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At least 109 records · Page 6
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NASA NTRS1985

Computations of unsteady transonic flows

During the last eight years, the subject of computational unsteady transonic aerodynamics has undergone a period of rapid growth. A brief survey of some of the fundamental advances during this period is provided, and some of the research done at NASA Ames Research Center is described in detail. The small-distance potential equation is considered, taking into account features of the unsteady transonic flow, the governing equation, the pressure coefficient, the wake condition, the airfoil tangency condition, the downstream boundary condition, the alternating direction implicit (ADI) algorithm, a grid system, boundary conditions, an airfoil with oscillating trailing edge flap, three types of shock-wave motion, and an example of a simple aeroelastic problem. A description is given of an implicit algorithm for the unsteady full potential equation in conservation form.

Goorjian, P. M.↗
NASA NTRS1985

A simple, accurate and efficient algorithm for unsteady transonic flow

The derivation of an algorithm for computing an airfoil's response to small unsteady perturbations is described. The analysis of the far-field boundary conditions for the flow field, and the application of the time-linearization technique to develop an accurate description of the flow field are discussed. The treatment of moving shock waves is examined. The alternating direction implicit scheme of Ballhaus and Steger (1975) is utilized for the discretization of the governing equations and boundary conditions. Numerical examples demonstrating the applicability of the time-linearization method to determine the correlation between airfoil and pressure distribution are provided. The effect of wind tunnel walls on unsteady transonic testing is studied.

Fung, K.-Y.↗
NASA NTRS1986

Unsteady transonic flow calculations for wing-fuselage configurations

The development of the XTRAN3S wing fuselage capability for predicting transonic unsteady aerodynamic loads for aeroplastic applications is described. The modifications of the XTRAN3S code, and XTRAN3S fuselage modeling based on an alternating-direction implicit finite-difference algorithm for solving a modified transonic small-disturbance equation, are analyzed. The XTRAN3S transonic code is applied to the steady and unsteady calculations for three wing-fuselage configurations and a transport-type wing-fuselage model. The effects of fuselage aerodynamic interference on the transonic unsteady air load and flutter characteristics of wings are investigated. Good correlation is detected for the calculated and experimental pressure distributions of the models confirming the validity of the code.

Batina, J. T.↗
NASA NTRS1986

Transonic potential flow in hyperbolic nozzles

The full potential equation for the classical problem of transonic flow through a hyperbolic nozzle (with or without a shock wave) is solved in conservation form using the finite volume method of Jameson and Caughey (1977). Either a firstor a second-order numerical viscosity is added in the direction of the flow, explicitly, in conservation form. A multigrid alternating direction implicit method is used to solve the difference equations, and the results obtained are compared with analytical and numerical results from previous researches.

Park, M.↗
NASA NTRS1987

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Walters, Robert W.↗
NASA NTRS1987

Relaxation algorithms for the Euler equations

The alternating direction implicit central-difference scheme algorithms may be replaced by successive-line-relaxation (SLR) procedures that are stable in three dimensions. Several Beamand Warming-type codes are presently modified on the basis of SLR solution procedures in order to compute the flows over a cylinder, a NACA-0012 airfoil, and a shock wave reflecting off a plate. Since the codes are written in a 'delta form', the implementation of relaxation procedures that rely only on the corrections is relatively easy; the steady state residual computation and any artificial viscosity terms may be left unchanged.

Wornom, S. F.↗
NASA NTRS1985

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Homicz, G. F.↗
NASA NTRS1987

Evaluation of a research circulation control airfoil using Navier-Stokes methods

The compressible Reynolds time averaged Navier-Stokes equations were used to obtain solutions for flows about a two dimensional circulation control airfoil. The governing equations were written in conservation form for a body-fitted coordinate system and solved using an Alternating Direction Implicit (ADI) procedure. A modified algebraic eddy viscosity model was used to define the turbulent characteristics of the flow, including the wall jet flow over the Coanda surface at the trailing edge. Numerical results are compared to experimental data obtained for a research circulation control airfoil geometry. Excellent agreement with the experimental results was obtained.

Shrewsbury, George D.↗
NASA NTRS1988

Computer modeling of convection in the liquid metal during solidification

Numerical methods are used to study thermally/gravitationally induced convection during solidification. The primary object is aimed at understanding the flow field in the liquid metal pool due to convection. An Al-0.5Fe weight percent alloy is assumed to fill a small scale vertical rectangular enclosure model for this study. The Alternating Direction Implicit method and Successive Overrelaxation method are employed to solve these equations, which include the energy balance equation coupled with the mass and momentum equations. Both transient and steady state conditions under 1 g and low gravity (0.001 g) are investigated. The solutions for the two-dimensional isotherms and streamlines under 1 g conditions are graphically presented. The quantitative results show that the convection which occurs in the liquid metal pool is very small and is likely to have a negligible effect on the solute redistribution ahead of the solid-liquid interface.

Lott, R. L., Jr.↗
NASA NTRS1988

Primitive numerical simulation of circular Couette flow - Carrousel wind tunnel nonturbulent solutions

The azimuthal-invariant, three-dimensional cylindrical, incompressible Navier-Stokes equations are solved to steady state for a finite-length, physically realistic model. The numerical method relies on an alternating-direction implicit scheme that is formally second-order accurate in space and first-order accurate in time. The equations are linearized and uncoupled by evaluating variable coefficients at the previous time iteration. Wall grid clustering is provided by a Roberts transformation in radial and axial directions. A vorticity-velocity formulation is found to be preferable to a vorticity-streamfunction approach. Subject to no-slip, Dirichlet boundary conditions, except for the inner cylinder rotation velocity (impulsive start-up) and zero-flow initial conditions, nonturbulent solutions are obtained for sub- and supercritical Reynolds numbers of 100 to 400 for a finite geometry where R(outer)/R(inner) = 1.5, H/R(inner) = 0.73, and H/Delta-R = 1.5. An axially-stretched model solution is shown to asymptotically approach the one-dimensional analytic Couette solution at the cylinder midheight. Flowfield change from laminar to Taylor-vortex flow is discussed as a function of Reynolds number. Three-dimensional velocities, vorticity, and streamfunction are presented via two-dimensional graphs and three-dimensional surface and contour plots.

Hasiuk, Jan↗
NASA NTRS1988

Solution of the Neumann pressure problem in general orthogonal coordinates using the multigrid technique

The multigrid (MG) technique has been advanced for use with Neumann boundary-value problems in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of incompressible flow using the velocity-pressure formulation of the Navier-Stokes equations. The finite-difference representation of the problem and the formulation of the restriction and coarse-grid correction operators are examined in detail. Maintaining consistency between these and the integral constraint associated with the Neumann problem is found to be critical for the success of the MG technique. The influence of the smoothing operator is examined by employing Gauss-Seidel, alternating-direction implicit, and strongly implicit techniques. The MG procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 14, depending on the type of smoothing operator employed and the values of the problem parameters.

Ghia, U.↗
NASA NTRS1989

Calculating Transonic Flows About Airfoils

Small disturbances and aeroelastic effects simulated. XTRAN2L computer program used to calculate two-dimensional transonic flows about airfoils. Uses time-accurate, alternating-direction, implicit (ADI) finite-difference scheme to solve two-dimensional complete unsteady transonic small-disturbance equation. Engquist-Osher monotone spatial differencing used in ADI solution algorithm to provide robust and efficient program. Written in FORTRAN V.

Seidel, David A.↗
NASA NTRS1989

Unsteady stagnation-point heat transfer during passage of a concentrated vortex

The unsteady boundary layer due to a single rectilinear vortex filament approaching a 2-D stagnation point is investigated. Assuming the vortex remains far from the surface, incompressible potential flow theory is used to determine the time dependent inviscid flow field. The unsteady boundary layer equations are solved by an alternating-direction-implicit finite-difference method. Two mechanisms which cause fluctuations in heat transfer are the unsteady velocity field in the boundary layer and secondly, the unsteady total temperature at the edge of the boundary layer. The relative importance of these mechanisms is dependent upon the total temperature fluctuations relative to the imposed temperature difference. As a vortex approaches a stagnation point it may be forced to one side of the stagnation line or the other, depending on its initial position. Results are presented for both of these cases.

Rigby, David L.↗
NASA NTRS1988

Unsteady transonic aerodynamics and aeroelastic calculations at low-supersonic freestreams

A computational procedure is presented to simulate transonic unsteady flows and corresponding aeroelasticity of wings at low-supersonic freestreams. The flow is modeled by using the transonic small-perturbation theory. The structural equations of motions are modeled using modal equations of motion directly coupled with aerodynamics. Supersonic freestreams are simulated by properly accounting for the boundary conditions based on pressure waves along the flow characteristics in streamwise planes. The flow equations are solved using the time-accurate, alternating-direction implicit finite-difference scheme. The coupled aeroelastic equations of motion are solved by an integration procedure based on the time-accurate, linear-acceleration method. The flow modeling is verified by comparing calculations with experiments for both steady and unsteady flows at supersonic freestreams. The unsteady computations are made for oscillating wings. Comparisons of computed results with experiments show good agreement. Aeroelastic responses are computed for a rectangular wing at Mach numbers ranging from subtransonic to upper-transonic (supersonic) freestreams. The extension of the transonic dip into the upper transonic regime is illustrated.

Guruswamy, Guru P.↗
NASA NTRS1989

Compressible studies on dynamic stall

The purpose of this work is to investigate the effects of compressibility on the dynamic stall phenomenon by numerical simulation of the unsteady flow. The full two-dimensional unsteady compressible Navier-Stokes equations are solved for flows over oscillating airfoils and airfoils pitching rapidly to high angles of attack. The free-stream speeds vary from low subsonic with mild compressibility effects, to moderate subsonic where strong compressibility effects appear close to the leading edge at high angles of attack. An Alternating Direction Implicit scheme is implemented for the numerical solution with the viscous terms retained in both directions. The numerical results are compared with available experimental data for a Sikorsky airfoil for compressible high Reynolds number flows. There is good agreement between the computed and measured unsteady lift and pitching moment coefficient time histories. The computed high-speed subsonic unsteady results give a good picture of the entire flow field, and the dynamic stall progression in the compressible flow regime. It was observed that compressibility effects are more severe close to the leading edge at moderate angles of attack, and that the dynamic stall vortex appears at lower angles of attack as the free-stream speed increases.

Ekaterinaris, J. A.↗
NASA NTRS1989

Unsteady stagnation-point heat transfer during passage of a concentrated vortex

The unsteady boundary layer due to a single rectilinear vortex filament approaching a two-dimensional stagnation point is investigated. The unsteady boundary-layer equations are solved by an alternating-direction-implicit finite-difference method. Two mechanisms which cause fluctuations in heat transfer are the unsteady velocity field in the boundary layer and secondly, the unsteady total temperature at the edge of the boundary layer. The relative importance of these mechanisms is dependent upon the total temperature fluctuations relative to the imposed temperature difference.

Rigby, David L.↗
NASA NTRS1989

Analysis of a second-order-accurate finite-volume method for temporally-growing compressible shear layers

A finite-volume method for solving the compressible laminar Navier-Stokes equation in two dimensions is assessed for use in the simulation of transitional flows. The method is second-order-accurate, uses alternating-direction-implicit time integration, and a total-variation-diminishing smoothing operator in the inviscid flux terms. The test problem was a free shear layer with a forced periodicity in x at a specified wavelength and with the parallel mean flow specified as a hyperbolic-tangent profile. A grid refinement investigation verified this method to be second-order-accurate with less than 4 percent error in the growth rate of isolated modes on a 32 by 64 grid. The interaction between modes of similar amplitude was small, less than 1 percent. However, in cases where there was a dominant mode, numerical phase error pumped energy into all other modes. This error results in nonphysical growth rate for modes whose energy content is several orders of magnitude below the dominant mode. In the case when the dominant mode saturates, the pumping action stops and the growth rate of the next largest growing mode regains physical significance.

Atkins, H. L.↗
NASA NTRS1990

Evolution of midplate hotspot swells: Numerical solutions

The evolution of midplate hotspot swells on an oceanic plate moving over a hot, upwelling mantle plume is numerically simulated. The plume supplies a Gaussian-shaped thermal perturbation and thermally-induced dynamic support. The lithosphere is treated as a thermal boundary layer with a strongly temperature-dependent viscosity. The two fundamental mechanisms of transferring heat, conduction and convection, during the interaction of the lithosphere with the mantle plume are considered. The transient heat transfer equations, with boundary conditions varying in both time and space, are solved in cylindrical coordinates using the finite difference ADI (alternating direction implicit) method on a 100 x 100 grid. The topography, geoid anomaly, and heat flow anomaly of the Hawaiian swell and the Bermuda rise are used to constrain the models. Results confirm the conclusion of previous works that the Hawaiian swell can not be explained by conductive heating alone, even if extremely high thermal perturbation is allowed. On the other hand, the model of convective thinning predicts successfully the topography, geoid anomaly, and the heat flow anomaly around the Hawaiian islands, as well as the changes in the topography and anomalous heat flow along the Hawaiian volcanic chain.

Liu, Mian↗