k-ε turbulent
model, taking into consideration the effect of gap ratio (L/Deq ) and Reynolds number , where the distance between
the centers of cylinders is L (L=30 mm and 37 mm), the equivalent diameter of cylinder is Deq=22.5mm and
the range of Reynolds number is 2x103
< Reeq < 21x103 .The commercial CFD software FLUENT was used to get
the thermofluid characteristics (temperature, velocity, kinetic energy and pressure contours ,coefficient of friction ,
heat transfer coefficient , Stanton number …… etc) of the flow around cylinders. The dependency of the heat transfer
coefficient, Stanton number (Sta), pressure drop, and friction factor for circular and elliptical cylinders on the gap
ratio is clear from the results. Results show that, for circular cross section, the heat transfer coefficient is increased as
velocity, and gap ratio increase. On the other hand Sta decreased as velocity increase. The pressure drop and hence
the friction factor increase for circular cylinder as gap ratio increases. For elliptical tube the heat transfer and Sta are
relatively equal to that for circular one at the same gap ratio, but the overall power consumption and friction factor
for elliptical tube is lower than that of circular one. As the elliptical cylinder fixed on the second position the heat
transfer and Sta
increase, on the other hand the pressure drop and hence the friction factor decreases. For all studied
arrangements the highest heat transfer is observed for the arrangement of circular-first and elliptical-second cylinder
and the minimum pressure drop and hence the friction factor are for the elliptical one
This document outlines an experiment to analyze converging-diverging (CD) nozzles. The experiment has two parts: 1) analyzing the outlet conditions of a single nozzle by comparing experimental and theoretical data, and 2) studying relationships between nozzle design parameters (area ratio, divergence angle) and flow characteristics (outlet speed, efficiency) for several nozzles. The document provides relevant theory, equipment descriptions, procedures, and methods to determine the success of each part. The goal is to better understand subsonic flow through CD nozzles and relationships between nozzle geometry and performance.
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Optimization of Closure Law of Guide Vanes for an Operational Hydropower Plan...Dr. Amarjeet Singh
This paper addresses the optimization of twostage closure law of guide vanes in an operational
hydropower plant of Nepal. The mathematical model
has been established in commercial software Bentley
Hammer, whose correctness has been validated by
comparing the results with the data of experimental
load rejection test. The validated mathematical model
has been employed to find the parameters of optimum
closure pattern, which minimizes the non-linear
objective function of maximum water pressure and
maximum rotational speed of turbine.
A fully integrated temperature compensation technique for piezoresistive pres...mayibit
This document describes a technique for fully integrating temperature compensation into piezoresistive pressure sensors. It presents a sensor model used to evaluate temperature and pressure characteristics with variations from the fabrication process. The technique aims to compensate for errors from a sensor's inherent cross-sensitivity to temperature and processing variations between sensors, allowing operation from -40°C to 130°C over a pressure range of 0-310 kPa. Hardware is specified to implement the technique, and an analysis discusses its effectiveness over the desired operating conditions.
A fully integrated temperature compensation technique for piezoresistive pres...
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1. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
Flow Analysis of Rocket Nozzle Using Computational Fluid
Dynamics (Cfd)
Pardhasaradhi Natta*, V.Ranjith Kumar**, Dr.Y.V.Hanumantha Rao***
*(Department of Mechanical Engineering, koneru lakshmiahUniversity, Guntur)
** (Assistant professor, Department of Mechanical Engineering, koneru lakshmiahUniversity, Guntur)
*** (professor, Department of Mechanical Engineering, koneru lakshmiahUniversity, Guntur)
ABSTRACT
A nozzle is used to give the direction to the gases Laval found that the most efficient conversion
coming out of the combustion chamber.Nozzle is occurred when the nozzle first narrowed, increasing
a tube with variable cross-sectional area. Nozzles the speed of the jet to the speed of sound, and then
are generally used to control the rate of flow, expanded again. Above the speed of sound (but not
speed, direction, mass, shape, and/or the pressure below it) this expansion caused a further increase in
of the exhaust stream that emerges from the speed of the jet and led to a very efficient
them.The nozzle is used to convert the chemical- conversion of heat energy to motion. The theory of
thermal energy generated in the combustion air resistance was first proposed by Sir Isaac
chamber into kinetic energy. The nozzle converts Newton in 1726. According to him, an aerodynamic
the low velocity, high pressure, high temperature force depends on the density and velocity of the
gas in the combustion chamber into high velocity fluid, and the shape and the size of the displacing
gas of lower pressure and low temperature.Our object. Newton’s theory was soon followed by other
study is carried using software’s like gambit 2.4 theoretical solution of fluid motion problems. All
for designing of the nozzle and fluent 6.3.2 for these were restricted to flow under idealized
analyzing the flows in the nozzle.Numerical study conditions, i.e. air was assumed to posses constant
has been conducted to understand the air flows density and to move in response to pressure
in a conical nozzle at different divergence degrees and inertia. Nowadays steam turbines are the
of angle using two-dimensional axisymmetric preferred power source of electric power stations
models, which solves the governing equations by and large ships, although they usually have a
a control volume method. The nozzle geometry different design-to make best use of the fast steam
co-ordinates are taken by using of method of jet, de Laval’s turbine had to run at an impractically
characteristics which usually designed for De- high speed. But for rockets the de Laval nozzle was
Laval nozzle. The present study is aimed at just what was needed.
investigating the supersonic flow in conical
nozzle for Mach number 3 at various divergence
degree of angle. The throat diameter and inlet II. MATERIAL AND METHODS
diameter is same for all nozzles with various MATHEMATICAL MODEL
divergence degree of angles. The flow is A mathematical model comprises equations
simulated using fluent software. The flow relating the dependent and the independent variables
parameters like pressure , Area of nozzle at exit and the relevant parameters that describe some
are defined prior to the simulation. physical phenomenon. Typically, a mathematical
The result shows the variation in the Mach model consists of differential equations that govern
number, pressure, temperature distribution and the behavior of the physical system, and the
turbulence intensity. associated boundary conditions. To start with fluent,
it is necessary to know if the meshed geometry is
Key words —conical nozzle, degree of angle, correct, so is checked. To ensue with, we are to
supersonic flow, Mach number, Control Volume define the model, material, operating condition and
boundary condition. Models are to be set in order to
I. INTRODUCTION define if any energy equation is dealt with our study,
Swedish engineer of French descent who, if the flow is viscous…etc. We have chosen coupled
in trying to develop a more efficient steam engine, solver, 2d implicit, absolute velocity formulation,
designed a turbine that was turned by jets of steam. cell based gradient option, superficial velocity
The critical component – the one in which heat porous formulation. As our flow is dealt with energy
energy of the hot high-pressure steam from the equation so is necessary to check them up. The
boiler was converted into kinetic energy – was the material is selected as air and the density as ideal
nozzle from which the jet blew onto the wheel. De gas to make the solution simpler. Under the solve
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2. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
command the control is selected for limiting the
pressure to a maximum of 5e+7 and Minimum of
1e+4. The initialization of value is computed from
the inlet. It is also necessary to select the appropriate The following are the results of nozzle with
approximation required in the residual command divergence angle of 7 degrees.
under monitors and check in plot to visualize the
progress of iteration. Once every parameter is VELOCITY COUNTOUR
described the iteration is performed till the value
gets converged to required approximation. The
Figures can be plotted between position in x-axis
and any other function in y-axis from plot command
or else to view vectors, contours or grid display
command is to be chosen.
III. RESULTS AND DISCUSSION
The geometry of the grid is designed by the
help of gambit tool and is made by using of method
of characteristics which usually designed for De-
Laval nozzle. On the same basic we take the throat
co-ordinates and exit co-ordinates for designing this
nozzle and after calculating, we get an angle nearly
7. and simulate it using Fluent software and after Figure: Velocity Contour For Nozzle With
this we take minimum degree of angle for conical Divergence Angle 7 Degrees.
nozzle i.e.7.0 and check the variation in Mach
Number and other properties to
CASE 1
Figure XY Plot for Velocity contours For Nozzle
with Divergence Angle of 7 Degrees.
In this, the nozzle is designed for Mach
no. 3. From Figure, it is clearly visualized that in the
convergent section at inlet point, Mach number, is in
the Sub-sonic region (=0.35) while at the throat,
Figure 1:nozzle at 70 grid display flow becomes Sonic (=1.02) and at the nozzle exit it
becomes Super-Sonic (=2.90) for which the nozzle
is designed. Near the wall, the Mach number is 1.65.
This is due to the viscosity and turbulence in the
fluid.
From the graph it is clearly observed that the
velocity is increased.
Figure 2:nozzle at 7 residual
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3. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
STATIC PRESSURE: TOTAL TEMPERATURE
Figure : Static Pressure Contour For Nozzle With
Divergence Angle Of 7 Degrees.
FIGURE: Temperature Contour For Nozzle With
Divergence Angle Of 7 Degrees
Figure: XY Plot For Static Pressure With
Divergence Angl Of 7 Degrees.
Static pressure is the pressure that is
exerted by a fluid. Specifically, it is the pressure
measured when the fluid is still, or at rest. The FIGURE : Xy Plot For Total Temperature With
above Figure reveals the fact that the gas gets Divergence Angle Of 7 Degrees.
expanded in the nozzle exit. The static pressure in
the inlet is observed to be 108 Pa and as we move The total temperature almost remains a
towards the throat there is a decrease and the value constant in the inlet up to the throat after which it
at the throat is found out to be 56 Pa. After the tends to increase. Near the walls the temperature
throat, there is sudden expansion and the static increases to 302 K. In the inlet and the throat the
pressure falls in a more rapid manner towards the temperature is 300 K. After the throat, the
exit of the nozzle. At the exit it is found to be 3.75 temperature increases to 301K at the exit. As we
Pa. move from the centre vertically upwards at the exit,
there is variation. At the centre it is 300 K, at the
walls it is 302 K and moving inward a little bit from
the wall the temperature reaches a maximum of 301
K.
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4. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
Turbulence intensity CASE 2:
The following are the results of nozzle with
divergence angle of 20 degrees.
VELOCITY COUNTOUR
Figure Turbulence Intensity Contour With
Divergence Angle Of 7 Degrees
Figure: Velocity contour For Nozzle with
Divergence Angle of 20 Degrees
Figure XY Plot For Turbulence Intensity
With Divergence Angle Of 7 Degrees.
The turbulent intensity at the convergent
section is very low (=1.01e+03 %). Almost till the
throat it remains almost a constant. At the throat Figure: XY Plot for Velocity contour With
there is a very small increase to 1.25e+03 %. As Divergence Angle of 20 Degrees
soon as it crosses the throat, there is a sudden
increase in the turbulent intensity due to the sudden From the Figure, it is clearly observed that
increase in the area. As we move towards the exit, Mach number in the convergent section is 0.24
there is a small patch in the centre where the (Sub-Sonic), at the throat it is 1.15(Sonic) and as we
turbulent intensity increases (1.48e+03 %) and then move in the divergent section, it keeps increasing
as the fluid stabilizes near the exit, there is a and at the exit it is 2.84(Super-Sonic). Parallel flow
decrease in the turbulent intensity (1.25e+03 %). is observed which is a characteristic of the conical
Near the walls the turbulent intensity is high due to nozzle and its design purpose (for Mach 3) is also
the reversals of flow. At the exit near the walls the solved. Mach number near the wall is less due to the
turbulent intensity reaches a maximum (=4.56e+03 viscosity and the turbulence (=1.54). The Mach
%). number for the default angle turns out to be 2.90 but
for a divergence angle of 20 degrees it comes out to
be 2.84. This is due to the change in the geometry
due to which flow also changes.
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5. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
STATIC PRESSURE
Figure: Static Pressure Contour with Divergence
Angle of 20 Degrees Figure: XY Plot For Total Temperature With
Divergence Angle Of 20 Degrees.
The total temperature almost remains a
constant in the inlet up to the throat. Increase is
observed after some distance from the throat
towards the exit as seen in the above Figure Near
the walls the temperature decreases to 298 K. In the
inlet and the throat the temperature is 300 K. After
the throat, the temperature increases to 302K at the
exit. At the exit, moving vertically upward there is
variation. The maximum value is not attained at the
centre but at some distance from the centre. At the
Figure: XY Plot for Static Pressure With centre it is 301 K and at the wall it is 298 K. The
Divergence Angle Of 20 Degrees. maximum value of 302 K is attained near the walls
but some distance away from it. There is not much
The above Figure shows that the gas gets difference in the total temperature contour when
over expanded in the nozzle exit. The static pressure compared to the default nozzle but the fact that in
in the inlet is observed to be 106 Pa and the value at the default nozzle, the temperature increases as soon
the throat is found out to be 65.2 Pa. At the exit the as the throat is crossed but in this it is clearly
pressure is found to be 8.85 Pa. Right from the inlet observed that there is a beginning in the rise in
to the throat to the exit the static pressure tends to temperature after some distance from the throat.
decrease. There is a considerable decrease observed
after the throat to the exit where there is a large drop Turbulence intensity
in the static pressure. As compared to the previous
case there is a change in the exit static pressure
value.
TOTAL TEMPERATURE
Figure Turbulence Intensity Contour With
Divergence Angle Of 20 Degrees.
Figure: Total Temperature Contour With Divergence
Angle Of 20 Degrees.
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6. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
Figure : XY plot for turbulence intensity With
Divergence Angle Of 20 Degrees. Figure : XY Plot For Velocity contour With
Divergence Angle Of 30 Degrees
The turbulent intensity at the convergent
section is 8.17e+01 % which is low. It remains a The region in the inlet is sub-sonic and has
constant almost up to the throat. At the throat it an inlet value of 0.23. As it nears the throat it
increases to 8.75e+02 %. Since there is an increase becomes sonic and at the throat it is 1.51 and the
in the area, there is also an increase in the turbulent exit is super-sonic and it exits with a Mach number
intensity as we move towards the exit from the of 3.06. The motive of the design of the conical
throat. There is a difference when compared to the nozzle is also achieved with parallel flow. There are
default nozzle. There is a larger increase in the area irregularities near the walls due to the reversals of
just after in the default case where as the increase in flow. The Mach number as observed in the previous
the area is more gradual in the divergence angle of 7 case of divergence angle of 20 degrees was 2.84
case. As we move towards the exit, there is a small which is less than the present case.
patch in the centre extending from the throat to
almost the centre between the throat and the exit STATIC PRESSURE:
where the turbulent intensity increases (1.93e+03 %)
and as we exit there is stabilization of the fluid near
the exit of the nozzle (1.67e+03 %). The turbulent
intensity reaches a maximum of 4.84e+03 % near
the walls as there is reversal of flow and turbulence
due to the walls.
CASE 3:
The following are the results of nozzle with
divergence angle of 30 degrees.
Figure: Static Pressure Contour With Divergence
Angle Of 30 Degrees
Figure : Velocity Contour With Divergence Angle
of 30 Degrees
Figure: XY Plot of Static Pressure With Divergence
Angle Of 30 Degrees
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7. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
The static pressure contour is also similar Turbulence intensity:
to that of the previous version. It decreases to the
throat and then continues to decrease till the exit.
The value at the inlet is 106 Pa and at the throat it is
55 Pa. There is also a steep decrease after the throat
where the static pressure reduces to 2.72 Pa at
halfway around outlet and remains the same till the
exit. There is a slight decrease in the minimum
value of static pressure from 8.8 to 2.24 pa.
Total temperature:
Figure Turbulence Intensity Contour With
Divergence Angle Of 30 Degrees
Figure : Total Temparature Contour With
Divergence Angle Of 30 Degrees
Figure XY Plot of Turbulence Intensity With
Divergence Angle of 30 Degrees
The turbulent intensity at the convergent
section is 1.01e+03 % which is very low. It remains
Figure: XY Plot of Total Temperature With a constant almost up to the throat. At the throat it
Divergence Angle of 30 Degrees increases to 1.25e+03%. There is an increase in the
value after the throat as there is a sudden expansion
There is a lot of variation in the total to a bigger area than the nozzle. There is also a
temperature plot. In the previous case it was difference in the pattern when compared to the 7
observed that there is an increment in the nozzle. There were patches in the 1st 2 nozzles
temperature after the throat and midway from the (default and 20) but here there are no patches and
exit but in this case, there is a difference. Here the the flow stabilization which was observed towards
temperature tends to increase just after inlet. After the end of the nozzle in the other nozzles is not
this it remains a constant till the exit except near the observed here as the increase is right from the throat
walls where it increases further and then decreases to the exit. The maximum value however is reached
as we move from the centre to the wall. The value at near the walls as the reversals cause more
the inlet is 300 K and then increases near the inlet to turbulence. The exit turbulent Intensity value at the
300.25 K. At the throat as well as the exit, the value centre is 1.49e+03%. Moving vertically upward (or)
remains the same. The maximum value attained is downward at the exit, at the centre it is 1.49e+03 %
301 K which is, moving vertically from the wall, which remains a constant up to some distance after
some distance from it before which the value steeply which there is a slight decrease to 1.73e+03% and
increases up to the maximum value and then again it decrease after which there is a steep increase
decreases a little. The maximum value has reduced a up to the wall where it attains a maximum value to
little by 1 K considering this case and the previous 5.32e+03 %. There is an increase in the maximum
case of divergence angle of 20 degrees. value when compared to the previous nozzle.
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8. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
Figure: Total Temperature Contour With
Divergence Angle of 40 Degrees
CASE 4:
The following are the results of nozzle with
divergence angle of 40 degrees.
VELOCITY COUNTOUR
Figure: XY Plot Of Total Temperature With
Divergence Angle Of 40 Degrees
The total temperature contour is also
similar to the previous version. There is uniformity
observed from the inlet to some distance from the
Figure : Velocity Contour With Divergence Angle throat where it remains a constant whose value is
of 40 Degrees 300 K. After which it increases to 301 K in the
centre. The maximum value of 302 K is attained
some distance from the wall. There is decrease near
the wall. Vertically moving from the centre, it is 301
K up to more than the upper (or) lower half after
which it reaches the maximum value of 302 K and
then it decreases to the wall where it has a value of
297 K. The variation is similar in the case of 30
nozzles also.
STATIC PRESSURE
Figure: XY Plot For Velocity contour With
Divergence Angle of 40 Degrees
From Figure it can be seen that there is
parallel flow. The Mach number at the inlet is 0.383
which is Sub-Sonic, 1.42 at the throat and 3.10 at
the exit. There is a decrease in the value of Mach
number near the walls. Its value is 1.71. Turbulence
and viscosity are the cause for this decrease. The
Mach number has increased in this case to 3.10
where as it was 2.84 in the case of divergence angle Figure: Static Pressure Contour With Divergence
of 30 degrees. Angle of 40 Degrees
TOTAL TEMPERATURE
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9. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
Figure: XY Plot For Static Pressure With wall. This is because there is reversal of flow as well
Divergence Angle Of 40 Degrees as turbulence near the wall.
There is a continuous decrease in the value
of static pressure from the inlet to the throat and to RESULT TABLE:
the exit. At the inlet it is 106 Pa. It then keeps on Conditions at exit:
decreasing to 75 Pa which is also observed in the
case of 30 nozzles. The main difference arises in the CA AN MAC TOTAL STATIC
exit where there is a deviation in the minimum value SE GL H TEMPARA PRESSUR
in 30 nozzle was 2.24 Pa same as 2.24 Pa for this E NUM TURE(K) E(Pascal)
nozzle. Other than that there is no major difference BER
between the two. The pattern is also similar.
1 7 2.9 301 3.24
Turbulence intensity 20 2.84 300.5 3.86
2
30 3.06 300 2.72
3
40 3.19 301 2.24
4
The above values are considered at the exit of the
nozzle.
Conditions at throat:
Figure: Turbulence Intensity Contour with CA AN MAC TOTAL STATIC
Divergence Angle of 40 Degrees SE GL H TEMPARA PRESSUR
E NUM TURE(K) E(Pascal)
BER
1 7 1.19 300 65.8
20 1.02 300 71
2
30 1.08 300 64.8
3
40 1.12 300.25 59.6
4
The above values are considered at the throat of the
Figure: XY Plot of Turbulence Intensity With nozzle.
Divergence Angle of 40 Degrees
After taking a look at the above Figure and
the one for the previous case, it can be said there is a
lot of difference in the contour especially in the
region after the throat where there is a steep increase
when compared to the last case. The exit value has
also changed from 1.49e+03 % which was in the
previous case to 1.09e+03 % which is in the current
one. The turbulent intensity at the inlet is 7.75e+02
% which decreases a little to 7.02e+02 % just after
the inlet and remains a constant up to the throat.
After the throat there is a sudden increase in the area
and hence there is increase in the turbulent intensity.
The fluid also does not stabilize here. The maximum
turbulent intensity (5.75e+03 %) is obtained near the
1234 | P a g e
10. Pardhasaradhi Natta, V.Ranjith Kumar, Dr.Y.V.Hanumantha Rao / International Journal of
Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 5, September- October 2012, pp.1226-1235
computational combustion Dynamics
CONCLUSION Division of Defence Research and
The following observations were found in the Development Laboratory, Hyderabad.
nozzles with different divergence angles considering 5. Yasuhiro Tani ―Fundamental study of
default divergence angle as 7 degrees supersonic combustion in pure air flow
In the nozzle with divergence angle of 20 with use of shock tunnel‖ Department of
degrees Mach number is 1.15 at throat and Aeronautics and stronautics, Kyushu
at divergence angle of 7 degrees Mach University, Japan, Acta Astronautica 57
number is 1.19. From Default angle Mach (2005) 384 – 389.
number is increasing up to 2.917 at the 6. Patankar, S.V. and spalding. D.B. (1974),
nozzle exit while for divergence angle of ― A calculation for the transient and steady
20 degrees the Mach number at exit is state behaviour of shell- and- tube Heat
nearly 2.84. Exchanger‖. Heat transfer design and
At the throat the velocity magnitude is theory sourcebook. Afghan A.A. and
same for all divergence degrees of angle Schluner E.U.. Washington. Pp. 155-176.
and it is 260 m/s..
Near the wall, the Mach number is
decreasing for all the nozzles. This is due
to the viscosity and turbulence in the fluid.
For a nozzle of divergence angle of 20
degrees the Mach number at exit is very
low compared to other nozzles.
While when the divergence angle is 30
degrees the Mach number at nozzle exit is
3.06 and but an divergence angle 40
degrees it gives the Mach number at
nozzle exit is 3.19 and it is lowest at an
divergence angle 20 degrees.
The turbulence intensity is very high for a
divergence angle of 20 degrees at exit.
For maximum velocity we can go with 30
or 40 degrees of divergence angle conical
nozzle.
The efficiency of the nozzle increases as
we increase the divergence angle of the
nozzle up to certain extent.
REFERENCES
1. K.M. Pandey, Member IACSIT and A.P.
Singh ‖CFD Analysis of Conical Nozzle
for Mach 3 at Various Angles of
Divergence with Fluent Software’’
2. K.M. Pandey, Member IACSIT and A.P.
SinghK.M.Pandey, Member, IACSIT and
S.K.YadavK.M.Pandey and S.K.Yadav,
―CFD Analysis of a Rocket Nozzle with
Two Inlets at Mach2.1‖, Journal of
Environmental Research and
Development, Vol 5, No 2, 2010, pp- 308-
321.
3. David R. Greatrix, Regression rate
estimation for standard-flow hybrid rocket
engines, Aerospace Science and
Technology 13, 358-363, (2009).
4. P Manna, D Chakraborty ―Numerical
Simulation of Transverse H2 Combustion
in Supersonic Airstream in a Constant
Area Duct‖, Vol. 86, November 2005,
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