flowlab-cimbala-imece2004-5987

1 Copyright © 2004 by ASME

Proceedings of IMECE’04: 2004 ASME International Mechanical Engineering Conference

November 13-19, 2004, Anaheim, California, USA

IMECE2004-59870

USING FLOWLAB, A COMPUTATIONAL FLUID DYNAMICS TOOL, TO FACILITATE THE TEACHING OF FLUID MECHANICS

John Cimbala The Pennsylvania State University

Mechanical Engineering Department 234 Reber Building

University Park, Pennsylvania 16802

Shane Moeykens Ashish Kulkarni

Ajay Parihar Fluent Inc.

10 Cavendish Court Lebanon, New Hampshire 03766

ABSTRACT Traditional fluid mechanics textbooks are generally written with problem sets comprised of closed, analytical solutions. However, it is recognized that complex flow fields are not easily represented in terms of a closed solution. A tool that allows the student to visualize complex flow phenomena in a virtual environment can significantly enhance the learning experience. Such a visualization tool allows the student to perform open-ended analyses and explore cause-effect relationships. Computational fluid dynamics (CFD) brings these benefits into the learning environment for fluid mechanics. With these benefits in mind, FlowLab was introduced by Fluent Inc. in 2002. FlowLab may be described as a virtual fluids laboratory – a computer-based analysis and visualization package. Using this software, students solve predefined CFD exercises, either as homework or in a supervised laboratory or practicum setting. Predefined exercises facilitate the teaching of fluid mechanics and provide students with hands-on CFD experience, while avoiding many of the difficulties associated with learning a generalized CFD package. A new fluid mechanics textbook is scheduled for release in early 2005. This book includes FlowLab as a textbook companion, where student-friendly CFD exercises are employed to convey important concepts to the student. Because of the unique design of end-of-chapter homework problems in this book and the intimate coupling between these problems and the CFD software,

students are introduced to engineering problems and concepts, as well as to CFD, via a structured learning process. The CFD exercises are not meant to stand alone; rather, they are designed to support and emphasize the theory and concepts taught in the textbook, which is the primary learning vehicle. Each homework problem has a specific fluid mechanics learning objective. Through use of the software, a second learning objective is also achieved, namely a CFD objective. The scope, content, and presentation of these CFD exercises are discussed in this paper. Additionally, one of the exercises is explained in detail to show the value of using CFD to teach introductory fluid mechanics to undergraduate engineers. INTRODUCTION In many engineering disciplines (aerospace, civil, mechanical, etc.), at least one introductory course in fluid mechanics is required for undergraduates. However, it is unusual for even the fundamentals of computational fluid dynamics (CFD) to be taught at the undergraduate level. In spite of this, many B.S. engineers end up using CFD at their workplace, often with little or no formal training, and engineering educators are beginning to see the importance of hands-on exposure to CFD in the undergraduate curriculum.

Proceedings of IMECE04 2004 ASME International Mechanical Engineering Congress and Exposition

November 13-20, 2004, Anaheim, California USA

IMECE2004-59870


While any intelligent, computer-literate person can run a CFD code, the results he or she obtains may not be physically correct. In fact, a poor choice of computational domain, an under-resolved grid, improper choice of laminar versus turbulent flow, inappropriate boundary conditions, and/or any of a number of other miscues can lead to CFD solutions that are physically incorrect, even though the colorful graphical output always looks pretty. Therefore, the goal of the exercises described here is to expose students to both the capabilities and limitations of CFD, while reinforcing or furthering their knowledge of fluid mechanics. The exercises emphasize the proper application of CFD to engineering problems, rather than details about grid generation techniques, discretization schemes, CFD algorithms, or numerical stability. Fluid mechanics is a highly visual subject; therefore, flow visualization photographs and video clips [1], in-class demonstrations, and hands-on laboratory exercises often accompany a traditional fluid mechanics course. Another tool with enormous potential for enhancing the learning experience is CFD [2, 3]. Like a traditional laboratory experiment, CFD allows the student to perform open-ended analyses and explore cause-effect relationships. Furthermore, CFD extends the analysis beyond what is possible using traditional physical experiments, because the student can easily visualize complex flow phenomena using color contour plots and vector plots. In addition, the post-processing modules in CFD codes provide the student with the capability of zooming in on a region of interest for detailed study. In the present paper, a synopsis of FlowLab [4] is provided first, followed by a description of the new FlowLab templates (exercises) that were jointly developed by Fluent Inc. and the authors of a new undergraduate fluid mechanics textbook [5]. Then, an end-of-chapter exercise and its corresponding FlowLab template created to illustrate flow through a conical diffuser are described in greater detail. Finally, we explain how another FlowLab template was successfully integrated into an undergraduate fluid mechanics laboratory in the spring semester of 2004 at Penn State University. FLOWLAB The introduction of CFD to engineering students at the undergraduate level has become more common in recent years, although there are significant barriers for doing so using a generalized CFD solver. A common restriction is the volume of material to be covered in a fixed amount of time, which leaves little time left for learning the use of a generalized CFD package. With this concern in mind, a computer based analysis and visualization package called FlowLab was created.

FlowLab is a virtual laboratory that facilitates the running of predefined fluid mechanics problems under a single interface. FlowLab is not a generalized CFD package. This software provides for the learning of fluid mechanics through an interface which is structured to control the process in which a problem is set up, converged, and post-processed. Using Flowlab, a student may visualize complex flow fields in a virtual environment. Geometric dimensions, material properties of the fluid, and boundary conditions can be varied by the user. Relevant reports, X-Y plots, contour plots, and vector diagrams can be displayed after the solution is converged. The primary advantage of using FlowLab in the classroom is that it is interactive. For each CFD template, students run the CFD solution from start to finish - generate the geometry, generate the grid, choose parameters and/or models, run the iterations, and post-process. While this approach is more challenging than simply post-processing previously run CFD solutions, FlowLab allows for CFD exercises to be set up such that the steps are easy to follow; there are not pages of instructions or directions to read. Each template contains one or more variables that students adjust with each run. In this sense, the CFD exercise becomes analogous to a physical experiment - students collect data after each run, plot and identify trends in the data, and learn something about both CFD and fluid mechanics in the process. Primarily because of it’s ease of use and minimal learning curve, FlowLab was recently chosen for use at Purdue University in a course on transport phenomena open to undergraduate students. Details about one CFD exercise used at Purdue, developing flow in a pipe with heat transfer, are provided by Curtis et al. [6]. They conclude that by using FlowLab, CFD can be incorporated easily into a course without requiring a large start-up time, and without taking valuable lecture time. It was also observed that CFD exercises are a natural complement to lecture material which discusses theory or develops analytical solutions to flow and heat transfer problems. Under National Science Foundation funding, FlowLab CFD exercises have recently been developed and applied in the classroom by a consortium of universities (Iowa, Iowa State, Cornell, and Howard) [7]. In the fall 2003 semester, three CFD exercises were tested by this consortium: pipe, nozzle, and airfoil flow. As part of the testing process, a self-evaluation was performed at each university with support from the Center for Evaluation and Assessment at the University of Iowa. The self-evaluation revealed that most students’ performance was very good, and students were cooperative and eager to learn CFD methods. Students appreciated the hands-on learning process gained via using a step-by-step method through the CFD interface, which enhanced their understanding of


analyzing and solving practical fluids engineering problems. Appendix A presents additional information relating to the self-evaluation conducted at Iowa State University, as an example. NEW FLOWLAB TEMPLATES The fluid mechanics textbook by Çengel and Cimbala [5] includes a chapter that introduces CFD to undergraduate students. The emphasis of the chapter is how to use CFD, rather than how to write CFD codes. The CFD chapter is more than a user’s manual, however, in that the fundamental steps required to obtain a useful CFD solution are explained at a level appropriate for undergraduate engineering students: define a computational domain; generate a grid; specify boundary conditions, fluid properties, and numerical parameters; define initial conditions; iterate towards a solution; and generate desired results through post-processing. Over the course of approximately one year, the authors of the textbook collaborated with developers at Fluent Inc. to create 43 new FlowLab templates that are used in conjunction with 46 end-of-chapter homework problems in the textbook. There is nearly one-to-one correspondence between each individual template and an end-of-chapter homework problem in the textbook, although a few of the templates are used for more than one homework problem. Each homework problem, along with its corresponding FlowLab template, has been carefully designed with two major learning objectives in mind: (1) enhance the student’s understanding of a specific fluid mechanics concept, and (2) introduce the student to a specific capability and/or limitation of CFD through hands-on practice. The FlowLab templates can also be used in stand-alone mode for CFD user training, provided that the corresponding end-of-chapter homework problems are provided. The FlowLab templates are categorized into 9 independent flow fields, as listed in Table 1. The flow fields include internal flows and external flows, laminar and turbulent flows, incompressible and compressible flows, flows with heat transfer, and low Reynolds number (creeping) flows. Each flow field has one or more templates, each of which contains both a fluid mechanics objective and a CFD objective, as listed in Table 1. Consider, for example, Flow field 2 – Turbulent flow through a conical diffuser. In the first template of this exercise (template number 8), students examine the pressure recovery through a 20o half-angle diffuser. From the point of view of teaching fluid mechanics, two basic physical concepts are reinforced: (1) a flow may separate from the wall in an adverse pressure gradient, and (2) the pressure increases through the diffuser, in spite of the irreversible losses due to flow separation. Both of these concepts are rather difficult for beginning students of fluid

mechanics to comprehend, but they are clearly demonstrated by this FlowLab template. The CFD objective is two-fold: learn to refine a mesh until grid independence is achieved, and learn how to plot streamlines for each grid resolution for comparison. FLOW THROUGH A CONICAL DIFFUSER Details about Template 10 of Flow field 2 – Turbulent flow through a conical diffuser (Table 1) − are provided in this section as an example of how FlowLab is used in conjunction with the new undergraduate fluid mechanics textbook. Adverse pressure gradients, flow separation, and pressure recovery through a diffuser are often difficult concepts for students studying introductory fluid mechanics. Therefore, the fluid mechanics objective is to study pressure recovery in conical diffusers of half-angle 5o to 90o. The CFD objectives are to observe streamline patterns and flow separation as diffuser half-angle increases, and to compute and compare pressure recovery for all cases. The end-of-chapter problem in the textbook is copied here, with minor modifications for clarity:

Barbara is designing a conical diffuser for an axisymmetric wind tunnel. She needs to achieve at least 40 Pa of pressure recovery through the diffuser, while keeping the diffuser length as small as possible. Barb decides to use CFD to compare the performance of various diffusers with half-angle θ ranging from 5o to 90o (see Fig. 1 for the definition of θ and other parameters in the problem.). In all cases, the diameter doubles through the diffuser – the inlet and outlet diameters are D1 = 0.50 m and D2 = 1.0 m respectively. The inlet velocity is nearly uniform at V = 10.0 m/s. The axial distance upstream of the diffuser is L1 = 1.50 m and the axial distance from the start of the diffuser to the outlet is L2 = 8.00 m. (The overall length of the computational domain is 9.50 m in all cases.) Run FlowLab with template “Diffuser_angle”. In addition to the axis and wall boundary conditions labeled in Fig. 1, the inlet is specified as a velocity inlet and the outlet is specified as a pressure outlet with Pout = 0 gage pressure for all cases. The fluid is air at default (room temperature) conditions. The flow is approximated as incompressible, axisymmetric, and turbulent, but steady in the mean. (a) Generate CFD solutions for half-angle θ = 5o, 7.5o, 10o,

12.5o, 15o, 17.5o, 20o, 25o, 30o, 45o, 60o, and 90o. Plot streamlines for each case. Describe how the flow field changes with diffuser half-angle, paying particular attention to flow separation on the diffuser wall. How small must θ be to avoid flow separation?

(b) For each case, calculate and record ∆P = Pin – Pout. Plot ∆P as a function of θ, and discuss your results. What is the maximum value of θ that achieves Barb’s design objectives?


Flow field 3 – Turbulent flow through a sudden conical expansion: # Template Name Fluid Mechanics Objective CFD Objective

11 Expansion_mesh Examine pressure recovery through a 90o sudden expansion.

Learn to refine a mesh until grid independence is achieved; examine streamlines.

Table 1: FlowLab templates and their learning objectives. Flow field 1 – Turbulent flow over a bluff body:

# Template Name Fluid Mechanics Objective CFD Objective 1 Block_domain Calculate drag coefficient on a bluff

body in free stream flow. Learn to extend the far-field boundary until solution is independent of far-field boundary.

2 Block_mesh Compare drag coefficient with empirical results.

Learn to refine a mesh until grid independence is achieved.

3 Block_fluid Show that drag coefficient is independent of fluid if Reynolds number is fixed.

Learn how to model a flow with different fluids, and how to apply nondimensional parameters.

4 Block_Reynolds Show that drag coefficient becomes independent of Re.

Observe how grid resolution needs to improve with increasing Re.

5 Block_turbulence _model

Examine effect of turbulence model on drag coefficient.

Learn that no turbulence model is universal, and results vary significantly between models.

6 Block_length Examine effect of block length on drag coefficient.

Observe streamline patterns and flow separation as block length increases.

7 Block_axisymmetric Compare 2-D and axisymmetric drag coefficients.

Compare axisymmetric far-field boundary requirement with that of 2-D flow.

Flow field 4 – Laminar and turbulent flow through a sudden conical contraction: # Template Name Fluid Mechanics Objective CFD Objective

12 Contraction_domain Examine flow separation and pressure drop through a sudden contraction; laminar flow.

Learn to extend the downstream pipe section until solution is independent of the length of the downstream section.

13 Contraction_zerolength Examine flow through a sudden contraction with no downstream section of pipe.

Examine the effects of eliminating the pipe extension, and replacing it with a simple constant pressure outlet boundary.

14 Contraction_pressure Reinforce concept that pressure differences drive an incompressible flow.

Examine the effect of varying the back pressure, and therefore the overall pressure magnitude.

15 Contraction_turbulent Examine flow separation and pressure drop through a sudden contraction; turbulent flow.

Compare the length of downstream pipe section required to properly model laminar versus turbulent flow through a sudden contraction.

16 Contraction_outflow Examine the importance of downstream boundary conditions.

Experiment with different types of outflow boundary conditions.

17 Contraction_2d Examine flow separation and pressure drop through a sudden 2-D contraction; turbulent flow.

Compare the length of downstream pipe section required to properly model axisymmetric versus 2-D flow through a sudden contraction.

Flow field 2 – Turbulent flow through a conical diffuser: # Template Name Fluid Mechanics Objective CFD Objective 8 Diffuser_mesh Examine pressure recovery through

a 20o conical diffuser. Learn to refine a mesh until grid independence is achieved; examine streamlines.

9 Diffuser_outflow Examine the importance of downstream boundary conditions.

Experiment with different types of outflow boundary conditions.

10 Diffuser_angle Compare pressure recovery in conical diffusers of half-angle 5o to 90o.

Observe streamline patterns and flow separation as diffuser half-angle increases; compute pressure recovery for all cases.


Flow field 9 – Velocity and thermal boundary layer over a flat plate: # Template Name Fluid Mechanics Objective CFD Objective

32 Plate_laminar Compare boundary layer thickness, drag, and profile shape to Blasius.

Examine how good the boundary layer approximation is, compared to Navier-Stokes.

33 Plate_turbulent Calculate boundary layer thickness, drag, and profile shape.

Examine how well CFD can predict turbulent boundary layer properties.

34 Plate_turbulence _models

Predict drag coefficient using several different turbulence models.


35 Plate_laminar _temperature

Compare velocity and thermal boundary layer thicknesses.

Learn that Prandtl number greatly influences thermal diffusion in a laminar boundary layer.

36 Plate_turbulent _temperature

Compare velocity and thermal boundary layer thicknesses.

Learn that Prandtl number is not as important in turbulent compared to laminar boundary layers.

Flow field 8 – Laminar and turbulent pipe flow: # Template Name Fluid Mechanics Objective CFD Objective

27 Pipe_laminar _developing

Calculate the entrance length required to achieve fully developed laminar flow in a pipe.

Learn how to plot and compare velocity profiles to determine if a flow is fully developed.

28 Pipe_turbulent _developing

Calculate the entrance length required to achieve fully developed turbulent flow in a pipe.

Learn how to plot and compare velocity profiles to determine if a flow is fully developed; compare laminar and turbulent flow results.

29 Pipe_laminar _developed

Calculate Darcy friction factor in fully developed laminar pipe flow.

Learn how to apply periodicity from outlet to inlet, including a pressure drop.

30 Pipe_turbulent _developed

Calculate Darcy friction factor in fully developed turbulent pipe flow.

Learn how to apply periodicity, including turbulence properties from outlet to inlet.

31 Pipe_turbulent_rough Compare Darcy friction factor for smooth and rough pipes.

Learn how to model wall roughness with a turbulence model.

Flow field 5 – Laminar and turbulent flow through a jog in a channel: # Template Name Fluid Mechanics Objective CFD Objective

18 Jog_turbulent_mesh Examine pressure drop and streamlines through a jog in a channel; turbulent flow.

Learn to refine a mesh until grid independence is achieved in turbulent flow; examine streamlines.

19 Jog_laminar_mesh Examine pressure drop and streamlines through a jog in a channel; laminar flow.

Learn to refine a mesh until grid independence is achieved in laminar flow; examine streamlines.

20 Jog_high_Re Examine pressure drop and streamlines through a jog in a channel; high Re laminar flow.

Learn that high Reynolds number laminar flows are unstable, and CFD is not able to converge on a steady solution, even with a fine mesh.

Flow field 6 – Inviscid compressible flow through a converging-diverging nozzle:

# Template Name Fluid Mechanics Objective CFD Objective 21 Nozzle_axisymmetric Examine choking and normal shocks

in a C-D nozzle. Learn how CFD is applied to compressible flows to predict choking and shock waves.

22 Nozzle_2d Compare axisymmetric and 2-D compressible flow features.

Learn how the r 2 area term in an axisymmetric geometry makes a big difference in a flow field.

Flow field 7 – Streamlining an automobile body shape:

# Template Name Fluid Mechanics Objective CFD Objective 23 Automobile_drag Calculate drag on a 2-D car shape

with variable rear-end shape. Learn to use velocity vectors to identify flow separation and increased drag.

24 Automobile_domain Learn that the blockage caused by an automobile extends far away.

Learn to extend the top domain boundary until car drag is independent of boundary location.

25 Automobile_turbulence _model

Examine effect of turbulence model on drag coefficient.


26 Automobile_3d Compare drag coefficients for a 2-D versus a 3-D car shape.

Learn to appreciate the enormous memory and CPU time increases in a 3-D flow simulation.


V

x

D1

L1

D2

θ

L2 (a)

V Axis x

Pin

Pout

Wall Wall

(b)

Figure 1: Flow through a conical diffuser; (a) geometry and dimensions, and (b) computational domain, assuming axisymmetric flow. Drawings not to scale. When the student runs FlowLab, he or she is greeted with a user-friendly interface consisting of a graphical display

window, operation options, display options, and a main working window, as shown in Figure 2. When the student selects the Problem Overview option, a window appears that describes the exercise in detail. In the main working window, the student selects a diffuser half-angle between 5 and 90 degrees, creates the geometry, and then generates the mesh, which is displayed on the graphical display window. The mesh for the 5o case is shown in Fig. 3; it is a hybrid mesh consisting of a structured rectangular mesh upstream and downstream of the diffuser section, and an unstructured quad mesh in the upstream portion of the diffuser section. There are more than 22,000 cells in this mesh.

Diffuser section x

Figure 3: Hybrid mesh for the 5o half-angle conical diffuser.

Graphical display window

Main working window

Overview window

Result table

Display options

Operation options

Figure 2: User interface for FlowLab, showing the operation options, main working window, result table, overview window, graphical display window, and display options. Colored pressure contours for a 5o half-angle conical diffuser are shown in the graphical display window.


When the student hits the Solve button, FlowLab iterates towards a converged solution. At this point, an X-Y plot of the residuals appears (Fig. 4), and the student watches the solution progress towards convergence. Convergence criteria are listed in the overview window, and are predefined for proper convergence.

Figure 4: X-Y plot of residuals for the conical diffuser case, θθθθ = 5o. After convergence, which takes only a few minutes on a 3 GHz PC, the student calculates and stores the pressure difference ∆P = Pin – Pout into a table. The table is displayed in a separate window called the Result Table (Fig. 2). At this point, the student may use the post-processing operation button to plot streamlines, velocity vectors, and contour plots of various flow variables (pressure, velocity magnitude, turbulent kinetic energy, etc.). In this particular exercise, students are asked to plot streamlines for each value of diffuser half-angle θ. Streamlines are plotted in Fig. 5 for the twelve requested values of half-angle θ.

x (a) θ = 5o

x (b) θ = 7.5o

x (c) θ = 10o

x (d) θ = 12.5o

x (e) θ = 15o

x (f) θ = 17.5o

x (g) θ = 20o

x (h) θ = 25o

x (i) θ = 30o

x (j) θ = 45o

x (k) θ = 60o

x (l) θ = 90o

Figure 5: Streamlines through conical diffusers of various half-angles.


From the streamlines shown in Fig. 5, students see that at θ = 5o and 7.5o, the flow does not separate along the diffuser wall (Figs. 5a and b), although separation appears imminent near the downstream corner of the diffuser for the latter case. As θ increases, the boundary layer is unable to remain attached in the adverse pressure gradient, and the flow separates. A very small separation bubble is apparent at θ = 10o (Fig. 5c). As θ continues to increase, the separation bubble grows in size, and the separation point moves upstream, closer and closer to the upstream corner of the diffuser (compare Figs. 5d through g). By θ = 30o (Fig. 5i), the flow separates very close to the start of the diffuser. From this point on, the diffuser angle is so sharp that the flow separates right at the upstream corner of the diffuser. The streamline patterns reveal that the separation bubble continues to grow in size somewhat as θ increases (Figs. 5i through j). Beyond θ ≈ 45o however, the streamline pattern changes very little in the separation bubble (compare Figs. 5k and l). The answer to Part (a) of the end-of-chapter problem is that θ must be smaller than about 10o to avoid flow separation in the diffuser. The pressure change from inlet to outlet is tabulated for each value of half-angle θ in Table 2. The student saves these data into a spreadsheet, and plots ∆P as a function of θ, as shown in Fig. 6 (four extra cases are solved for improved resolution). Table 2: Pressure difference from inlet to outlet of a conical diffuser as a function of diffuser half-angle.

θθθθ ∆∆∆∆P 5 -49.1371

7.5 -47.7787 10 -44.9927

12.5 -42.4013 15 -39.6981

17.5 -37.6431 20 -36.0981 25 -32.7173 30 -29.9919

32.5 -23.2118 35 -21.6434

37.5 -21.0490 45 -19.6571 60 -18.7252 75 -18.1364 90 -18.3018

-50.0

-40.0

-30.0

-20.0

-10.0

0 50 100

θ (degrees)

∆P (Pa)

Figure 6: Pressure difference from inlet to outlet of a conical diffuser as a function of diffuser half-angle. The student learns that as θ increases, Pin increases, reflecting the effect of the larger separation bubble. Physically, less pressure recovery is achieved as the separation bubble grows. The student also sees that ∆P flattens out at high values of θ, becoming nearly independent of θ beyond θ ≈ 60o. There is a sharp rise in ∆P above 30o. The reason for this is not certain, but is probably related to the fact that when θ is greater than about 30o, the flow separates at the same point, the upstream corner of the diffuser. The pressure rise is greater than 40 Pa for all angles below 15o. Thus, the answer to Part (b) of the end-of-chapter problem is that to ensure a pressure recovery of at least 40 Pa, Barb should recommend a diffuser half-angle of 12.5o or less. Completion of this exercise has achieved both the fluid mechanics and the CFD objectives. Alert students will also notice that even for the case of a sudden expansion (θ = 90o), there is still a pressure recovery through the diffuser (Pin is less than Pout), and the air still flows from left to right in spite of the fact that the pressure rises from the inlet to the outlet. Instructors may ask their students to analyze a FlowLab problem in more detail using the post-processing options. For example, one may look at colored contour plots of pressure, as compared in Fig. 7 for θ = 5o, 300, and 45o. The same color legend is used in all three plots for consistency. One can immediately see that the pressure just upstream of the 5o diffuser is much lower than that upstream of the other two cases. In addition, the differences between the 300 and 45o cases are not as dramatic as those between the 5o case and either of the other two.


(a) θ = 5o

(b) θ = 30o

(c) θ = 45o

Figure 7: Pressure contours through a conical diffuser of three different half-angles. Colors range from dark blue at -60 Pa to bright red at 0 Pa gage pressure, and are consistent among the three plots. Students may also be asked to plot contours of turbulent kinetic energy (tke), as shown in Fig. 8 for the same three values of θ. Again we see a marked difference between the 5o diffuser and the other two cases. As θ increases and flow separation occurs, the level of turbulence within and downstream of the separation bubble rises significantly. Finally, other than overall magnitude of tke, the differences between the 300 and 45o cases are not as great as those between either of these and the 5o case.

(a) θ = 5o

(b) θ = 30o

(c) θ = 45o

Figure 8: Contours of turbulent kinetic energy through a conical diffuser of three different half-angles. Colors range from dark blue at 0 m2/s2 to bright red at 3.5 m2/s2, and are consistent among the three plots. In summary, this end-of-chapter exercise and corresponding FlowLab template clearly demonstrate that a hands-on computer-based analysis and visualization package can be used effectively to enhance the learning of complex fluid mechanics concepts, while at the same

time exposing undergraduate students to CFD. Furthermore, the post-processing capabilities enable instructors to go beyond the end-of-chapter exercises provided in the textbook to enhance learning. IMPLEMENTATION OF FLOWLAB AT PENN STATE The end-of-chapter problems in the textbook [5] can be used either as homework problems in a fluid mechanics course, or as part of a CFD lab in a fluid mechanics laboratory. The latter approach was implemented in the spring semester of 2004 at Penn State University as part of the ME 83 Fluid Flow Laboratory course – an optional one-credit lab that follows the required three-credit introductory fluid mechanics course. Of the ten lab exercises conducted by the students in this course, one is a CFD lab that introduces students to the fundamentals of CFD. As part of the CFD exercise, students run through Flowlab templates 1 and 5 of Flow field 1, Table 1 – Turbulent flow over a bluff body. A 5-page introduction to CFD is given prior to the lab, and this was found to be sufficient for the students to run FlowLab successfully, with comprehension of the results, and meeting both the fluid mechanics and the CFD objectives. Using FlowLab template 1, students calculate drag coefficient CD on a rectangular block for values of R/D between 5 and 500, where R is the radius of the outer domain boundary and D is the block height normal to the freestream flow (Figs. 9a and 9b). They find that CD decreases with R/D, leveling off to three significant digits beyond R/D ≈ 100. They plot and compare streamlines for two cases, R/D = 5 and 500, and find that the flow is constricted by the outer boundaries for the R/D = 5 case, leading to a drag coefficient that is more than 30% too high compared to the R/D = 500 case.

V

L

D x

y Block

(a)

Figure 9a: Flow over a rectangular block; geometry and dimensions. Drawing not to scale.


V

Symmetry x

y

Symmetry

Wall Wall

Block

Outlet Inlet

R

Figure 9b: Flow over a rectangular block; computational domain. Drawing not to scale. From a fluid mechanics perspective, students gain a more clear understanding of flow separation and the source of pressure drag. From a CFD perspective, they learn that in order to properly model flow over a body in an infinite free stream, the far-field boundaries of the computational domain must be quite far away to avoid adverse effects of these boundaries. In addition, the students gain some appreciation for the appropriateness of the approximations made in the CFD computations. For example, only the upper half of the block is modeled, with a plane of symmetry assumed through the block centerline. In reality, a bluff body like this sheds vortices in an alternating periodic fashion; since the CFD simulation is steady and symmetric, it cannot predict this kind of unsteadiness. Part of the discrepancy between the calculated and experimental values of CD is due to this approximation. The students then use FlowLab template 5 to compare CFD predictions using four turbulence models – Spallart-Allmaras (1 eq.), k-ε (2 eq.), k-ω (2 eq.), and a Reynolds stress model (5 eq.). The calculated value of CD differs by as much as -30% to +20% compared to the experimentally obtained value. Again, this reinforces the fact that enforced symmetry and steady flow on an inherently unsymmetric, unsteady flow field leads to incorrect results. It also reinforces the fact that no turbulence model is universal, and exact agreement with experiment is not to be expected from CFD calculations with turbulence models. CONCLUSIONS Because of its short learning curve and the ease of set-up and usage, FlowLab is a nice supplement to an existing undergraduate fluid mechanics course or lab. Several new FlowLab templates have been created in conjunction with end-of-chapter problems in a new undergraduate fluid mechanics book, but the templates themselves can be used with or without the textbook, provided that the homework problem statement is provided. These FlowLab templates are unique in that each has a dual

objective – namely, to emphasize a fluid mechanics concept and to introduce a CFD concept. Each template, along with its fluid mechanics and CFD learning objectives, is listed and discussed briefly, and the template of one sample flow field, flow through a conical diffuser, is discussed in greater detail in this paper. Finally, the successful integration of a FlowLab template into an undergraduate fluid flow laboratory at Penn State is discussed. There are pedagogical advantages to the approach presented here. Specifically, the dual learning objectives of each exercise (both a fluid mechanics and a CFD objective) enable students to learn more than one thing at the same time. Furthermore, while textbooks remain the primary tool for teaching theory and fundamentals, computer software packages offer the opportunity for interactive learning, and help to fill the gap in situations where budget restrictions have forced departments to cut back on hands-on laboratories. The homework problems and CFD templates developed here help students learn fluid mechanics, while at the same time teach them about the capabilities and limitations of CFD via hands-on experience. REFERENCES 1 Homsy, G. M., 2001, “Multi-Media Fluid Mechanics”, ASEE Annual Conference Proceedings, Session 2793. 2 Caughey, D. A., and Liggett, J. A., 1998, “A Computer-based Textbook for Introductory Fluid Mechanics”, ASEE Annual Conference Proceedings, Session 2520. 3 Wankat, P. C., 2002, “Integrating the Use of Commercial Simulators into Lecture Courses”, Journal of Engineering Education. 4 FLUENT/FLOWLAB, a registered trademark of Fluent Inc., www.flowlab.fluent.com. 5 Çengel, Y. A. and Cimbala, J. M., Fluid Mechanics: Fundamentals and Applications, McGraw-Hill, NY, 2006. 6 Curtis, J. S., Henthorn, K. Moeykens, S., and Krishnan, M., 2004, “Enhancing the Teaching of Fluid Mechanics and Transport Phenomena via FlowLab – a Computational Fluid Dynamics Tool”, ASME Heat Transfer/Fluids Engineering Summer Conference, July 11-15, 2004, Charlotte, NC, Paper number HT-FED2004-56164. 7 Stern, F., Xing, T, Yarbrough, D., Rothmayer, A. Rajagopalan, G., Otta, S., Caughey, D., Bhaskaran, R., Smith, S., Hutchings, B. and Moeykens, S., “Development of Hands-On CFD Educational Interface for Undergraduate Engineering Courses and Laboratories”, 2004 ASEE Annual Conf. & Exposition.


APPENDIX A In the fall 2003 semester, a FlowLab CFD exercise was integrated into Aerodynamics Lab 1 (AERO E. 243L), a required laboratory class in the Aeronautical Engineering program at Iowa State University. The CFD exercise was used by students to simulate external flow around airfoil geometries. A summary of ‘end-of-class’ survey responses from students in AERO E. 243L is presented in Table A.1. Student responses were analyzed using statistical techniques with support from the Center for Evaluation and Assessment at the University of Iowa, and the following observations were drawn from the AERO E. 243L survey [7]:

• respondents on average “mildly to moderately” agreed that their overall learning needs were met (cluster score M=4.20 out of a possible 6.0, SD=.85),

• respondents “mildly to moderately” agreed that their knowledge and skills improved as a result of the CFD lab (cluster score M=4.62, SD=1.07),

• students, on average, mildly agreed that the quality of the hands-on experience in the CFD lab either helped them learn valuable skills and knowledge or worked well for them (cluster score M=4.14, SD=1.06).

Table A.1: Iowa State Student Survey Summary

Key results from AERO E. 243L survey Question SA A a d D SD Nop

N 1 10 12 3 1 2 0 FlowLab is an easy to use CFD tool.

% 3 34 41 10 3 7 0

N 5 9 10 1 1 2 1 The hands-on aspects of the CFD lab helped me learn valuable skills and knowledge. % 17 31 34 3 3 7 3

N 1 6 12 4 1 2 3 CFD taught me things that I could not learn through EFD* or AFD** alone. % 3 21 41 14 3 7 10

N 4 5 16 2 0 2 0 The CFD lab contributed to my understanding of Aerodynamics. % 14 17 55 7 0 7 0

N 1 7 16 1 2 1 1 EFD and CFD results from this lab helped my basic understanding of AFD and the underlying theory. % 3 24 55 3 7 3 3

N 4 7 16 0 0 2 0 CFD is a useful addition to the EFD lab.

% 14 24 55 0 0 7 0

N 2 6 12 3 0 3 3 I would recommend the CFD lab to others.

% 7 21 41 10 0 10 10

N 5 2 2 4 3 12 1 I have used CFD in some form before this class.

% 17 7 7 14 10 41 3

N 9 7 12 1 0 0 0 As a result of my learning in this course, I have run one or more simulations with Flowlab. % 31 24 41 3 0 0 0

N 8 10 9 0 1 0 1 As a result of my learning in this course, I can appreciate the connection between EFD, AFD & CFD. % 28 34 31 0 3 0 3

N 3 6 12 5 1 1 1 As a result of my learning in this course, I have a basic understanding of CFD methodology and procedures. % 10 21 41 17 3 3 3

* Experimental Fluid Mechanics ** Analytical Fluid Mechanics

flowlab-cimbala-imece2004-5987

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