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NASA NTRS1988

Application of advanced grid generation techniques for flow field computations about complex configurations

In the computation of flowfields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach; its applications are investigated. The method conservative providing conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid system is not possible.

Kathong, Monchai↗
NASA NTRS1991

Use of finite volume schemes for transition simulation

The use of finite-volume methods in the study of spatially and temporally evolving transitional flows over a flat plate is investigated. Schemes are developed with both central and upwind differencing. The compressible Navier-Stokes equations are solved with a Runge-Kutta time stepping scheme. Disturbances are determined using linear theory and superimposed at the inflow boundary. Time accurate integration is then used to allow temporal and spatial disturbance evolution. Characteristic-based boundary conditions are employed. The requirements of using finite-volume algorithms are studied in detail. Special emphasis is placed on difference schemes, grid resolution, and disturbance amplitudes. Moreover, comparisons are made with linear theory for small amplitude disturbances. Both subsonic and supersonic flows are considered, and it is shown that the locations of branch 1 and branch 2 of the neutral stability curve are well predicted, given sufficient resolution.

Fenno, Charles C., Jr.↗
NASA NTRSDate not supplied

Wall-Modeled Large Eddy Simulation Method for Unstructured-Grid Navier-Stokes Solvers

This paper reports on the implementation and assessment of a Wall-Modeled Large-Eddy Simulation (WMLES) methodology in an unstructured-grid, node-centered flow solver, FUN3D that is developed and supported at the NASA Langley Research Center. Finite-volume (FV) and finite-element (FE) discretization schemes considered in the study provide formal second-order spatial accuracy. Large-Eddy Simulations (LES) resolve large-scale turbulent-flow features and filter out small-scale effects using the Vreman subgrid-scale model. At solid-wall boundaries, a shear-stress model is employed to provide a proper boundary-flux closure. The nonlinear equations are integrated in time using either an optimized backward difference formula or an implicit multistage Runge-Kutta temporal scheme. The implicit equations at each time step are solved by strong nonlinear iteration schemes. WMLES demonstrations are shown for two high-lift configurations, namely, the McDonnell Douglas 30P30N multielement airfoil and a NASA High-Lift Common Research Model. Results show that the WMLES approaches implemented in the FV and FE discretization methods produce consistent solutions and are capable of capturing key aerodynamic characteristics and flow structures for high-lift configurations at a wide range of angles of attack including maximum-lift conditions. In the 30P30N example, correct trends in the variations of integrated aerodynamic forces and moments, surface pressure distributions, and boundary-layer profiles are captured as the Reynolds number is increased.

CFD; turbulence modeling; High-Lift flow simulatio↗
NASA NTRS1994

Fourth-order 2N-storage Runge-Kutta schemes

A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes.

Carpenter, Mark H.↗
NASA NTRS1988

Essentially non-oscillatory shock capturing methods applied to turbulence amplification in shock wave calculations

ENO (essentially non-oscillatory) schemes can provide uniformly high order accuracy right up to discontinuities while keeping sharp, essentially non-oscillatory shock transitions. Recently, an efficient implementation of ENO schemes was obtained based on fluxes and TVD Runge-Kutta time discretizations. The resulting code is very simple to program for multi-dimensions. ENO schemes are especially suitable for computing problems with both discontinuities and fine structures in smooth regions, such as shock interaction with turbulence, for which results for 1-D and 2-D Euler equations are presented. Much better resolution is observed by using third order ENO schemes than by using second order TVD schemes for such problems.

Osher, Stanley↗
NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the 'multiple grids' or 'zonal grids' approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, M.↗
NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, Monchai↗
NASA NTRS1990

Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations

An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.

Jentink, Thomas Neil↗
NASA NTRS1992

Propulsion-related flowfields using the preconditioned Navier-Stokes equations

A previous time-derivative preconditioning procedure for solving the Navier-Stokes is extended to the chemical species equations. The scheme is implemented using both the implicit ADI and the explicit Runge-Kutta algorithms. A new definition for time-step is proposed to enable grid-independent convergence. Several examples of both reacting and non-reacting propulsion-related flowfields are considered. In all cases, convergence that is superior to conventional methods is demonstrated. Accuracy is verified using the example of a backward facing step. These results demonstrate that preconditioning can enhance the capability of density-based methods over a wide range of Mach and Reynolds numbers.

Venkateswaran, S.↗
NASA NTRS1984

A new method for determining acoustic-liner admittance in a rectangular duct with grazing flow from experimental data

A method is developed for determining acoustic liner admittance in a rectangular duct with grazing flow. The axial propagation constant, cross mode order, and mean flow profile is measured. These measured data are then input into an analytical program which determines the unknown admittance value. The analytical program is based upon a finite element discretization of the acoustic field and a reposing of the unknown admittance value as a linear eigenvalue problem on the admittance value. Gaussian elimination is employed to solve this eigenvalue problem. The method used is extendable to grazing flows with boundary layers in both transverse directions of an impedance tube (or duct). Predicted admittance values are compared both with exact values that can be obtained for uniform mean flow profiles and with those from a Runge Kutta integration technique for cases involving a one dimensional boundary layer.

Watson, W. R.↗
NASA NTRS1986

Euler solutions for high-speed flow about complex three-dimensional configurations

A numerical algorithm based on a finite-volume explicit scheme with Runge-Kutta time integration of the Euler equations is presented for calculating high-speed three-dimensional flow about complex aerospace configurations. The use of enhancing factors such as artificial dissipative terms, enthalpy damping and local time-stepping are described. An algebraic method for generating quasi-three-dimensional computational grids for realistic aerospace configurations is presented. Computed results for various three-dimensional bodies at different Mach numbers and angles of attack have been obtained using the methods for grid-generation and flow simulation. Comparison of computed and experimental data for an advanced tactical aircraft-like configuration is presented, and a reasonable agreement of the data is noticed.

Moitra, A.↗
NASA NTRS1988

Efficient implementation of essentially non-oscillatory shock capturing schemes, 2

Earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock capturing schemes is continued. A new simplified expression is provided for the ENO construction procedure based again on numerical fluxes rather than cell averages. Also considered are two improvements which are labeled ENO-LLF (local Lax-Friedrichs) and ENO-Roe, which yield sharper shock transitions, improved overall efficiency, and lower computational cost than previous implementation of the ENO schemes. Two methods of sharpening contact discontinuities, i.e., the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors used originally in the cell-average framework, are supplied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations. The implementation for nonlinear systems and multi-dimensions is given. Finally, many numerical examples, including a compressible shock turbulence interaction flow calculation, are given.

Shu, Chi-Wang↗
NASA NTRS1986

Development of an explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbomachinery

A rapid quasi three-dimensional analysis was developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations which are solved b a two-stage Runge-Kutta scheme made efficient by use of vectorization, a variable time-step, and a flux-based multigrid scheme, are described. A stability analysis is presented for the two-stage. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi three-dimensional viscous analysis can be a practical design tool.

Chima, R. V.↗
NASA NTRS1985

Development of an explicit multigrid algorithm for quasi-three-dimensional viscous flows in turbo-machinery

A rapid quasi three-dimensional analysis was developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations which are solved by a two-stage Runge-Kutta scheme made efficient by use of vectorization, a variable time-step, and a flux-based multigrid scheme, are described. A stability analysis is presented for the two-stage scheme. Results for a flat-plate model problem show the applicability of the method to axial, radial, and rotating geometries. Results for a centrifugal impeller and a radial diffuser show that the quasi three-dimensional viscous analysis can be a practical design tool.

Chima, R. V.↗
NASA NTRS1997

Numerical Simulation of Turbulent Jets with Rectangular Cross-Section

Three-dimensional turbulent jets with rectangular cross-section are simulated with a finite-difference numerical method. The full Navier-Stokes equations are solved at low Reynolds numbers, whereas at the high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporal discretization and a fourth-order compact scheme is used for spatial discretization. Computations are performed for different inlet conditions which represent different types of jet forcing. The phenomenon of axis-switching is observed, and it is confirmed that this is based on self-induction of the vorticity field. Budgets of the mean streamwise velocity show that convection is balanced by gradients of the Reynolds stresses and the pressure.

Wilson, Robert V.↗
NASA NTRS2005

Computations of Flow over a Hump Model Using Higher Order Method with Turbulence Modeling

Turbulent separated flow over a two-dimensional hump is computed by solving the RANS equations with k - omega (SST) turbulence model for the baseline, steady suction and oscillatory blowing/suction flow control cases. The flow equations and the turbulent model equations are solved using a fifth-order accurate weighted essentially. nonoscillatory (WENO) scheme for space discretization and a third order, total variation diminishing (TVD) Runge-Kutta scheme for time integration. Qualitatively the computed pressure distributions exhibit the same behavior as those observed in the experiments. The computed separation regions are much longer than those observed experimentally. However, the percentage reduction in the separation region in the steady suction case is closer to what was measured in the experiment. The computations did not predict the expected reduction in the separation length in the oscillatory case. The predicted turbulent quantities are two to three times smaller than the measured values pointing towards the deficiencies in the existing turbulent models when they are applied to strong steady/unsteady separated flows.

Balakumar, P.↗
NASA NTRS1990

Application of the computational aeroacoustics method to an advanced counterrotating propfan configuration

The acoustical near field of a counterrotating propeller configuration of unducted fan (UDF) type is presently predicted by means of a numerical methodology employing the transonic flow field generated by the three-dimensional numerical flow solver designated SSTAGE. This numerical approach simulates the time-averaged, three-dimensional inviscid flow field of the UDF by means of a four-stage Runge-Kutta integration scheme which marches the equations forward in time toward an asymptotic limit. The near field pressure time history is obtained directly from the flow field solution; by converting these histories with a Fourier series representation, specific data on the acoustic signal frequency spectra can be obtained.

Kim, Jinhan↗
NASA NTRS2004

Computations of Flow Over a Hump Model Using Higher Order Method With Turbulence Modeling

Turbulent separated flow over a two-dimensional hump is computed by solving the RANS equations with k-omega (SST) turbulence model for the baseline, steady suction and oscillatory blowing/suction flow control cases. The flow equations and the turbulent model equations are solved using a fifth-order accurate weighted essentially nonoscillatory (WENO) scheme for space discretization and a third order, total variation diminishing (TVD) Runge-Kutta scheme for time integration. Qualitatively the computed pressure distributions exhibit the same behavior as they are observed in the experiments. The computed separation regions are much longer than that are observed. However, the percentage reduction in the separation region in the steady suction case is closer to that was measured in the experiment. The computations did not predict the expected reduction in the separation length in the oscillatory case. The predicted turbulent quantities are two to three times smaller than that are measured and it points towards the deficiencies in the existing turbulent models when they are applied to strong steady/unsteady separated flows.

Balakumar, Ponnampalam↗