Teaching Computational Fluid Mechanics Over The Internet

Session 2793

Teaching Computational Fluid MechanicsOver the Internet

Phillip R. SmithNew Mexico State University

Abstract

New Mexico State University's Mechanical Engineering Department provides a distanceeducation Master of Science degree program for Boeing Aircraft Company. As part of thisprogram, students were o�ered a trial version of a computational uid mechanics courseover the internet. The Summer Session and Fall 2000 Semester inaugurated this course un-der a special projects designation. Lecture notes on computational methods for uid me-chanics were provided on the course web site for the students to download. They also weregiven access to the video streamed lectures of a separate intermediate uid mechanics courseby the same instructor. Concurrent with viewing lectures and lecture notes, the studentsfamiliarized themselves with a sophisticated uid mechanics computer package, called CFXprovided by AEA, Inc., housed on the NMSU-ME computer system. This was accomplishedby working through a series of 10 fairly complicated tutorials which treated a range of prob-lems from laminar, incompressible ows through compressible, turbulent ows.

The grade for the course was based upon homework, the CFX tutorial results and a�nal course project using CFX. Homework assignments provided on the course web sitecould be returned by the students to the instructor either electronically or by FAX. Sincethe CFX package was run remotely by the students, the tutorial and the project could bemonitored continuously by the instructor who had access to the student's �les.

The CFX project required the students to do a diÆcult compressible, turbulent uidsproblem completely on their own. This included creating the ow geometry, meshing of the ow �eld, setting up the boundary and initial conditions, and solving the problem on a par-allel Unix machine. Graded output consisted of the geometry �le, the mesh, the results �leand a multitude of color plots which included temperature and pressure contour plots, ve-locity contour plots, velocity vector plots, and streamline plots.

Our initial o�ering of Computational Fluid Mechanics over the internet was not with-out diÆculties, mainly with equipment and software. Despite these diÆculties, the studentsat Boeing performed just as well as our students on the NMSU campus who have taken thiscourse in the past, but with 'live' lectures and direct access to the computers. We feel thiscourse should now become a regular part of our distance education program at the Masterof Science level.

I. Introduction

The Master of Science program o�ered by New Mexico State University to employees ofBoeing Aircraft Company in Seattle, Washington began in 1997. This program allows stu-dents to work toward a Master of Science degree either in Mechanical Engineering or in In-dustrial Engineering with a minor in Manufacturing Engineering for both degrees. Studentswho enroll in the program are required to have an undergraduate degree in Mechanical En-gineering or Industrial Engineering or equivalent undergraduate background in the subjectscovered in these curricula. The program consists of 31 semester hours of course work, of

Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition

Copyright c 2002, American Society for Engineeing Education

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which all but one semester hour can be taken through distance education methods, i.e. byinteractive video courses, taped video courses or video streamed courses. The remainingsemester hour is ful�lled when a student presents a required seminar on the NMSU campusimmediately proceeding or following his or her �nal oral examination. A student's programof study for the Mechanical Engineering degree consists of 18 semester hours of ME courses,9 semester hours of Manufacturing Engineering courses, a 3 hour Special Project related totheir work at Boeing, and 1 hour of seminar. If the student opts for a non-project degree,then these 3 hours may be replaced by 3 hours of further course work. Each student mustwork out his or her program of study with their assigned faculty advisor.

In general, students work full time at Boeing and take only one course each semesterand one course during the summer. Therefore, it takes three to three and a half years forthem to earn the Master of Science degree through this program. To date (January, 2002),18 students have been graduated.

Within the Mechanical Engineering program, students are required to take at leastone course in Fluid Mechanics. Because of the extensive use of computational methods atBoeing, students were o�ered a trial version of a computational uids mechanics course be-ginning in the 2000 Summer Session and extending through the 2000 Fall Semester. Thecourse was drawn out over this extended period of time to allow the students to become fa-miliarized with very sophisticated computational uids software. In order to facilitate this,the course was o�ered under a Special Research Project designation because these type ofcourses can be continued over more that one enrollment period and are allowed to carry asub-title indicating their content. A detailed discussion of the course follows in the next sec-tion.

II. Computational Fluids Mechanics Course

The computational uids mechanics course o�ered to our Boeing graduate studentsconsisted of two parts: Computational Methods and Theoretical Fluid Mechanics. Lecturenotes on computational uid mechanics were provided on the course web site for the stu-dents to download. They were also given access to video streamed lectures of a intermediate uids mechanics course taught previously by the same instructor. Lecture notes for the the-oretical portion of the course also were made available for downloading. A text book1 forthe course was recommended, but not required. The content of the combined course is out-lined in Table No. 1.

Table No. 1, Topics Covered

Theoretical Computational

Fluid Kinematics Finite ElementsConservation Laws Finite Di�erences

Navier-Stokes Equations Finite VolumesViscous and Non-Viscous Flow AEA-CFX CFDS Package

Compressible and Hypersonic Flows Grid GenerationTurbulent Flow Boundary Fitted CoordinatesExact Solutions Numerical Solutions

As can be seen from Table No. 1, the course was designed to present a comprehensiveoverview of both computational and theoretical uid mechanics. Because of the extensive



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material the students were expected to cover, the lecture notes for the course were fairlydetailed. An example of the notes for one of the early lectures dealing with �nite di�erencemethods follows.

1. Typical Excerpt from Lecture Notes

Computational and Theoretical Fluid MechanicsSummer Session, 2000

Lecture No.2, June 27, 2000A Heat Transfer Example

Consider the time dependent heat transfer in a slab, as shown below.

T(0,t) = 0

L

ρT(L,t) = 500

T(x,0)=f(x)

k Cpx0

Assuming constant coeÆcients, the conduction heat transfer equation is

�Cp

@T (x; t)

@t= k

@2T (x; t)

@x20 � x � L; t > 0

with boundary conditions1:) T (0; t) = TÆ(t)

2:) T (L; t) = TL(t)

and an initial condition3:) T (x; 0) = f(x)

where we will consider the functions TÆ(t), TL(t) and f(x) as known. Notice that the heat

conduction equation is a parabolic equation.

We let � = k=�Cp which is called the thermal di�usivity. Since we know the initialcondition, we use a backward di�erence approximation for the time derivative term. Againassume x = i�x, and t = j�t, so

@T

@t�

Ti;j � Ti;j�1

�t

Further, we use a central di�erence approximation for the second derivative, i.e.

@2T

@x2�

Ti+1:j � 2Ti;j + Ti�1;j

�x2



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2. The Computational Fluids Mechanics Software

Concurrent with viewing lectures and lecture notes, the students were required to fa-miliarize themselves with a sophisticated uid mechanics computer software package. Thissoftware, CFX provided by AEA, Inc., is a �nite volume based code which can treat prob-lems ranging from laminar, incompressible ows through compressible, turbulent ows. TheCFX software is installed on the Mechanical Engineering Department's Sun network andis capable of running on up to 8 parallel processors. Each student received a CFX user'smanual2 which allowed them to learn the software package by working through a series of 10tutorials. Table No. 2 lists these tutorials.

Table No. 2, Required Tutorials

Tutorial No. Title

1 Flow in a Static Mixer2 Static Mixer - Re�ned Mesh3 Flow in a Process Injector Mixing Pipe4 Flow through a Circular Vent5 Flow around a Blunt Body6 Supersonic Flow in a Laval Nozzle7 Supersonic Flow over a Wing8 Flow through a Butter y Valve9 Flow through a Catalytic Converter10 2D Flow of a Shear-Thicking Fluid

The students accessed the Sun network remotely and could run CFX either in interactivemode or in batch mode. The instructor of the course had access to each of the student'sCFX computer accounts and continuously monitored their progress on the tutorials (Thiswas arranged at the student's request). Figure 1 is

Fig. 1, Mach Number Contours for Laval Nozzle



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a typical student result for Tutorial No. 6 showing the Mach number contours for super-sonic ow in a Laval nozzle. Flow is from left to right.

Once the students had become familiar with utilizing CFX, they were required to do adiÆcult compressible turbulent ow problem completely on their own. This included creat-ing the ow geometry, meshing the resulting ow �eld, setting up the boundary conditionsand the initial conditions, and then solving the problem on the parallel Sun network. Thefollowing is the description of the project given to the students.

3. Course Final Project

Consider the two-dimensional Chimney/Ejector system shown below. The object of theanalysis is to determine the characteristics of the thermal plume produced by the systemand how these characteristics are a�ected by a uniform wind blowing horizontally from theleft toward the right. The three cross- ow velocities to consider are (1) 0.0 ft/s, (2) 10.0ft/s, and 20 ft/s. Assume a steady ow and produce contour plots of the temperature andcontour and vector plots of the velocity for the xy-centerline plane shown in the de�nitionsketch. The uid properties , simulation type, and the boundary conditions are given in thetables below.

1’

1’

2’

2’

3’’

1’

Chimney

Ejector

Opening

Opening

Inlet

Ground Plane Ground Plane

Uniform Chimney Exhaust Velocity

1.5’

Uniform Cross-Flow

x

y

Fluid Properties

Fluid Type: Air (Ideal Gas)Molecular Weight: 28.959999Viscosity: 1:79� 10�5 kg m�1sec�1

Speci�c Heat Capacity: 10000:06 kg�1K�1

Thermal Conductivity: 0:0252 W m�1K�1



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Simulation Type

Turbulence: K � � modelFully CompressibleBuoyancy along y-axis gy = �9:81499 m s�2

Reference Pressure: 1:01� 105 kg m�1s�2 (14.696 psi)

Boundary Conditions

Atmosphere:

Relative Pressure: 0:0kg m�1s�2 (0.0 psi)Static Temperature: 293:9 K (529:66ÆR)

Chimney Exhaust Plane:

Velocity (Uniform): 91:8 ms�1 (300:0 fts�1)Static Temperature: 533:3 K (960:0ÆR)

Solid Surfaces:Chimney: No SlipEjector: No SlipGround Plane: No Slip

Openings:Left Boundary:Assigned Uniform Cross-Flow Velocity Atmospheric Pressure and TemperatureAll Others:No Velocities Assigned Atmospheric Pressure and Temperature

Hints

Begin running your calculations assuming laminar ow and when it appears to convergeto steady ow change to turbulent ow. You may need to have a very �ne grid in the ex-haust area.

4. Typical Student Result for Final Project

The following is a typical student result plot for the �nal project which shows the tem-perature pro�les in the chimney plume.



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Fig.2 Temperature Contours in Chimney Plume for a 20 ft/sec Cross-Flow

5. Grading Scheme.

The grade for the course was based upon homework, the CFX tutorial results and a �-nal course project using CFX. The �nal grade for the course was equally weighted betweenthese three elements. Homework assignments, which covered the theoretical portion of thecourse, were provided on the course web site and could be returned to the instructor eitherelectronically or by FAX. The homework assignments, for the most part, were not computeroriented but were designed as learning experiences and to evaluate the students understand-ing of theoretical uid mechanics. The CFX tutorials not only brought the students up tospeed in the utilization of the CFX software package, but also demonstrated their under-standing of the �nite volume computational method. The �nal course project required thestudents to begin from the written description of the ow �eld (as described above), and ontheir own to set up the problem in CFX and solve it with no directions from the instructor.This experience included creating the ow geometry, meshing of the the ow �eld, deter-mining and setting up of boundary and initial conditions, and solving the uids problemson parallel Unix machines. Graded output for the tutorials and the �nal project could con-sist of geometry �les, the mesh, results �les and a great number of color plots of the results,including temperature and pressure contour plots, velocity contour plots , velocity vectorplots, Mach number contour plots, Mach number vector plots, and streamline plots.

6. Course DiÆculties

The main diÆculties we experienced in o�ering computational uid mechanics overthe internet lay in the areas of equipment and software. The Boeing students encounteredproblems with the �rewall at di�erent Boeing facilities in the Seattle area. In some casesit took several weeks to modify the hardware or software to allow CFX to be run remotelyfrom these locations. Once on-line, students found that the preprocessing module and thesolution module of CFX ran very quickly. But the post processing visualization module,which had to be run interactively, was very slow (apparently due to the local port at their



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location). This was overcome by providing the students with local postprocessing software.They could then transfer �les from the NMSU-ME computer system to themselves at theirparticular Boeing location and very quickly reduce their data and produce their desired out-put plots.

Another diÆculty that one might envision for the distance education students was theirlack of face-to-face personal contact with the course instructor. The Boeing students over-came this through repeated viewing of the course video taped or video streamed lectures ofsubjects which at �rst were unclear to them and by extensive use of telephone conversationsand e-mail with the instructor.

III. Conclusion

The students from Boeing taking the computational uid mechanics course over theinternet during the Summer and Fall of 2000 performed as well or better than the on cam-pus Mechanical Engineering graduate students who took the course having direct access to'live' lectures and to the on campus computer network (the Boeing student's actually hada slightly higher grade point than the on campus students who most recently had takenthis course, but the statistical signi�cance of this is uncertain because of the small size ofthe classes and the fact that these courses were not o�ered in the same semester). Some ofthese Boeing students have gone on to use the knowledge gained from this course to com-plete their required Master of Science project related to their work at Boeing and have re-ceived their MS degrees from NMSU. As a result, we feel that this computational uidscourse should be made a regular part of our distance education program at the Master ofScience level.

Bibliography

1. White, F., Viscous Fluid Flow, McGraw-Hill, Inc., New York, (1991).

2. Using CFX-5, CFX International, AEA Technology, Harwell, UK, (1998).

Phillip R. Smith is currently an Emeritus Professor of Mechanical Engineering at New Mexico State Uni-versity in Las Cruces, New Mexico. He received his B.S. in Mechanical Engineering and his M.S. in Aeronauti-cal Engineering from Purdue University in West Lafayette, Indiana. In 1966 he received a Ph.D. in EngineeringMechanics from the University of Kansas. Dr. Smith has been actively involved in teaching and research in uid mechanics and computational uid mechanics since joining the faculty of NMSU in 1964.



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Teaching Computational Fluid Mechanics Over The Internet