Our model analyzed air flow through varying degrees of tracheal stenosis (0%, 75%, 90%) using computational fluid dynamics software. We found that velocity increased with higher stenosis, consistent with literature. Pressure dropped more significantly between 75-90% stenosis. While our values did not match literature exactly due to model limitations, trends were similar, showing the model can represent tracheal fluid dynamics. Further refinement could improve accuracy by incorporating turbulence, time-dependence, and realistic tracheal geometry from medical imaging.
The document discusses the design of a steel pipeline submerged in moving water. It analyzes the forces on the pipeline from the flowing water, including drag force. Experiments using a wind tunnel were conducted to determine the coefficient of drag on cylindrical objects at different flow velocities. This was then used to calculate the drag force on the 10-inch diameter pipeline placed 200 inches below the surface of water flowing at 10 in/s. The calculated drag force and weight of the pipeline and water above it were then used to design the pipeline to withstand these forces.
TrainingTranscripts- Truong Mai-861178899 (1)TRUONG MAI
This document is a training transcript for Truong Mai that lists safety trainings completed from October 2014 through November 2014. It shows the training topics, estimated credit hours, start and completion dates, scores and grades. Truong Mai completed trainings in hazardous waste management, bloodborne pathogens, biosafety, laser safety, and various chemical, laboratory and tool safety topics, scoring between 79-100% on assessments.
Our device uses doppler ultrasound and an Android app to locate arteries for medical procedures like arterial line placement. The app analyzes the audio signal from the doppler ultrasound to identify the location of the artery, displaying it with changing colors. The device also includes a marker attached to the ultrasound probe that allows the user to mark the location of the detected artery. Our low-cost solution aims to improve artery location compared to existing techniques like manual palpation, which can cause injury. We tested our device on phantoms and human subjects to demonstrate its accuracy in arterial detection.
The document describes the development of a smartphone-compatible hydrogen breathalyzer to detect lactose and fructose intolerance. It discusses the current clinic-based hydrogen breath testing process, limitations of existing home testing kits, and the team's work to create an accurate, fast, user-friendly and low-cost device. The team has developed initial prototypes under $25 using an inexpensive hydrogen sensor, Arduino programming, and a phone app for real-time results and feedback. Their goal is to match the accuracy of a $811 clinical-grade detector at lower cost.
Troponin_T_monitoring_BIEN 167 MINI PROJECT 2TRUONG MAI
- Troponin T detection strips work by having blood flow through a paper strip with sensor and control bands. At least 0.18 ug/L of troponin T is needed in the blood sample for a positive reading.
- COMSOL was used to simulate the diffusion and flow of troponin T through the paper strip at different pressures.
- Calculations were done to determine the minimum pressure needed to drive flow through the strip based on parameters like strip dimensions, diffusion rate, and viscosity.
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.
The document describes a study that investigated the depth-wise profiles of velocity and turbulence parameters in the proximity of a mid-channel bar using experimental and computational fluid dynamics (CFD) modeling methods. Velocity measurements were taken at various depths and locations near the mid-channel bar using an acoustic Doppler velocimeter (ADV). The study found changes in the velocity and turbulence profiles due to interactions between the fluid flow and the mid-channel bar. CFD modeling with the Reynolds stress model was also used to validate the experimental results.
Atmospheric turbulent layer simulation for cfd unsteady inlet conditionsStephane Meteodyn
The aim of this work is to bridge the gap between experimental approaches in wind tunnel testing and numerical computations, in the field of structural design against strong winds. This paper focuses on the generation of an unsteady flow field, representative of a natural wind field, but still compatible with CFD inlet requirements. A simple and “naïve” procedure is explained, and the results are successfully compared to some standards.
The document discusses the design of a steel pipeline submerged in moving water. It analyzes the forces on the pipeline from the flowing water, including drag force. Experiments using a wind tunnel were conducted to determine the coefficient of drag on cylindrical objects at different flow velocities. This was then used to calculate the drag force on the 10-inch diameter pipeline placed 200 inches below the surface of water flowing at 10 in/s. The calculated drag force and weight of the pipeline and water above it were then used to design the pipeline to withstand these forces.
TrainingTranscripts- Truong Mai-861178899 (1)TRUONG MAI
This document is a training transcript for Truong Mai that lists safety trainings completed from October 2014 through November 2014. It shows the training topics, estimated credit hours, start and completion dates, scores and grades. Truong Mai completed trainings in hazardous waste management, bloodborne pathogens, biosafety, laser safety, and various chemical, laboratory and tool safety topics, scoring between 79-100% on assessments.
Our device uses doppler ultrasound and an Android app to locate arteries for medical procedures like arterial line placement. The app analyzes the audio signal from the doppler ultrasound to identify the location of the artery, displaying it with changing colors. The device also includes a marker attached to the ultrasound probe that allows the user to mark the location of the detected artery. Our low-cost solution aims to improve artery location compared to existing techniques like manual palpation, which can cause injury. We tested our device on phantoms and human subjects to demonstrate its accuracy in arterial detection.
The document describes the development of a smartphone-compatible hydrogen breathalyzer to detect lactose and fructose intolerance. It discusses the current clinic-based hydrogen breath testing process, limitations of existing home testing kits, and the team's work to create an accurate, fast, user-friendly and low-cost device. The team has developed initial prototypes under $25 using an inexpensive hydrogen sensor, Arduino programming, and a phone app for real-time results and feedback. Their goal is to match the accuracy of a $811 clinical-grade detector at lower cost.
Troponin_T_monitoring_BIEN 167 MINI PROJECT 2TRUONG MAI
- Troponin T detection strips work by having blood flow through a paper strip with sensor and control bands. At least 0.18 ug/L of troponin T is needed in the blood sample for a positive reading.
- COMSOL was used to simulate the diffusion and flow of troponin T through the paper strip at different pressures.
- Calculations were done to determine the minimum pressure needed to drive flow through the strip based on parameters like strip dimensions, diffusion rate, and viscosity.
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.
The document describes a study that investigated the depth-wise profiles of velocity and turbulence parameters in the proximity of a mid-channel bar using experimental and computational fluid dynamics (CFD) modeling methods. Velocity measurements were taken at various depths and locations near the mid-channel bar using an acoustic Doppler velocimeter (ADV). The study found changes in the velocity and turbulence profiles due to interactions between the fluid flow and the mid-channel bar. CFD modeling with the Reynolds stress model was also used to validate the experimental results.
Atmospheric turbulent layer simulation for cfd unsteady inlet conditionsStephane Meteodyn
The aim of this work is to bridge the gap between experimental approaches in wind tunnel testing and numerical computations, in the field of structural design against strong winds. This paper focuses on the generation of an unsteady flow field, representative of a natural wind field, but still compatible with CFD inlet requirements. A simple and “naïve” procedure is explained, and the results are successfully compared to some standards.
This document summarizes an experimental, numerical, and theoretical analysis of supersonic flow over a solid diamond wedge. The study examines boundary layer shockwave effects and pressure coefficients (Cp) for supersonic flow past the wedge. Experimental data is collected from a wind tunnel test using a diamond wedge model. Pressure readings are recorded for various angles of attack and used to calculate Cp. The experimental results are compared to theoretical analyses using Ackeret's linear theory and computational fluid dynamics simulations. Limitations of each method are discussed along with discrepancies between experimental and theoretical results.
The document is a project report for developing a simple lung equivalent circuit. It includes:
- An introduction describing the purpose of creating an artificial lung model for early testing of an organ preservation system.
- Research on lung structure and blood flow, leading to the design of a circuit to mimic zones with different blood pressures.
- A concept development process including initial concepts, a system block diagram, and the final design with four zones to replicate different vein properties.
- Details of pressure measurement using a transducer and circuitry to measure the desired 10-15 mmHg pressure drop.
- Considerations for usability including adjustable designs, pressure readings, and variable inlet pressure.
- A project
This document discusses various methods for measuring pressure and volume flow rate in heating, ventilation and air conditioning systems. It describes fundamental pressure measurement principles and defines terms like static pressure, total pressure and velocity pressure. It then provides details on several instruments that can be used to measure pressure, including U-tube manometers, single limb manometers, dial gauges, and pressure transducers. The document also discusses methods for measuring volume flow rate, such as in-line flowmeters, pitot-static tube traverses, anemometer traverses, thermal anemometers, and Wilson flow grids. Conversion factors between common pressure and flow units are also provided.
The document summarizes numerical simulations of the flow inside a centrifugal compressor's vaneless diffuser and volute. Gambit was used to generate meshes of the geometries, and Fluent was used to simulate the flows. Results from simulations at different speeds and mass flows agreed well with experimental data. The simulations showed separated flow on the diffuser hub wall at low mass flows. Inside the volute, swirling flow structures like vortices were observed. The tongue region caused static pressure distortions that affected the flow.
1. The document describes a shock-expansion theory for calculating the surface pressure distribution on three-dimensional wings with attached shock waves at high supersonic speeds.
2. The method divides the wing into regions and treats how flow changes between facets and within each facet. It is applicable to wings with surfaces made of straight generators where the local flow is supersonic.
3. The method is based on disturbances transmitted to shock waves from the wing not being significantly reflected back at high supersonic Mach numbers. Comparisons with experiments and linearized theory show the method is valid when the wing leading edge is highly supersonic.
This document summarizes a numerical study on free-surface flow conducted using a computational fluid dynamics (CFD) solver. The study examines the wave profile generated by a submerged hydrofoil through several test cases varying parameters like the turbulence model, grid resolution, and hydrofoil depth. The document provides background on the governing equations solved by the CFD solver and the interface capturing technique used to model the free surface. Five test cases are described that investigate grid convergence, the impact of laminar vs turbulent models, the relationship between hydrofoil depth and wave height, and the effect of discretization schemes.
REVIEW VProfiles Koutsiaris 2010b BULLETIN of PSHMKoutsiaris Aris
This document reviews equations that describe the velocity profile of blood flow in mammalian microvessels. It divides the equations into two groups: those that can be reduced to the classic parabolic equation (Group A), and those that cannot (Group B). Group A includes the parabolic, Roevros, and Koutsiaris equations. The Koutsiaris equation best approximates experimental mouse venule velocity profile data with errors under 1%, while the parabolic equation underestimates by up to 72% and the Roevros overestimates by up to 48%. Group B includes the Damiano equation, which fits mouse venule data very well using non-linear regression. However, it remains unclear whether these equations, validated
1. The document numerically investigates turbulent air flow in a coaxial jet burner using Reynolds Averaged Navier Stokes (RANS) modeling.
2. It compares predicted results of air axial velocity, air swirl velocity, and turbulent kinetic energy at different axial positions to experimental measurements from a previous study.
3. The simulation results show good agreement with experimental data, except at side regions where air velocity is under estimated, demonstrating RANS is a reasonably accurate approach for modeling industrial turbulent flows.
This document describes an experiment on conservation of mass in fluid mechanics. The experiment uses a Pressurized Flow System (PFS) to determine the volume flow rate and discharge coefficient of the PFS inlet and stack. It is broken into two parts: 1) measuring leakage to account for it in calculations, and 2) finding the stack discharge coefficient as a function of the ratio of the stack and cap diameters. Equations are derived for mass conservation, discharge coefficient, and volume flow rate. The experiment aims to demonstrate these concepts and relationships between variables.
This project analyzed subsonic flow over a blended wing body (BWB) aircraft model based on Lockheed Martin's X-56A/MUTT using computational fluid dynamics (CFD). Aerodynamic coefficients were obtained for angles of attack of 0, 5, and 10 degrees. The CFD analysis found lift-to-drag ratios up to 14.61 and low drag coefficients, validating the aerodynamic efficiency of BWB designs. Skin friction and pressure drag breakdowns showed drag contributions varied reasonably with angle of attack. Results provide validation data for stability augmentation system design for a tailless BWB configuration.
AJK2011-03023 (Conference Paper DR) Modelling Multiphase Jet Flows for High V...David Ryan
This document summarizes CFD simulations of flow inside an industrial static mixer called a Sonolator. Single-phase steady-state simulations were performed for three mass flow rates through a fixed nozzle orifice. Streamline data was used to calculate residence times and turbulent energy dissipation rates, which can provide insight into droplet breakup for emulsification processes. Validation was done against experimental discharge coefficients and predicted droplet sizes may depend on inlet conditions for multiphase mixtures.
This document describes research using Creo Parametric 2.0 software to design corner fillets and microramps to test their efficacy in mitigating corner separation in supersonic wind tunnels. Corner separation can reduce airflow uniformity and intake. The researcher modeled tapered corner fillets and microramps of varying sizes and shapes within a wind tunnel model. The goal was to simulate different geometries to analyze using computational fluid dynamics and potentially improve wind tunnel design.
1. The document presents a pressure transient analysis method for a reservoir with an internal circular boundary, such as a gas cap.
2. The problem is modeled using the Laplace transform solution of the diffusivity equation with boundary conditions. This allows developing a generalized type curve solution.
3. A new generalized type curve is presented, which allows estimating the permeability of the reservoir section within the boundary and the transient time to reach the boundary through type curve matching, without using the double straight line technique.
This document summarizes an experimental study on controlling base pressure in a suddenly expanded flow using micro jets. The study varied the area ratio of the enlarged duct, the length to diameter ratio of the duct from 10 to 1, and nozzle pressure ratios from 1.5 to 3.0. Micro jets located around the base region were used for active control. Results found that micro jets were effective at increasing base pressure and did not disturb the wall pressure distribution. For length to diameter ratios from 4 to 2, oscillations in pressure were observed at nozzle pressure ratios of 2.5 to 3.0, but these were reduced by increasing the length to diameter ratio or decreasing the nozzle pressure ratio. The micro jets provided effective control of base pressure under
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).
Perfusion System Controller Strategies during an ECMO Support ijsc
This document summarizes a research paper that models and simulates control strategies for regulating partial pressures of oxygen and carbon dioxide during extracorporeal membrane oxygenation (ECMO) support. It presents models for the gas blender, oxygenator, and blood gas analyzer. It designs proportional-integral-derivative (PID) controllers for oxygen and carbon dioxide based on these models. Simulations show the controllers provide fast reference tracking and good disturbance rejection under varying conditions. The control strategy could help improve patient safety during ECMO by automatic rather than manual control of blood gas levels.
AIAA Student Competition 2015 Research PaperKalendrix Cook
1) Tests were conducted in a wind tunnel to measure the interference drag between two axisymmetric bodies placed in tandem at varying horizontal and vertical spacing, representing stores separating from an aircraft.
2) Data showed that drag forces were strongly correlated to the spacing between the bodies and remained insensitive to changes in Reynolds number until a threshold was reached.
3) Key findings were that drag was highest when bodies were closest horizontally, and changing the vertical spacing altered the drag and moment coefficients in sinusoidal patterns, with implications for store stability during separation.
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.
Asme2009 82287 - Porous Media - Forced Convection FlowHIIO
In this study the flow field and heat transfer properties of a
steady, two-dimensional flow field in a porous domain between
two parallel plates is investigated numerically by using a
discretized numeric code. Analysis has been carried for
Reynolds number based on particle sizes ranging from 60 to
1000. Numerical results are compared with different numerical
methods used for predicting this kind of flow. Results are
obtained for different regime, various p Re numbers and the
effect of Particles size is also investigated. Solutions indicate
that by increasing the
p Re , the flow in the porous media
remains laminar where the flow has turbulence characteristics
for p Re <50. Moreover, by increasing p Re , the value of
average Nusselt number increases. Also, reducing the particle
size affects the Nusselt number and it increases while the
porosity remains the same.
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This document summarizes an experimental, numerical, and theoretical analysis of supersonic flow over a solid diamond wedge. The study examines boundary layer shockwave effects and pressure coefficients (Cp) for supersonic flow past the wedge. Experimental data is collected from a wind tunnel test using a diamond wedge model. Pressure readings are recorded for various angles of attack and used to calculate Cp. The experimental results are compared to theoretical analyses using Ackeret's linear theory and computational fluid dynamics simulations. Limitations of each method are discussed along with discrepancies between experimental and theoretical results.
The document is a project report for developing a simple lung equivalent circuit. It includes:
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- Research on lung structure and blood flow, leading to the design of a circuit to mimic zones with different blood pressures.
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- Considerations for usability including adjustable designs, pressure readings, and variable inlet pressure.
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This document discusses various methods for measuring pressure and volume flow rate in heating, ventilation and air conditioning systems. It describes fundamental pressure measurement principles and defines terms like static pressure, total pressure and velocity pressure. It then provides details on several instruments that can be used to measure pressure, including U-tube manometers, single limb manometers, dial gauges, and pressure transducers. The document also discusses methods for measuring volume flow rate, such as in-line flowmeters, pitot-static tube traverses, anemometer traverses, thermal anemometers, and Wilson flow grids. Conversion factors between common pressure and flow units are also provided.
The document summarizes numerical simulations of the flow inside a centrifugal compressor's vaneless diffuser and volute. Gambit was used to generate meshes of the geometries, and Fluent was used to simulate the flows. Results from simulations at different speeds and mass flows agreed well with experimental data. The simulations showed separated flow on the diffuser hub wall at low mass flows. Inside the volute, swirling flow structures like vortices were observed. The tongue region caused static pressure distortions that affected the flow.
1. The document describes a shock-expansion theory for calculating the surface pressure distribution on three-dimensional wings with attached shock waves at high supersonic speeds.
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This document summarizes a numerical study on free-surface flow conducted using a computational fluid dynamics (CFD) solver. The study examines the wave profile generated by a submerged hydrofoil through several test cases varying parameters like the turbulence model, grid resolution, and hydrofoil depth. The document provides background on the governing equations solved by the CFD solver and the interface capturing technique used to model the free surface. Five test cases are described that investigate grid convergence, the impact of laminar vs turbulent models, the relationship between hydrofoil depth and wave height, and the effect of discretization schemes.
REVIEW VProfiles Koutsiaris 2010b BULLETIN of PSHMKoutsiaris Aris
This document reviews equations that describe the velocity profile of blood flow in mammalian microvessels. It divides the equations into two groups: those that can be reduced to the classic parabolic equation (Group A), and those that cannot (Group B). Group A includes the parabolic, Roevros, and Koutsiaris equations. The Koutsiaris equation best approximates experimental mouse venule velocity profile data with errors under 1%, while the parabolic equation underestimates by up to 72% and the Roevros overestimates by up to 48%. Group B includes the Damiano equation, which fits mouse venule data very well using non-linear regression. However, it remains unclear whether these equations, validated
1. The document numerically investigates turbulent air flow in a coaxial jet burner using Reynolds Averaged Navier Stokes (RANS) modeling.
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3. The simulation results show good agreement with experimental data, except at side regions where air velocity is under estimated, demonstrating RANS is a reasonably accurate approach for modeling industrial turbulent flows.
This document describes an experiment on conservation of mass in fluid mechanics. The experiment uses a Pressurized Flow System (PFS) to determine the volume flow rate and discharge coefficient of the PFS inlet and stack. It is broken into two parts: 1) measuring leakage to account for it in calculations, and 2) finding the stack discharge coefficient as a function of the ratio of the stack and cap diameters. Equations are derived for mass conservation, discharge coefficient, and volume flow rate. The experiment aims to demonstrate these concepts and relationships between variables.
This project analyzed subsonic flow over a blended wing body (BWB) aircraft model based on Lockheed Martin's X-56A/MUTT using computational fluid dynamics (CFD). Aerodynamic coefficients were obtained for angles of attack of 0, 5, and 10 degrees. The CFD analysis found lift-to-drag ratios up to 14.61 and low drag coefficients, validating the aerodynamic efficiency of BWB designs. Skin friction and pressure drag breakdowns showed drag contributions varied reasonably with angle of attack. Results provide validation data for stability augmentation system design for a tailless BWB configuration.
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This document summarizes CFD simulations of flow inside an industrial static mixer called a Sonolator. Single-phase steady-state simulations were performed for three mass flow rates through a fixed nozzle orifice. Streamline data was used to calculate residence times and turbulent energy dissipation rates, which can provide insight into droplet breakup for emulsification processes. Validation was done against experimental discharge coefficients and predicted droplet sizes may depend on inlet conditions for multiphase mixtures.
This document describes research using Creo Parametric 2.0 software to design corner fillets and microramps to test their efficacy in mitigating corner separation in supersonic wind tunnels. Corner separation can reduce airflow uniformity and intake. The researcher modeled tapered corner fillets and microramps of varying sizes and shapes within a wind tunnel model. The goal was to simulate different geometries to analyze using computational fluid dynamics and potentially improve wind tunnel design.
1. The document presents a pressure transient analysis method for a reservoir with an internal circular boundary, such as a gas cap.
2. The problem is modeled using the Laplace transform solution of the diffusivity equation with boundary conditions. This allows developing a generalized type curve solution.
3. A new generalized type curve is presented, which allows estimating the permeability of the reservoir section within the boundary and the transient time to reach the boundary through type curve matching, without using the double straight line technique.
This document summarizes an experimental study on controlling base pressure in a suddenly expanded flow using micro jets. The study varied the area ratio of the enlarged duct, the length to diameter ratio of the duct from 10 to 1, and nozzle pressure ratios from 1.5 to 3.0. Micro jets located around the base region were used for active control. Results found that micro jets were effective at increasing base pressure and did not disturb the wall pressure distribution. For length to diameter ratios from 4 to 2, oscillations in pressure were observed at nozzle pressure ratios of 2.5 to 3.0, but these were reduced by increasing the length to diameter ratio or decreasing the nozzle pressure ratio. The micro jets provided effective control of base pressure under
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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).
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This document summarizes a research paper that models and simulates control strategies for regulating partial pressures of oxygen and carbon dioxide during extracorporeal membrane oxygenation (ECMO) support. It presents models for the gas blender, oxygenator, and blood gas analyzer. It designs proportional-integral-derivative (PID) controllers for oxygen and carbon dioxide based on these models. Simulations show the controllers provide fast reference tracking and good disturbance rejection under varying conditions. The control strategy could help improve patient safety during ECMO by automatic rather than manual control of blood gas levels.
AIAA Student Competition 2015 Research PaperKalendrix Cook
1) Tests were conducted in a wind tunnel to measure the interference drag between two axisymmetric bodies placed in tandem at varying horizontal and vertical spacing, representing stores separating from an aircraft.
2) Data showed that drag forces were strongly correlated to the spacing between the bodies and remained insensitive to changes in Reynolds number until a threshold was reached.
3) Key findings were that drag was highest when bodies were closest horizontally, and changing the vertical spacing altered the drag and moment coefficients in sinusoidal patterns, with implications for store stability during separation.
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.
Asme2009 82287 - Porous Media - Forced Convection FlowHIIO
In this study the flow field and heat transfer properties of a
steady, two-dimensional flow field in a porous domain between
two parallel plates is investigated numerically by using a
discretized numeric code. Analysis has been carried for
Reynolds number based on particle sizes ranging from 60 to
1000. Numerical results are compared with different numerical
methods used for predicting this kind of flow. Results are
obtained for different regime, various p Re numbers and the
effect of Particles size is also investigated. Solutions indicate
that by increasing the
p Re , the flow in the porous media
remains laminar where the flow has turbulence characteristics
for p Re <50. Moreover, by increasing p Re , the value of
average Nusselt number increases. Also, reducing the particle
size affects the Nusselt number and it increases while the
porosity remains the same.
Similar to Fluid Dynamic Model Analysis_report_ENGR_105 (20)
2. 2
When a patient undergoes a condition of tracheal stenosis, the windpipe
experiences a narrowing that prevents an individual from breathing normally. The
causes of this are trauma, inflammatory diseases, and collagen vascular diseases[1].
Stenosis impedes the air to the lungs and causes abnormal flow and pressure.
However, often times symptoms do not arise until the condition becomes so severe that
immediate attention is required. Patients do not usually experience breathing trouble
until the stenosis takes over around seventy-five percent of the trachea. This leads to
the question of why breathing troubles are reported well after the stenosis has
appeared. In order to answer this question, it seems most apparent to look at the air
flow in the trachea, around the stenosis area.
Because of the intricacy of computing the air flow field has been very challenging
for scientists to do using experimental measurements, research is slow for this area.
However, the understanding of fluid dynamic studies in the upper airways has regained
a new sense of interest because of the vast possibilities offered by computational fluid
dynamics applied to this area[5]. Computational fluid dynamics allows you to use the
Navier-Stokes equations in order analyze and solve problems related to fluid flow.
Recently, Brouns & Jayaraju modeled the airflow characteristics on tracheal flow, mainly
using Reynolds-averaged Navier-Stokes modeling methods because of its low
computational costs. He noticed that the pressure drop in the trachea is dominated by
the cross-sectional area that the stenosis occupies.
Our report will simulate several models of air flowing downwards through
simplified tracheal models. We will first start with a normal trachea without a stenosis,
then move on to stenosis of varying sizes applied to the trachea model. The velocity
and pressure will be computed for the air flowing through the stenosis, as well as the
vorticity each size of the stenosis creates. The overall purpose of this experiment is to
explain why patients only state breathing troubles starting at a certain percentage that
the stenosis populates in the trachea.
Method
Using the Navier-Stokes equation incorporated in COMSOL, we planned our
experiment around finding the velocity profile and pressure drop downwards through the
trachea with and without the stenosis.
We are able to model the velocity field and the pressure in our model because these
values are located within the Navier-Stokes equation, as shown here:
It can be assumed that this model is not time dependent, making the model much
simpler and making it faster to compute and solve.
3. 3
Along with the Navier-Stokes equation, we use the continuity equation in order to
determine the boundary conditions and to show that our fluid model is incompressible:
Because we are defining the relationship between the velocity and pressure, we will
also include Bernoulli’s equation to show the connection:
The last equation we will use for this model is Reynold’s equation:
We will use Reynold’s number to determine the kind of flow along a certain point within
the system at varying sizes of stenosis.
Assumptions: The assumptions that we were required for us to make the model on
COMSOL simplify the human trachea because an actual trachea isn’t perfectly
cylindrical. Our model consisted of five varying blocks that were smoothed out to
replicate the bronchi and the cartilage rings. These blocks are lined along the rotating
axis which will later create a 3-dimensional mode. A trachea of this kind will not
physiologically be correct because a trachea isn’t a straight tube. The trachea has a flat
back and it has slight curves rather than being completely straight as in our model. To
simplify the Navier-Stokes equation, we conducted a stationary model to simulate a
steady-state model. We also assumed that the fluid was Newtonian and incompressible
so that the fluid – in our case air – has a constant viscosity and density respectively.
The flow was also assumed to be laminar rather than turbulent due to a limitation in
COMSOL, and the walls are taken with a no-slip condition.
Geometry: The dimensions for our 2-dimensional model are taken from the upper limit a
normal human male trachea of with a radius 1.35 cm (Breatnach et al.). This radius
was used to depict the bronchi and the cartilage ring was found to be 1.25 cm according
to Patel et al. Rather than looking at a full length trachea, we analyzed a segment of
the trachea with a 6.5 cm length to further simplify the anatomy of the trachea. The
three bronchi “rings” have a height of 1.5 cm and the height for the two cartilage rings
are 1 cm. For the normal trachea with 0% stenosis, the five “rings” are combined
together through a union. A circle with its center placed along the bronchi wall at 3.25
cm is made and subtracted to create a stenosis. The radii of the circle is adjusted and
subtracted from the tracheal wall to simulate various percentages of stenosis. The
geometry of this model is shown at Figure 1.
4. 4
Subdomain: The density of air was found to be 1.177 kg·m-3 (“Air Properties
Definitions”). Assuming air as a Newtonian Fluid is significantly important in our model
because the viscosity of air will be held constant at 0.00002 Pa·s (“Viscosity”).
Boundary: The walls of the trachea were set to be no-slip and have inlet velocity at the
top of the trachea with 0.87 m/s. The inlet velocity used was calculated by using a
volumetric flow rate of 30 L/min which was provided by Jayaraju et al. Knowing the
cross-sectional area of the inlet, we divided the volumetric flow rate with cross-sectional
area of the inlet and was able to calculate the inlet velocity. COMSOL could not
produce an answer without an outlet value so we set the outlet to have a velocity of 0.5
m/s.
Figure 1: The diagram above depicts the dimensions of the trachea on 2D axi-
symmetrical over r-axis of our COMSOL model. The air will flow from the left to right.
This is a 2D symmetrical model over z-axis, so it is not necessary to make 3D model.
This is There is airflow from the left and air out on the right side of the model. Initial
velocity is 0.8732m/s and zero pressure. Some assumption is incompressible, no slip,
gravitational force neglected, and velocity on z-direction only and at steady state. Our
geometry is RCCS. Boundary condition is at x = 0, v(z) is finite; at x=r, v(z) is zero.
Table 1: Material properties of air.
Density 1.177 kg/m3
5. 5
Viscosity 0.00002 Pa·s
Figure 2: This figure illustrates the finer mesh that was applied to our model to obtain
more accurate results.
Results:
Table 2: Comparison of initial conditions from literature and the values applied to our
model.
Literature Values Our Values
Stenosis Size Depends on
Degree of Severity
1 mm (100% stenosis) Radius of 1.35 cm (100%
stenosis)
Stenosis Shape Trapezoid Semi-circle
Inlet Velocity 0.8732 m/s 0.8732 m/s
Mesh 750,000 cells, hexahedral
shaped
Finer
Table 3: This table shows the values of velocity at the point of interest (r,z) = (0, 3.25).
Percent Stenosis Velocity (m/s) Percent Stenosis Velocity (m/s)
0 0.8732 70 9.8000
25 1.5000 75 14.0000
50 3.4000 80 22.0000
55 4.2000 85 39.5000
6. 6
60 5.3500 90 88.0000
65 7.2300
Figure 3: Velocity field at zero percent stenosis (m/s). Goes straight downwards with
laminar flow. This is our control variable for the report.
7. 7
Figure 4: The figure above displays the pressure at 0% stenosis (Pa). This is our
control variable for the report.
Graph 5: This graph shows the values of the small pressure drop in the stenosis from
top to bottom for 0% stenosis. Control variable.
Figure 6: Velocity is at 75% stenosis (m/s). Velocity after stenosis become bigger
because the pressure drops after stenosis larger.
8. 8
Figure 7: Pressure’s trend at 75% stenosis. At the z= 0.75, pressure’s trend is curl
shape, this predicts that the velocity will move in different directions.
Figure 8: Pressure at 75% stenosis (Pa). There is a lot pressure before the stenosis
and drops significantly after stenosis.
9. 9
Graph 9: Graph for the pressure at 75% stenosis (Pa). The pressure begins from the
right to the left because the airflow from top to bottom of trachea. Pressure drops show
the flow from high pressure to low pressure. Then pressure stabilizes from 3 to 0.
10. 10
Figure 10: Velocity at 90% stenosis (m/s). As explanation in figure 6, the velocity is
higher after stenosis. Velocity becomes weaker from z=0 to 1.35 and expresses the no-
slip condition. The vorticity is developed at the end of the trachea.
Figure 11: Pressure’s trend at 90% stenosis. In this figure, it is much easier to see the
vorticity at the bottom of the trachea
11. 11
Figure 12: Pressure at 90% stenosis (Pa).
Graph 13: Pressure at 90% stenosis (Pa).
Figure 14: The figure shows velocity increases proportional to the percentage of
stenosis at point (0,3.25)
12. 12
Table 4: Velocity from our Comsol model and from literature data
Percent Stenosis of
our data (%)
Our velocity at
stenosis area (m/s)
Percent Stenosis
from literature data
(%) [15]
Velocity at cross-
section D in
literature (m/s) [15]
50 1.62 49 7.5
75 3.37 75 10.5
85 5.94 84 12.5
90 8.7 91 21.5
Table 5: Percent error between velocity of our data and literature data
Percent Stenosis (%) Percent Error (%)
50 78.3
75 67.9
85 52.5
89 59.5
Table 6: Difference pressure of our data and literature data and percent error
Our difference
pressure (Pa)
Literature difference
pressure (Pa)
Percent Error (%)
Percent Stenosis (%)
75 7 51 86.27
90 57 680 91.61
Discussion (Sarah and Vincent) - why these results could be significant (what the
reasons might be for the patterns found or not found)
Velocity Analysis:
Looking at our 2-D axi-symmetric model, we were able to show that the
magnitude of the velocity increased as the degree of stenosis increased. Comparing our
velocity values for varying sizes of stenosis with the literature values, we were not able
to reproduce the results of Jayaraju’s simulation. For Jayaraju’s simulation, he got a
max velocity of 91 m/s for 90% stenosis at a volumetric flow rate of 30 L/min, while we
13. 13
got a max velocity of 9.63 m/s at the same volumetric flow rate and stenosis. Even
though we could not get the same values, our model at least followed the same trend
for increasing velocity as Jayaraju’s model. In our study, there was only a slight
increase in velocity for the 0-75% stenosis cases. However, after 75%, there were
significant increases in velocity for the model. This also occurs in Jayaraju’s study,
showing that our model can accurately represent the velocity field through the trachea.
Vorticity Analysis:
In laminar flow, the vorticity will be 0 at the axis. Our model with a 75% stenosis
shows a vorticity below the stenosis which is indicated by the stream lines. In the
trachea model with a 90% stenosis, the streamlines indicated that there was also
vorticity. The further away from the axis, the higher the vorticity will be. The vorticity
found does not mean there is turbulent flow as swirling can happen in laminar flow.
Pressure Analysis:
The pressure drops we found at a 75% stenosis and 90% stenosis was 7 Pa and
57 Pa respectively. Jayaraju found that at a 75% stenosis the pressure drop was 51 Pa
and a 90% stenosis produced a 680 Pa pressure drop from the inlet to the outlet. The
small change in pressure relates to why our velocity values at these stenosis
percentages are lower compared to the values found by Jayaraju et al. The fluid
requires a pressure drop in order to move down the trachea. With low pressure drops,
the velocity of the fluid will be lower. Our small pressure drops may have been due to a
lower inlet pressure. The size of the stenosis is the cause in the pressure drops, but if
the inlet pressure isn’t high enough, then the pressure drop cannot replicate the values
found from Jayaraju et al. In the study by Jayaraju et al, the pressure drop significantly
increased between 75% and 90%. Though not as significant of a change, we found that
the pressure drop in our 75% and 90% stenosis model showed a sizeable increase.
Error Analysis
There is error in our velocity and pressure difference due to limitations. The
method used to find our values at the point of interest (r,z) of (0,3.25) was picked by
clicking on the surface of the velocity graph on comsol which hold to be very accurate.
The errors found in with these values can be due to the geometry of our model. Our
model is very simplified compared a real human trachea. The literature model we
compared to was created using a CT scan of the upper respiratory tract. Unlike the CT
scanned model, our model is more of a straight cylinder with ridges. Another reason is
that COMSOL is limited to only using a Laminar Flow Study. According to Jayaraju et
al., a trachea with a volumetric flow rate of 30 L/min will already have a turbulent flow
before the air reaches the stenosis. Because of this COMSOL limitation, the values
obtained from COMSOL may have been affected. Since we cannot observe the
turbulent flow in a laminar flow study, we examined the vorticity after the point of
14. 14
stenosis. A Time-Dependent Study may give us a more accurate pressure drop
because the pressure may change over time. Also, we didn’t corporate the Young’s
Modulus and Poisson’s Ratio to our model, so our model lost viscoelastic properties.
The trachea in both our model and literature model didn’t simplify the surface tension
because of assuming the trachea as a dry airflow. Lastly, the accuracy of our values
are mesh dependent. The finest mesh we were able to run our model simulation was a
finer mesh. Coarser meshes produced lower velocity and pressure values.
Conclusion
In this report, it has been determined that:
(1) As velocity increased, there was a pressure drop within the trachea. This is known to
be due to their relationship in the Bernoulli equation.
(2) The vorticity in the trachea after the stenosis increased as the stenosis was made
bigger
Some of our values compared to literature are different in the model, however they both
share the same trend that we were looking for. If we were able to modify our model in
Comsol to be a little more realistic of the trachea, it can represent an efficient way of
studying how a stenosis affects airflow.
Acknowledgements
We would like to thank Dr. V.G.J. Rodgers for consistently supporting and motivating us
to perform at our highest potential.
References
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Appendix
1) Calculation
a) Inlet velocity
Q= 30L/min = 0.0005m3/s [10]
r=1.35cm = 0.0135m
This value makes sense because the real value from literature is about 0.8 to
1.3m/s [12]
b) Difference pressure
2) Reynold number [10]
17. 17
(assuming the velocity is function of z only)
7) Percent Error (%)
In figure 3, the maximum velocity is about 1m/s and uniform in the whole trachea. this
happens because of two reasons. The inlet velocity is 0.8732m/s. There is an increase
in velocity because the radius of the bronchi is larger than cartilage. As the result, the
cross-section area increase back and forth.
In figure 4, there is a