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NASA NTRS1990

A numerical study of the effects of wind tunnel wall proximity on an airfoil model

A procedure was developed for modeling wind tunnel flows using computational fluid dynamics. Using this method, a numerical study was undertaken to explore the effects of solid wind tunnel wall proximity and Reynolds number on a two-dimensional airfoil model at low speed. Wind tunnel walls are located at varying wind tunnel height to airfoil chord ratios and the results are compared with freestream flow in the absence of wind tunnel walls. Discrepancies between the constrained and unconstrained flows can be attributed to the presence of the walls. Results are for a Mach Number of 0.25 at angles of attack through stall. A typical wind tunnel Reynolds number of 1,200,000 and full-scale flight Reynolds number of 6,000,000 were investigated. At this low Mach number, wind tunnel wall corrections to Mach number and angle of attack are supported. Reynolds number effects are seen to be a consideration in wind tunnel testing and wall interference correction methods. An unstructured grid Navier-Stokes code is used with a Baldwin-Lomax turbulence model. The numerical method is described since unstructured flow solvers present several difficulties and fundamental differences from structured grid codes, especially in the area of turbulence modeling and grid generation.

Potsdam, Mark↗

NASA NTRS1990

Numerical investigations in three-dimensional internal flows

The application of the SCRAM2D code to investigating the flow fields that might be expected to occur in a representative Mach 10, two dimensional (ramp-compression) inlet is described. This Mach number allows the use of existing Navier-Stokes codes without the additional complexity of air chemistry and the associated large increases in computational time required to achieve numerical simulations of such flow fields. The CFD simulation consists of a two-dimensional inlet geometry that has an overall geometric turning of 36 degrees. The cowl for this inlet is assumed to be aligned with the oncoming freestream flow, turning the ramp flow field back parallel to the freestream, thus producing the overall 36 degree turning angle. The primary subject is the cowl shock wave-ramp boundary layer interaction effects. The results of numerical simulations carried out at the design Mach number of 10 and two other off-design Mach numbers, 7.2 and 5.0 are described.

Rose, William C.↗

NASA NTRS1991

GEOSIM: A numerical model for geophysical fluid flow simulation

A numerical model which simulates geophysical fluid flow in a wide range of problems is described in detail, and comparisons of some of the model's results are made with previous experimental and numerical studies. The model is based upon the Boussinesq Navier-Stokes equations in spherical coordinates, which can be reduced to a cylindrical system when latitudinal walls are used near the pole and the ratio of latitudinal length to the radius of the sphere is small. The equations are approximated by finite differences in the meridional plane and spectral decomposition in the azimuthal direction. The user can specify a variety of boundary and initial conditions, and there are five different spectral truncation options. The results of five validation cases are presented: (1) the transition between axisymmetric flow and baroclinic wave flow in the side heated annulus; (2) the steady baroclinic wave of the side heated annulus; (3) the wave amplitude vacillation of the side heated annulus; (4) transition to baroclinic wave flow in a bottom heated annulus; and (5) the Spacelab Geophysical Fluid Flow Cell (spherical) experiment.

Butler, Karen A.↗

NASA NTRS1991

Numerical prediction of turbulent oscillating flow and associated heat transfer

A crucial point for further development of engines is the optimization of its heat exchangers which operate under oscillatory flow conditions. It has been found that the most important thermodynamic uncertainties in the Stirling engine designs for space power are in the heat transfer between gas and metal in all engine components and in the pressure drop across the heat exchanger components. So far, performance codes cannot predict the power output of a Stirling engine reasonably enough if used for a wide variety of engines. Thus, there is a strong need for better performance codes. However, a performance code is not concerned with the details of the flow. This information must be provided externally. While analytical relationships exist for laminar oscillating flow, there has been hardly any information about transitional and turbulent oscillating flow, which could be introduced into the performance codes. In 1986, a survey by Seume and Simon revealed that most Stirling engine heat exchangers operate in the transitional and turbulent regime. Consequently, research has since focused on the unresolved issue of transitional and turbulent oscillating flow and heat transfer. Since 1988, the University of Minnesota oscillating flow facility has obtained experimental data about transitional and turbulent oscillating flow. However, since the experiments in this field are extremely difficult, lengthy, and expensive, it is advantageous to numerically simulate the flow and heat transfer accurately from first principles. Work done at the University of Minnesota on the development of such a numerical simulation is summarized.

Koehler, W. J.↗

NASA NTRS1991

A new numerical framework for solving conservation laws: The method of space-time conservation element and solution element

A new numerical framework for solving conservation laws is being developed. It employs: (1) a nontraditional formulation of the conservation laws in which space and time are treated on the same footing, and (2) a nontraditional use of discrete variables such as numerical marching can be carried out by using a set of relations that represents both local and global flux conservation.

Chang, Sin-Chung↗

NASA NTRS1990

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case.

Wu, S. T.↗

NASA NTRS1990

Efficient numerical simulation of electron states in quantum wires

A new algorithm is presented for the numerical simulation of electrons in a quantum wire as described by a two-dimensional eigenvalue problem for Schroedinger's equation coupled with Poisson's equation. Initially, the algorithm employs an underrelaxed fixed point iteration to generate an approximation which is reasonably close to the solution. Subsequently, this approximate solution is employed as an initial guess for a Jacobian-free implementation of an approximate Newton method. In this manner the nonlinearity in the model is dealt with effectively. The effectiveness of this approach is demonstrated in a set of numerical experiments which study the electron states on the cross section of a quantum wire structure based on III-V semiconductors at 4.2 and 77 K.

Kerkhoven, Thomas↗

NASA NTRS1990

Numerical derivation of forced nutation terms for a rigid earth

The results of a numerical integration of the Euler equations for a rigid earth model covering a time span of 250 years are compared with Kinoshita's (1977) theory for the forced nutations and with a new nutation series by Kinoshita and Souchay. Numerical corrections to some of the analytically derived nutation terms are presented.

Schastok, J.↗

NASA NTRS1990

A numerical study of the outflow layer of tropical cyclones

Numerical simulations of idealized tropical cyclones with special emphasis on the outflow layer are presented. The quasi-steady state outflow layers of weak and strong cyclones are found to exhibit similar characteristics. The circulations are anticyclonic and asymmetric about the center; the outflow layer is dominated by a narrow, elongated outflow-jet contributing up to 50 percent of the angular momentum transport; the air particles in the outflow jet mostly originate from the lower level. Secondary circulations are found to influence the relative humidity and the potential vorticity at the outflow levels. In order to study the effect of upper tropospheric forcings, two variational numerical experiments using cumulus convection as the major link between the upper-level forcing and the tropical cyclone's response are conducted.

Shi, Jainn-Jong↗

NASA NTRS1991

Numerical prediction of the unsteady flowfield around the F-18 aircraft at large incidence

This paper describes a numerical method capable of solving the steady and unsteady viscous flow around complete aircraft configurations at high angles of attack. This method is used to simulate the external flow around the F-18 aircraft, including deflected control surfaces. The current technique employs a generalized overset zonal grid scheme to decompose the computational space around the aircraft. The grid around various components of the aircraft are created numerically using a three-dimensional hyperbolic grid generation procedure. The Reynolds-averaged Navier-Stokes equations are integrated using a time-accurate, implicit procedure. Results for the turbulent flow around the F-18 aircraft at 30 degrees angle of attack show the details of the flowfield structure, including the unsteadiness created by the vortex burst and the resulting fluctuating airloads exerted on the vertical tail. The computed results agree fairly well with flight data for surface pressure, surface flow pattern, vortex burst location, and the dominant frequency for tail load fluctuations.

Rizk, Yehia M.↗

NASA NTRS1991

A novel gas-droplet numerical method for spray combustion

This paper presents a non-iterative numerical technique for computing time-dependent gas-droplet flows. The method is a fully-interacting combination of Eulerian fluid and Lagrangian particle calculation. The interaction calculations between the two phases are formulated on a pressure-velocity coupling procedure based on the operator-splitting technique. This procedure eliminates the global iterations required in the conventional particle-source-in-cell (PSIC) procedure. Turbulent dispersion calculations are treated by a stochastic procedure. Numerical calculations and comparisons with available experimental data, as well as efficiency assessments are given for some sprays typical of spray combustion applications.

Chen, C. P.↗

NASA NTRS1991

Numerical investigation of the flow over a double delta wing at high incidence

The vortical flowfield over a double-delta wing configuration, consisting of a sharp leading edge 76 deg sweep strake and a 40 deg sweep wing section is investigated. The governing equations are solved numerically with a partially upwind, finite-difference, factorized algorithm. The leeward side vortex system resulting from the strake and wing vortices is investigated for subsonic, high-Reynolds-number flow at various angles of incidence. At low angles of attack the strake and wing vortices remain separate over the wing section, while for flows at higher angles of attack the two vortices merge and vortex breakdown develops. Vortex breakdown appears initially at the trailing edge region of the wing section. As the angle of attack increases bursting occurs further upstream closer to the strake section. The effect of numerical grid density is investigated, and the solutions are compared with available experimental data.

Ekaterinaris, John A.↗

NASA NTRS1991

Numerical simulation of transition in wall-bounded shear flows

The current status of numerical simulation techniques for the transition to turbulence in incompressible channel and boundary-layer flows is surveyed, and typical results are presented graphically. The focus is on direct numerical simulations based on the full nonlinear time-dependent Navier-Stokes equations without empirical closure assumptions for prescribed initial and boundary conditions. Topics addressed include the vibrating ribbon problem, space and time discretization, initial and boundary conditions, alternative methods based on the triple-deck approximation, two-dimensional channel and boundary-layer flows, three-dimensional boundary layers, wave packets and turbulent spots, compressible flows, transition control, and transition modeling.

Kleiser, Leonhard↗

NASA NTRS1990

Numerical computation of transition to turbulence

Current applications of numerical simulations, including studies of mildly nonlinear and strongly nonlinear effects, and incipient turbulence are reviewed, and it is observed that one mildly nonlinear application for which direct simulations need to take a leading part is in establishing confidence in the dominant instability of a flow, while direct simulations are the primary tool when nonlinear effects are stronger than can be handled by existing asymptotic methods. The characteristics of existing algorithms for transition simulations are discussed, along with algorithmic improvements which would extend the range of problems amenable to numerical simulations. Current and future issues and problems are outlined.

Zang, Thomas A.↗

NASA NTRS1990

Numerical study of subcritical flow with fluid injection

It is suggested that the study of synthetic flows, where controlled experiments can be performed, is useful in understanding turbulent flow structures. The early states of formation of hairpin structures in shear flows and the subsequent evolution of these structures is studied in shear flows and the subsequent evolution of these structures is studied through numerical simulations, by developing full-time dependent three-dimensional flow solution of an initially laminar (subcritical) flow in which injection of fluid through a narrow streamwise slot from the bottom wall of a plate is carried out. Details of the numerical approach and significance of the present findings are reported in this work.

Balasubramanian, R.↗

NASA NTRS1990

Numerical simulation of turbulent flows around airfoil and wing

During the last years the simulation of compressible viscous flows has received much attention. While the numerical methods were improved drastically, a satisfactory modeling of the Reynolds stresses is still missing. In this paper, after a short description of the numerical procedure used for solving the Reynolds equations, experiments with a promising simple turbulence model are discussed.

Marx, Yves P.↗

NASA NTRS1991

Numerical simulations of the nonlinear kink modes in linearly stable supersonic slip surfaces

High-resolution numerical simulations of supersonic slip surfaces were performed using the Cray 2 at the Minnesota Supercomputer Center to confirm earlier analytic nonlinear stability calculations of such structures. The present study presents a numerical solution for the problem solved analytically by Artola and Majda (1987) and follows growing modes well into the large-amplitude regime. The response of an equal-density Mach-4 slip surface to a variety of impinging nonlinear sound wave trains is computed using the piecewise-parabolic method (PPM). The nature of the nonlinear kink modes observed in the simulations was found to be similar to that discussed by Artola and Majda. Most of the speeds moved in either direction, with speeds near the predicted value. It is suggested that the stationary modes will eventually dominate the flow at much later times, and it is argued that the stationary modes are more disruptive than the propagating kink modes.

Pedelty, Jeffrey A.↗

NASA NTRS1990

Numerical simulation of actively controlled space structures

The numerical simulation of large, actively controlled space structures is a problem that has received considerable attention. A new computational method is presented in this paper, which simulates the vibration suppression of a large space structure by a linear compensator. The structure is assumed to be modeled by a large linear finite element model. Nested circularly linked lists and the trapezoidal rule are key aspects of this algorithm. There is an emphasis on generality, while establishing an equivalence between numerical stability and system stability.

Quan, Ralph↗