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NASA NTRS1984

Evaluation of a velocity-split solution of the Navier-Stokes equations for fighter forebodies

A velocity-splitting method of solving the three-dimensional Navier-Stokes equations, originally designed for afterbody flows, is examined for its applicability for predicting fighter forebody flows. Results from the AFTEND Code are compared with wind tunnel data for two fighter configurations at a Mach number of 0.9 and angles-of-attack from 0 deg to 20 deg. Results compare well with data, and in areas where data do not exist, the viscous AFTEND results show realistic effects of viscosity compared to inviscid predictions. The inviscid results themselves are in general superior to results obtained from a small-disturbance transonic potential code.

Yaros, S. F.↗

NASA NTRS1984

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Hall, P.↗

NASA NTRS1985

Numerical simulation of self-excited oscillations in a ramjet inlet-diffuser flow

This paper describes numerical simulations of self-excited oscillations in a two-dimensional transonic inlet-diffuser flow by solving the Navier-Stokes equations with a two-equation turbulence model. The calculated amplitudes of oscillations for the terminal shock and the velocity fields compare well with experimental measurements; however, the predicted frequency of oscillations is about 50 percent higher. The formation of a pair of downstream-traveling, counter-rotating vortices at each cycle of velocity fluctuations, as reported experimentally, is vividly revealed by the numerical results.

Hsieh, T.↗

NASA NTRS1984

Multi-grid technique for the solution of incompressible Navier-Stokes equations

A computationally efficient method is proposed for obtaining fine-mesh solutions of the Navier-Stokes equations for high-Re flow, including separation. The method involves implementing a multi-grid solution procedure with suitably chosen elements, such that the resulting overall solution technique is efficient as well as robust. The robustness and efficiency of the solution technique are demonstrated by applying it to three model problems: flow in a driven cavity, downstream asymptotic flow in curved ducts of square and polar sections, and Newmann boundary-value problem in clustered curvilinear orthogonal coordinates.

Ghia, K. N.↗

NASA NTRS1985

The effects of compliant walls on transition and turbulence

Two theoretical approaches to the phenomenon of drag reduction by a compliant wall are proposed. One is to study the limit cycle oscillations of the Navier-Stokes equations for a boundary layer flow over a compliant wall or a Poiseuille flow in a channel with a compliant wall. The other is a complementary study of a simpler, sequential model, which partially decouples the fluid and wall motions. In this approach, a 'Total Model' is constructed from suitable component models. While the first study is more rigorously based, it will be initially limited, by computational constraints, to relatively low Reynolds numbers. The second, more approximate approach, will allow consideration of a fully developed turbulent flow. The Total Model will predict the compliant wall motion accurately, but will not per se be sufficient to predict the skin friction drag. However, once the wall motion is known, the skin friction drag and the pressure drag can be computed separately, using one of the existing models.

Dowell, E. H.↗

NASA NTRS1987

CSCM methodology for slot injection cooled cavity flow design in a high enthalpic stream

The CSCM method for the compressible Navier-Stokes equations is applied to study design factors in a slot injection cooled cavity flow in the side of a 2-D wedge body in a high enthalpy free stream. The flow geometry is being designed and will be tested in an arc jet tunnel at NASA-Ames Research Center. Objectives of the design are to provide adequate thermal protection for and minimize aero-optical distortion in the path above a window located in the bottom of the cavity. Among design issues, are the geometry of and flow conditions in the expanding section of the supersonic slot injection nozzle. Here, for straight walled nozzles, two geometries are considered for the upper nozzle lip between the hot, high speed outer flow and the colder, denser cooling flow. The two lip geometries - thick, square and thin, wedge - as the result of associated widely differing base/wake flows also exhibit different and interesting viscous-inviscid flow structures near the ramp termination to the cavity. For the thin lip case, the consequences on flow quality of off design nozzle conditions relative to matching pressure with the outer flow are explored.

Bardina, Jorge↗

NASA NTRS1988

Fluid-thermal-structural study of aerodynamically heated leading edges

A finite element approach for integrated fluid-thermal-structural analysis of aerodynamically heated leading edges is presented. The Navier-Stokes equations for high speed compressible flow, the energy equation, and the quasi-static equilibrium equations for the leading edge are solved using a single finite element approach in one integrated, vectorized computer program called LIFTS. The fluid-thermal-structural coupling is studied for Mach 6.47 flow over a 3-in diam cylinder for which the flow behavior and the aerothermal loads are calibrated by experimental data. Issues of the thermal-structural response are studied for hydrogen-cooled, super thermal conducting leading edges subjected to intense aerodynamic heating.

Deuchamphai, Pramote↗

NASA NTRS1987

Vectorizable implicit algorithms for the flux-difference split, three-dimensional Navier-Stokes equations

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computation of vortical flow over a sharp-edged, thin delta wing has been chosen as a common numerical test case. The convergence of the algorithms is discussed and the accuracy of the computed flow-field results is assessed. The validity of the present results are demonstrated by a comparison with experimental data.

Hartwich, P. M.↗

NASA NTRS1989

Fluid-thermal-structural interaction of aerodynamically heated leading edges

A two-dimensional finite element approach is presented for the integrated fluid-thermal-structural analysis of aerodynamically heated leading edges. The approach is combined with an adaptive unstructured remeshing technique to solve the Navier-Stokes equations for high speed compressible flow, the energy equation for the structure thermal response, and the quasi-static equilibrium equations for the structural response. Coupling and interaction between the three disciplines are demonstrated using two applications for high speed flow over a cylinder and a simulated engine leading edge verification test.

Dechaumphai, Pramote↗

NASA NTRS1990

Shock interference studies on a circular cylinder at Mach 16

This paper presents the results of a computational study on the shock interference problems on a cylindrical body typical of an engine inlet cowl leading edge at a nominal Mach number of 16. The two-dimensional Navier-Stokes equations are solved assuming the flow to be in chemical and thermal equilibrium and using a finite element method. The algorithm employs a cell-centered fully implicit upwind scheme. Adaptively generated unstructured meshes of triangles and quadrilaterals are employed. Under certain conditions the finite element code resulted in oscillatory solutions for shock interference at Mach 16. Some of the causes of the unsteady behavior are identified, and to the extent possible, such situations are avoided in the present application. Two shock interference conditions involving a Type IV (supersonic jet) and a Type III (attaching shear layer) are solved. The results are compared with available experimental data and reasonable agreement is observed. A semi-empirical method is also used to estimate the maximum surface heat flux and static pressure.

Prabhu, Ramadas K.↗

NASA NTRS1990

Numerical prediction of turbulent flow over airfoil sections with a new nonequilibrium turbulence model

A new nonequilibrium turbulence closure model has been developed for computing wall bounded two-dimensional turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present model has been evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated turbulent flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the new nonequilibrium turbulence model accurately captures the history effects of convection and diffusion on turbulence.

Ahmed, S.↗

NASA NTRS1990

Algebraic turbulence modeling for unstructured and adaptive meshes

An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

Mavriplis, Dimitri J.↗

NASA NTRS1990

Numerical simulation of particle-wave interaction in boundary layers

The effects of wall injection and particle motion on the spatial stability of two-dimensional plane channel flow are investigated. For this purpose, an accurate Navier-Stokes solver to simulate the space-time evolution of disturbances in three-dimensional flows has been developed. The code is operational on the NASA Langley CRAY2 and can be ported to any other supercomputer. The code has been tested extensively in tracking the spatial evolution of two-dimensional disturbances in plane channel flow and provided excellent agreement with the linear theory including at the inflow/outflow boundaries. Preliminary calculations have been performed to investigate the effects of stationary and moving sources of vortical disturbances simulating a particle traveling in the flow field. Results suggest that even at very low amplitudes, vortical disturbances act as amplifiers on the Tollmien-Schlichting waves promoting rapid instability. It is also found that slow moving particles are more dangerous than both stationary and fast moving particles for the same disturbance levels.

Biringen, S.↗

NASA NTRS1991

Navier-Stokes simulation of a close-coupled canard-wing-body configuration

The thin-layer Navier-Stokes equations are solved for the flow about a coplanar close-coupled canard-wing-body configuration at a transonic Mach number of 0.90 and at angles of attack ranging from 0 to 12 degrees. The influence of the canard on the wing flowfield, including canard-wing vortex interaction and wing vortex breakdown, is investigated. A study of canard downwash and canard leading-edge vortex effects, which are the primary mechanisms of the canard-wing interaction, is emphasized. Comparisons between the computations and experimental measurements of surface pressure coefficients, lift, drag and pitching moment data are favorable. A grid refinement study for configurations with and without canard shows that accurate results are obtained using a refined grid for angles of attack where vortex burst is present. At an angle of attack of approximately 12 deg, favorable canard-wing interaction which delays wing vortex breakdown is indicated by the computations and is in good agreement with experimental findings.

Tu, Eugene L.↗

NASA NTRS1991

Unsteady Navier-Stokes computations on a wing-body configuration in ramp motions

Unsteady Navier-Stokes computations are conducted for transonic flows over a wing-body configuration undergoing prescribed ramp motions. The ramp motion from 0 to 15 deg includes angles of attack where vortex breakdown is observed experimentally. The vortex breakdown is found to be delayed until after the ramp motion ends. The dynamic effects on the loads are also demonstrated. The moment coefficient is found to be sensitive to the effect of the virtual mass of the fluid. To verify the numerical results, a grid refinement study has been performed for both steady and unsteady flow conditions, by using up to approximately one million grid points. The results show that the coarse grid can give integrated quantities reasonably well, whereas the finer grids give a more detailed flow structure. Comparisons are also made with available steady-state experimental data.

Obayashi, Shigeru↗

NASA NTRS1991

A Navier-Stokes Solution of Hull-Ring Wing-Thruster Interaction

Navier-Stokes simulations of high Reynolds number flow around an axisymmetric body supported in a water tunnel were made. The numerical method is based on a finite-differencing high resolution second-order accurate implicit upwind scheme. Four different configurations were investigated, these are: (1) barebody; (2) body with an operating propeller; (3) body with a ring wing; and (4) body with a ring wing and an operating propeller. Pressure and velocity components near the stern region were obtained computationally and are shown to compare favorably with the experimental data. The method correctly predicts the existence and extent of stern flow separation for the barebody and the absence of flow separation for the three other configurations with ring wing and/or propeller.

Yang, C.-I.↗

NASA NTRS1992

A systematic experimental and computational investigation of a class of contoured wall fuel injectors

The performance of contoured wall fuel injectors for scramjet engine applications is considered. These fuel injectors were aimed at augmenting mixing through axial vorticity production arising from interaction of the fuel/air interface with an oblique shock. The effects of incoming boundary layer height, injector spacing, and injectant to freestream pressure and velocity ratios are examined. Results from 3D flow field surveys and Navier-Stokes simulations are presented.

Waitz, Ian A.↗

NASA NTRS1992

Effect of canard deflection on close-coupled canard-wing-body aerodynamics

The thin-layer Navier-Stokes equations are solved for the flow about a canard-wing-body configuration at transonic Mach numbers of 0.85 and 0.90, angles of attack from -4 to 10 degrees and canard deflection angles from -10 to +10 degrees. Effects of canard deflection on aerodynamic performance, including canard-wing vortex interaction, are investigated. Comparisons with experimental measurements of surface pressures, lift, drag and pitching moments are made to verify the accuracy of the computations. The results of the study show that the deflected canard downwash not only influences the formation of the wing leading-edge vortex, but can cause the formation of an unfavorable vortex on the wing lower surface as well.

Tu, Eugene L.↗