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CFD-Mature Technology?Dochan Kwak*

KeyWords: Computational fluid dynamics, hemodynamics, numerical simulationAbstract

Over the past 30 years, numerical methods and simulation tools for fluid dynamic problems haveadvanced as a new discipline, namely, computational fluid dynamics (CFD). Although a wide spectrum offlow regimes are encountered in many areas of science and engineering, simulation of compressible flow hasbeen the major driver for developing computational algorithms and tools. This is probably due to a largedemand for predicting the aerodynamic performance characteristics of flight vehicles, such as commercial,military, and space vehicles. As flow analysis is required to be more accurate and computationally efficientfor both commercial and mission-oriented applications (such as those encountered in meteorology, aerospacevehicle development, general fluid engineering and biofluid analysis) CFD tools for engineering becomeincreasingly important for predicting safety, performance and cost. This paper presents the authorsperspective on the maturity of CFD, especially from an aerospace engineering point of view.

1. IntroductionThe computational study of flow problems forboth basic research and engineering applicationshas been performed for several decades.Numerical solutions for sueh basic fluid dynamicsproblems as flow past a circular cylinder; flowthrough channels, ducts, and pipes; and flow overa backward facing step were presented as early asthe 1930s (for example, Thom [l] for a circularcylinder). In the computational fluid dynamics(CFD) community-especially in aerospace-CFD is synonymous with computationalaerodynamics. Computational analysis ofaerospace vehicles is required to produce highlyaccurate results for predicting aerodynamicperformance characteristics, while flow devices ina wide range of fluid engineering applicationscould be reasonably well designed empiricallywithout resorting to accurate numericalsimulations; for example, hydraulic turbines forhydroelectric power plants were designed withoutthe CFD approach. As flow devices becomeincreasingly compact, efficient, and sophisticated,pushing the conventional operating envelope,

* NASA Advanced Supercomputing (NAS)Division, Applications BranchNASA Ames Research Center, Mail Stop T27B-1,Moffett Field, CA 94035, USAE-mail: [email protected] L . : (1-650) 604-6743; FAX (1-650) 604-4377

requirements on CFD tools have become moredemanding, just as aerodynamic performanceprediction tools require quantitative predictioncapability. This trend is reflected in thedevelopment of various flow solution methods,tools, and physical modeling, especially inconjunction with high-fidelity computations usinghigh-end computing facilities.2. Evolution of CF D Capabilities

Over the past several decades, many reviewarticles and books on CFD have discussednumerical algorithm, grid generation, andboundary condition procedures. For morecomprehensive reviews of computational methodsin general, see: Roach [2]; Peyret and Taylor [3];Hirsch [4]; Kwak [5]; Gunzburger and Nicolades[6]; Hafez and Oshima [7]; Gresho and Sani [SI;and Hafez [9]. These books and articles providefairly extensive formulations, numerical methods,and solutions to fundamental fluid dynamicsproblems. After thirty-some years of CFDmethods development and application, industrialproblems involving complex systems are nowsolved routinely. There are a vast number of caseswhere the CFD approach has made significantimpact. This paper gives a short summary ofprogress from a historical perspective and lists afew pacing challenges. The examples mentionedhere represent samples to illustrate the level ofcomplexities researchers have encountered in fluid

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engineering as CFD technology has evolved. Theyinclude the following:CFD in Aeronautics:Application of CFD tools to engineering problemsbecame realistic in the early 1970s, as high-speedcomputers (such as the Control Data Corp. 7600and the ILLIACIV, followed by early series ofGay computers) became available. Algorithmsthat had been developed earlier were furtherextended utilizing then high-speed processors.However, computer speeds were still too limitedto produce solutions to complicated geometryproblems. To obtain solutions in a reasonableturnaround time, simplifications at the formulationlevel were made. For example, Navier-Stokes (N-S) equations were reduced to small disturbanceequations, full potential equations, andparabolized N-S equations.Numerous successful methods and tools weredeveloped and applied to real-world designproblems, with the most notable success incommercial airplane designs. In the late OS,computer speed increased with the advent of theCray-2-and Cray Y-MI?, followed by the Cray C90in the early 1990s. Processor speed increased froma fraction of a gigaflop in the early '80s to tens ofgigaflops in the '90s. With this increasedcomputer speed, full Navier-Stokes solutions to acomplete aircraft configuration became one of themost exciting challenges of the '80s. For example,Transonic Navier-Stokes (TNS) project at NASAAmes Research Center established the goal ofsimulating a full F-16 fighter aircraft geometrywith N-S equations.In t h e 1 9 9 0 ~ ~he goal for CFD simulationadvanced one step further to tackle unsteady andmultidisciplinary N-S computations for a fullaircraft geometry. As computer speeds increasedfurther, through faster processor speed andparallel architectures such as SGI Origin system,more complexities (such as bodies with relativemotions) could be added to simulations. Manyreview articles have been written in this area (forexample, see Johnson et. a1 [lo], Jameson [ll],MacCormack [12])PropulsionCFD:Numerical methods and boundary conditionprocedures have advanced since the 1980s tohandle complex rotor-stator interaction problemsencountered in turbine engines. Yet the processorrequirements for computing limited rows of a

rotor-stator were so huge that it took months tocomplete just one simulation involving a singlestage of a rotor-stator-making it impossible toapply CFD simulation to a turbine or compressordesign. Primarily due to the computer hardwarespeedup, it became possible to analyze multi-stageturbine flow in the 1990s and 2000s. Yet despitethese advances, impacts on engine design are stilllimited to the component level.Rocket propulsion CFD has, in general, laggedbehind airplane applications. Complexity of theflow physics and hardware geometry involved inrocket engines probably delayed the application ofCFD to this area. One of the most significantapplications of CFD simulation to rocket enginesbegan in the early 1980s, when NASA carried outa series of upgrades to the Space Shuttle mainengine (SSME), developed in the 1970s.One such effort involved the powerhead redesign.Considered the backbone of the engine, thepowerhead consists of the main injector assemblyand pre-burners. Partially burned hot gas passesthrough the Hot Gas Manifold (HGM) to the maininjector assembly. The powerhead redesign wasundertaken from 1983-84, focusing on a two-ductHGM. NASA Ames and Rocketdyne collaboratedin applying the CFD approach to this task (usingthe INS3D code [13]). The team of researcherssuccessfully applied a CFD simulation procedureto this task for enhancing the performance of theSSME powerhead. This two-duct design replacedthe previous three-duct engine, resulting inreduced pressure and turbulence, and decreasedtemperatures in the engine during operation. Thetwo-duct design, which first flew on the shuttle inJuly 1995, significantly improved fluid flow in thesystem, thus reducing maintenance and enhancingoverall engine performance. This pioneering workwas probably the first major application of CFD toa rocket propulsion system (see [14] for moredetail). A rocket propulsion CFD consortium wasthen formed at NASA Marshall Space FlightCenter in 1983 and continued until the mid-1990s.Biomedical/Biofluid Applications:Extension of CFD methods to blood flow has beenof interest to biomedical researchers for manyyears. However, lack of a complete analysiscapability kept it from making significant impactson medical research and practices for many years.Limited success on blood flow simulations wererealized in the 1980s. More significantapplications have been made since the O OS, such

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as in the area of mechanical devices and localmodeling for surgical planning. For thecardiovascular system, the brain, and other partsof the human body, branching of blood vesselsinvolves bifurcations, most of which are non-symmetric. Therefore, bifurcation has been apopular subject for blood flow simulations.Bifurcation problems offer the opportunity toaddress numerical issues involving gridgeneration, as well as to study basic fluid dynamicphenomena relevant to blood circulationsimulation. When the size of a blood vesselbecomes very small (as in capillaries), non-Newtonian characteristics become significant,thus requiring physical modeling. In addition, thevessel wall is elastic, requiring a structural modelto account for geometric changes, depending onwall stresses. Pioneering work on this subject wasdone by Womersley [15] in the '50s. Moresophisticated computations have since beenperformed for regular and non-regular bifurcatingarteries, including stenotic vessels (see Berger[161for a review).The human circulatory system is like a huge treewith many branches of various sizes. Therefore,many computatioaal studies have been performedusing a truncated geometric model. One difficultyin simulating a truncated arterial system resultsfrom setting proper boundary conditions,especially at the downstream boundary. Toaccount for the large arterial network, Quarteroniand his colleagues have developed a circuit analogthat has been applied to more inclusive circulatorysystems modeling, such as the cardiovascularsystem and the Circle of Willis (Cow) in the brain(see [17] among many other publications). Analternative way of imposing downstreamboundary conditions has been developed by TimDavid et. al. [18] and Peskin and his colleagues[19]. One crucial step in blood flow simulation isto construct the computational geometry startingfrom anatomical data. Kim et al. [20]reconstructed a 3-D, anatomically realistic COWgeometry from human-specific magneticresonance angiography (MRA). With a non-Newtonian blood model, a model for deformableblood vessels, truncated downstream boundaryconditions, and an auto-regulation model, Kim etal. simulated unsteady blood circulation throughthis COWunder various gravitational conditions.Because of its importance in biomedical research,modeling and simulation of the cardiovascularsystem has been the subject of many

investigations. Peter Hunter and his colleagueshave been modeling cardiovascular systems,including multidisciplinary aspects, producing oneof the most impressive results to date (forexample, see [21]). An earlier, and perhaps themost elaborate physical model of the heart, waspioneered by Peskin and his colleagues (see [22]for example) in the 1970s. This model includedblood, wall structures, and an electrical fieldactivating heart muscles.Another interesting application of blood flowsimulation is related to artificial devices such asartificial hearts, ventricular assist devices (VADs),and heart valves. Because the demand fortransplant organs far exceeds the number ofdonors, the need for artificial devices-to be usedeither as a temporary device or as a permanentreplacement for a natural organ-becomesincreasingly high. Accurate quantification ofblood flow plays a crucial role in developing thesedevices. Thus, CFD simulation of blood flow inand around these artificial devices has become anindispensable part of the design. One suchexample is the recent CFD-aided design of theDeBakey VAD, where CFD-aided designimprovements enabled human implantation byremoving thrombus formation and loweringhemolysis to an acceptable level for humanapplication. This and an earlier effort set a newmilestone for CFD applications in the biomedicalarea [23,24].All such blood flow computations may beregarded as a branch of CFD. The number of CFDapplications for blood flow and biomedicalproblems are increasing rapidly, and the workcited here represents only a small sample of thevast amount of ongoing work.3. Challenges and Possibilities

CFD capabilities have been advanced along withcomputational technologies in general. Many fluidengineering problems can now be simulated;however, these are mostly at a single-componentlevel. For example, it is possible to generatesolutions to problems like a turbopump (inducer-impeller-diffuser), a naval vehicle at a steadymotion including propulsor by a model, and atruncated model of the brain or heart. To realizethe full benefits of CFD, more inclusive modelingwill be required, such as systems of pumps,including: multiple pumps and feed lines; vehiclein maneuver with propulsor; and a complete or

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more inclusive human circulatory system from theheart through the aorta and all the way to the brainand kidney capillaries. Attempts to solve thesetypes of problems have been made with somequalitative successes. However, the predictivecapability is still very limited, and prediction withaccurate physics is yet to be accomplished. Thiswill require inclusion of not only fluid dynamicmodeling but modeling of other quantities likethermal loading, struchral properties (such asstructural behavior of arterial walls), turbulenceand transition prediction and cavitation physics.These computations will require not only largecomputing resources but large data storage andmanagement technologies, as well.Flow solver codes and software tools have beendeveloped to the point that many daily fluidengineering problems can now be computedroutinely. Some of the physical models, such asthose for turbulence and transition, however, havenot advanced much since the 70s or 80s. Othermodels, like the cavitation model, have yet to beadvanced to produce quantitative results forengineering. In aerospace design, the mostproductive aspect of CFD applications has been topredict relative change among design variations.To push the limit of operation and try bold newideas, more predictive capabilities will be neededfor complicated flows involving transientphenomena, separation, tip vortex, and cavitation.For example, without accurate predictioncapabilities for such quantities as cavitation anddamaging frequencies, back flow, and rotationalstall, CFD cant be of much help in thedevelopment of an advance turbopump system. Tomake these advances, high-fidelity computationsusing high-end computing facilities are still a

References(1) Thom, A., 1933, The Flow Past CircularCylinder at Low Speeds, Procedures, RoyalSociety Of London, Series A, Vol. 141, pp. 651-666.Dynamics, Hermosa Publishers, Albuquerque,New Mexico.Computational Methods for Fluid Flow, SpringerSeries in a m p . Physics, Springer-Verlag.Internal and External Flows, John Wiley& Sons.

(2) Roach, P.J., 1972, Computational Fluid(3) Peyret,R. and Taylor, T.D., 1983,

(4) Hirsch, C., 1989, Numerical Computation of

musf-despite the current euphoria about PCclusters and grid computing.4.0 Rema rks on Parallel Computing andHuman Resources

A typical process of flow simulation, especiallyfor high-fidelity unsteady flow, requires largeamounts of both computing time and human timein problem setting and data processing. Asubstantial reduction in computational time for3-D unsteady flow simulations is needed to reducethe design-cycle time of, for example, a pumpsystem. Part of this speedup will be due toenhancements in computer hardware. Theremaining portion of the speedup must becontributed by advances in grid-generationprocedures, flow solution algorithms, and byefficient parallel implementations. These andother procedural and computer science aspects arenot presented in this report. However, the humanresource aspect of CFD work must be noted. Foreven though CFD has advanced remarkably, manychallenging cases require CFD experts. Computerscience can automate a good portion of the CFDsimulation processes, thus saving much humantime required to obtain solutions. However, blindapplication of tools without understanding thecapabilities and limitations of the methodsinvolved could lead to catastrophic engineeringresults. As in many other engineering and sciencedisciplines, CFD researchers and practitionersneed to understand the physics and engineeringsystems being simulated. Future experts need tobe cultivated who are willing to think through theflow physics in addition to the softwareengineering aspects of fluid dynamics work.

( 5 ) Kwak, D., Mar. 1989, Computation ofViscous Incompressible Flows, von KarmanInstitute for Fluid Dynamics, Lecture Series,1989-2004, Also NASA TM 101090.(6) Gunzburger, M.D. and Nicolades,R. A.,1993, Incompressible ComputationalFluidDynamics Trends and Advances, ed. CambridgeUniversity Press.ComputationalFluid Dynamics Review 1998,World Scientific.(8) Gresho, P. M., and Sani, R. L., April 1998,Incompressible flow and the finite elementmethod, John Wiley and Sons.

(7)Hafez, M. and Oshima, K., 1998,

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(9) Hafez, M., 2002, Numerical Simulation of(10) Johnson, F.T., Tinoco, E.N., andYu, N.J.,Incompressible Flows, World Scientific.Thirty Years of Development and Applicationof CFD at Boeing Commercial Airplanes,Seattle, AZAA paper 2003-3439, AIAA 16CFD conference, Orlando, FL, June 23-26,2003.(1 1) Jameson, A., Numerical wind tunnel-visionof Reality, AIAA paper 93-3021, AIAA 24&Fluid Dynamics Conference, Orlando, FL, July6-9,1993.(12) MacCormack, R., A Perspective on aQuarter Century of CFD Research, AIAA paper93-3291, AIAA 11* CFD conference, Orlando,

(13) Kwak, D., Chang, J. L. C., Shanks, S. P., andChakravarthy,S., Mar. 1986, A Three-Dimensional Incompressible Navier-Stokes FlowSolver Using Primitive Variables,&A ., Vol.24, no. 3, pp. 390-396.Yang, R-J, 1988, Numerical SimulationMethods of Incompressible Flows and anApplication to the Space Shuttle Maine Engine,Int. J . Numer. Methods Fluids,Vol. 8, pp. 1241-1268.Theory of Pulse Transmission and OscillatoryFlow in Mammalian Arteries, Wright-PattersonAir Force Base, OH.

Stenotic Vessels,Ann. Rev. Fluid Mech.

FL, July 6-9, 1993.

(14) Chang, J.L.C., Kwak, D., Rogers, S . E. and

(15) Womersley J. R., 1957, An Elastic Tube

(16) Berger, S . A. and Jou, L-D., 2000, Flow in32~347-382.(17) Quarteroni, A., October 9,2001, Modelingthe Cardiovascular System: A MathematicalChallenge, Mathematics Unlimited-200 1 andBeyond, Enquist& Schmid (eds).

(18) Fernandez, A., David, T. and Brown, M. D.,2002, Numerical Models of Auto-regulation andblood Flow in the Cerebral Circulation, Comp.Methods in Biomechanics and Engineering,Vol.,5 (l) , pp. 7-20.

(19) Oluffesen, M.S., Peskin, C.S., Kim, W.Y.,Pedersen, E.M., Nadim, A., and Larsen, J., 2000,Numerical Simulation and ExperimentalValidation of Blood Flow in Arteries withStructured-Tree Outflow Conditions,AnnaZs ofBiomedical engineering,Vol. 28, pp.1281-1299.(20) Kim, C.S., Kiris, C., Kwak, D., WumericalModels of Human Circulatory System underAltered Gravity: Brain circulation, AIAA PaperNo. 2004-1092, AIAA 42nd Aerospace SciencesMeeting and Exhibit, Reno,NV, January 5-8,2004.(21) Smith, N. P., Pullan, A. J., and Hunter, P. J.,2002, An Anatomically Based Model ofTransient Coronary Blood Flow in the Heart,S UM J . Appl, Math., Vol. 62, No. 3, pp. 990-1018.Computational Biofluid Dynamics, FluidDynamics in Biology, Seattle WA, AmericanMath. Society, pp. 161-186.(23) Kiris, C., Kwak, D., Rogers, S . , and Chang,I-D, November 1997, Computational Approachfor Probing the Flow Through Artificial HeartDevices, Transactionof the ASME, Vol. 119,

(22) Peskin, C. S . , McQueen, M., 1993,

pp. 452-460.(24) Kiris, C., Kwak, D., and Benkowski, R., 1998,Incompressible Navier-Stokes Calculations forthe Development of a Ventricular Assist Device,Computer and Fluids,Vol. 27, Nos. 5-6, pp. 709-719.

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Source of Acquisition NASA Ames Research Center