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NASA NTRS1992

Transonic aeroelastic computations on wings using Navier-Stokes equations

Aeroelastic computations are made on fighter type wings in the transonic regime. The flow is modeled using the Navier-Stokes equations and is coupled with structural equations of motion. The flow equations are solved by a time accurate finite difference scheme with moving grids. The coupled aeroelastic equations of motion are solved using the linear acceleration method. The configuration adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. Computations are made for oscillating rigid wings with moving shock waves in the presence of leading edge vortices. The computed results compare well with the experiment. Unsteady computations are made to demonstrate the shock-vortex interaction phenomenon on wings in ramp motion. Effects of flexibility and pitch rate are demonstrated for flows with vortices.

Guruswamy, Guru P.↗

NASA NTRS1992

Surface tension and buoyancy-driven flow in a non-isothermal liquid bridge

The Navier-Stokes-Boussinesq equations governing the transport of momentum, mass and heat in a nonisothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a nonorthogonal coordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.

Zhang, Yiqiang↗

NASA NTRS1991

Effect of convection on the microstructure of a lamellar eutectic growing with a stepped interface

A two dimensional model developed to study the influence of convective flow on the concentration field ahead of a growing lamellar eutectic is described when one phase projects out into the melt creating a stepped interface. The two dimensional convective flow field, which is periodic in the horizontal direction, was computed numerically using the software FLUENT. The velocity field generated due to the flow of melt over the steps was then incorporated into a finite difference scheme employed to solve the concentration field. The average interfacial composition was calculated and converted to lamellar spacing using the Jackson and Hunt minimum supercooling criterion. It was found that a stepped interface is more sensitive to convection than a planar interface.

Seth, Jayshree↗

NASA NTRS1992

Thermochemical nonequilibrium and radiative interactions in supersonic hydrogen-air combustion

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with nonequilibrium chemistry and thermodynamics, coupled with radiation, for hydrogen-air systems. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed, expanding flow in a supersonic nozzle. The reacting flow consists of seven species, one of which is the inert N2 molecule. The thermal state of the gas is modeled with one translational-rotational temperature and five vibrational temperatures. The harmonic oscillator model is used in the formulation for vibrational relaxation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate the presence of nonequilibrium in the expansion region. This reduces the radiative interactions and can have a significant influence on the flowfield.

Chandrasekhar, R.↗

NASA NTRS1991

Towards large eddy and direct simulation of complex turbulent flows

Recent advances in the methodology for direct numerical simulation of turbulent flows and some of the current applications are reviewed. It is argued that high-order finite difference schemes yield solutions with comparable accuracy to the spectral methods with the same number of degrees of freedom. The effects of random inflow conditions on the downstream evolution of turbulence are discussed.

Moin, Parviz↗

NASA NTRS1992

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Fan, Mark S.↗

NASA NTRS1992

A hybrid multigrid technique for computing steady-state solutions to supersonic flows

Recently, Li and Sanders have introduced a class of finite difference schemes to approximate generally discontinuous solutions to hyperbolic systems of conservation laws. These equations have the form together with relevant boundary conditions. When modelling hypersonic spacecraft reentry, the differential equations above are frequently given by the compressible Euler equations coupled with a nonequilibrium chemistry model. For these applications, steady state solutions are often sought. Many tens (to hundreds) of super computer hours can be devoted to a single three space dimensional simulation. The primary difficulty is the inability to rapidly and reliably capture the steady state. In these notes, we demonstrate that a particular variant from the schemes presented can be combined with a particular multigrid approach to capture steady state solutions to the compressible Euler equations in one space dimension. We show that the rate of convergence to steady state coming from this multigrid implementation is vastly superior to the traditional approach of artificial time relaxation. Moreover, we demonstrate virtual grid independence. That is, the rate of convergence does not depend on the degree of spatial grid refinement.

Sanders, Richard↗

NASA NTRS1992

Progress on single barrier varactors for submillimeter wave power generation

Theoretical work on Single Barrier Varactor (SBV) diodes, indicate that the efficiency for a multiplier has a maximum for a considerably smaller capacitance variation than previously thought. The theoretical calculations are performed, both with a simple theoretical model and a complete computer simulation using the method of harmonic balance. Modeling of the SBV is carried out in two steps. First, the semiconductor transport equations are solved simultaneously using a finite difference scheme in one dimension. Secondly, the calculated I-V, and C-V characteristics are input to a multiplier simulator which calculates the optimum impedances, and output powers at the frequencies of interest. Multiple barrier varactors can also be modeled in this way. Several examples on how to design the semiconductor layers to obtain certain characteristics are given. The calculated conversion efficiencies of the modeled structures, in a multiplier circuit, are also presented. Computer simulations for a case study of a 750 GHz multiplier show that InAs diodes perform favorably compared to GaAs diodes. InAs and InGaAs SBV diodes have been fabricated and their current vs. voltage characteristics are presented. In the InAs diode, was the large bandgap semiconductor AlSb used as barrier. The InGaAs diode was grown lattice matched to an InP substrate with InAlAs as a barrier material. The current density is greatly reduced for these two material combinations, compared to that of GaAs/AlGaAs SBV diodes. GaAs based diodes can be biased to higher voltages than InAs diodes.

Nilsen, Svein M.↗

NASA NTRS1992

Effect of free surface shape on combined thermocapillary and natural convection

Combined thermocapillary and natural convection in an open square cavity with differentially-heated side walls is studied numerically as well as experimentally. The test fluid is silicone oil with Prandtl number of 105. The shape of fluid-free surface is made either flat or curved to study its effect on the flow. A finite difference scheme to deal with a curved free surface is developed. The experimental results shown agree with the numerical results. With the curved-free surface, the flow and local heat transfer rate are reduced in the corner regions, and a sharp peak in heat transfer rate at the top edge of the cold wall disappears.

Kamotani, Yasuhiro↗

NASA NTRS1993

Effects of icing on the aerodynamic performance of high lift airfoils

A 2D compressible Navier-Stokes solver capable of analyzing multi-element airfoils is described. The flow field is divided into multiple zones. In each zone, the governing equations are solved using an implicit finite difference scheme. The flow solver is validated through a study of the aerodynamic characteristics of a GA(W)-1 configuration, for which good quality measured surface pressure data and load data are available. The solver is next applied to a study of the effects of icing on an iced 5-element airfoil configuration, experimentally studied at NASA Lewis Research Center. It is demonstrated that the formation of ice over the leading edge slat and the main airfoil can lead to significant flow separation, and a significant loss in lift, compared to clean configurations.

Sankar, L. N.↗

NASA NTRS1993

Numerical investigation of receptivity to freestream vorticity

The receptivity to freestream vorticity of the boundary layer over a flat plate with an elliptic leading edge is studied numerically. A finite-difference scheme that is second-order accurate in both time and space is utilized to solve the incompressible Navier-Stokes system in general curvilinear coordinates with the vorticity and stream function as dependent variables. Simulations show, for the conditions considered, a linear variation in the Tollmien-Schlichting response with forcing amplitude for perturbations of freestream velocity that are either symmetrical or asymmetrical with respect to the basic state stagnation streamline.

Buter, Thomas A.↗

NASA NTRS1992

Calculations of separated vortex flows at low speed for low-aspect-ratio wings

An implicit finite-difference scheme has been developed for solving three-dimensional incompressible Navier-Stokes equations. Computations for complicated vortical flows past several sharp- and round-edged delta and double-delta wings at high angles of attack and sideslip are discussed. Computed results demonstrate the effectiveness of the present method and show good agreement with experimental data.

Liu, C. H.↗

NASA NTRS1992

The eigenvalue spectrum of the Rayleigh equation for a plane shear layer

The eigenvalue spectrum of the Rayleigh equation is examined using three different solution techniques. In particular, a simple second-order finite difference scheme and two spectral methods, the Chebyshev tau and Chebyshev collocation methods, are used to discretize the equation. All of the approximation methods are shown to be capable of predicting the discrete spectrum as well as the continuous spectrum associated with the critical point singularity for the Rayleigh equation. The global eigenvalue methods considered here provide an efficient way of obtaining either an approximation to the complete eigenvalue spectrum or initial guesses for a local shooting procedure for the discrete part of the spectrum.

Liou, William W.-W.↗

NASA NTRS1993

Source term evaluation for combustion modeling

A modification is developed for application to the source terms used in combustion modeling. The modification accounts for the error of the finite difference scheme in regions where chain-branching chemical reactions produce exponential growth of species densities. The modification is first applied to a one-dimensional scalar model problem. It is then generalized to multiple chemical species, and used in quasi-one-dimensional computations of shock-induced combustion in a channel. Grid refinement studies demonstrate the improved accuracy of the method using this modification. The algorithm is applied in two spatial dimensions and used in simulations of steady and unsteady shock-induced combustion. Comparisons with ballistic range experiments give confidence in the numerical technique and the 9-species hydrogen-air chemistry model.

Sussman, Myles A.↗

NASA NTRS1993

Numerical simulation of thermocapillary flow under zero and low gravity conditions

This paper discusses the numerical solution methods and results of steady and unsteady thermocapillary (surface-tension) and buoyancy driven flows in 2D cavities and liquid columns. The 2D cavity was assumed to be square with one free surface with a zero Capillary number (i.e., the free surface was constrained to be flat). A pseudospectral method was used to solve steady and unsteady surface tension-driven and mixed buoyancy-surface tension flows in a square cavity. For the liquid column a finite-difference scheme based on a Picard iteration was used to solve for the flow, temperature and free surface shape. The surface of the liquid column was allowed to deform and, as for the 2D cavity, the surface tension was assumed to depend on temperature.

Alexander, J. I. D.↗

NASA NTRS1993

Numerical simulations of a high Mach number jet flow

The present 2D simulations of plane and axisymmetric jets, which are relevant to current efforts to suppress the jet exhaust noise of prospective high-speed civil transports, were conducted by solving full Navier-Stokes equations by means of a high-order finite-difference scheme. The results obtained, which were able to generate the correct mode shape after an adjustment region of about 10 diameters, are in good agreement with linear-theory predictions of the growth of instability waves.

Hayder, M. E.↗

NASA NTRS1992

Investigation of vortex breakdown on delta wings using Navier-Stokes equations

An efficient finite-difference scheme solving for the three-dimensional incompressible Navier-Stokes equations is described. Numerical simulations of vortex breakdown are then carried out for a sharp-edged delta wing and a round-edged double-delta wing at high Reynolds numbers. Computed results show that several major features of vortex breakdown are qualitatively in agreement with observations made in experiments.

Hsu, C.-H.↗

NASA NTRS1993

High order finite difference and multigrid methods for spatially evolving instability in a planar channel

The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.

Liu, C.↗