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NASA NTRS1985

Use of a hyperbolic grid generation scheme in simulating supersonic viscous flow about three-dimensional winged configuration

The present paper describes a numerical mesh generation technique to be used with an implicit finite difference method for simulating visous supersonic flow about low-aspect-ratio wing body configurations using a single grid strategy. The computational domain is segmented into multiple regions, with borders located in supersonic areas to avoid the otherwise costly interfacing procedure between adjacent segments. The numerical procedure is applied to calculate the turbulent flow around the shuttle orbiter and a canard projectile at supersonic free stream Mach number.

Rizk, Y. M.↗

NASA NTRS1985

CAG12 - A CSCM based procedure for flow of an equilibrium chemically reacting gas

The Conservative Supra Characteristic Method (CSCM), an implicit upwind Navier-Stokes algorithm, is extended to the numerical simulation of flows in chemical equilibrium. The resulting computer code known as Chemistry and Gasdynamics Implicit - Version 2 (CAG12) is described. First-order accurate results are presented for inviscid and viscous Mach 20 flows of air past a hemisphere-cylinder. The solution procedure captures the bow shock in a chemically reacting gas, a technique that is needed for simulating high altitude, rarefied flows. In an initial effort to validate the code, the inviscid results are compared with published gasdynamic and chemistry solutions and satisfactorily agreement is obtained.

Green, M. J.↗

NASA NTRS1986

Navier-Stokes computations for circulation controlled airfoils

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Pulliam, T. H.↗

NASA NTRS1986

Wall reflection of a viscous vortex ring

The behavior of a viscous axisymmetric vortex ring being reflected from a wall is investigated. The incompressible Navier-Stokes equations formulated in terms of the vorticity function and vector potential are numerically integrated by implicit finite difference methods. To specify the vector potential at a far boundary from the wall, the existing integral method used so far only for an unbounded domain is modified by a kind of image method. The trajectory of the vortex ring calcualted as a result closely resembles that observable from the experiment.

Sa, J. Y.↗

NASA NTRS1986

Hierarchial implicit dynamic least-square solution algorithm

This paper develops an implicit type transient solution strategy which possesses hierarchial levels of application. In particular, due to the manner of formulation, stiffness updating, assembly inversion, solution constraint, as well as iteration are all performed at a localized level. The level of iterative calculations depends on the type of hierarchial partitioning employed, namely degree of freedom, nodal, elemental, material/nonlinear group, substructural, and so on. Since the iterative solution process and application of constraints are applied at a local level, the resulting so-called hierarchial implicit solution algorithm possesses very stable and efficient numerical properties and is highly storage efficient. To demonstrate the scheme, the results of several benchmark examples are presented. These enable comparisons with the Newton-Raphson solved implicit transient solution method. Overall the comparisons illustrate the superior stability and efficiency of the hierarchial scheme.

Padovan, J.↗

NASA NTRS1986

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Imlay, S. T.↗

NASA NTRS1987

Development of upwind schemes for the Euler equations

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct relaxation methods for unfactored implicit upwind schemes, which in turn can be exploited to construct space-marching procedures for even the unsteady Euler equations. A major part of the report describes time- and space-marching procedures for solving the Euler equations in 2-D, 3-D, Cartesian, and curvilinear coordinates. Along with many illustrative examples, several results of efficient computations on 3-D supersonic flows with subsonic pockets are presented.

Chakravarthy, Sukumar R.↗

NASA NTRS1987

Navier-Stokes computations for circulation control airfoils

Pulliam, Thomas H.↗

NASA NTRS1988

Liquid sprays and flow studies in the direct-injection diesel engine under motored conditions

A two dimensional, implicit finite difference method of the control volume variety, a two equation model of turbulence, and a discrete droplet model were used to study the flow field, turbulence levels, fuel penetration, vaporization, and mixing in diesel engine environments. The model was also used to study the effects of engine speed, injection angle, spray cone angle, droplet distribution, and intake swirl angle on the flow field, spray penetration and vaporization, and turbulence in motored two-stroke diesel engines. It is shown that there are optimum conditions for injection, which depend on droplet distribution, swirl, spray cone angle, and injection angle. The optimum conditions result in good spray penetration and vaporization and in good fuel mixing. The calculation presented clearly indicates that internal combustion engine models can be used to assess, at least qualitatively, the effects of injection characteristics and engine operating conditions on the flow field and on the spray penetration and vaporization in diesel engines.

Nguyen, Hung Lee↗

NASA NTRS1988

An algorithm for unsteady flows with strong convection

An implicit ADI numerical method for the calculation of 2-D unsteady flows with strong convection effects is described. The method is based on the conventional Crank-Nicholson approach for parabolic equations but an upwind-downwind differencing is used for the first order spatial derivatives associated with convection. The differencing is carried out in the current and previous time plane in such a way that the algorithm is second order accurate in both space and time. The difference equations are factored into sequential operators, one in each independent spatial variable; the solution at each time step may then be computed as a sequence of tridiagonal matrix problems. The method may be used in a noniterative manner although iteration at each time step is recommended in situations where the effects of convection are strong.

Peridier, Vallorie↗

NASA NTRS1989

Unsteady Navier-Stokes computations over airfoils using both fixed and dynamic meshes

A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Rumsey, Christopher L.↗

NASA NTRS1989

Numerical investigation of the control of the secondary instability process in boundary layers

A numerical model has been developed for investigating boundary layer transition control for a flat plate boundary layer. Active control of a periodically forced boundary layer in an incompressible fluid is studied using surface heating techniques. The spatially evolving boundary layer is simulated. The Navier-Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. Temperature perturbations are introduced locally along finite heater strips to directly attenuate the instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Active control of small amplitude two-dimensional and three-dimensional disturbances is numerically simulated. With proper phase control, in-phase reinforcement and out-of-phase attenuation are demonstrated. A receptivity study of the localized temperature perturbations is made. It is shown that narrow heater strips are more receptive in that they maximize the amplitude level of the disturbances in the flow. Active control of the early stages of the fundamental breakdown process is also numerically simulated. Control is achieved with either two-dimensional or three-dimensional control inputs.

Kral, L. D.↗

NASA NTRS1990

Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows

A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.

Hsu, C.-H.↗

NASA NTRS1990

Numerical study of vortical flow over a sideslipping delta wing

The three-dimensional vortical viscous flow past a sideslipping delta wing at a high angle of attack is numerically investigated. A computational method for calculating low-speed viscous flowfields is developed. The time-iterative method uses an implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. An algebraic turbulence model is implemented to account for the eddy viscosity. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. Computed results are compared with experimental data.

Hsu, C.-H.↗

NASA NTRS1990

Mapping unstructured grid problems to the connection machine

We present a highly parallel graph mapping technique that enables one to solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretizated partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit the high performance promised by massively parallel computing. To eliminate this bottleneck, we map the graph of the irregular problem to the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. We show that, in comparison to a naive assignment of processors, our heuristic mapping algorithm significantly reduces the communication time on the Connection Machine, CM-2.

Hammond, Steven W.↗

NASA NTRS1990

Numerical simulation of the control of the three-dimensional transition process in boundary layers

Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.

Kral, L. D.↗

NASA NTRS1991

An assessment of computational fluid dynamic techniques in the analysis and design of turbomachinery - The 1990 Freeman Scholar Lecture

Various computational fluid dynamic techniques are reviewed focusing on the Euler and Navier-Stokes solvers with a brief assessment of boundary layer solutions, and quasi-3D and quasi-viscous techniques. Particular attention is given to a pressure-based method, explicit and implicit time marching techniques, a pseudocompressibility technique for incompressible flow, and zonal techniques. Recommendations are presented with regard to the most appropriate technique for various flow regimes and types of turbomachinery, incompressible and compressible flows, cascades, rotors, stators, liquid-handling, and gas-handling turbomachinery.

Lakshminarayana, B.↗

NASA NTRS1991

Elliptic flow computation by low Reynolds number two-equation turbulence models

A detailed comparison of ten low-Reynolds-number k-epsilon models is carried out. The flow solver, based on an implicit approximate factorization method, is designed for incompressible, steady two-dimensional flows. The conservation of mass is enforced by the artificial compressibility approach and the computational domain is discretized using centered finite differences. The turbulence model predictions of the flow past a hill are compared with experiments at Re = 10 exp 6. The effects of the grid spacing together with the numerical efficiency of the various formulations are investigated. The results show that the models provide a satisfactory prediction of the flow field in the presence of a favorable pressure gradient, while the accuracy rapidly deteriorates when a strong adverse pressure gradient is encountered. A newly proposed model form that does not explicitly depend on the wall distance seems promising for application to complex geometries.

Michelassi, V.↗