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At least 109 records · Page 6

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NASA NTRS1993

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Steinthorsson, E.↗

NASA NTRS1992

The impact of time step definition on code convergence and robustness

We have implemented preconditioning for multi-species reacting flows in two independent codes, an implicit (ADI) code developed in-house and the RPLUS code (developed at LeRC). The RPLUS code was modified to work on a four-stage Runge-Kutta scheme. The performance of both the codes was tested, and it was shown that preconditioning can improve convergence by a factor of two to a hundred depending on the problem. Our efforts are currently focused on evaluating the effect of chemical sources and on assessing how preconditioning may be applied to improve convergence and robustness in the calculation of reacting flows.

Venkateswaran, S.↗

NASA NTRS1996

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Zingg, David W.↗

NASA NTRS1993

Computational techniques for high-speed flows with viscous and chemical effects

Algorithms for solving the Euler and the Navier-Stokes equations in conjunction with chemical kinetic equations are presented. The convective flux is estimated from a quasi one dimensional interpolation procedure. Shock, contact, and expansion waves and thermochemical nonequilibrium phenomena are captured by the Lax-Friedrichs technique. Relaxation techniques were developed to enhance their effectiveness in dealing with spatial and temporal stiffness associated with the physical problems. Both explicit and implicit smoothers were implemented into the standard multigrid time stepping method. Unsteady and steady scalar problems are discussed. A perfect gas and equilibrium air shock tube problem is investigated. Numerical schemes and techniques are compared for the problems of shock and boundary layer interaction and three dimensional viscous, nonequilibrium flow encompassing an aerobrake. The results are comparable in accuracy against other high order non-oscillatory techniques. The multigrid methods are assessed using a Mach 8 flow over a complete planar body, a sphere, and a blunt delta wing at 20 deg incidence. Applying an implicit multigrid method on a nested grid of 128 by 64 nodes the reduction factor is 0.25. The central processing unit reduction factor is 2.2 after both the single and multigrid Runge-Kutta solutions converged to machine zero on a grid of 37 by 41 by 73 nodes.

Li, C. P.↗

NASA NTRS1991

Time-dependent aerodynamic analysis of ducted and unducted propfans at angle of attack

A three-dimensional unsteady aerodynamic analysis is described for predicting the time-dependent flow about ducted and unducted propfans operating at angle of attack. Although the freestream is assumed to be uniform, the flow relative to the rotating blades varies with circumferential position, resulting in an inherent unsteadiness due to the nonaxial inflow. The time-dependent Euler equations are solved utilizing a Runge-Kutta time-stepping scheme. The analysis is based on a finite-volume discretization employing a multiple-block grid network. To permit the use of large calculation time steps, an implicit residual smoothing scheme previously tested for unsteady flow calculations in two dimensions is extended to three spatial dimensions. For unducted propfans, a single H-type grid block is used for each blade passage to determine the time-periodic flowfield. For ducted propfans (ultra-high bypass fans) a body-centered C-type grid is wrapped about the cowl to improve the accuracy of the analysis in the high gradient flow region near the cowl leading edge. Numerical results are compared with available data for both ducted and unducted propfans operating at angle of attack.

Hall, Edward J.↗

NASA NTRS1985

Spectral methods for modeling supersonic chemically reacting flow fields

A numerical algorithm was developed for solving the equations describing chemically reacting supersonic flows. The algorithm employs a two-stage Runge-Kutta method for integrating the equations in time and a Chebyshev spectral method for integrating the equations in space. The accuracy and efficiency of the technique were assessed by comparison with an existing implicit finite-difference procedure for modeling chemically reacting flows. The comparison showed that the procedure presented yields equivalent accuracy on much coarser grids as compared to the finite-difference procedure with resultant significant gains in computational efficiency.

Drummond, J. P.↗

NASA NTRS1992

Three-dimensional simulation of slender delta wing rock and divergence

Computational simulation of three-dimensional flows around a delta wing undergoing rock and roll-divergence motions is presented. The problem is a multidisciplinary one where fluid-dynamics equations and rigid-body-dynamics equations are sequentially solved. For the fluid-dynamics part, the unsteady Euler equations, which are written relative to a moving frame of reference, are solved using an implicit, approximately-factored, central-difference, finite-volume scheme. For the rigid-body dynamics part, the Euler equation of rigid-body rolling motion is solved using a four-stage Runge-Kutta scheme. Since the applications do not include deforming wings or relative-rigid-body motions, the computational-fluid-dynamics grid, which is fixed in the moving frame of reference, does not need to be updated once it is generated.

Kandil, Osama A.↗

NASA NTRS1993

Simulation of tail buffet using delta wing-vertical tail configuration

Computational simulation of the vertical tail buffet problem is accomplished using a delta wing-vertical tail configuration. Flow conditions are selected such that the wing primary-vortex cores experience vortex breakdown and the resulting flow interacts with the vertical tail. This multidisciplinary problem is solved successively using three sets of equations for the fluid flow, aeroelastic deflections and grid displacements. For the fluid dynamics part, the unsteady, compressible, full Navier-Stokes equations are solved accurately in time using an implicit, upwind, flux-difference splitting, finite-volume scheme. For the aeroelastic part, the aeroelastic equation for bending vibrations is solved accurately in time using the Galerkin method and the four-stage Runge-Kutta scheme. The grid for the fluid dynamics computations is updated every few time steps using a third set of interpolation equations. The computational application includes a delta wing of aspect ratio 1 and a rectangular vertical tail of aspect ratio 2, which is placed at 0.5 root-chord length downstream of the wing trailing edge. The wing angle of attack is 35 deg and the flow Mach number and Reynolds number are 0.4 and 10,000, respectively.

Kandil, Osama A.↗

NASA NTRS1988

An explicit Runge-Kutta method for 3D turbulent incompressible flows

A computer code has been developed to solve for the steady-state solution of the 3D incompressible Reynolds-averaged Navier-Stokes equations. The approach is based on the cell-center, central-difference, finite-volume formulation and an explicit one-step, multistage Runge-Kutta time-stepping scheme. The Baldwin-Lomax turbulence model is used. Techniques to accelerate the rate of convergence to a steady-state solution include the preconditioned method, the local time stepping, and the implicit residual smoothing. Improvements in computational efficiency have been demonstrated in several areas. This numerical procedure has been used to simulate the turbulent horseshoe vortex flow around an airfoil/flat-plate juncture.

Sung, Chao-Ho↗

NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗

NASA NTRS1987

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Chima, Rodrick V.↗

NASA NTRS1987

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

Chima, Rodrick V.↗

NASA NTRS1998

Computational Investigation and Validation of Twin-Tail Buffet Response Including Dynamics and Control

Multidisciplinary tools for prediction of single rectangular-tail buffet are extended to single swept-back-tail buffet in transonic-speed flow, and multidisciplinary tools for prediction and control of twin-tail buffet are developed and presented. The configuration model consists of a sharp-edged delta wing with single or twin tails that are oriented normal to the wing surface. The tails are treated as cantilevered beams fixed at the root and allowed to oscillate in both bending and torsion. This complex multidisciplinary problem is solved sequentially using three sets of equations on a dynamic single or multi-block grid structure. The first set is the unsteady, compressible, Reynolds-averaged Navier-Stokes equations which are used for obtaining the flow field vector and the aerodynamic loads on the tails. The Navier-Stokes equations are solved accurately in time using the implicit, upwind, flux-difference splitting, finite volume scheme. The second set is the coupled bending and torsion aeroelastic equations of cantilevered beams which are used for obtaining the bending and torsion deflections of the tails. The aeroelastic equations'are solved accurately in time using, a fifth-order-accurate Runge-Kutta scheme. The third set is the grid-displacement equations and the rigid-body dynamics equations, which are used for updating the grid coordinates due to the tail deflections and rigid-body motions. The tail-buffet phenomenon is predicted for highly-swept, single vertical tail placed at the plane of geometric symmetry, and for highly-swept, vertical twin tails placed at three different spanwise separation distances. The investigation demonstrates the effects of structural inertial coupling and uncoupling of the bending and torsion modes of vibration, spanwise positions of the twin-tail, angle of attack, and pitching and rolling dynamic motions of the configuration model on the tail buffet loading and response. The fundamental issue of twin-tail buffet alleviation is addressed using two active flow-control methods. These methods are the tangential leading-edge blowing and the flow suction from the leading-edge vortex cores along their paths. Qualitative and quantitative comparisons with the available experimental data are presented. The comparisons indicate that the present multidisciplinary aeroelastic analysis tools are robust, accurate and efficient.

Kandil, Osama A.↗

NASA NTRS1985

Accuracy of schemes for the Euler equations with non-uniform meshes

The effect of non-uniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme based on a finite volume formulation is considered. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are presented in both two- and three-space dimensions. Applications to finite difference and implicit algorithms are also given.

Turkel, E.↗

NASA NTRS1991

Effects of leading-edge flap oscillation on unsteady delta wing flow and rock control

The isolated and interdisciplinary problems of unsteady fluid dynamics and rigid-body dynamics and control of delta wings with and without leading-edge flap oscillation are considered. For the fluid dynamics problem, the unsteady, compressible, thin-layer Navier-Stokes (NS) equations, which are written relative to a moving frame of reference, are solved along with the unsteady, linearized, Navier-displacement (ND) equations. The NS equations are solved for the flowfield using an implicit finite-volume scheme. The ND equations are solved for the grid deformation, if the leading-edge flaps oscillate, using an ADI scheme. For the dynamics and control problem, the Euler equation of rigid-body rolling motion for a wing and its flaps are solved interactively with the fluid dynamics equations for the wing-rock motion and subsequently for its control. A four-stage Runge-Kutta scheme is used to explicitly integrate the dynamics equation.

Kandil, Osama A.↗

NASA NTRS1992

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Cannizzaro, Frank E.↗

NASA NTRS1994

Fourth order difference methods for hyperbolic IBVP's

Fourth order difference approximations of initial-boundary value problems for hyperbolic partial differential equations are considered. We use the method of lines approach with both explicit and compact implicit difference operators in space. The explicit operator satisfies an energy estimate leading to strict stability. For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique. We also present numerical experiments for the linear advection equation and Burgers' equation with discontinuities in the solution or in its derivative. The first equation is used for modeling contact discontinuities in fluid dynamics, the second one for modeling shocks and rarefaction waves. The time discretization is done with a third order Runge-Kutta TVD method. For solutions with discontinuities in the solution itself we add a filter based on second order viscosity. In case of the non-linear Burger's equation we use a flux splitting technique that results in an energy estimate for certain different approximations, in which case also an entropy condition is fulfilled. In particular we shall demonstrate that the unsplit conservative form produces a non-physical shock instead of the physically correct rarefaction wave. In the numerical experiments we compare our fourth order methods with a standard second order one and with a third order TVD-method. The results show that the fourth order methods are the only ones that give good results for all the considered test problems.

Gustafsson, Bertil↗

NASA NTRS1993

A multigrid nonoscillatory method for computing high speed flows

A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.

Li, C. P.↗