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NASA NTRS1990

Computational results for flows over 2-D ramp and 3-D obstacle with an upwind Navier-Stokes solver

An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spacially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.

Venkatapathy, Ethiraj↗

NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗

NASA NTRS1991

Navier-Stokes computation of wing/rotor interaction for a tilt rotor in hover

A method has been developed to analyze the wing/rotor interaction of tilt rotor aircraft in hover. The unsteady, thin-layer compressible Navier-Stokes equations are solved using an implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts a radial and azimuthal distribution of pressure rise and swirl to the flowfield. The 'chimera' approach of grid point blanking is used to update the rotor boundary conditions. Results are presented for both a rotor alone and for wing/rotor interaction where the thrust coefficient is 0.0164 and wing flap deflection is 67 degrees. Many of the complex flow features are captured including the fountain effect, leading and trailing edge separation, and the unsteady wake beneath the wing. Wing surface pressures compare fairly well with experimental data although the time-averaged download is about twenty percent higher than the measured value. This discrepancy is due to a combination of factors that are discussed.

Fejtek, Ian↗

NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗

NASA NTRS1991

Computational aspects of chemically reacting flows

An implicit, time-dependent approach is taken to solve the inviscid conservative equations in a vertex-based finite-volume formulation. The convective fluxes are estimated by a modified Riemann solver, and higher-order accuracy is obtained by means of the MUSCL. Implicit techniques are adopted to deal with the equation stiffness as a result of the clustered grid and chemical source term. The real-gas Roe matrix and the ADI and LU schemes have been tested on the sample problems: hypersonic flow over blunt configurations, such as the forebody of a double ellipse, and the near wake of a conic aerobrake. Temperature distribution and standoff distance are validated against the shock-fitting, central-differencing results. Equilibrium temperature may be recovered by artificially increasing the chemical rates at the wall. The present method satisfactorily resolves the flow structure, including the strong expansion behind the flat base. The relative merits and performance of the real-gas TVD and implicit schemes are discussed briefly.

Li, C. P.↗

NASA NTRS1991

Three-dimensional incompressible Navier-Stokes solver using lower-upper symmetric-Gauss-Seidel algorithm

A numerical method based on the pseudocompressibility concept is developed for solving the three-dimensional incompressible Navier-Stokes equations using the lower-upper symmetric-Gauss-Seidel implicit scheme. Very high efficiency is achieved in a new flow solver, INS3D-LU code, by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

Yoon, Seokkwan↗

NASA NTRS1991

Computations of the three-dimensional flow and heat transfer within a coolant passage of a radial turbine blade

A numerical code is developed for computing three-dimensional, turbulent, compressible flow within coolant passages of turbine blades. The code is based on a formulation of the compressible Navier-Stokes equations in a rotating frame of reference in which the velocity dependent variable is specified with respect to the rotating frame instead of the inertial frame. The algorithm employed to obtain solutions to the governing equation is a finite-volume LU algorithm that allows convection, source, as well as diffusion terms to be treated implicitly. In this study, all convection terms are upwind differenced by using flux-vector splitting, and all diffusion terms are centrally differenced. This paper describes the formulation and algorithm employed in the code. Some computed solutions for the flow within a coolant passage of a radial turbine are also presented.

Shih, T. I.-P.↗

NASA NTRS1991

Low thrust viscous nozzle flow fields prediction

A Navier-Stokes code was developed for low thrust viscous nozzle flow field prediction. An implicit finite volume in an arbitrary curvilinear coordinate system lower-upper (LU) scheme is used to solve the governing Navier-Stokes equations and species transportation equations. Sample calculations of carbon dioxide nozzle flow are presented to verify the validity and efficiency of this code. The computer results are in reasonable agreement with the experimental data.

Liaw, G. S.↗

NASA NTRS1991

Turbulence modeling in supersonic combusting flows

To support the National Aerospace Plane project, the RPLUS3D CFD code has been developed at NASA Lewis. The code has the ability to solve three-dimensional flowfields with finite rate combustion of hydrogen and air. The combustion processes of the hydrogen-air system are simulated by an 18-reaction path, 8-species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though it uses a fully implicit numerical algorithm. A k-epsilon (two equation) turbulence model is incorporated into the RPLUS3D code.

Chitsomboon, Tawit↗

NASA NTRS1991

Progress of simulations for reacting shear layers

An attempt was made to develop a high speed, chemically reactive shear layer test rig. The purpose of the experiment was to study the mixing of oxidizer and fuel streams in reacting shear layers for various density, velocity, and Mach number. The primary goal was to understand the effects of the compressibility upon mixing and combustion in a fundamental way. Therefore, a two-dimensional shear layer is highly desirable for its simplicity to quantify the compressibility effects. The RPLUS 2D code is used to calculate the flow fields of different sections of the test rig. The emphasis was on the supersonic nozzle design, the vitiation process for the hot air stream and the overall thermodynamic conditions of the test matrix. The k-epsilon turbulence model with wall function was successfully implemented in the RPLUS code. The k and epsilon equations are solved simultaneously and the LU scheme is used to make it compatible with the flow solver.

Yu, Sheng-Tao↗

NASA NTRS1992

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Chitsomboon, Tawit↗

NASA NTRS1993

Development Of A Navier-Stokes Computer Code

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Yoon, Seokkwan↗

NASA NTRS1992

Geochemistry and petrology of primitive achondrite meteorites LEW 88280, MAC 88177, ALHA 81187, EET 84302, and LEW 88663

Primitive achondrites are meteorites that have mineral and bulk chemical compositions similar to the most primitive meteorites (chondrites) but have textures similar to more evolved meteorites (achondrites). The unique geochemistry and texture of the primitive achondrites suggest these meteorites may be genetic intermediates between chondrites and achondrites and may preserve evidence of processes occurring in the early solar system. Five primitive achondrites LEW 88280, MAC 88177, ALHA 81187, EET 84302, and LEW 88663 were examined in this study in order to classify the meteorites and to determine processes that have affected them. Bulk chemical analyses of Nap, K2O, CaO, FeO, Cr, Co, Ni, Sc, Ir, Au, As, Sb, Se, Br, Cs, Ba, La, Ce, Nd, Sm, Eu, Tb, Yb, and Lu were determined for each meteorite by Instrumental Neutron Activation Analysis (INAA). Concentrations of Hf, U, and Th were determined for some meteorites. Polished thin sections of the five meteorites were examined in transmitted and reflected light microscopy to identify minerals and examine petrographic relationships. Minerals found in the meteorites include olivine, orthopyroxene, clinopyroxene, plagioclase, Cr-spinel, phosphates, troilite, kamecite, and taenite along with other minor phases. Mineral compositions were determined with an electron microprobe. The initial study suggests that the meteorites have been altered by metamorphic processes although igneous processes may also have played a role in the evolution of these rocks. Further studies of isotope and bulk chemistry are planned for these meteorites.

Field, Stephen W.↗

NASA NTRS1993

A simple parallel prefix algorithm for compact finite-difference schemes

A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiagonal systems that are difficult to solve efficiently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel prefix (SPP), is proposed. The SPP algorithm requires less memory than the conventional LU decomposition and is highly efficient on parallel machines. It consists of a prefix communication pattern and AXPY operations. Both the computation and the communication can be truncated without degrading the accuracy when the system is diagonally dominant. A formal accuracy study was conducted to provide a simple truncation formula. Experimental results were measured on a MasPar MP-1 SIMD machine and on a Cray 2 vector machine. Experimental results show that the simple parallel prefix algorithm is a good algorithm for the compact scheme on high-performance computers.

Sun, Xian-He↗

NASA NTRS1993

Computational analysis of methods for reduction of induced drag

The purpose of this effort was to perform a computational flow analysis of a design concept centered around induced drag reduction and tip-vortex energy recovery. The flow model solves the unsteady three-dimensional Euler equations, discretized as a finite-volume method, utilizing a high-resolution approximate Riemann solver for cell interface flux definitions. The numerical scheme is an approximately-factored block LU implicit Newton iterative-refinement method. Multiblock domain decomposition is used to partition the field into an ordered arrangement of blocks. Three configurations are analyzed: a baseline fuselage-wing, a fuselage-wing-nacelle, and a fuselage-wing-nacelle-propfan. Aerodynamic force coefficients, propfan performance coefficients, and flowfield maps are used to qualitatively access design efficacy. Where appropriate, comparisons are made with available experimental data.

Janus, J. M.↗

NASA NTRS1991

Computational results for 2-D and 3-D ramp flows with an upwind Navier-Stokes solver

An implicit, finite-difference, upwind, full Navier-Stokes solver was applied to supersonic/hypersonic flows over two-dimensional ramps and three-dimensional obstacle. Some of the computed results are presented. The numerical scheme used in the study is an implicit, spatially second order accurate, upwind, LU-ADI scheme based on Roe's approximate Reimann solver with MUSCL differencing of Van Leer. An algebraic grid generation scheme based on generalized interpolation scheme was used in generating the grids for the various 2-D and 3-D problems.

Venkatapathy, Ethiraj↗

NASA NTRS1993

Navier-Stokes flowfield computation of wing/rotor interaction for a tilt rotor aircraft in hover

The download on the wing produced by the rotor-induced downwash of a tilt rotor aircraft in hover is of major concern because of its severe impact on payload-carrying capability. A method has been developed to help gain a better understanding of the fundamental fluid dynamics that causes this download, and to help find ways to reduce it. In particular, the method is employed in this work to analyze the effect of a tangential leading edge circulation-control jet on download reduction. Because of the complexities associated with modeling the complete configuration, this work focuses specifically on the wing/rotor interaction of a tilt rotor aircraft in hover. The three-dimensional, unsteady, thin-layer compressible Navier-Stokes equations are solved using a time-accurate, implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts both a radical and an azimuthal distribution of pressure rise and swirl to the flowfield. A momentum theory blade element analysis of the rotor is incorporated into the Navier-Stokes solution method. Solution blanking at interior points of the mesh has been shown here to be an effective technique in introducing the effects of the rotor and tangential leading edge jet. Results are presented both for a rotor alone and for wing/rotor interaction. The overall mean characteristics of the rotor flowfield are computed including the flow acceleration through the rotor disk, the axial and swirl velocities in the rotor downwash, and the slipstream contraction. Many of the complex tilt rotor flow features are captured including the highly three-dimensional flow over the wing, the recirculation fountain at the plane of symmetry, wing leading and trailing edge separation, and the large region of separated flow beneath the wing. Mean wing surface pressures compare fairly well with available experimental data, but the time-averaged download/thrust ratio is 20-30 percent higher than the measured value. The discrepancy is due to a combination of factors that are discussed. Leading edge tangential blowing, of constant strength along the wing span, is shown to be effective in reducing download. The jet serves primarily to reduce the pressure on the wing upper surface. The computation clearly shows that, because of the three-dimensionality of the flowfield, optimum blowing would involve a spanwise variation in blowing strength.

Fejtek, Ian G.↗

NASA NTRS1993

An experimental study of trace element partitioning between perovskite, hibonite and melt: Equilibrium values

The presence of perovskite (CATiO3) and hibonite (Ca Al12O19) within different regions of Calcium-, Aluminum-rich Inclusions (CAI) and the trace element concentrations of these minerals in each circumstance, constrain models of precursor formation, nebular condensation, the thermal history of inclusions with relict perovskite and hibonite, and the formation of the Wark-Lovering rim. At present mineral/melt partition coefficient data for hibonite are limited to a few elements in simple experimental systems, or to those derived from hibonite-glass pairs in hibonite/glass microspherules. Similarly, there is only limited data on perovskite D that are applicable to meteorite compositions. Apart from the importance of partitioning studies to meteorite research, D values also are invaluable in the development of thermodynamic models, especially when data is available for a large number of elements that have different ionic charge and radii. In addition, study of the effect of rapid cooling on partitioning is crucial to our understanding of meteorite inclusions. To expand our knowledge of mineral/melt D for perovskite and hibonite, a study was instituted where D values are obtained in both equilibrium and dynamic cooling experiments. As an initial phase of this study mineral/melt D was measured for major elements (Ca, Mg, Al, Ti, and Si), 15 rare earth elements (La-Lu) and 8 other elements (Ba, Sr, U, Th, Nb, Zr, Hf, and Ge) in perovskite and hibonite grown under equilibrium conditions, in bulk compositions that are respectively similar to Compact Type A (CTA) CAI and to a hibonite/glass microspherule. Experimental mixes were doped with REE at 20-50x chondritic (ch) abundances, Ba at 50 ppm, Sr, Hf, Nb, and Zr at 100 ppm and, U and Th at 200 ppm. Trace element abundances were measured with the PANURGE ion microprobe. Major element compositions were obtained by electron microprobe analysis.

Kennedy, A. K.↗