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NASA NTRS1984

Fast solutions to the steady state compressible and incompressible fluid dynamic equations

For low speed flows the use of the compressible fluid dynamic equations is inefficient. The use of an explicit scheme requires delta t to be bounded by 1/c. However, the physical parameters change over time scales of order 1/u which is much larger. Hence, it is not appropriate to use explicit schemes for very subsonic flows. Implicit schemes are hard to vectorize and frequently do not converge quickly for very subsonic flows. If one is only interested in the steady state then a minor change to an existing code can greatly increase the efficiency of an explicit method. Even when using an implicit method the proposed changes increase the efficiency of the scheme. The Euler equations for low speed flows will be considered first and then incompressible flows. The method is generalized to include viscous effects. Supersonic flow is accelerated by essentially decoupling the equations.

Turkel, E.↗

NASA NTRS1983

The efficient solution of transonic wing flow fields

An evaluation of the transonic-wing-analysis computer code TWING is presented. TWING utilizes a fully implicit, approximate-factorization iteration scheme to solve the full-potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations have been analyzed, and comparisons of computed results have been made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative, full-potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations, including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

Holst, T. L.↗

NASA NTRS1984

Transonic analysis of canted winglets

A computational method developed to provide a transonic analysis for upper/lower surface wing-tip mounted winglets is described. Winglets with arbitrary planform, cant and toe angle, and airfoil section can be modeled. The embedded grid approach provides high flow field resolution and the required geometric flexibility. In particular, coupled Cartesian/cylindrical grid systems are used to model the complex geometry presented by canted upper/lower surface winglets. A new rotated difference scheme is introduced in order to maintain the stability of the small-disturbance formulation in the presence of large spanwise velocities. Wing and winglet viscous effects are modeled using a two-dimensional 'strip' boundary layer analysis. Correlations with wind tunnel and flight test data for three transport configurations are included.

Rosen, B. S.↗

NASA NTRS1984

Euler and Navier-Stokes solutions for supersonic shear flow past a circular cylinder

Euler and Navier-Stokes solutions of the supersonic shear flow past a circular cylinder are obtained. These solutions are used to study the basic flow structure around the cylinder. Both the inviscid and viscous calculations show the formation of a large recirculating flow region around the front stagnation point. The calculations further show that the overall size of the recirculating region is approximately the same for the Euler and Navier-Stokes solutions but the inside structure is quite different. The inviscid flow shows only one vortex whereas the viscous flow shows two vortices inside the recirculating flow region. The inner vortex in the Navier-Stokes solution is formed primarily due to the viscous effects near the body surface and its size depends upon the Reynolds number. It is found that with increasing Reynolds number, the inner vortex diminishes in size and the Navier-Stokes solution asymptotically approaches the Euler solution. These results indicate that the Euler equations may correctly predict certain high Reynolds number separation phenomenon in flows with natural inviscid vorticity source.

Kumar, A.↗

NASA NTRS1984

Interference from slotted walls

Wall interference is made predominant in tunnel models and by wall geometries to facilitate the study of slot flow. The viscous effects in slots are studied by two dimensional measurements of flow. Wall interference is assessed by measuring pressure distributions at two levels near the walls. Interference on lifting delta wings is calculated. Pressure distributions at inner boundaries show basis axisymetries between the pressure side and the suction side, pointing to the necessity of having wider slots on the pressure side.

Berndt, S. B.↗

NASA NTRS1984

Thrust chamber performance using Navier-Stokes solution

The viscous, axisymmetric flow in the thrust chamber of the space shuttle main engine (SSME) was computed on the CRAY 205 computer using the general interpolants method (GIM) code. Results show that the Navier-Stokes codes can be used for these flows to study trends and viscous effects as well as determine flow patterns; but further research and development is needed before they can be used as production tools for nozzle performance calculations. The GIM formulation, numerical scheme, and computer code are described. The actual SSME nozzle computation showing grid points, flow contours, and flow parameter plots is discussed. The computer system and run times/costs are detailed.

Chan, J. S.↗

NASA NTRS1985

NAS - Supercomputing master tool for aeronautics

Features, performance objectives and applications planned for the NASA National Aerodynamics Simulator (NAS) are outlined. NAS was conceived in the 1970s as a means to performing numerical aerodynamic simulations beyond the scope of wind tunnel testing for high-speed flight. Present supercomputers cannot deal with problems exhibiting strongly coupled viscous effects, which are being increasingly more accurately represented by approximations to the full Navier-Stokes equations. Located at the NASA-Ames Center, the NAS will by 1990 comprise a distributed computer network capable of a 4 Gflop computing rate and have a memory capacity of 1 billion 64-bit words. Remote access to the system through UNIX-based microcomputers will be available through land lines and satellite links. New supercomputers will be tested on the system without disturbing ongoing work. The core machine will be a Cray-2 with a 2 Gflop rate.

Bailey, F. R.↗

NASA NTRS1985

Radiative viscous-shock-layer analysis of Fire, Apollo, and PAET flight data

Equilibrium, radiating viscous-shock-layer solutions are obtained for a number of trajectory points of the Fire II, Apollo 4, and PAET experimental flight vehicles. Convective heating rates calculated by a benchmark code agree well, except at high altitudes corresponding to low densities, with two engineering correlations. Calculated radiation intensities are compared with the flight radiometer data and with inviscid flow results. Differences as great as 70 percent are observed between measured data and the viscous calculations. Viscous effects reduce the intensity toward the wall, because of boundary-layer absorption, by as much as 30 percent, compared with inviscid intensities. Preliminary chemical and thermal nonequilibrium flow calculations along a stagnation streamline for a PAET trajectory predict enhancement of radiation owing to chemical relaxation. Stagnation point solutions are also presented for future air-assisted orbital transfer vehicle geometries with nose radii ranging from 0.3 to 15 m.

Balakrishnan, A.↗

NASA NTRS1983

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

The prediction of the complete flow field in a turbine passage is an extremely difficult task due to the complex three dimensional pattern which contains separation and attachment lines, a saddle point and horseshoe vortex. Whereas, in principle such a problem can be solved using full Navier-Stokes equations, in reality methods based on a Navier-Stokes solution procedure encounter difficulty in accurately predicting surface quantities (e.g., heat transfer) due to grid limitations imposed by the speed and size of the existing computers. On the other hand the overall problem is strongly three dimensional and too complex to be analyzed by the current design methods based on inviscid and/or viscous strip theories. Thus there is a strong need for enhancing the current prediction techniques through inclusion of 3-D viscous effects. A potentially simple and cost effective way to achieve this is to use a prediction method based on three dimensional boundary layer (3-DBL) theory. The major objective of this program is to assess the applicability of such a 3-DBL approach for the prediction of heat loads, boundary layer growth, pressure losses and streamline skewing in critical areas of a turbine passage. A brief discussion of the physical problem addressed here along with the overall approach is presented.

Vatsa, V. N.↗

NASA NTRS1985

Theoretical and experimental flow fields for a supersonic cruise fighter forebody

The capability of two numerical methods to predict the flow field about a representative supersonic cruise aircraft was examined. The two codes were a small-disturbance transonic program of Boppe and a conservative form full-potential transonic program of Shankar and Szema. For the former code, comparisons were made with wind-tunnel data at Mach numbers of 0.6, 0.9, and 1.2 and angles of attack of 0 deg, 5 deg, and 10 deg (7.5 deg instead of 10 deg at a Mach number of 1.2). Predictions from the two codes were compared at a Mach number of 1.2 and an angle of attack of 7.5 deg. The comparison criteria were contours of local angle of attack, local angle of sideslip, and local Mach number. The comparisons indicated that both codes may be considered useful for design applications, depending on the degree of accuracy required by the user's solution. Both solutions show an inaccuracy in their predictions, particularly as Mach number and/or angle of attack increases, because of their lack of viscous effects and any mechanisms to predict vortex development.

Yaros, S. F.↗

NASA NTRS1986

Energetics and optimum motion of oscillating lifting surfaces of finite span

In certain modes of animal propulsion in nature, such as bird flight and fish swimming, the efficiency compared to man-made vehicles is very high. In such cases, wing and tail motions are typically associated with relatively high Reynolds numbers, where viscous effects are confined to a thin boundary layer at the surface and a thin trailing wake. The propulsive forces, which are generated primarily by the inertial forces, can be calculated from potential-flow theory using linearized unsteady-wing theory (for small-amplitude oscillations). In the present study, a recently developed linearized, low-frequency, unsteady lifting-line theory is employed to calculate the (sectional and total) energetic quantities and optimum motion of an oscillating wing of finite span.

Ahmadi, A. R.↗

NASA NTRS1986

A numerical study of shock wave diffraction by a circular cylinder

The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross (1961) which included both experimental schlieren pictures and theoretical calculations using Whitham's ray-shock theory and results of the present finite difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects which are not accounted for by the Euler equations.

Yang, J.-Y.↗

NASA NTRS1987

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗

NASA NTRS1987

A study of multi-body aerodynamic interference at transonic Mach numbers

A wind tunnel experiment involving single, double, and triple combinations of mutually interfering generic, unfinned aircraft stores has been conducted. Each combination of stores was tested at Mach numbers from 0.60 to 1.20 and at angles of attack from 0 to 25 deg for the single store and from 0 to 6 deg for the double and triple store configurations. Extensive axial and circumferential pressure and flow visualization data at each store location were obtained. Euler solutions for each configuration at 0 deg incidence have been generated and compared with experimental data. This comparison indicates an Euler flow solver can yield accurate predictions of the location and magnitude of multibody interference provided an appropriate grid is used and the viscous effects associated with these configurations remain small. The data indicate multibody interference in the transonic region increases as the freestream Mach number approaches 1 from either direction, and subsides as the Mach number moves away from sonic conditions. This interference is characterized by a large, localized reduction in pressure on the inboard surfaces of the bodies which results in forces that draw the configuration closer together.

Cottrell, Charles J.↗

NASA NTRS1987

The rationale for an aeroassist flight experiment

The states of several technologies are reviewed which are critical to the design of an aeroassisted orbital transfer vehicle. In these technologies, advancements are needed which hinge on obtaining new flight data. While some of the work can be done with the wind tunnel and computational disciplines, much of the required new data are tied to finite chemical reaction rates, possible thermal nonequilibrium, high flow enthalpy, and strong viscous effects. Because these effects cannot be modeled adequately in ground-based facilities, computational methods lack adequate verification to allow committing to the design of an aeroassist vehicle. Thus a new flight experiment is being planned by NASA to gather the required data. The flight experiment and associated instrumentation which NASA is proposing is discussed briefly.

Jones, Jim J.↗

NASA NTRS1986

Time-dependent mixed convection heat transfer from a sphere in a micro-gravity environment

A fundamental problem of interest for crystal growth in micro-gravity applications involves the mixed convection heat transfer from a sphere in a uniform flow of fluid at a differing temperature. Under the combined influence of the imposed free stream as well as an induced buoyancy force due to thermal expansion of the fluid, the heat transfer from the sphere will be different from that of either the pure forced convection flow or the pure free convection flow. For the present study, the method of matched asymptotic expansions is applied to the laminar flow problem of an impulsively heated, impulsively started sphere in an originally quiescent fluid. Time series expansions are developed for the dependent variables by acknowledging the existence of two distinct regions: one, an inner region, near the sphere, in which viscous effects are significant; and two, an outer region in which the fluid may be treated as inviscid. The time series expansions are developed in terms of the Reynolds number and Richardson number (Buoyancy Parameter), and the relevant heat transfer and drag coefficients are calculated and plotted.

Hommel, Mark J.↗

NASA NTRS1987

On the confinement of planetary arcs

The necessary conditions for planetary arc confinement are investigated, concentrating on the limiting case where the arc is marginally confined. It is shown that periodic perturbations due to a discrete Lindblad resonance can induce a secular change of Jacobian energy as well as orbital eccentricity. If the particles are subject to the perturbation of only one inner (outer) Lindblad resonance, the Lindblad resonance's location must be exterior (interior) to that of the corotation resonance if the perturbations are to lead to confinement. The trajectories of particles that are subject to inelastic collisions and pertubations due to corotation and Lindblad resonances are computed, showing that the confinement mechanism can indeed operate provided the perturbation due to the Lindblad resonance is sufficiently strong to balance viscous effects. The possibility that internal nonradial oscillations of Neptune may provide the necessary perturbations for arc confinement is considered.

Lin, D. N. C.↗

NASA NTRS1988

Euler equation computations for the flow over a hovering helicopter rotor

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Roberts, Thomas Wesley↗