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NASA NTRS1977

Computational techniques for solar wind flows past terrestrial planets: Theory and computer programs

The interaction of the solar wind with terrestrial planets can be predicted using a computer program based on a single fluid, steady, dissipationless, magnetohydrodynamic model to calculate the axisymmetric, supersonic, super-Alfvenic solar wind flow past both magnetic and nonmagnetic planets. The actual calculations are implemented by an assemblage of computer codes organized into one program. These include finite difference codes which determine the gas-dynamic solution, together with a variety of special purpose output codes for determining and automatically plotting both flow field and magnetic field results. Comparisons are made with previous results, and results are presented for a number of solar wind flows. The computational programs developed are documented and are presented in a general user's manual which is included.

Stahara, S. S.↗
NASA NTRS1977

Numerical solution of the compressible Navier-Stokes equations using density gradients as additional dependent variables

Numerical solution of two dimensional, time dependent, compressible viscous Navier-Stokes equations about arbitrary bodies was treated using density gradients as additional dependent variables. Thus, six dependent variables were computed with the SOR iteration method. Besides formulation for pressure gradient terms, a formulation for computing the body density was presented. To approximate the governing equations, an implicit finite difference method was employed. In computing the solution for the flow about a circular cylinder, a problem arose near the wall at both stagnation points. Thus, computations with various conditions were tried to examine the problem. Also, computations with and without formulations are compared. The flow variables were computed on 37 by 40 field first, then on an 81 by 40 field.

Kwon, J. H.↗
NASA NTRS1978

CAVE3: A general transient heat transfer computer code utilizing eigenvectors and eigenvalues

The method of solution is a hybrid analytical numerical technique which utilizes eigenvalues and eigenvectors. The method is inherently stable, permitting large time steps even with the best of conductors with the finest of mesh sizes which can provide a factor of five reduction in machine time compared to conventional explicit finite difference methods when structures with small time constants are analyzed over long time periods. This code will find utility in analyzing hypersonic missile and aircraft structures which fall naturally into this class. The code is a completely general one in that problems involving any geometry, boundary conditions and materials can be analyzed. This is made possible by requiring the user to establish the thermal network conductances between nodes. Dynamic storage allocation is used to minimize core storage requirements. This report is primarily a user's manual for CAVE3 code. Input and output formats are presented and explained. Sample problems are included which illustrate the usage of the code as well as establish the validity and accuracy of the method.

Palmieri, J. V.↗
NASA NTRS1978

A computer program for calculating laminar and turbulent boundary layers for two-dimensional time-dependent flows

A computer program is described which provides solutions of two dimensional equations appropriate to laminar and turbulent boundary layers for boundary conditions with an external flow which fluctuates in magnitude. The program is based on the numerical solution of the governing boundary layer equations by an efficient two point finite difference method. An eddy viscosity formulation was used to model the Reynolds shear stress term. The main features of the method are briefly described and instructions for the computer program with a listing are provided. Sample calculations to demonstrate its usage and capabilities for laminar and turbulent unsteady boundary layers with an external flow which fluctuated in magnitude are presented.

Cebeci, T.↗
NASA NTRS1978

Geological applications of thermal-inertia mapping from satellite

The author has identified the following significant results. A more efficient algorithm for calculating surface temperature was developed. This algorithm was determined to be essentially exact, and relative accuracies in determining thermal inertia of the finite difference and the linear Fourier series algorithms were approximately 5% for both. A procedure for performing geometric registration was developed.

Offield, T. W.↗
NASA NTRS1978

Modeling of the Reynolds stresses

In their most general form, the Reynolds averaged conservation equations result from ensemble or time averages of the instantaneous Navier-Stokes equations or their compressible counterparts. For these averaging processes to be consistent, the averaging time period must exceed the periods identified with the largest time scales of the turbulence, and yet be shorter than the characteristic times of the flow field. With these equations long period variations in the flow fields are deterministic, provided initial conditions are known. The average dependent variables are sufficiently smooth to be resolvable by finite difference techniques consistent with the size and speed of modern computers.

Rubesin, M. W.↗
NASA NTRS1978

Computational advances in fluid dynamics

An office size digital computer with capabilities exceeding a CDC 7600 can be constructed for less than 300 K and spectral methods offer a factor ten improvement over finite difference methods. Integration of these facts can produce two orders of magnitude reduction in cost of fluid dynamic computations and permit solution of 3-D problems which were not previously feasible.

Taylor, T. D.↗
NASA NTRS1978

Conservative implicit schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) were investigated for the solution of matrix equations resulting from finite difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, was introduced by an upwind bias of the density. Two implicit AF procedures are presented and their convergence performance is compared with that of the standard transonic solution procedure, successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. The results indicate that the AF schemes are substantially faster than SLOR.

Holst, T. L.↗
NASA NTRS1977

Computation of unsteady transonic flows through rotating and stationary cascades. 1: Method of analysis

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator) or a single blade row of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite difference method is employed in the interior of the passage, and a method of characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors and compared with available experimental data, consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗
NASA NTRS1978

Numerical study of transonic flow over oscillating airfoils using the full potential equation

The behavior of unsteady aerodynamic loadings on airfoils oscillating in transonic flow has been investigated numerically with particular attention given to supercritical airfoil sections. A previously developed finite difference method, which is based on the full potential equation and which uses a quasi-conservative scheme for proper capture of a shock wave motion, was employed for the present study. The unsteady aerodynamic pressure and load distributions on several different airfoil sections are presented with particular emphasis on the effects of free-stream Mach number, reduced frequency, and mean angle of attack. These parameters are demonstrated to have a significant effect on the behavior of the unsteady aerodynamic loadings. Comparisons of the present calculations with the exact inviscid solution and with the experimental results are also presented.

Isogai, K.↗
NASA NTRS1978

Two-dimensional computer code for design assessment of SRM aft closure environment

A general interpolants method for constructing numerical analogs of the partial differential equations of continuum mechanics and which combines the best features of both finite element and finite difference methods was used in a two dimensional axisymmetric analysis of the space shuttle solid motor aft closure region flowfield. The numerical technique used is discussed as well as the results of the analysis. A steady state solution for the submerged nozzle nose region indicates the development of an area gas flow recirculation near the propellant burning surface boundary and in the region of the underside of the nozzle nose. This recirculation region remains spatially fixed for successive iterations (greater than 800) of the solution.

Freeman, J. A.↗
NASA NTRS1978

Efficiency of unconstrained minimization techniques in nonlinear analysis

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Kamat, M. P.↗
NASA NTRS1978

Analysis of turbulent free jet hydrogen-air diffusion flames with finite chemical reaction rates

The nonequilibrium flow field resulting from the turbulent mixing and combustion of a supersonic axisymmetric hydrogen jet in a supersonic parallel coflowing air stream is analyzed. Effective turbulent transport properties are determined using the (K-epsilon) model. The finite-rate chemistry model considers eight reactions between six chemical species, H, O, H2O, OH, O2, and H2. The governing set of nonlinear partial differential equations is solved by an implicit finite-difference procedure. Radial distributions are obtained at two downstream locations of variables such as turbulent kinetic energy, turbulent dissipation rate, turbulent scale length, and viscosity. The results show that these variables attain peak values at the axis of symmetry. Computed distributions of velocity, temperature, and mass fraction are also given. A direct analytical approach to account for the effect of species concentration fluctuations on the mean production rate of species (the phenomenon of unmixedness) is also presented. However, the use of the method does not seem justified in view of the excessive computer time required to solve the resulting system of equations.

Sislian, J. P.↗
NASA NTRS1978

Large eddy simulation of incompressible turbulent channel flow

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Moin, P.↗
NASA NTRS1978

Inverse boundary-layer theory and comparison with experiment

Inverse boundary layer computational procedures, which permit nonsingular solutions at separation and reattachment, are presented. In the first technique, which is for incompressible flow, the displacement thickness is prescribed; in the second technique, for compressible flow, a perturbation mass flow is the prescribed condition. The pressure is deduced implicitly along with the solution in each of these techniques. Laminar and turbulent computations, which are typical of separated flow, are presented and comparisons are made with experimental data. In both inverse procedures, finite difference techniques are used along with Newton iteration. The resulting procedure is no more complicated than conventional boundary layer computations. These separated boundary layer techniques appear to be well suited for complete viscous-inviscid interaction computations.

Carter, J. E.↗
NASA NTRS1978

An old integration scheme for compressible flows revisited, refurbished and put to work

A scheme for integrating the Euler equations of compressible flow in any hyperbolic case is presented. The scheme relies on the concept of characteristics but is strictly a finite difference scheme. Improvements in accuracy and physical consistence due to the scheme are discussed and results of its application to complex flows are shown.

Moretti, G.↗
NASA NTRS1978

Direct measurements and analysis of skin friction and cooling downstream of multiple flush-slot injection into a turbulent Mach 6 boundary layer

Experiments were conducted to determine the reduction in surface skin friction and the effectiveness of surface cooling downstream of one to four successive flush slots injecting cold air at an angle of 10 deg into a turbulent Mach 6 boundary layer. Data were obtained by direct measurement of surface shear and equilibrium temperatures, respectively. Increasing the number of slots decreased the skin friction, but the incremental improvement in skin-friction reduction decreased as the number of slots was increased. Cooling effectiveness was found to improve, for a given total mass injection, as the number of slots was increased from one to four. Comparison with previously reported step-slot data, however, indicated that step slots with tangential injection are more effective for both reducing skin friction and cooling than the present flush-slot configuration. Finite-difference predictions are in reasonable agreement with skin-friction data and with boundary-layer profile data.

Howard, F. G.↗