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NASA NTRS1987

Calculating rotordynamic coefficients of seals by finite-difference techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.

Dietzen, F. J.↗

NASA NTRS1986

Finite-element reentry heat-transfer analysis of space shuttle Orbiter

A structural performance and resizing (SPAR) finite-element thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR finite-element solutions agreed reasonably well with those obtained from the conventional finite-difference method.

Ko, William L.↗

NASA NTRS1986

Dislocation dynamics during the growth of silicon ribbon

The thermal viscoplastic stresses and the dislocation densities in silicon ribbon are computed for an axially changing thermal profile by using an iterative finite difference method. A material constitutive equation (Haasen-Sumino model) which involves an internal variable (mobile dislocation density) is used. The results are interpreted as showing that there is a maximum width of silicon ribbon that can be grown when viscoplasticity and dislocations are considered. This maximum width limitation does not exist if the material behavior is elastic.

Dillon, O. W., Jr.↗

NASA NTRS1987

A new PNS code for chemical nonequilibrium flows

A new parabolized Navier-Stokes (PNS) code has been developed to compute the hypersonic laminar flow of a multicomponent, chemically reacting mixture of thermally perfect gases over two-dimensional and axisymmetric bodies. The new PNS code solves the gas dynamic and species conservation equations in a coupled manner using a noniterative, implicit, space-marching finite-difference method. The conditions for well-posedness of the space-marching method have been derived from an eigenvalue analysis of the governing equations. The code has been used to compute hypersonic laminar flow of chemically reacting air over wedges and cones. The results of these computations are in good agreement with the results of reacting boundary-layer calculations.

Prabhu, D. K.↗

NASA NTRS1987

Computer-based phosphoric acid fuel cell analytical tools Descriptions and usages

Simulation models have been developed for the prediction of phosphoric acid fuel cell (PAFC) powerplant system performance under both transient and steady operation conditions, as well as for the design of component configurations and for optimal systems synthesis. These models, which are presently computer-implemented, are an engineering and a system model; the former being solved by the finite difference method to determine the balances and properties of different sections, and the latter using thermodynamic balances to set up algebraic equations that yield physical and chemical properties of the stream for one operating condition.

Lu, C.↗

NASA NTRS1987

Modeling and calculation of turbulent transport in free-shear flows

In this work the applicability of the combined bulk convection and gradient transport hypotheses for modeling turbulent diffusion is investigated. The resulting model equation, namely the one-equation model, is solved for free-shear flows by an implicit finite-difference method. Results indicate that significant improvements over previous models can be achieved with this new formulation of turbulent diffusion for both heat and momentum transport.

Biringen, S.↗

NASA NTRS1987

A simultaneous viscous-inviscid interaction calculation procedure for transonic turbulent flows

A new simultaneous viscous-inviscid interaction scheme has been developed for the analysis of steady turbulent transonic separated flows. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity. The local solutions of the full potential and boundary-layer equations are treated simultaneously using the finite-difference method. The displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure of the space marching scheme. The Cebeci-Smith and Johnson-King models are used to simulate the turbulence. The computational examples showed that the simultaneous method is more efficient and robust than the semi-inverse method for transonic flows with a strong interaction.

Lee, D.↗

NASA NTRS1987

An adaptive grid, unsteady model for two-dimensional magnetohydrodynamic (MHD) flow

An adaptive grid finite difference method for solving multi-dimensional, time-dependent, magnetohydrodynamic (MHD) equations is developed. The method is capable of solving problems that include high gradients due to geometry, propagation of shock waves and unsteady boundary conditions. The grid generation technique is based on variational principles with direct control over grid concentration, smoothness and skewness. An example for a two-dimensional MHD simulation of the propagation of a solar-flare-generated shock wave in solar wind flow in the heliographic equatorial plane is selected for illustration of this method.

Panitchob, Supat↗

NASA NTRS1987

Study of instability and active control of boundary layers using Navier-Stokes equations

Spatial stability of a three-dimensional growing boundary layer is studied using Navier-Stokes equations. The finite difference method used is an explicit, predictor-corrector type which is fourth-order accurate in space and second-order in time. Active control of two-dimensional disturbances is simulated by localized surface heating. The computations show features of the flow relevant to early stages of transition such as lifting of vorticity away from the wall and localized regions of intense shear. Active control with single heating strip is only marginally effective, but may be improved by multiple strips.

Parikh, Paresh↗

NASA NTRS1987

Linear stability analysis of three-dimensional compressible boundary layers

A compressible stability analysis computer code is developed. The code uses a matrix finite-difference method for local eigenvale solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used inital-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed that may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, Mujeeb R.↗

NASA NTRS1987

Concepts for radically increasing the numerical convergence rate of the Euler equations

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow.

Nixon, David↗

NASA NTRS1987

Navier-Stokes computations for circulation control 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, 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

Solving time-dependent two-dimensional eddy current problems

Results of transient eddy current calculations are reported. For simplicity, a two-dimensional transverse magnetic field which is incident on an infinitely long conductor is considered. The conductor is assumed to be a good but not perfect conductor. The resulting problem is an interface initial boundary value problem with the boundary of the conductor being the interface. A finite difference method is used to march the solution explicitly in time. The method is shown. Treatment of appropriate radiation conditions is given special consideration. Results are validated with approximate analytic solutions. Two stringent test cases of high and low frequency incident waves are considered to validate the results.

Lee, Min Eig↗

NASA NTRS1987

Nonplanar interface morphologies during unidirectional solidification of a binary alloy. II - Three-dimensional computations

A finite difference method is used to obtain three-dimensional steady-state solutions for nonplanar interface morphologies in order to study the situation of equal thermal properties in the crystal and melt with negligible latent heat release. Stable steady-state solutions corresponding to two-dimensional bands and three-dimensional hexagonal nodes, as well as to rectangular interface planiforms, are found using a model of an aluminum-chromium alloy with a distribution coefficient of greater than one. Hexagonal nodes are predicted near the onset of instability, in agreement with weakly nonlinear theory.

Mcfadden, G. B.↗

NASA NTRS1988

A Three-Dimensional, Time-Dependent Numerical Modeling of Super-Sonic, Super-Alfvenic MHD Flow

A three-dimensional, time-dependent, MHD disturbance propagating through a steady inhomogeneous MHD flow is analyzed by a numerical model based on the Lax-Wendroff finite difference method. The initial steady MHD flow is assumed to be supersonic and super-Alfvenic. The background steady MHD flow is obtained by dropping the time-dependent terms in the unsteady MHD equations. A transient MHD disturbance corresponding to a MHD shock is generated at the lower radial boundary surface. The resulting development and propagation of 3-D MHD disturbances interacting with the background steady MHD flow are numerically simulated in this first application to the field of interplanetary physics. Detailed descriptions of the mathematical formulation and numerical methodology are presented. Example computations are performed to demonstrate the validity of the formulation and the capabilities of the model.

Han, S. M.↗

NASA NTRS1988

Numerical investigation of three-dimensional flow separation using the boundary layer equations

The steady, incompressible, three-dimensional laminar and turbulent boundary-layer equations are solved in a streamline coordinate system and in a self-adaptive grid system using Matsuno's finite difference method. Techniques are described for calculating laminar and turbulent separation using the boundary-layer equations. Any type (bubble type or free vortex-layer type) of major separation line can be calculated at an angle of attack on ellipsoids of revolution by this boundary layer code. Results are presented for ellipsoids of revolution at angles of attack up to 45 degrees. Agreements with other numerical and experimental results are very good for laminar flows. Turbulent flows are also investigated with algebraic turbulence models proposed by Rotta and Cebeci and Smith. Good agreement with experimental results was obtained at a small angle of attack (10 degrees) but only qualitative agreement was obtained at a high angle of attack (30 degrees) for turbulent flow on a 6:1 ellipsoid of revolution.

Wie, Yong-Sun↗

NASA NTRS1986

Interface procedures for overlapping grids

The solution of partial differential equations by means of either implicit or conservative explicit finite-difference methods, on the one hand, or multicomponent overlapping grid schemes on the other, is presently subjected to interpolation at grid boundaries in an attempt to eliminate the time lag. The accuracy of the transient solution of a hyperbolic or parabolic partial differential equation is dependent on the procedures used to transfer information between grids in a composite grid system. The present techniques reduce numerical solution errors.

Mastin, C. Wayne↗