Tom Shih’s Research Group

Current Students and Projects:

MS Students:

1. “RANS and URANS on the Effects on Endwall Contouring on Secondary Flows,” Zhouyi Wang, August 2017.

2. “Conjugate Heat Transfer with Film and Internal Cooling,” James Peck, May 2018.

Ph.D. Sudents:

1. “Flow and Heat Transfer in High-Aspect Ratio U-Ducts under Rotating and Non-rotating Conditions,” Shih-Yung (Kenny) Hu, May 2018 (expected).

2. “Multiphase Flow in a Clutch Assembly,” Irsha Pardeshi, May 2018.

3. “Controlling Leakage Flows into Wheelspace between Rotors and Stators,” Jason Liu, May 2018.

4. “Large-Eddy Simulations of Film-Cooling Flow and Heat Transfer,” Zach Stratton, May 2018.

5. “Modelling and Simulations of Statistically Stationary and Nonstationary Turbulent Flows by Using Hybrid Methods,” Wanjia Zhang, May 2018.

6. “Inflow Boundary Conditions for LES of Convective Heat Transfer,” Yongkai Chen, May 2019.

7. “Time-Accurate CFD Analysis of the Multiphase Flow in a Liquid-Ring Vacuum Pump,” Ashutosh Pandel, May 2019.

8. “Large-Eddy-Simulation of Flow about a Blade Tip with Rotor-Stator Interactions,” Adwiteey Raj Shishodia, May 2019.

Research Staff:

Dr. Chien-Shing Lee.

Tom Shih’s research group focuses on research in computational fluid dynamics and heat transfer (CFD) – both in developing and improving it as a tool and in using it to study physical problems to understand flow and heat-transfer mechanisms and to impact design in aerodynamics and propulsion.  Some examples of their work are given below.

Grid Generation (funded by NASA Ames, Lewis/Glenn, Ford, GM, DaimlerChrysler, DOE; students:  Julio Dulce, Robert Bailey, Erlendur Steinthorrson, Mark Stephens, Mark Rimlinger, Xubin Gu, Xuehui “Christine” Qin, Xingkai “Kyle” Chi, Brandon Williams).  Grid generation is important to CFD because without a good grid or mesh, one cannot generate a high-quality CFD solution.  Even with today’s automatic grid generation tools, grid generation is the most time-consuming part of CFD if a high-quality grid is needed and its generation requires a high-level of user expertise of CFD and in understanding the problem being studied because the grid/mesh and the flow physics are intimately connected.  Contributions made include:  (1) Developed a highly efficient and versatile algebraic surface generator (referred to as 3-D bidirectional Hermite interpolation) that ensures C¹ continuity across patches without the need to solve systems of equations. This method is ideal for time-dependent problems with moving and deforming geometries, and was applied to study the flow fields in the combustion chambers of reciprocating piston and Wankel rotary engines.  (2) Developed several techniques to enhance control of grid-point distribution in algebraic grid generation methods based on transfinite interpolation, including orthogonality of grid lines at boundaries and smoothness in r-refinement.  (3) Developed a code called GRID2D/3D to generate grid systems in complex-shaped two- and three-dimensional spatial domains that can deform in time and be single- or multi-block.  (4) Developed a knowledge-based automatic grid generator involving patched/overlapped grids for CFD analyses of shock-wave/boundary-layer interactions with bleed through rows of circular holes (this tool can be used by non-experts in CFD to generate high-quality grids along with all other inputs needed to generate a solution in the OVERFLOW code in seconds).(5) Developed grid-quality measures for structured and unstructured meshes that take into account the vector and tensor nature of CFD solutions as well as the geometry/shape of the cells in the mesh and showed their correlation to errors in the computed solutions.  (6) Developed the concept and the formulation of the discrete-error-transport equation (DETE) for estimating grid-induced errors in steady and unsteady CFD solutions.  (7) Developed an efficient solution-adaptive mesh refinement strategy based on the concept that error source and error location may not coincide.  (8) Developed a method to generate “smooth” high quality grids for rough surfaces with discontinuities in the boundary geometry such as iced airfoils and wings by using algebraic grid generation with partial elliptic smoothing (methods developed were incorporated into NASA’s SmagICE code).

Representative papers in this area are as follows:

• Steinthorsson, E., Shih, T.I-P., Schock, H.J., and Stegeman, J., “Calculations of the Unsteady, Three-Dimensional Flow Field inside a Motored Wankel Engine,” SAE 1988 Transactions Journal of Engines, Vol. 97, Section 6, 1988, pp. 6.1160-6.1188.
• Dolce, J.S. and Shih, T. I-P., “A Solution-Adaptive Algebraic Grid Generation Technique Based on Variational Principles,” X Congresso Ibero-Latino-Americano Sobre Metodos Computacionais em Engenharia, September 25-27, 1989, Portugal.
• Shih, T. I-P., Bailey. R.T., Nguyen, H.L., and Roelke, R.J., “GRID2D3D -- A Computer Program for Generating Grid Systems in Complex-Shaped Two- and Three-Dimensional Spatial Domains:  Part 1 - Theory and Method,”  NASA Technical Memorandum 102453, 1990.
• Bailey. R.T., Shih, T. I-P., Nguyen, H.L., and Roelke, R.J., “GRID2D3D -- A Computer Program for Generating Grid Systems in Complex-Shaped Two- and Three Dimensional Spatial Domains:  Part 2 - User's Manual,”  NASA Technical Memorandum 102454, 1990.
• Steinthorsson, E., Shih, T.I-P., and Roelke, R.J., “GRID2D3D -- A Computer Program for Generating Grid Systems in Complex-Shaped Two- and Three-Dimensional Spatial Domains, An Updated Version: GRID3D-v2,” NASA Technical Memorandum 103766, 1991.
• Shih, T.I-P., Bailey, R.T., Nguyen, H.L., and Roelke, R.J., “Algebraic Grid Generation for Complex Geometries,” International Journal for Numerical Methods in Fluids, Vol. 13, 1991, pp. 1-31.
• Steinthorsson, E., Shih, T.I-P., and Roelke, R.J., “Enhancing Control of Grid Distribution in Algebraic Grid Generation,” International Journal for Numerical Methods in Fluids, Vol. 15, 1992, pp. 297-311.
• Stephens, M.A., Rimlinger, M.J., Shih, T.I-P., and Civinskas, K.C., “Chimera Grids in Computing Flow and Heat Transfer in Blade Cooling,” AIAA Journal of Propulsion and Power, Vol. 11, No. 2, 1995, pp. 213-220.
• Chyu, W.J., Rimlinger, M.J., and Shih, T.I-P., “A Procedure for Automating CFD Simulations of an Inlet-Bleed Problem,” NASA Workshop on Surface Modelling, Grid Generation, and Related Issues in CFD Solutions,” NASA CP-3291, NASA - Lewis Research Center, May 1995, pp. 731-749.
• Shih, T. I-P., Lin, Y.-L., Flores, A.J., Stephens, M.A., Rimlinger, M.J., and Willis, B.P., “An Automated CFD Design and Analysis Tool for Inlet-Bleed Systems,” ASME DETC98/CIE-6033, Pittsburgh, Pennsylvania, September 1998.
• Shih, T.I-P., Gu, X., and Chu, D., “Grid-Quality Measures and Error Estimates,” Proceedings of the 7th International Conference on Grid Generation for Computational Field Simulations, September 25-28, 2000.
• Gu, X., Schock, H.J., Shih, T.I-P., Hernandez, E.C., Chu, D., Keller, P.S., and Sun, R.L., “Grid-Quality Measures for Structured and Unstructured Meshes,” AIAA Paper 2001-0652, Aerospace Sciences Meeting, Reno, Jan. 2001.
• Gu, X. and Shih, T.I-P., “Differentiating between Error Source and Error Location in Solution-Adaptive Mesh Refinement,” AIAA Paper 2001-2660, 15th Computational Fluid Dynamics Conference, Anaheim, June 2001.
• Gu, X., Hernandez, E., Chu, D., Sun, R., Keller, P., and Shih, T.I-P., “Grid-Quality Measures for Error Estimation of CFD Solutions,” Computational Fluid and Solid Mechanics, Vol. 1, Edited by K.J. Bathe, Elsevier, 2001, pp. 843-846.
• Shih, T.I-P., “Overset Grids: Fundamental and Practical Issues,” AIAA Paper 2002-3259, an invited paper, Applied Aerodynamics Conference, St Louis, June 2002.
• Chi, X., Zhu, B., Shih, T.I-P., Slater, J.W., Addy, H.E., and Choo, Y.K., “Computing Aerodynamic Performance of 2D Iced Airfoils: Blocking Topology and Grid Generation,” AIAA Paper 2002-0381, Aerospace Sciences Meeting, Reno, January 2002.
• Qin, Y. and Shih, T.I-P., “A Discrete Transport Equation for Error Estimation in CFD,” AIAA Paper 2002-0906, Aerospace Sciences Meeting, Reno, January 2002.
• Qin, Y. and Shih, T.I-P., “A Method for Estimating Grid-Induced Errors in Finite-Difference and Finite-Volume Methods,” AIAA Paper 2003-0845, Aerospace Sciences Meeting, Reno, January 2003.
• Qin, Y., Chi, X., and Shih, T. I-P., “Estimating Grid-Induced Errors in Navier-Stokes Solutions by Euler Discrete-Error-Transport Equations,” AIAA Paper 2005-0567, Aerospace Sciences Meeting, Reno, Nevada, January 2005.
• Shih, T.I-P., “Estimating Grid-Induced Errors in CFD Solutions,” Frontiers of Computational Fluid Dynamics 2006, Editors: D.A. Caughey and M. M. Hafez, Chapter 9, World Scientific, Singapore (ISBN: 981-256-527-2), 2005, Chapter 9, pp. 183-198.
• Shih, T.I-P., “Error Estimation in CFD Solutions,” invited plenary keynote, 13th National CFD Conference, Taiwan, August 14, 2006.  Proceedings of the 13th National Conference on Computational Fluid Dynamics, August 2006, pp. 1-14.
• Shih, T. I-P. and Williams, B., “Development and Evaluation of an à Posteriori Method for Estimating and Correcting Grid-Induced Errors in Solutions of the Navier-Stokes Equations,” AIAA Paper 2009-1499, Jan. 2009.

“Navier-Stokes” Solvers (funded by NASA Ames, NASA Lewis/Glenn, ALCOA (electrodeposition), ANYSIS (multiphase flow), Ford (IC engine flows), NSF (sprays & liquid atomization); students: Erlendur Steinthorrson, Joe Li, Adnan Karadag, Arindam Dasgupta, Asghar Afshari, Wanjia Zhang; colleagues: Farhad Jaberi and Glenn Sinclair).  This research is important because it determines the accuracy of the computed solutions, the efficiency with which they can be obtained, and the range of problems that can be studied by CFD.  Contributions made include:  (1) Developed a flux-vector splitting algorithm for conservation equations cast in chain-rule conservation-law form for spatial domains that deform in time and for PDEs that cannot be cast in strong conservation-law form (e.g., multi-fluid models of multiphase flows). (2) Developed a finite-volume algorithm based on the AUSM scheme for chemically reacting flows that can handle extremely low Mach number compressible flows (pre-conditioning was found to be not needed). (3) Developed a noniterative implicit algorithm for tracking particles in mixed Lagrangian-Eulerian formulations, which enables much larger time-step sizes to be used.  (4) Developed an approximate factorization method for PDEs with source terms, where the approximate factorization is a minimum for time-accurate simulations. (5) Developed a predictor-corrector method to stabilize three-factored schemes such as the Beam-Warming approximate-factorization method. (6) Developed an efficient LU factorization method for the “full” compressible Navier-Stokes equations in which the viscous terms are also factored.  (7) Developed and validated several codes for computing two- and three-dimensional flows that can be compressible or incompressible, laminar or turbulent, reacting or nonreacting, steady or unsteady, and single- or multi-phase, including an algorithm and a code (developed in 1994) for the direct simulation of particle-particle interactions in which the flow around each moving particle can be resolved.  (8) Discovered and performed asymptotic analysis to verify stress and pressure singularities induced by steady flows of viscous incompressible fluids, where solution quality decreases as grid resolution increases.

Current research is on hybrid methods for computing turbulent flows with focus on inflow boundary conditions for LES and boundary conditions at the interface between LES and RANS.

Representative papers in this area are as follows:

• Steinthorsson, E., Li, Z., Shih, T.I-P., Nguyen, H.L., and Willis, E.A., “A Flux-Vector Splitting Algorithm for Chain-Rule Conservation-Law Form,” AIAA Journal, Vol. 29, 1991, pp. 1101-1107.
• Shih, T.I-P. and Chyu, W.J., “Approximate-Factorization with Source Terms,” AIAA Journal, Vol. 29, 1991, pp. 1759-1760.
• Shih, T. I-P. and Dasgupta, A., “A Noniterative Implicit Algorithm for Tracking Particles for Mixed Lagrangian-Eulerian Formulations,” AIAA Journal, Vol. 31, No. 4, 1993, pp. 782-784.
• Shih, T.I-P., Steinthorsson, E., and Chyu, W.J., “Implicit Treatment of Diffusion Terms in Lower-Upper Algorithms,” AIAA Journal, Vol. 31, No. 4, 1993, pp. 788-791.
• Steinthorsson, E. and Shih, T.I-P., “Methods for Reducing Approximate-Factorization Errors in Two- and Three-Factored Schemes,” SIAM Journal on Scientific Computing, Vol. 14, No. 5, 1993, pp. 1214-1236.
• Dasgupta, A., Shih, T.I-P., Kundu, K.P., and Deur, J.M., “Numerical Simulation of Flow past an Array of Moving Spherical Particles,” AIAA Paper 94-3283, Joint Propulsion Conference, June 27-29, 1994.
• Shih, T.I-P., “Modeling Multiphase Flows through Direct Numerical Simulation,” ASME Paper 98-5039, an invited paper, ASME Fluids Engineering Summer Meeting, Washington, D.C., June 1998.
• Karadag, A., Ganjoo, D., Ostergaard, D., and Shih, T. I-P., “A Density-Based Method for Computing Incompressible Multiphase Flows – Part 1: Formulation and Solution Algorithm,” AIAA Paper 2000-0459, Aerospace Sciences Meeting, Jan. 2000.
• Karadag, A., Ganjoo, D., Ostergaard, D., and Shih, T. I-P., “A Density-Based Method for Computing Incompressible Multiphase Flows – Part 2: Verification and Application,” AIAA Paper 2000-0460, Aerospace Sciences Meeting, Jan. 2000.
• Li, Z., Jaberi, F., and Shih, T.I-P., “A Hybrid Lagrangian-Eulerian Particle-Level Set Method for Numerical Simulations of Two-Fluid Turbulent Flows,” International Journal for Numerical Methods in Fluids, Vol. 56, Oct. 2007, pp. 2271-2300.
• Afshari, A., Jaberi, F.A., and Shih, T.I-P., “Large-Eddy Simulations of Turbulent Flows in an Axisymmetric Dump Combustor,” AIAA Journal, Vol. 46, No. 7, July 2008, pp. 1576-1592.
• Sinclair, G.B., Chi, X., and Shih, T.I-P., “On the Pressure and Stress Singularities Induced by Steady Flows of an Incompressible Viscous Fluid,” Acta Mechanica Sinica, Vol. 25, No. 4, August 2009, pp. 451-462.
• Zhang, W. and Shih, T.I-P., “An Adaptive Downstream Anisotropic Eddy-Viscosity Model for Hybrid RANS/LES Simulations,” AIAA 2017-0977, AIAA Sci Tech, Jan. 2017.

Control of Shock-Wave/Boundary-Layer Interactions by Bleed for External and Mixed Compression Inlets (funded by NASA Ames, NASA Glenn; students: Tom Hahn, Mark Rimlinger, Yu-Liang Lin, Mark Stephens, Andrew Flores, Dave Benson, E-Jieh Teh).  Our focus is on understanding the nature of shock-wave/boundary-layer interactions and their control through bleed.  Contributions made include:  (1) Developed and validated CFD tools to study details of shock-wave/boundary-layer interactions with bleed in which flow through each bleed hole or slot is resolved. (2) Discovered and quantified the structure of “barrier shocks” (a name that we coined) and the mechanism that created it when bleeding a supersonic boundary layer. (3) Developed design concepts that utilize the “barrier shocks” to control shock-induced flow separations in inlet bleed systems. (4) Performed CFD studies to understand shock-wave/boundary-layer interactions with bleed as a function of hole arrangement, hole inclination, incident shock position, and plenum back pressure, including passive bleed and bleed through micro holes.  (5) Developed and evaluated boundary conditions for the bleed region that account for the physics of the bleed process but do not require the bleed holes or plenum to be resolved.  The evaluation was accomplished by comparing predictions from bleed boundary conditions with CFD solutions that resolved the flow through each bleed hole into the plenum and experimental data when they exist.

Representative papers in this area are as follows:

• Chyu, W.J., Howe, G.W., and Shih, T.I-P., “Bleed Boundary Conditions for Numerically Simulated Mixed-Compression Supersonic Inlet Flows,” AIAA Paper 88-0270, Aerospace Sciences Meeting, Jan. 11-14, 1988.  Also, AIAA Journal of Propulsion and Power, Vol. 8, 1992, pp. 862-868.
• Hahn, T.O., Shih, T.I-P., and Chyu, W.J., “Numerical Study of Shock-Wave / Boundary-Layer Interactions with Bleed,” AIAA Journal, Vol. 31, No. 5, 1993, pp. 869-876.
• Shih, T.I-P., Rimlinger, M.J., and Chyu, W.J., “Three-Dimensional Shock-Wave/Boundary-Layer Interactions with Bleed,” AIAA Journal, Vol. 31, No. 10, 1993, pp. 1819-1826.
• Chyu, W.J., Rimlinger, M.J., and Shih, T.I-P., “Control of Shock-Wave/Boundary-Layer Interactions by Bleed,” AIAA Journal, Vol. 33, No. 7, 1995, pp. 1239-1247.
• Rimlinger, M.J., Shih, T.I-P., and Chyu, W.J., “Three-Dimensional Shock-Wave/Boundary-Layer Interactions with Bleed through Rows of Holes,” AIAA Journal of Propulsion and Power, Vol. 12, No. 2, 1996, pp. 217-224.
• Lin, Y.-L., Stephens, M.A., Shih, T.I-P., and Willis, B.P., “Effects of Plenum Size on Bleeding a Supersonic Boundary Layer,” AIAA Paper 97-0609, Aerospace Sciences Meeting, Jan. 1997.
• Lin, Y.-L., Shih, T.I-P., and Willis, B.P., “Control of Shock-Wave/Boundary-Layer Interactions with Passive Blowing and Bleeding,” AIAA Paper 97-3002, Joint Propulsion Conference, July 1997.
• Flores, A.J., Shih, T.I-P., Davis, D.O., and Willis, B.P., “Bleed of Supersonic Boundary-Layer Flow through Rows of Normal and Inclined Holes,” AIAA Paper 99-2112, Joint Propulsion Conference, June 1999.
• Benson, D., Shih, T.I-P., Davis, D.O., and Willis, B.P., “Boundary Conditions for CFD Simulations of Supersonic Boundary-Layer Bleed through Discrete Holes,” AIAA Paper 2000-0888, Aerospace Sciences Meeting, Jan. 2000.
• Benson, D.B., Shih, T.I-P., Davis, D.O., and Willis, B.P., “Bleed Boundary Conditions for CFD Simulations of Supersonic Flows with Embedded Shocks and Boundary-Layer Bleed,” ASME Paper FEDSM-2001-18116, ASME Fluids Engineering Summer Meeting, New Orleans, May 2001.
• Benson, D.B, Shih, T.I-P., and Davis, D.O., “CFD Simulations of an Axisymmetric Mixed-Compression Inlet with Bleed through Discrete Holes,” ASME Paper FEDSM 2003-45076, 4th ASME/FED & JSME 2003 Joint Fluids Conference, July 6-10, 2003, Honolulu, Hawaii.
• Shih, T.I-P., “Control of Shock-Wave/Boundary-Layer Interaction by Bleed,” invited keynote, 9th Asian International Conference on Fluid Machinery (AICFM-9), Paper NO. AICFM9-IL01, Jeju, Korea, October 16-19, 2007.  Also, International Journal of Fluid Machinery and System (inaugural issue), Vol. 1, No. 1, Oct.-Dec. 2008, pp. 24-32.
• Teh, E-J. and Shih, T.I-P., “Reynolds-Averaged Simulations of Shock-Wave/Boundary-Layer Interactions with Bleed,” AIAA Paper 2013-0423 (an invited paper), AIAA Aerospace Sciences Meeting, Jan. 2013.

Aircraft Icing (funded by NASA Glenn). Ice accrued on wings will greatly reduced lift, and ice accretion and its subsequent breakup in engines could cause engine failure or roll out. Thus, aircraft icing is a serious safety issue. Contributions made include: (1) Developed an algorithm and code to generate high-quality single and multi-block structured grids for rime and glaze ice shapes with highly complicated surface geometries including horns and feathers, which enabled CFD studies of turbulence models because now solutions will converge. The grid- generation algorithm developed is the basis of NASA’s SmaggICE code. (2) Performed CFD studies to understand when CFD will yield reliable and meaningful solutions for different ice shapes. It was found that CFD could predict lift and drag as a function of angle of attack almost perfectly for airfoils and wings with accrued “rime” ice. For airfoils/wings with “glaze” ice, the predictions can have considerable uncertainty. (3) Developed a highly efficient reduced-order method to predict the aerodynamic performance of wings with accrued ice that could be used to guide flight control of aircraft in icing conditions in real time.

Representative papers in this area are as follows:

• Chi, X., Zhu, B., Shih, T.I-P., Slater, J.W., Addy, H.E., and Choo, Y.K., “Computing Aerodynamic Performance of 2D Iced Airfoils: Blocking Topology and Grid Generation,” AIAA Paper 2002-0381, Aerospace Sciences Meeting, Reno, January 2002.
• Zhu, B., Chi, X., Shih, T.I-P., and Slater, J.W., “Computing Aerodynamic Performance of 2D Iced Airfoils:  Blocking Strategies and Convergence Rate,” AIAA Paper 2002-3049, Applied Aerodynamics Conference, St Louis, June 2002.
• Zhu, B., Chi, X., Shih, T.I-P., Slater, J.W., Addy, H.E., and Choo, Y., “Computing Aerodynamic Performance of 2-D Iced Airfoils with Structured Grids,” AIAA Paper 2003-1071, Aerospace Sciences Meeting, Reno, January 2003.
• Chi, X., Zhu, B., Shih, T.I-P., Addy, H.E., and Choo, Y.K., “CFD Analysis of the Aerodynamics of a Business-Jet Airfoil with Leading-Edge Ice Accretion,” AIAA Paper 2004-0560, Aerospace Sciences Meeting, Reno, January 2004.
• Chi, X., Li, Y., Chen, H., Addy, H.E., Choo, Y.K., and Shih, T.I-P., “A Comparative Study Using CFD to Predict Iced Airfoil Aerodynamics,” AIAA Paper 2005-1371, Aerospace Sciences Meeting, Reno, Nevada, January 2005.
• Chi, X., Crist, N., Williams, B., Hindman, R., Kreeger, R.E., and Shih, T.I-P., “2-D and 3-D CFD Simulations of Clean and Iced Wings,” AIAA Paper 2006-1267, Aerospace Sciences Meeting, Reno, Nevada, January 2006.
• Hindman, R., Crist, N., Williams, B., Chi, X., and Shih, T.I-P., “Q3D Wing: Validation of a Modern Lifting-Line Method for Clean and Iced Wings,” AIAA Paper 2006-1268, Aerospace Sciences Meeting, Reno, Nevada, January 2006.
• Williams, B., Lu, P., Shih, T.I-P., “Q3D-Wing for Flight Control of Aircraft with Ice Accretion,” AIAA Paper 2007-503, Aerospace Science Meeting, Reno, Jan. 2007.

Gas Turbine Heat Transfer and Aerodynamics (funded by NASA Lewis, Pratt & Whitney, Siemens-Westinghouse, Solar Turbines, NSF, Exa, and DOE; students: Erlendur Steinthorrson, Mark Stephens, Yu-Liang Lin, Michael Gu, Xingkai Chi, Sangkwon Na, Bin Zhu, Leo Li, Kenny Hu, Chien-Shing Lee, Saiprashanth Gomatam Ramachandran, Christelle Wanko, Srisudarshan Krishna Sathyanarayanan, Zach Stratton, Jsason Liu, Adwiteey Raj Shishodia, James Peck).  Turbine efficiency increases with turbine inlet temperature. The temperatures sought today far exceed allowable material temperatures for strength and durability.  Thus, effective and efficient cooling is needed for all components that come in contact with the hot gases to maintain structural integrity and reasonable service life.  Contributions made include:  (1) Developed and validated CFD tools for studying three-dimensional (3-D) flow and heat transfer involved in internal and film cooling of turbine blades/vanes. (2) Performed CFD studies that showed how the 3-D flow induced by heat-transfer enhancement devices (square and rounded ribs, 90 degree and inclined ribs, hemispherical concavities, pin fins, and pedestals) affect surface heat transfer in rotating and non-rotating ducts (the first to do simulations of this type that resolve the turbulent flow in the near-wall region with a low-Reynolds number turbulence model (SST) in 1993 and the first to describe the flow mechanisms induced by centrifugal buoyancy in 1996). (3) Performed CFD studies that showed how secondary flows formed by Coriolis force in a rotating duct interact with secondary flows formed by inclined ribs and 180-degree bends and streamwise flow separation from centrifugal buoyancy (1996). (4) Performed CFD studies that showed the mechanism by which film cooling of the turbine-airfoil leading edge by rows of compound-angle holes could produce hot spots (1997) and developed a design to eliminate hot spot on the blades’ leading edges that is used in one company’s aircraft engines.  (6) Developed a number of design concepts to improve film-cooling effectiveness for the leading edge and the main body of the turbine airfoil (trench, strut in film-cooling holes, upstream ramp, flow aligned blockers (patented), and momentum-preserving W-shaped shape holes (patented)).  (7) The first to perform CFD studies that showed the mechanisms responsible for reducing secondary flows in nozzle guide vanes by contouring the endwall from the combustor to the first-stage stator.  (8) Develop a method to reduce secondary flows in a blade passage by blade-surface contouring (among the first to work on fillets about the leading edge) and by inlet swirl (first to do swirl). (9) Developed a design of experiment technique based on the Biot number analogy to enable experimental studies of cooling designs to be conducted at near room temperatures and near atmospheric pressures to reveal temperature distributions in turbine materials at realistic turbine operating conditions.  (10) Showed the effects of local Biot number distribution on temperature distribution in turbine materials with cooling on one side and external heat transfer from the hot gases on the other side and how hot spots could form.  (11) Showed the effects of using incorrect bulk temperatures on the measured heat-transfer coefficient (HTC) and that such HTC cannot be used in design – though still useful to validate CFD as long as the authors clearly state how the bulk temperature is defined in their measurements (typically omitted in all papers because they are hard to measure).  (12) Showed transient methods for measuring the HTC can yield large relative errors under certain conditions and provided guidelines to help assess when that happens. (13) Showed averaging the heat-transfer coefficient in design tools, a widely-used practice in industry, can severely under predict maximum material temperature and temperature gradients and developed a reduced-order model to correct for that error.  (14)  Showed that the Reynolds number in gas-turbine cooling passages can change significantly along the passage because wall-to-bulk temperature can be as high as 2 or more.  Thus, measurements of the HTC made at wall-to-bulk temperature near unity in laboratory conditions cannot be applied to engine-operating conditions as is commonly done.  (15) Developed a mathematical procedure to scale HTC measured under laboratory conditions, where wall-to-bulk temperature is near unity, to engine operating conditions, where the wall-to-bulk temperature cam be up to 2.  (16) Showed transient operations can lead to overheating of the turbine material even though there is cooling because of the slow time response of the material and proposed a way to ensure no overheating.  (17) Developed reduced-order model to estimate the maximum temperature and the duration of overheating in turbine material during transient operations.

Current research incudes: (1) Understand and quantify uncertainty issues that arise from errors in experimental and computational methods as well as from reduced-order methods for systems-level analysis.  (2) Understand and formulate meaningful dimensionless parameters to connect measurements made under laboratory conditions (i.e., in a scaled-up models operating near room temperature, atmospheric pressure, and low rotational speeds) to engine-relevant conditions (i.e., “small” actual configurations operating under high temperature, pressure, and rotational speeds) for turbine cooling.  (3) Turbine cooling during transient operations.  (4) Understand how design and operating parameters affect ingress through rim seals between rotor and stator disks and leakage flows through blade tips and their control.

Representative papers in this area are as follows:

Internal Cooling:

• Stephens, M.A., Shih, T.I-P., and Civinskas, K.C., “Effects of Inclined Rounded Ribs on Flow and Heat Transfer in a Square Duct,” AIAA Paper 95-2115, Thermal Physics Conference, June 19-22, 1995.
• Stephens, M.A., Shih, T.I-P., and Civinskas, K.C., “Computations of Flow and Heat Transfer in a Rotating U-Shaped Square Duct with Smooth Walls,” AIAA Paper 96-3161, Joint Propulsion Conference, July 1996.
• Shih, T. I-P. and Chyu, M.K., “Computation of Flow and Heat Transfer in a Rotating Passage with Ribs and a U-Bend,” Proceedings of the Tenth International Symposium on Transport Phenomena, Vol. 3, pp. 601-606, 1997.
• Stephens, M.A., Shih, T.I-P., “Computations of Flow and Heat Transfer in a Smooth U-Shaped Square Duct with and without Rotation,” AIAA Journal of Propulsion and Power, Vol. 15, No. 2, March-April 1999, pp. 272-279.
• Lin, Y.-L., Shih, T.I-P., Stephens, M.A., and Chyu, M.K., “A Numerical Study of Flow and Heat Transfer in a Smooth and a Ribbed U-Duct with and without Rotation,” ASME Journal of Heat Transfer, Vol. 123, April 2001, pp. 219-232.
• Lin, Y.-L. and Shih, T.I-P., “Flow and Heat Transfer induced by Rows of Hemispherical Cavities,” International Journal of Transport Phenomena, Vol. 3, 2001, pp. 1-11.
• Shih, T.I-P., Lin, Y.-L., and Stephens, M.A., “Flow and Heat Transfer in an Internal Coolant Passage,” International Journal for Rotating Machinery, Vol. 7, No. 5, September 2001, pp351-364.
• Hu, S.-Y., Chi, X., Shih, T.I-P., Bryden, K.M., Chyu, M.K., Ames, R., and Dennis, R.A., “Flow and Heat Transfer in the Tip-Turn Region of a U-Duct under Rotating and Non-Rotating Conditions.” ASME Paper GT-2011-46013, June 2011, Vancouver, Canada.
• Chi, X., Shih, T.I-P., Bryden, K.M., Chyu, M., Ames, R., and Dennis, R.A., “Effects of Pin-Fin Height on Flow and Heat Transfer in a Rectangular Duct,” ASME Paper GT-2011-46014, June 2011, Vancouver, Canada.
• Liu, J., Weaver, A., Lee, C.S., Shih, T.I-P., Klinger, J., Ames, R., and Dennis, R.A., “Flow and Heat Transfer in a Triple-Impingement Configuration for Trailing-Edge Cooling,” ASME Paper GT-2012-70075, June 2012, Copenhagen, Denmark.
• Lee, C.-S., Shih, T.I-P., Bryden, K.M., Ames, R., and Dennis, R.A., “Flow and Heat Transfer in a Jet-Impingement Configuration with No-Cross Flow about Jets,” ASME Paper GT-2012-70080, June 2012, Copenhagen, Denmark.
• Pardeshi, I., Shih, T.I-P., Bryden, K.M., Ames, R., Dennis, R.A., Ding, S., Xu, G., Deng, H., and Lu, R., “Flow and Heat Transfer in a Rotating and Non-Rotating Wedge-Shaped Cooling Passage with Ribs and Pin Fins,” AIAA Paper 2015-1444, AIAA Sci Tech, Jan. 2015.
• Weaver, A.M., Liu, J., and Shih, T.I-P., “A Weave Design for Trailing-Edge Cooling,” AIAA Paper 2015-1446, AIAA Sci Tech, Jan. 2015.

Film Cooling:

• Lin, Y.-L. and Shih, T.I-P., “Film Cooling over Flat, Convex, and Concave Surfaces,” AIAA Paper 99-0344, Aerospace Sciences Meeting, January 1999.
• Yu, Y., Yen, C.-H., Shih, T. I-P., Chyu, M.K., and Gogineni, S., “Film Cooling Effectiveness and Heat Transfer Coefficient around Diffusion Shaped Holes,” ASME Paper 99-GT-034, June 1999.
• Lin, Y.-L. and Shih, T.I-P., “Film Cooling of a Semi-Cylindrical Leading Edge with Injection through Rows of Compound-Angled Holes,” ASME Journal of Heat Transfer, Vol. 123, August 2001, pp. 645-654.
• Yu, Y., Yen, C-H., Shih, T. I-P., Chyu, M.K., and Gogineni, S., “Film Cooling Effectiveness and Heat Transfer Coefficient around Diffusion Shaped Holes,” ASME Journal of Heat Transfer, Vol. 124, No. 5, October 2002, pp. 820-827.
• Na, S., Cunha, F.J., Chyu, M.K., and Shih, T.I-P., “Effects of Coating Blockage and Deposit on Film Cooling Effectiveness and Surface Heat Transfer,” AIAA Paper 2006-0024, Aerospace Sciences Meeting, Reno, Nevada, January 2006.
• Shih, T.I-P., Na, S., and Chyu, M.K., “Prevent Hot-Gas Entrainment by Film-Cooling Jets via Flow-Aligned Blockers,” ASME Paper GT-2006-91161, IGTI Conference and Expo, Barcelona, Spain, May 8-11, 2006.
• Na, S. and Shih, T.I-P., “Increasing Film-Cooling Adiabatic Effectiveness by Using an Upstream Ramp,” ASME Paper GT-2006-91163, IGTI Conference and Expo, Barcelona, Spain, May 8-11, 2006. Also,  ASME Journal of Heat Transfer, Vol. 129, No. 4, April 2007, pp. 464-471.
• Shih, T.I-P., “Enhancing the Effectiveness of Film Cooling,” invited plenary keynote, 1st International Symposium on Jet Propulsion and Power Generation, Kunming, China, 20 September 2006.  Proceedings of the 1st International Symposium on Jet Propulsion and Power Generation, Vol. 1, 2006, pp. 28-34.  Also, Journal of Aerospace Power, Vol. 22, No. 4, April 2007, pp. 531-539.
• Shih, T.I-P. and Na, S., “Momentum-Preserving Shaped Holes for Film Cooling,” ASME IGTI Paper GT-2007-27600, IGTI Conference and Expo, Montreal, Canada, May 14-17, 2007.
• Chen, S.P., Chyu, M.K., and Shih, T.I-P., “Effects of Upstream Ramp on the Performance of Film Cooling,” ASME Paper GT2007-28137, Montreal, Canada, May 14-17, 2007.  Also, International Journal Thermal Sciences, Vol. 50, June 2011, pp. 1085-1094.
• Siw, S.C., Chyu, M.K., Shih, T.I-P., and Alvin, M.A., “Effects of Pin Detached Space on Heat Transfer and Pin-Fin Arrays,”  ASME J. of Heat Transfer, Vol. 134, No. 8, 2012, pp. 081902-1 to 081902-9.
• Stratton, Z., Shih, T.I-P., Laskowski, G., Briggs, R., and Barr, B., “Effects of Cross Flow in an Internal-Cooling Channel on Film Cooling of a Flat Plate through Compound-Angle Holes,” ASME Paper GT-2015-42771, Montreal, Canada, June 2015.

Conjugate Heat Transfer

• Na, S., Williams, B., Dennis, R.A., Bryden, K.M., and Shih, T. I-P., “Internal and Film Cooling of a Flat Plate with Conjugate Heat Transfer,” ASME IGTI Paper GT-2007-27599, IGTI Conference and Expo, Montreal, Canada, May 14-17, 2007.
• Shih, T.I-P., Chi, X., Bryden, K.M., Alsup, C., and Dennis, R.A., “Effects of Biot Number on Temperature Distribution in a Flat Plate Cooled by Rib-Enhanced Internal Cooling,” ASME Paper GT2009-59726, IGTI Conference, Orlando, June 2009.
• Na, S., Dennis, R.A., Alsup, C., Bryden, K.M., Shih, T. I-P., “Effects of Hot-Gas Composition on Temperature Distribution in a Flat Plate Cooled by Internal and Film Cooling,” ASME Paper GT2009-59727, IGTI Conference, Orlando, June 2009.

Secondary Flows and Rim Seals:

• Shih, T. I-P., Lin, Y.-L., and Simon, T.W., “Control of Secondary Flow in Turbine Nozzle Guide Vane by Endwall Contouring,” ASME Paper 2000-GT-0556, IGTI Conference, Munich, May 2000.
• Lin, Y.-L., Shih, T.I-P., Chyu, M.K., and Bunker, R.S., “Effects of Gap Leakage on Fluid Flow in a Contoured Turbine Nozzle Guide Vane,” ASME Paper 2000-GT-0555, IGTI Conference, Munich, May 2000.
• Lin, Y.-L. and Shih, T.I-P., “Flow and Heat Transfer in a Turbine Nozzle Guide Vane with Endwall Contouring,” AIAA Paper 2000-3002, 35^th Intersociety Energy Conversion Engineering, Las Vegas, July 2000
• Zhu, B., Shih, T.I-P., Oke, R., Simon, T.W., and Chyu, M.K., “Computational Study of a Two-Passage Turbine Guide-Vane Cascade with Endwall Contouring,” ASME Paper DETC-CIE 21762, September 2001.
• Shih, T.I-P. and Lin, Y.-L., “Controlling Secondary-Flow Structure by Leading-Edge Airfoil Fillet and Inlet Swirl to Reduce Aerodynamic Loss and Surface Heat Transfer,” ASME Journal of Turbomachinery, Vol. 125, January 2003, pp. 48-56.
• Liu, J., Weaver, A., Shih, T. I-P., Sangan, C.M., and Lock, G.D., “Modelling and Simulation of Ingress into the Rim Seal and Wheelspace of a Gas-Turbine Rotor-Stator Configuration,” AIAA Paper 2015-1445, AIAA Sci Tech, Jan. 2015.

Transient Operations:

• Lee, C.-S. and Shih, T. I-P., and Bryden, K.M., “CFD Conjugate Analysis of a Jet-Impingement Configuration with Sudden Changes in Heating and Cooling Loads,” Proceedings of the ASME 2013 International Mechanical Engineering Congress & Exposition, Paper IMECE2013-65542, November 2013, San Diego.
• Lee, C.-S., Shih, T.I-P., and Bryden, K.M., “Estimating Over Temperature and Its Duration in a Flat Plate with Sudden Changes in Heating and Cooling,” ASME Paper GT-2015-43526, Montreal, Canada, June 2015.  Also, ASME Journal of Turbomachinery, Vol. 138, June 2016, 061007-1 to 061007-12.

Fundamental Issues:

• Shih, T.I-P. and Sultanian, B., “Computations of Internal and Film Cooling,” Heat Transfer in Gas Turbines, Editors: B. Sundén and M. Faghri, WIT Press, Southhampton, 2001, Chapter 5, pp. 175-225.
• Durbin, P.A. and Shih, T.I-P., “An Overview of Turbulence Modeling,” Modelling and Simulation of Turbulent Heat Transfer, Edited by B. Sundén and M. Faghri, WIT Press, Southhampton, 2005, Chapter 1, pp. 3-31.
• Chi, X. and Shih, T.I-P., “Bulk Temperature, Heat-Transfer Coefficient, and Nusselt Number – Revisited,” AIAA Paper 2012-0807, Jan. 2012, Nashville.
• Shih, T.I-P., Gomatam-Ramachandran, S., and Chyu, M.K., “Time-Accurate CFD Conjugate Analysis of Transient Measurements of the Heat-Transfer Coefficient in a Channel with Pin Fins,” Journal of Propulsion and Power Research, Vol. 2, Issue 1, 2013, pp. 10-19.  DOI information: http://dx.doi.org: 10.1016/j.jppr.2013.01.003.
• Shih, T. I-P. and Durbin, P., “Modeling and Simulation of Turbine Cooling,” in Turbine Aerodynamics, Heat Transfer, Materials, and Mechanics, Editors:  T. Shih and V. Yang, Progress in Astronautics and Aeronautics, Vol. 243, American Institute of Aeronautics and Astronautics, 2014, pp. 389-421.
• Ramachandran, S.G. and Shih, T. I-P., “Biot-Number Analogy for Design of Experiments in Turbine Cooling,” ASME Journal of Turbomachinery, Vol. 137, June 2015, pp. 061002-1 to 061002-14.
• Lee, C.-S., Shih, T.I-P., and Bryden, K.M., “Effects of Averaging the Heat-Transfer Coefficient on the Predicted Material Temperature and Its Gradient,” ASME Journal of Heat Transfer, Vol. 139, Feb. 2017, 022002-1 to 022002-14.
• Sathyanarayanan, S.K. and Shih, T.I-P., “Time-Accurate Conjugate Analysis of Transient Measurements of Heat-Transfer Coefficients,” AIAA Journal of Thermophysics and Heat Transfer, Vol. 31, April 2017, DOI: 10.2514/1.T4723.
• Shih, T.I-P., Lee, C.-S., and Bryden, K.M., “Scaling Heat-Transfer Coefficients Measured under Laboratory Conditions to Engine-Relevant Conditions,” ASME Paper GT2017-64039, June 2017.

Automotive Related Flows (funded by NASA Lewis, DaimlerChrysler, Ford, GM, EPA, DOE; students: Erlendur Steinthorrson, Joe Li, Leo Li, Xingkai Chi, Kenny Hu, Chien-Shing Lee, Irsha Pardeshi, Ashutosh Pandey):  Contributions made include:  (1) Developed algorithms and codes to study the flow, fuel-air mixing, and combustion in Wankel rotary engines. (2) Developed grid-generation tools for KIVA to enable the analysis highly convoluted cylinder head and piston bowls for efficient and low emission direct-injection IC engines. (3) Assessed the performance of KIVA, Fluent, Star-CD, and FIRE for computing flow in the combustion chamber of three 4-value internal combustion engines (a generic pan-cake chamber, a Ford commercial engine, and a DaimlerChrysler engine) via comparison with experimental data. (4) Evaluated and validated models and codes for computing flow of water over car roofs. (5) Evaluated CFD models and codes for computing flows in torque converters. (6) Performed CFD simulations of a full torque converter with all blade/vane passages in the pump, turbine, and stator that accounted for leakage flow up to the clutch (first to do this and the first to show the effects of models for rotor-stator interactions for one passage versus all passages and the important role played by seal leakages).  (7) Developed a reduced-order model to predict aeration in clutches in automatic transmissions to reduce drag torque.  (8) Developed CFD tools to study flow physics connected to aeration and its onstart  in clutches.  (9) Develop CFD tools to study the multiphase flow inside liquid-ring vaccum pumps.

Water Flow on Car Roofs

Automotive Torque Converter

Flow in IC Engine Combustion Chamber Intake and Exhaust Manifolds

Liquid-Ring Vacuum Pumps

Representative papers in this area are as follows:

• Ramos, J.I., Shih, T.I-P., and Schock, H.J., “Wankel Engine Modelling,” Heat and Mass Transfer in Gasoline and Diesel Engines, Editors: D.B. Spalding and N.H. Afgan, Hemisphere Publishing Co., 1989, pp. 201-214.
• Shih, T.I-P., Schock, H.J., Nguyen, H.L., and Stegeman, J.D., “Numerical Simulation of the Flowfield in a Motored, Two-Dimensional Wankel Engine,” AIAA Journal of Propulsion and Power, Vol. 3, 1987, pp. 269-276.
• Steinthorsson, E., Shih, T.I-P., Schock, H.J., and Stegeman, J., “Calculations of the Unsteady, Three-Dimensional Flow Field inside a Motored Wankel Engine,” SAE 1988 Transactions Journal of Engines, Vol. 97, Section 6, 1988, pp. 6.1160-6.1188.
• Li, Z., Steinthorsson, E., Shih, T.I-P., and Nguyen, H.L., “Modelling and Simulation of Wankel Engine Flow Fields,” SAE 1990 Transactions Journal of Engines, Vol. 99, Section 3, Part 1, 1990, pp. 138-162.

Heat Transfer Issues in Thermoelectric Power Generation (funded by ONR MURI, DOE; students: Bob Harris, Kenny Hu, Chien-Shing Lee; faculty:  Professor Harold Schock at Michigan State):  One challenge is extracting energy from waste heat in hot gases such as the exhaust of a car engine because gases do not transfer heat very efficiently.  Another challenge is thermal stress when the hot and cold temperature difference across the TE couple is large (300 K or more) over a short distance (< 5 mm).  Contributions made include:  (1) Developed an algorithm and code to study the 3-D heat-transfer and electric current generation in thermoelectric (TE) couples that include conducting plates and insulation material. (2) Performed CFD studies to understand free convection and radiation heat transfer in the cavities between TE legs in TE couples.  (3) Performed CFD studies to develop compact heat exchangers for waste-heat recovery that can extract up to 50% of the available energy from the hot gas with reasonable pressure loss.

Representative papers in this area are as follows:

• Hogan, T. and Shih, T.I-P., “Modeling and Characterization of Power Generation Modules Based on Bulk Materials,” Thermoelectric Handbook:  Macro to Nano-Structured Materials, Editor: M. Rowe, Taylor and Francis Books, 2005.
• Zhu, B., Schock, H.J., Hogan, T., and Shih, T. I-P., “Natural Convection and Radiation Heat Transfer in High-Temperature Thermoelectric Couples,” AIAA Paper 2006-0574, Aerospace Sciences Meeting, Reno, Nevada, January 2006.
• Harris, R., Schock, H.J., and Hogan, T., and Shih, T., “Heat Transfer and Electric Current Flow in a Thermoelectric Couple,” AIAA Paper 2006-0575, Aerospace Sciences Meeting, Reno, Nevada, January 2006.
• Hu, K., Chi, X., Shih, T.I-P., and Schock, H.J., “Heat Transfer Enhancement in Thermoelectric Power Generation,” AIAA 2009-1210, Jan. 2009.

Capability in CFD Codes

Government and Commercial Codes Used by Shih & His Students:

Government:  OVERFLOW+PEGASUS, CFL3D+MAGGIE & RONNIE, USM3D, Wind, FDL3D

Commercial:  Gambit, GridGen, ICEM, CFX, Fluent, PowerFlow, Tecplot, FieldView

Open Source:  HiFiLES, SU2

In-House Codes Developed by Shih with His Students:

UM-IC2D (Tom Shih with his M.S. & Ph.D. thesis advisor, Dr. George S. Springer, now at Stanford):  This code uses the implicit-factored method of Beam and Warming to analyze the unsteady, compressible Navier-Stokes equations in r-z coordinates.  This code is configured to analyze axisymmetric flowfields inside piston-cylinder configurations that model internal combustion engines.

Lewis-2D (with graduate students: Song-Lin Yang, Erlendur Steinthorsson, & Zhi (Joe) Li):  This code uses an implicit finite-difference method based on approximate-factorization and flux-vector splitting to analyze the "unsteady, compressible" Navier-Stokes equations in two-dimensional generalized coordinates with domains that deform with time.  This code is written in modular form and can be used to study a wide range of problems with different boundary conditions and geometries.

Lewis-3D (with graduate students: Erlendur Steinthorsson & Zhi (Joe) Li):  This code is similar to Lewis-2D except that it can analyze unsteady, three-dimensional flows.

LeRC3D/CmuFD3D (with graduate students: Greg W. Howe, Erlendur Steinthorsson, Zhi (Joe) Li, Adnan Karadag, & Asghar Afshari; Professor Farhad Jaberi at Michigan State University was involved in the LES part):  This code uses a finite-volume method which can be a point or a line iterative process (including Runge-Kutta with implicit residual smoothing) with multigrid and a variety of differencing schemes for the convection terms (including several different flux-vector and flux-difference splitting schemes) to analyze steady or unsteady, three-dimensional compressible flows that can be single- or multi-component gas mixture, reacting or nonreacting, laminar or turbulent, single or multi-phase, and compressible or incompressible.  For the LES and DNS, 3^rd-order low-storage RK is used for time differencing, and 4^th-order compact differencing is used for spatial derivatives.  LES models coded include the Smagorinsky model, the modified kinetic energy viscosity (MKEV) model, the dynamic Smagorinsky model, and the algebraic renormalization group (RNG) SGS closure.

RAAKE (with Dr. W.J. Chyu of NASA Ames):  This code uses an implicit finite-volume method based on a quasi-Newton algorithm which includes the LU algorithm as a special case with flux-vector splitting to analyze four different two-equations models of turbulence: the low-Reynolds number k-e model of Chen and Patel, the low-Reynolds number k-e model of Jones and Launders, a k-e model based on renormalization group theory, and the k-w model of Wilcox.  The user of this code can choose to use any one of these models.  This code can be attached to any code, which analyzes the conservation equations of mass, momentum, and total energy such as ARC3D, F3D, and OVERFLOW, three well-known codes developed at NASA Ames Research Center.

PPPFIN (with graduate student Arindam Dasgupta):  This code uses OVERFLOW and PEGASUS to perform direct numerical simulations of particle-particle/particle-fluid interactions, where the flow past each particle is resolved (i.e., particles are not treated as point masses).  The method utilizes an iterative solution procedure on moving overlapping grids, one attached to each moving particle. Stencil construction and data transfer between the grids were accelerated through a knowledge-based algorithm.

GRID2D/3D (with graduate students: Robert T. Bailey & Erlendur Steinthorsson):  This code generates grid systems in complex-shaped, two- and three-dimensional spatial domains.  The code uses bi-directional Hermite interpolation to construct surfaces with C¹ continuity across patches.  Surface and volume grids are generated by algebraic techniques based transfinite interpolation with controls for stretching and orthogonality.

AUTOMAT (with W.J. Chyu of NASA Ames, Brian P. Willis of NASA Lewis, and graduate students, Mark J. Rimlinger, Mark A. Stephens, Yu-Liang Lin, and Andrew Flores):  This code automatically generates grid systems based on overlapping Chimera grids as well as all other input files needed to perform CFD simulations of a bleed system for mixed compression supersonic inlets by using the OVERFLOW/PEGSUS or the CFL3D/RONNIE/MAGGIE codes.

TRACKER (with graduate student: Arindam Dasgupta):  This code computes the position, velocity, and thermal energy of discrete particles in three-dimensional particle-laden flows that is modelled by a Lagrangian-Eulerian formulation.  This code also identifies the cell in which each particle is located as well as interpolates the data needed by the particles from the continuum phase.  This code is configured to be used with LeRC3D, and can track efficiently particles as small as 10-9 m because of a noniterative implicit algorithm employed.  The particles can be solids or evaporating liquid droplets.

ALCOA.electrodeposition (proprietary):  This code calculates the fluid mechanics of colloidal dispersions in water in which the electric double layer about each colloidal particle is accounted for and time-varying electromagnetic field is imposed.

AV-GRADIENT (still under development with Shlomo Ta-asan of Carnegie Mellon, Nizar Trigui of Ford Motor Co., and graduate student: Taek Choi):  This code solves the adjoint variable equations along with a set of boundary conditions for the full compressible Navier-Stokes equations on an unstructured grid to be used in CFD-based shape optimization.

EBE (Error-Bound Estimation with graduate student Xubin Gu):  This code provides an error-bound estimate on computed CFD solutions.  The code is based on two hypotheses.  First, relative error = F(formulation, numerical method, and grid-quality measures).  Second, the function F is general for a class of flows.  Considerable research has been conducted to search, develop, and evaluate solution-based grid-quality measures for structured and unstructured mesh that account for the vector and tensor nature of fluid mechanics.  Also, databases have been developed to construct the function F.

DETE-1 (Discrete-Error Transport Equation with graduate student Christine Yuehui Qin):  This code solves the discrete-error-transport equation for three model equations:  advection-diffusion, linear wave equation, and Burger’s equation.  Residual is modeled by the leading term of the modified equation and a number of physics-based grid-quality measures.

DETE-2 (Discrete-Error Transport Equation with graduate student Brandon Williams):  This code solves the discrete-error-transport equation to estimate grid-induced errors in steady and time-accurate solutions of the compressible Euler and Navier-Stokes equations (can be attached to any CFD code).  Residual is modeled by a multigrid-sequencing method, the leading term in the truncation error of an approximate modified equation, and a high-order interpolant constructed from a lower order solution.

TECA (Thermoelectric Couple Analysis with graduate student Rob Harris):  This code solves the energy and electric-potential equations in thermoelectric (TE) couples to predict the three-dimensional distributions of temperature, heat flow, electric potential, and current flow.  This code accounts for temperature-dependent material properties, electrical and heat transfer contact resistances, and heat transfer from the TE legs via convection or through insulation material with nonzero thermal conductivity.

Q3D-Wing (Quasi Three-Dimensional Analysis of Clean and Iced Wings with colleague Rich Hindman and graduate students Nick Crist and Brandon Williams):  This code uses a reduced-order method to estimate lift and drag as function of angle of attack for wings with accrued ice.  This reduced-order method and code were validated by full 3-D simulations.  This reduced-order method couples 2-D CFD or EFD results for lift and drag as a function of angle of attack with a modern version of the lifting-line theory to predict the aerodynamic performance of clean and iced 3-D wings with sweep, taper, and twist.