A Comparison of Analytical and Finite Element Solutions for Laminar Flow Conditions Near Gaussian Constrictions


 Clifton Craig
 2 years ago
 Views:
Transcription
1 A Comparison of Analytical and Finite Element Solutions for Laminar Flow Conditions Near Gaussian Constrictions by Laura Noelle Race An Engineering Project Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the degree of MASTER OF ENGINEERING Major Subject: Mechanical Engineering Approved: Professor Ernesto GutierrezMiravete, Project Adviser Rensselaer Polytechnic Institute Hartford, CT December, 2014 i
2 Copyright 2014 by Laura Noelle Race All Rights Reserved ii
3 CONTENTS LIST OF TABLES AND CHARTS... v LIST OF FIGURES... vi LIST OF SYMBOLS... vii ACKNOWLEDGMENT... viii ABSTRACT... ix 1. Introduction Fluid Flow Near Constrictions and Expansions in Capillary Tubes Prior Work Methodology Problem Description Analytical Setup Mathematical Theory of Flow Near Gaussian Constrictions Final Analytical Equations Fluent Setup Geometry Mesh Fluent Solutions No Constriction Case Case Case Case Case Case Case Case iii
4 3.10 Case Results and Discussion Conclusions References APPENDIX A Curve Coordinates APPENDIX B Mesh Settings APPENDIX C Maple Worksheet For Analytical Solutions iv
5 LIST OF TABLES AND CHARTS Table 1 Description of Geometry Cases... 3 Table 2 Description of Fluid Parameters and Flow Cases... 4 Table 3 Maple Input Parameters for Constriction Amplitude and Width Table 4 Analytical Solutions for ΔP ex Table 5 Finite Element Solutions for ΔP ex *Figure out how to add charts in here* v
6 LIST OF FIGURES Figure 1 HagenPoiseuille Flow... 5 Figure 2 Gaussian Constriction Geometry... 5 Figure 3 Base Mesh (No Constriction)... 9 Figure mm Constriction Mesh, 5 mm Width... 9 Figure mm Constriction Mesh, 5 mm Width... 9 Figure mm Constriction Mesh, 5 mm Width Figure mm Constriction Mesh, Width 10 mm Figure mm Constriction Mesh, Width 10 mm Figure mm Constriction Mesh, Width 10 mm Figure 10 Pressure Contour, No Constriction Figure 11 Velocity Vectors, No Constriction Figure 12 Pressure Contour, Case Figure 13 Velocity Vectors, Case Figure 14 Pressure Contour, Case Figure 15 Velocity Vectors, Case Figure 16 Pressure Contour, Case Figure 17 Velocity Vectors, Case Figure 18 Pressure Contour, Case Figure 19 Velocity Vectors, Case Figure 20 Pressure Contour, Case Figure 21 Velocity Vectors, Case Figure 22 Pressure Contour, Case Figure 23 Velocity Vectors, Case Figure 24 Pressure Contour, Case Figure 25 Velocity Vectors, Case Figure 26 Pressure Contour, Case Figure 27 Velocity Vectors, Case Figure 28 Pressure Contour, Case Figure 29 Velocity Vectors, Case vi
7 LIST OF SYMBOLS Symbol Description Units g z Gravity (Axial Direction) m/s 2 p Pressure Pa Δp ex Excess Pressure Drop Pa R Constriction Radius m R o Initial Radius m r Radial Position m s Radial Position Variable [dimensionless] U o Axial Velocity Scale [dimensionless] u r Radial Velocity m/s u z Axial Velocity m/s Radial Velocity [dimensionless] Axial Velocity [dimensionless] V o Radial Velocity Scale [dimensionless] z Axial Position m Π Pressure Scale [dimensionless] ε Ratio of Constriction Radius to Flow Radius [dimensionless] ζ Axial Position Variable [dimensionless] µ Dynamic Viscosity Kg/(ms) ρ Density Kg/m 3 vii
8 ACKNOWLEDGMENT I would like to thank my husband, Andy, for being supportive throughout my entire academic career and especially while I complete the last semester of my degree program. I would also like to thank my employer, The Lee Company, for financing my degree. Lastly, I would like to thank my adviser, Ernesto GutierrezMiravete for supplying the necessary guidance while I completed this report. viii
9 ABSTRACT This report evaluates the relationship between the analytical solution and the finite element solution of steady state laminar flow through a Gaussian constriction. The analytical solution of the excess pressure drop between Poiseuille Flow and the flow through a Gaussian constriction has been determined utilizing the continuity and momentum equations. The analytical solution is then compared with finite element solutions obtained using ANSYS Fluent. A variety of various cases for the size of constriction have been considered with water as the fluid. In general, it is found for a low Reynold s number of 2, the finite element solutions are within 10% of the analytical solutions. The lowest percentage difference for the actual pressure drop between the analytical and the finite element solutions are when the amplitude is its smallest at 25% of the tube radius. ix
10 1. Introduction 1.1 Fluid Flow Near Constrictions and Expansions in Capillary Tubes Fluid flow through a pipe with a constant internal radius and surface is expected in the theoretical world. However, many applications arise where the flow path is locally interrupted by some sort of constriction or expansion. In general, the larger the pipe or tube inner radius, the easier it is to disregard any internal surface inconsistencies. In the case of smaller inner diameter tubes, such as capillaries, the effect of such a constriction or expansion cannot be neglected so easily. Capillary tubes can be used in multiple applications ranging from the medical field to refrigeration and to plant life. A capillary tube depends on the phenomena of capillary action, which is when a fluid can be drawn up a tube against gravity without the need for help from external forces. Examples of real applications in which the inner diameter of a capillary tube varies include peristaltic pumps, viscometers, and the medical investigation of Aeterioscelerosis. A peristaltic pump is a medical device in which. Even though capillary action may not be the dominant phenomena, many analyses of constricting and expanding tubes can be applied. The example of a viscometer only relates to a tube in which an expansion takes place. Fluid is drawn up a capillary tube into a bulb (expansion) and then is allowed to flow to another bulb in the ushaped capillary tube. Two marks are made on the capillary tube and the time that it takes for the known volume of fluid to pass through the two marks yields the kinematic viscosity. Lastly, the example in which the radius of a tube constricts is in the cardiovascular disease of Aeterioscelerosis. The disease causes fat to build up on the artery walls (constriction) and can cause serious health problems by preventing proper blood flow. 1.2 Prior Work Prior work on varying axial internal constricting radii has been investigated as far back as 1970, where Lee and Fung determined numerical techniques determining the fluid parameter distributions near the varied radius. It is possible that the investigation began 1
11 before Lee and Fung. It is shown that the most efficient way to perform an analytical solution to the flow regime is to assume a fixed shape of how the internal radius varies in relation to the initial radius. However, applying a fixed shape limits the analysis that can be completed. In 1971, M.J. Manton determined that the numerical techniques could be expanded to apply to an arbitrarily shaped constriction. The solution considers an internal radius that is slowly varying and is not shape dependent. As mentioned in Section 1.1, the application of radii varying axially is usually seen in the medical field where capillary tubes are of large use. Not only is the situation of Aeterioscelerosis considered, but additionally Expansions of the internal crosssection of the tube have practical applications in viscometric capillary tubes and peristaltic pumping. In the case of peristaltic pumping The most common shapes that are chosen appear to be that of normal (Gaussian) or sinusoidal curves. The Gaussian constriction has been adequately investigated and it will be used in this study. 2
12 2. Methodology 2.1 Problem Description The problem at hand is to compare the analytical solution to the finite element solution for the pressure drop through a tube with a Gaussian constriction. The analytical solution will be evaluated for varying cases of Reynold s numbers, but within the laminar flow regime. The geometry of the Gaussian constriction will be varied appropriately while the radius of the tube will be kept constant. The tube radius will be chosen as such to ensure that the flow path at r = 0 will be unaltered and the flow directly near the Gaussian constriction will be analyzed. The analysis will also include the size at which the Gaussian constriction needs to be as a percentage of the tube radius in order to affect the flow at r = 0. This project will also evaluate the flow path variation with multiple fluids and flow conditions. The fluid under consideration will be that of water. The fluid chosen has a practical application and is typically seen used with capillary tubes. The analytical solution to the Gaussian constriction should reveal approximate solutions to the velocity and pressure in local areas. These solutions will then be compared with the flow characteristics that are calculated utilizing finite element analysis modeled in Fluent. The constriction length will be varied between 5, 10, and 15 mm. For each length of constriction, the amplitude will be varied to be 0.25, 0.50, and 0.75 mm. Table 1 depicts the length and amplitude combination on how each case will be analyzed. Case Number Parameter Amplitude (mm) Width (mm) Table 1 Description of Geometry Cases Even though a capillary tube with a inch radius seems small, it is actually quite large compared to blood capillaries. Only one red blood cell is allowed to pass through the capillary at a time, leaving the capillary diameter at about 7 micrometers (about inch). At these diameters, fluid flow is quite slow and is practical for this report. 3
13 Because of approximate size of a capillary tube, each geometry case will then be analyzed with the fluid properties shown in Table 2. Parameter Water Density 1000 kg/m 3 Dynamic Viscosity kg/ms Velocity m/s Reynold s Number 2 Table 2 Description of Fluid Parameters and Flow Cases A velocity of m/s, yielding a Reynold s Number of 2, is higher than what is typically seen in capillary tubes. A typical volumetric flow rate in a capillary tube is on the order of 1 x m 3 /s while the flow rate utilized for this report is approximately 3.14 x 109 m 3 /s. Utilizing a slightly faster velocity will check the ability of the analytical solution and the finite element solution to accurately predict the required system parameters. 4
14 2.2 Analytical Setup Mathematical Theory of Flow Near Gaussian Constrictions The most basic form of steady state laminar fluid flow through a tube has a parabolic velocity profile. The equation for the velocity profile is known as the HagenPoiseuille equation. The velocity profile typically will look similar to the profile shown in Figure 1. Figure 1 HagenPoiseuille Flow In theory, all flows through pipes and tubes would resemble the flow profile of Hagen Poiseuille flow. However, the reality of all flows having a similar profile is impractical. The flow path may exhibit a constriction that disturbs local flow paths from the standard HagenPoiseuille flow. One example is defined as the Gaussian constriction, as shown in Figure 2. r =0 Figure 2 Gaussian Constriction Geometry A Gaussian constriction takes the form of a Gaussian, or normal distribution bell curve. In this report, the continuity and momentum equations will be solved on the basis 5
15 of a defined geometry change to the radius. Equation 1 shows how the radius varies in the case of the Gaussian constriction. (1) The parameters ε and λ represent the dimensionless amplitude of the curve at any point and a measure of the width of the constriction, respectively. The continuity and momentum equations will need to be simplified to include dimensionless parameters so that different approximate solutions do not need to be found for each value of ε and λ. The continuity and momentum equations for steady flow without dimensionless parameters are shown in Equation 2 through Equation 4. (2) (3) (4) Once the proper continuity and momentum equations are determined for the flow characteristics, the equations can now be simplified. The first step is to define dimensionless parameters for each variable and substitute those values into the original equations. Dimensionless parameters are defined for the axial and radial distances, axial and radial velocities, and the pressure. Equation 5 through Equation 7 exhibits the new continuity and momentum equations with the substitutions. (5) 6
16 (6) (7) These equations can then be simplified even further, with the differentiation of equations for low (Laminar Flow < 2000) and high (Turbulent Flow > 2000) Reynold s numbers. The final simplified continuity and momentum equations for low Reynold s numbers are shown in Equation 8 through Equation 10. (8) (9) (10) These equations now represent the system of equations that can be solved in order to obtain the analytical solution for flow near a Gaussian constriction Final Analytical Equations In order to complete the study, the analytical solutions to the continuity and momentum equations for low Reynolds numbers need to be determined. The analytical solution will been determined by integrating Equation 8 through Equation 10. Since no heat transfer is taking place, no energy equation is necessary. Boundary conditions need to be determined and the technique utilized for integration is similar to the integral boundary layer technique of von Karman and Pohlhausen. A perturbation method is utilized to find an equation for the excess pressure drop (Equation 11). 7
17 (11) The excess pressure drop is not defined as the pressure drop through the tube, but as the difference in pressure drop between a tube with no constriction (Poiseuille flow) and a tube with a constriction. Equation 12 shows how to determine the pressure drop in a tube with no constriction. (12) Equation 13 shows how to determine the pressure drop in a tube with a defined Gaussian constriction. (13) In the following sections, the finite element results will be obtained for the pressure drops and then compared to the analytical solutions. 2.3 Fluent Setup The model setup in Fluent will be similar to Figure 2, except that the area below r = 0 will not be modeled. The geometry will be treated as a symmetrical 2d geometry in spherical coordinates except for the inclusion of the constriction. The constriction is expected to be modeled utilizing coordinate inputs as a curve into Fluent 2. The boundaries will consist of an inlet, outlet, and two nonpermeable walls that simulate the tube. The mesh will be refined near the constriction so that accurate results are obtained. Additionally, mesh verification will be run to validate the mesh size in all other areas of the flow path. The length of the tube will be chosen as such to ensure that accurate fully developed flow is obtained prior to the flow reaching the constriction. This method will also ensure that is it known when the baseline flow is being affected by the constriction. The constriction will be varied by length and amplitude. The size of the Gaussian constriction will be varied both in the analytical solution and the finite element solution. 8
18 The length of the entire tube will be set 40 mm, with the appropriate geometry modifications as stated in Table Geometry The geometry setups utilizing the values in Table 1 are created by importing coordinates as a 3D curve into Fluent. Two different curves are needed in order to create the constriction as a surface. The coordinate inputs for each case s curve are listed in Appendix A. The two curves can then be used to create a Surface from Edges, which creates a surface body. A rectangle is then drawn that is meters long and meters wide. The curve ends up being positioned in the center of the tube. A surface body is then created with the rectangle using the option Surface from Sketches. The surface body of the curve can then be treated as an area that will be removed from the surface body of the rectangle. The option to complete this action is to select Body Operation and then select Cut Material. The curve area is selected and when the body operation is applied, the geometry leftover is the flow area for a tube with a constriction Mesh Using the geometries specified in the aforementioned sections, the appropriate meshes were generated. The mesh is defined as a number of divisions in the axial and radial directions. This fine mesh allows the velocity and pressure throughout the flow region to be modeled accurately with the set conditions. Examples of the meshes generated for the base case and Cases 1 through 3 are shown in Figure 3 through Figure 6. Figure 3 Base Mesh (No Constriction) Figure mm Constriction Mesh, 5 mm Width Figure mm Constriction Mesh, 5 mm Width 9
19 Figure mm Constriction Mesh, 5 mm Width The cases where the constriction is 10 mm wide or greater require different mesh settings to ensure that the area near the constriction is properly meshed. Sample meshes for Cases 4 through 6 are shown in Figure 7 through Figure 9. Figure mm Constriction Mesh, Width 10 mm Figure mm Constriction Mesh, Width 10 mm Figure mm Constriction Mesh, Width 10 mm The mesh settings that were utilized for each case can be found in Appendix B. 10
20 3. Fluent Solutions In the following sections, the finite element solution results are shown in terms of the pressure contours and velocity vectors near the constriction. 3.1 No Constriction To accurately evaluate the flow characteristics through a Gaussian constriction, it is necessary to understand what normal Poiseuille flow looks like in a capillary tube with no constriction. The pressure contour and the velocity vectors for a tube with no constriction can be seen in Figure 10 and Figure 11, respectively. Figure 10 Pressure Contour, No Constriction Figure 11 Velocity Vectors, No Constriction 11
21 3.2 Case 1 With a constriction amplitude of 0.25 mm, the flow path is not interrupted severely from the normal pressure gradient. Figure 12 shows the pressure drop through the constriction. Figure 12 Pressure Contour, Case 1 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 13 shows the velocity vectors near the area of the constriction. Figure 13 Velocity Vectors, Case 1 It is shown that the flow path varies only slightly as it passes through the constriction. There is a slight increase of velocity to approximately m/s for a short period, but it quickly returns to the constant velocity of m/s. 12
22 3.3 Case 2 Keeping the constriction width the same and increasing the amplitude to 0.50 mm yields a slightly higher pressure drop. Figure 14 shows the pressure drop through the constriction. Figure 14 Pressure Contour, Case 2 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 15 shows the velocity vectors near the area of the constriction. Figure 15 Velocity Vectors, Case 2 In Case 2, the velocity increases to approximately m/s as it passes through the constriction 13
23 3.4 Case 3 With an amplitude of 0.75 mm, the pressure drop is significantly higher than with Case 1 or Case 2. Figure 16 shows the pressure drop through the constriction. Figure 16 Pressure Contour, Case 3 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 17 shows the velocity vectors near the area of the constriction. Figure 17 Velocity Vectors, Case 3 14
24 3.5 Case 4 Figure 18 Pressure Contour, Case 4 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 19 shows the velocity vectors near the area of the constriction. Figure 19 Velocity Vectors, Case 4 15
25 3.6 Case 5 Pressure and velocity contours Case 5 Figure 20 Pressure Contour, Case 5 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 21 shows the velocity vectors near the area of the constriction. Figure 21 Velocity Vectors, Case 5 16
26 3.7 Case 6 Figure 22 Pressure Contour, Case 6 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 23 shows the velocity vectors near the area of the constriction. Figure 23 Velocity Vectors, Case 6 17
27 3.8 Case 7 Figure 24 Pressure Contour, Case 7 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 25 shows the velocity vectors near the area of the constriction. Figure 25 Velocity Vectors, Case 7 18
28 3.9 Case 8 Figure 26 Pressure Contour, Case 8 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 27 shows the velocity vectors near the area of the constriction. Figure 27 Velocity Vectors, Case 8 19
29 3.10 Case 9 Figure 28 Pressure Contour, Case 9 The pressure drop along the entire length of the tube is increased to approximately Pa, which equals an excess pressure drop over a tube with no constriction of Pa. Figure 29 shows the velocity vectors near the area of the constriction. Figure 29 Velocity Vectors, Case 9 20
30 21
31 4. Results and Discussion The analytical solutions were determined utilizing a Maple worksheet and plugging in the necessary parameters to obtain the pressure drop values. The Maple worksheet utilized to determine the analytical results (Case 1 shown) can be seen in Appendix C. The main parameters that need to be changed for each case are the amplitude and width of the constriction. The velocity, tube radius, fluid density and fluid kinematic viscosity are the same for each case. Table 4 shows the input parameters for the amplitude (a) and the width (b) for each case. Case # a b Table 3 Maple Input Parameters for Constriction Amplitude and Width The values of b were determined to yield the constriction width required based on Equation X. The actual analytical results for each case obtained from the Maple worksheet and utilizing the above parameters is shown in Table 4. Case Pressure Drop  No Pressure Drop  ΔP ex Number Constriction (Pa) Constriction (Pa) Table 4 Analytical Solutions for ΔP ex 22
32 Percentage Difference Case Pressure Drop  No Pressure Drop  ΔP ex Number Constriction (Pa) Constriction (Pa) Table 5 Finite Element Solutions for ΔP ex The pressure values utilized for comparison from Fluent were the static pressure values listed at the inlet of the centerline. This value does not take into account the rise in pressure that occurs as the fluid is entering the tube since the flow is not fully developed at this point. However, the flow is fully developed at approximately m from the inlet, allowing the point of fully developed flow to take place before the area of the constriction begins % Percentage Difference of Analytical vs. Finite Element Pressure Drop Values With Constriction 8.00% 6.00% 4.00% 2.00% 0.00% Case Number Chart 1 Percentage Difference of Analytical vs. Finite Element Pressure Drop Values With Constriction 23
33 Percentage Difference Percentage Difference Between Analytical and Finite Element Excess Pressure Drop Values 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% Case Number Chart 2 Percentage Difference Between Analytical and Finite Element Excess Pressure Drop Values 24
34 5. Conclusions In general, the analytical and the finite element solutions were fairly close to one another. It was found that for the geometry and fluid properties chosen, the percentage difference of the finite element solution was within 10% of the analytical solution at all times. Typically, the lowest percentage differences of the actual pressure drop through the constriction occurred when the constriction width was limited to 5 mm, despite the amplitude being up to 75% of the tube radius. 25
35 6. References *Need to still assign references to spots in the text and put in order of appearance. Additional references for some theory, etc. are still required. [1] Middleman, Stanley. "Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops." Academic Press, n.d. [2] Lee, T. S. "Numerical Study of Fluid Flow through Double BellShaped Constrictions in a Tube." International Journal of Numerical Methods for Heat & Fluid Flow 12.2 (2002): ProQuest. Web. 7 Sep [3] Manton, M.J. "Low Reynolds Number Flow in Slowly Varying Axisymmetric Tubes." Fluid Mechanics (1971): Document. [4] Haber Shimon, Clark Alys, Tawhai Merryn. Blood Flow in Capillaries of the Human Lung J Biomech Eng 135, (2013) (11 pages); Paper No: BIO ; doi: / [5] a.pdf&code=b34ee34ac92a df0a7aa58, accessed September 29, 2014 [6] accessed October 17, 2014 [7] w, accessed September XX,
36 APPENDIX A Curve Coordinates The coordinates for each curve were obtained from the following sample code in Maple: > > > > > > The equation for how a radius varies axially due to a constriction is defined (Equation 1). Then, the parameters are chosen based on the curve that is to be plotted. The program then provides twentyone coordinates over the entire length of the 40 mm tube in order to build the curve. Since the program gives the coordinates for a length of meters to meters, the x values were adjusted accordingly to put the peak of the curve in the center of a length of 0 meters to meters. The following shows the adjusted coordinates that were used for plotting each curve in order to build the finite element flow domain, with the first coordinates being those that created the straight line curve used in all models. 27
37 Straight Line (Used For All Curves) #group #point #x_coord #y_coord #z_coord Amplitude 0.25 mm, Width 5 mm #group #point #x_coord #y_coord #z_coord
38 Amplitude 0.25 mm, Width 10 mm #group #point #x_coord #y_coord #z_coord Amplitude 0.25 mm, Width 15 mm #group #point #x_coord #y_coord #z_coord
39 Amplitude 0.5 mm, Width 5 mm #group #point #x_coord #y_coord #z_coord Amplitude 0.5 mm, Width 10 mm #group #point #x_coord #y_coord #z_coord
40 Amplitude 0.5 mm, Width 15 mm #group #point #x_coord #y_coord #z_coord Amplitude 0.75 mm, Width 5 mm #group #point #x_coord #y_coord #z_coord
41 Amplitude 0.75 mm, Width 10 mm #group #point #x_coord #y_coord #z_coord Amplitude 0.75 mm, Width 15 mm #group #point #x_coord #y_coord #z_coord
42 APPENDIX B Mesh Settings *Need to input mesh settings and also show a diagram of the geometry with corresponding named elements* Number of Divisions Case # Axial Centerline Pipewall
43 APPENDIX C Maple Worksheet For Analytical Solutions > > > > > > > > 34
44 > > > > > > 35
NavierStokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering Computing, Wiley (2006).
Introduction to Chemical Engineering Computing Copyright, Bruce A. Finlayson, 2004 1 NavierStokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering
More informationExperiment 3 Pipe Friction
EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A crosssectional
More informationANALYSIS OF FULLY DEVELOPED TURBULENT FLOW IN A PIPE USING COMPUTATIONAL FLUID DYNAMICS D. Bhandari 1, Dr. S. Singh 2
ANALYSIS OF FULLY DEVELOPED TURBULENT FLOW IN A PIPE USING COMPUTATIONAL FLUID DYNAMICS D. Bhandari 1, Dr. S. Singh 2 1 M. Tech Scholar, 2 Associate Professor Department of Mechanical Engineering, Bipin
More informationAbaqus/CFD Sample Problems. Abaqus 6.10
Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More informationLecture 5 Hemodynamics. Description of fluid flow. The equation of continuity
1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood
More informationPipe FlowFriction Factor Calculations with Excel
Pipe FlowFriction Factor Calculations with Excel Course No: C03022 Credit: 3 PDH Harlan H. Bengtson, PhD, P.E. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980
More informationME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts
ME 305 Fluid Mechanics I Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey csert@metu.edu.tr
More informationThe Use Of CFD To Simulate Capillary Rise And Comparison To Experimental Data
The Use Of CFD To Simulate Capillary Rise And Comparison To Experimental Data Hong Xu, Chokri Guetari ANSYS INC. Abstract In a microgravity environment liquid can be pumped and positioned by cohesion
More informationExergy Analysis of a Water Heat Storage Tank
Exergy Analysis of a Water Heat Storage Tank F. Dammel *1, J. Winterling 1, K.J. Langeheinecke 3, and P. Stephan 1,2 1 Institute of Technical Thermodynamics, Technische Universität Darmstadt, 2 Center
More informationCommercial CFD Software Modelling
Commercial CFD Software Modelling Dr. Nor Azwadi bin Che Sidik Faculty of Mechanical Engineering Universiti Teknologi Malaysia INSPIRING CREATIVE AND INNOVATIVE MINDS 1 CFD Modeling CFD modeling can be
More informationDiffusion and Fluid Flow
Diffusion and Fluid Flow What determines the diffusion coefficient? What determines fluid flow? 1. Diffusion: Diffusion refers to the transport of substance against a concentration gradient. ΔS>0 Mass
More informationMercury Flow through a Long Curved Pipe
Mercury Flow through a Long Curved Pipe Wenhai Li & Foluso Ladeinde Department of Mechanical Engineering Stony Brook University Summary The flow of mercury in a long, curved pipe is simulated in this task,
More informationAN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL
14 th European Conference on Mixing Warszawa, 1013 September 2012 AN EFFECT OF GRID QUALITY ON THE RESULTS OF NUMERICAL SIMULATIONS OF THE FLUID FLOW FIELD IN AN AGITATED VESSEL Joanna Karcz, Lukasz Kacperski
More informationFLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER
VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER? What type of fluid flow is observed? The above pictures show how the effect
More informationIntroduction to COMSOL. The NavierStokes Equations
Flow Between Parallel Plates Modified from the COMSOL ChE Library module rev 10/13/08 Modified by Robert P. Hesketh, Chemical Engineering, Rowan University Fall 2008 Introduction to COMSOL The following
More informationSteady Flow: Laminar and Turbulent in an SBend
STARCCM+ User Guide 6663 Steady Flow: Laminar and Turbulent in an SBend This tutorial demonstrates the flow of an incompressible gas through an sbend of constant diameter (2 cm), for both laminar and
More informationE 490 Fundamentals of Engineering Review. Fluid Mechanics. M. A. Boles, PhD. Department of Mechanical & Aerospace Engineering
E 490 Fundamentals of Engineering Review Fluid Mechanics By M. A. Boles, PhD Department of Mechanical & Aerospace Engineering North Carolina State University Archimedes Principle and Buoyancy 1. A block
More informationModeling and Numerical Blood Flow Analysis of Tibial Artery using CFD
Modeling and Numerical Blood Flow Analysis of Tibial Artery using CFD S.Manimaran Department of Biomedical Engineering C.Muralidharan M.E Assistant Professor Department of Biomedical Engineering Surendra
More informationFluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems
Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today
More informationModule 2 : Convection. Lecture 20a : Illustrative examples
Module 2 : Convection Lecture 20a : Illustrative examples Objectives In this class: Examples will be taken where the concepts discussed for heat transfer for tubular geometries in earlier classes will
More informationA LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW. 1998 ASME Fluids Engineering Division Summer Meeting
TELEDYNE HASTINGS TECHNICAL PAPERS INSTRUMENTS A LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW Proceedings of FEDSM 98: June 5, 998, Washington, DC FEDSM98 49 ABSTRACT The pressure
More informationTurbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine
HEFAT2012 9 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 16 18 July 2012 Malta Turbulence Modeling in CFD Simulation of Intake Manifold for a 4 Cylinder Engine Dr MK
More informationGEOMETRIC, THERMODYNAMIC AND CFD ANALYSES OF A REAL SCROLL EXPANDER FOR MICRO ORC APPLICATIONS
2 nd International Seminar on ORC Power Systems October 7 th & 8 th, 213 De Doelen, Rotterdam, NL GEOMETRIC, THERMODYNAMIC AND CFD ANALYSES OF A REAL SCROLL EXPANDER FOR MICRO ORC APPLICATIONS M. Morini,
More informationCivil Engineering Hydraulics Mechanics of Fluids. Flow in Pipes
Civil Engineering Hydraulics Mechanics of Fluids Flow in Pipes 2 Now we will move from the purely theoretical discussion of nondimensional parameters to a topic with a bit more that you can see and feel
More informationChapter 8: Flow in Pipes
Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks
More informationLaminar flow in a baffled stirred mixer (COMSOL)
AALTO UNIVERSITY School of Chemical Technology CHEME7160 Fluid Flow in Process Units Laminar flow in a baffled stirred mixer (COMSOL) Sanna Hyvönen, 355551 Nelli Jämsä, 223188 Abstract In this simulation
More informationAdaptation of General Purpose CFD Code for Fusion MHD Applications*
Adaptation of General Purpose CFD Code for Fusion MHD Applications* Andrei Khodak Princeton Plasma Physics Laboratory P.O. Box 451 Princeton, NJ, 08540 USA akhodak@pppl.gov Abstract Analysis of many fusion
More informationChapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any
Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass
More informationBasic Principles in Microfluidics
Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces
More informationPage It varies from being high at the inlet to low at the outlet. 2. It varies from being low at the inlet to high at the outlet
A water is pulled through a very narrow, straight tube by a pump. The inlet and outlet of the tube are at the same height. What do we know about the pressure of the water in the tube? 1. It varies from
More informationPractice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22
BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =
More informationApplied Fluid Mechanics
Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and
More informationCBE 6333, R. Levicky 1. Potential Flow
CBE 6333, R. Levicky Part I. Theoretical Background. Potential Flow Potential Flow. Potential flow is irrotational flow. Irrotational flows are often characterized by negligible viscosity effects. Viscous
More informationEXAMPLE: Water Flow in a Pipe
EXAMPLE: Water Flow in a Pipe P 1 > P 2 Velocity profile is parabolic (we will learn why it is parabolic later, but since friction comes from walls the shape is intuitive) The pressure drops linearly along
More informationME6130 An introduction to CFD 11
ME6130 An introduction to CFD 11 What is CFD? Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically
More informationLearning Module 4  Thermal Fluid Analysis Note: LM4 is still in progress. This version contains only 3 tutorials.
Learning Module 4  Thermal Fluid Analysis Note: LM4 is still in progress. This version contains only 3 tutorials. Attachment C1. SolidWorksSpecific FEM Tutorial 1... 2 Attachment C2. SolidWorksSpecific
More informationFLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS  CB0235 2014_1
COURSE CODE INTENSITY PREREQUISITE COREQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT
More informationINVESTIGATION OF FALLING BALL VISCOMETRY AND ITS ACCURACY GROUP R1 Evelyn Chou, Julia Glaser, Bella Goyal, Sherri Wykosky
INVESTIGATION OF FALLING BALL VISCOMETRY AND ITS ACCURACY GROUP R1 Evelyn Chou, Julia Glaser, Bella Goyal, Sherri Wykosky ABSTRACT: A falling ball viscometer and its associated equations were studied in
More informationEntrance Conditions. Chapter 8. Islamic Azad University
Chapter 8 Convection: Internal Flow Islamic Azad University Karaj Branch Entrance Conditions Must distinguish between entrance and fully developed regions. Hydrodynamic Effects: Assume laminar flow with
More informationFLUID FLOW Introduction General Description
FLUID FLOW Introduction Fluid flow is an important part of many processes, including transporting materials from one point to another, mixing of materials, and chemical reactions. In this experiment, you
More informationFlow Loss in Screens: A Fresh Look at Old Correlation. Ramakumar Venkata Naga Bommisetty, Dhanvantri Shankarananda Joshi and Vighneswara Rao Kollati
Journal of Mechanics Engineering and Automation 3 (013) 934 D DAVID PUBLISHING Ramakumar Venkata Naga Bommisetty, Dhanvantri Shankarananda Joshi and Vighneswara Rao Kollati Engineering Aerospace, MCOE,
More informationDimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena.
Dimensional Analysis and Similarity Dimensional analysis is very useful for planning, presentation, and interpretation of experimental data. As discussed previously, most practical fluid mechanics problems
More informationNUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES
Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics
More informationHEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi
HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi 2 Rajesh Dudi 1 Scholar and 2 Assistant Professor,Department of Mechanical Engineering, OITM, Hisar (Haryana)
More informationPrediction of Pressure Drop in Chilled Water Piping System Using Theoretical and CFD Analysis
Shirish P. Patil et.al / International Journal o Engineering and Technology (IJET) Prediction o Pressure Drop in Chilled Water Piping System Using Theoretical and CFD Analysis Shirish P. Patil #1, Abhijeet
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture  22 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture  22 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. So
More informationCFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER
International Journal of Advancements in Research & Technology, Volume 1, Issue2, July2012 1 CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER ABSTRACT (1) Mr. Mainak Bhaumik M.E. (Thermal Engg.)
More informationBLOOD CIRCULATION. Department of Biomedical Sciences Medical University of Lodz
BLOOD CIRCULATION Department of Biomedical Sciences Medical University of Lodz CONSTRUCTION OF THE CIRCULATORY SYSTEM Circulatory System VESSELS CONSTRUCTION HEART The primary function of the heart is
More information4.What is the appropriate dimensionless parameter to use in comparing flow types? YOUR ANSWER: The Reynolds Number, Re.
CHAPTER 08 1. What is most likely to be the main driving force in pipe flow? A. Gravity B. A pressure gradient C. Vacuum 2.What is a general description of the flow rate in laminar flow? A. Small B. Large
More informationBattery Thermal Management System Design Modeling
Battery Thermal Management System Design Modeling GiHeon Kim, Ph.D Ahmad Pesaran, Ph.D (ahmad_pesaran@nrel.gov) National Renewable Energy Laboratory, Golden, Colorado, U.S.A. EVS October 8, 8, 006 Yokohama,
More informationDimensional Analysis
Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous
More informationChapter Six. NonNewtonian Liquid
Chapter Six NonNewtonian Liquid For many fluids a plot of shear stress against shear rate does not give a straight line. These are socalled NonNewtonian Fluids. Plots of shear stress against shear rate
More informationHead Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids
Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness
More informationAUTOMOTIVE COMPUTATIONAL FLUID DYNAMICS SIMULATION OF A CAR USING ANSYS
International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 2, MarchApril 2016, pp. 91 104, Article ID: IJMET_07_02_013 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=2
More informationFluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01
Boundary Conditions C1 Overview Inlet and Outlet Boundaries Velocity Outline Profiles Turbulence Parameters Pressure Boundaries and others... Wall, Symmetry, Periodic and Axis Boundaries Internal Cell
More informationFLOW ANALYSIS OF EFFECT OF STRUTS IN AN ANNULAR DIFFUSER
FLOW ANALYSIS OF EFFECT OF STRUTS IN AN ANNULAR DIFFUSER 1, 2, 3 Raghul., DANUSHKOTTI., Nanda Gopal. B.E Student, Department of Mechanical Engineering, Velammal Engg College, Chennai ABSTRACT Some recent
More informationFLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions
FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or
More informationsensors ISSN 14248220 www.mdpi.com/journal/sensors
Sensors 2010, 10, 1056010570; doi:10.3390/s101210560 OPEN ACCESS sensors ISSN 14248220 www.mdpi.com/journal/sensors Article A New Approach to Laminar Flowmeters Fernando Lopez Pena *, Alvaro Deibe Diaz,
More informationTutorial 1. Flow over a Cylinder Two Dimensional Case. Using ANSYS Workbench. Simple Mesh
Tutorial 1. Flow over a Cylinder Two Dimensional Case Using ANSYS Workbench Simple Mesh The primary objective of this Tutorial is to guide the student using Fluent for first time through the very basics
More informationFluids in Motion Supplement I
Fluids in Motion Supplement I Cutnell & Johnson describe a number of different types of flow: Compressible vs incompressible (most liquids are very close to incompressible) Steady vs Unsteady Viscous or
More informationVISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries?
VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW VISCOSITY POISEUILLE'S LAW? Why do cars need different oils in hot and cold countries? Why does the engine runs more freely as
More informationBoundary Conditions in Fluid Mechanics
Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial
More informationTutorial 1. Introduction to Using ANSYS FLUENT in ANSYS Workbench: Fluid Flow and Heat Transfer in a Mixing Elbow
Tutorial 1. Introduction to Using ANSYS FLUENT in ANSYS Workbench: Fluid Flow and Heat Transfer in a Mixing Elbow Introduction This tutorial illustrates using ANSYS Workbench to set up and solve a threedimensional
More informationTHE PSEUDO SINGLE ROW RADIATOR DESIGN
International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, JanFeb 2016, pp. 146153, Article ID: IJMET_07_01_015 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1
More informationChapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations
Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.
More informationHEAVY OIL FLOW MEASUREMENT CHALLENGES
HEAVY OIL FLOW MEASUREMENT CHALLENGES 1 INTRODUCTION The vast majority of the world s remaining oil reserves are categorised as heavy / unconventional oils (high viscosity). Due to diminishing conventional
More informationPressure drop in pipes...
Pressure drop in pipes... PRESSURE DROP CALCULATIONS Pressure drop or head loss, occurs in all piping systems because of elevation changes, turbulence caused by abrupt changes in direction, and friction
More informationDEVELOPMENT OF HIGH SPEED RESPONSE LAMINAR FLOW METER FOR AIR CONDITIONING
DEVELOPMENT OF HIGH SPEED RESPONSE LAMINAR FLOW METER FOR AIR CONDITIONING Toshiharu Kagawa 1, Yukako Saisu 2, Riki Nishimura 3 and Chongho Youn 4 ABSTRACT In this paper, we developed a new laminar flow
More informationINVESTIGATION OF FLUID FLOW IN AXIAL HYDROSTATIC BEARING
INVESTIGATION OF FLUID FLOW IN AXIAL HYDROSTATIC BEARING Michal KOZDERA VŠB Technical University of Ostrava, Faculty of Mechanical Engineering, Department of hydromechanics and hydraulic equipment, 17.
More informationAnalysis of Mash Tun Flow: Recommendations for Home Brewers
Analysis of Mash Tun Flow: Recommendations for Home Brewers Conor J. Walsh 1 and Ernesto GutierrezMiravete* 2 1 General DynamicsElectric Boat, Groton, CT 2 Rensselaer at Hartford, Hartford, CT *Corresponding
More informationFluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment
Fluid Structure Interaction VI 3 Fluid structure interaction of a vibrating circular plate in a bounded fluid volume: simulation and experiment J. Hengstler & J. Dual Department of Mechanical and Process
More informationOpen Channel Flow. M. Siavashi. School of Mechanical Engineering Iran University of Science and Technology
M. Siavashi School of Mechanical Engineering Iran University of Science and Technology W ebpage: webpages.iust.ac.ir/msiavashi Email: msiavashi@iust.ac.ir Landline: +98 21 77240391 Fall 2013 Introduction
More informationAdvanced Differential Pressure Flowmeter Technology VCONE FLOW METER TECHNICAL BRIEF
Advanced Differential Pressure Flowmeter Technology VCONE FLOW METER TECHNICAL BRIEF Table of Contents Section 1  General Introduction 1.1 1 Principles Of Operation 1.2 1 Reshaping The Velocity Profile
More informationTechnology of EHIS (stamping) applied to the automotive parts production
Laboratory of Applied Mathematics and Mechanics Technology of EHIS (stamping) applied to the automotive parts production Churilova Maria, SaintPetersburg State Polytechnical University Department of Applied
More informationdu u U 0 U dy y b 0 b
BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:
More informationRavi Kumar Singh*, K. B. Sahu**, Thakur Debasis Mishra***
Ravi Kumar Singh, K. B. Sahu, Thakur Debasis Mishra / International Journal of Engineering Research and Applications (IJERA) ISSN: 4896 www.ijera.com Vol. 3, Issue 3, MayJun 3, pp.76677 Analysis of
More informationXI / PHYSICS FLUIDS IN MOTION 11/PA
Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A
More informationLaminar and Turbulent flow. Flow Sensors. Reynolds Number. Thermal flow Sensor. Flow and Flow rate. R = Mass Flow controllers
Flow and Flow rate. Laminar and Turbulent flow Laminar flow: smooth, orderly and regular Mechanical sensors have inertia, which can integrate out small variations due to turbulence Turbulent flow: chaotic
More informationFREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES
FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the
More informationCalculating resistance to flow in open channels
Alternative Hydraulics Paper 2, 5 April 2010 Calculating resistance to flow in open channels http://johndfenton.com/alternativehydraulics.html johndfenton@gmail.com Abstract The DarcyWeisbach formulation
More informationPipe Loss Experimental Apparatus
Pipe Loss Experimental Apparatus Kathleen Lifer, Ryan Oberst, Benjamin Wibberley Ohio Northern University Ada, OH 45810 Email: bwibberley@onu.edu Abstract The objective of this project was to develop
More informationCOMPUTATIONAL FLOW MODEL OF WESTFALL'S 4000 OPEN CHANNEL MIXER 4115271R1. By Kimbal A. Hall, PE. Submitted to: WESTFALL MANUFACTURING COMPANY
COMPUTATIONAL FLOW MODEL OF WESTFALL'S 4000 OPEN CHANNEL MIXER 4115271R1 By Kimbal A. Hall, PE Submitted to: WESTFALL MANUFACTURING COMPANY FEBRUARY 2012 ALDEN RESEARCH LABORATORY, INC. 30 Shrewsbury
More informationFREE CONVECTION FROM OPTIMUM SINUSOIDAL SURFACE EXPOSED TO VERTICAL VIBRATIONS
International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, JanFeb 2016, pp. 214224, Article ID: IJMET_07_01_022 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1
More informationChapter 1. Governing Equations of Fluid Flow and Heat Transfer
Chapter 1 Governing Equations of Fluid Flow and Heat Transfer Following fundamental laws can be used to derive governing differential equations that are solved in a Computational Fluid Dynamics (CFD) study
More informationHydraulic losses in pipes
Hydraulic losses in pipes Henryk Kudela Contents 1 Viscous flows in pipes 1 1.1 Moody Chart.................................... 2 1.2 Types of Fluid Flow Problems........................... 5 1.3 Minor
More informationProblem Statement In order to satisfy production and storage requirements, small and mediumscale industrial
Problem Statement In order to satisfy production and storage requirements, small and mediumscale industrial facilities commonly occupy spaces with ceilings ranging between twenty and thirty feet in height.
More informationViscous Flow in Pipes
Viscous Flow in Pipes Excerpted from supplemental materials of Prof. KuangAn Chang, Dept. of Civil Engin., Texas A&M Univ., for his spring 2008 course CVEN 311, Fluid Dynamics. (See a related handout
More informationWhat is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation)
OPEN CHANNEL FLOW 1 3 Question What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation) Typical open channel shapes Figure
More informationThe ratio of inertial to viscous forces is commonly used to scale fluid flow, and is called the Reynolds number, given as:
12.001 LAB 3C: STOKES FLOW DUE: WEDNESDAY, MARCH 9 Lab Overview and Background The viscosity of a fluid describes its resistance to deformation. Water has a very low viscosity; the force of gravity causes
More informationLecture 16  Free Surface Flows. Applied Computational Fluid Dynamics
Lecture 16  Free Surface Flows Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (20022006) Fluent Inc. (2002) 1 Example: spinning bowl Example: flow in
More informationIntroduction to Microfluidics. Date: 2013/04/26. Dr. YiChung Tung. Outline
Introduction to Microfluidics Date: 2013/04/26 Dr. YiChung Tung Outline Introduction to Microfluidics Basic Fluid Mechanics Concepts Equivalent Fluidic Circuit Model Conclusion What is Microfluidics Microfluidics
More informationCHAPTER 4 CFD ANALYSIS OF THE MIXER
98 CHAPTER 4 CFD ANALYSIS OF THE MIXER This section presents CFD results for the venturijet mixer and compares the predicted mixing pattern with the present experimental results and correlation results
More informationCE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART  A
CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART  A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density
More informationExpress Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology
Express Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology Dimitrios Sofialidis Technical Manager, SimTec Ltd. Mechanical Engineer, PhD PRACE Autumn School 2013  Industry
More informationBlasius solution. Chapter 19. 19.1 Boundary layer over a semiinfinite flat plate
Chapter 19 Blasius solution 191 Boundary layer over a semiinfinite flat plate Let us consider a uniform and stationary flow impinging tangentially upon a vertical flat plate of semiinfinite length Fig
More information. Address the following issues in your solution:
CM 3110 COMSOL INSTRUCTIONS Faith Morrison and Maria Tafur Department of Chemical Engineering Michigan Technological University, Houghton, MI USA 22 November 2012 Zhichao Wang edits 21 November 2013 revised
More informationCFD Analysis of Supersonic Exhaust Diffuser System for Higher Altitude Simulation
Page1 CFD Analysis of Supersonic Exhaust Diffuser System for Higher Altitude Simulation ABSTRACT Alan Vincent E V P G Scholar, Nehru Institute of Engineering and Technology, Coimbatore Tamil Nadu A high
More informationLecture 6  Boundary Conditions. Applied Computational Fluid Dynamics
Lecture 6  Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (20022006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.
More informationContents. Microfluidics  Jens Ducrée Physics: NavierStokes Equation 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. InkJet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More information