Results for “TRANSONIC FLOW” — Page 19

NASA NTRS1983

Transonic flow simulation of prop-fan configurations

This paper presents the results of a study that used a three-dimensional transonic analysis method to analyze flow around a wing-mounted prop-fan configuration. The transonic analysis method employs a cell-oriented finite volume approach to solve the full potential equation in conservative form over a numerically generated surface-fitted grid. The propeller slipstream effects are simulated using a linearized transpiration boundary condition. The results of analyses of flow over clean wing/body, wing/body/nacelle, and wing/body nacelle with slipstream are compared to test data.

Samant, S. S.↗

NASA NTRS1984

Newton like: Minimal residual methods applied to transonic flow calculations

A computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iterate is based on a Newton like algorithm, and a preconditioned Minimal Residual method is used to seek an approximate solution of the system of linear equations arising at each inner iterate. The present iterative scheme is formulated so that the uncertainties and difficulties associated with many iterative techniques, namely the requirements of acceleration parameters and the treatment of additional boundary conditions for the intermediate variables, are eliminated. Numerical experiments based on the new method for transonic potential flows around the NACA 0012 airfoil at different Mach numbers and different angles of attack are presented, and these results are compared with those obtained by the Approximate Factorization technique. Extention to three dimensional flow calculations and application in finite element methods for fluid dynamics problems by the present method are also discussed. The Inexact Newton like method produces a smoother reduction in the residual norm, and the number of supersonic points and circulations are rapidly established as the number of iterations is increased.

Wong, Y. S.↗

NASA NTRS1985

Newton-like minimal residual methods applied to transonic flow calculations

A computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iterate is based on a Newton like algorithm, and a preconditioned Minimal Residual method is used to seek an approximate solution of the system of linear equations arising at each inner iterate. The present iterative scheme is formulated so that the uncertainties and difficulties associated with many iterative techniques, namely the requirements of acceleration parameters and the treatment of additional boundary conditions for the intermediate variables, are eliminated. Numerical experiments based on the new method for transonic potential flows around the NACA 0012 airfoil at different Mach numbers and different angles of attack are presented, and these results are compared with those obtained by the Approximate Factorization technique. Extention to three dimensional flow calculations and application in finite element methods for fluid dynamics problems by the present method are also discussed. The Inexact Newton like method produces a smoother reduction in the residual norm, and the number of supersonic points and circulations are rapidly established as the number of iterations is increased.

Wong, Y. S.↗

NASA NTRS1985

Status and prospects of computational fluid dynamics for unsteady transonic flow

Applications of computational aerodynamics to aeronautical research, design, and analysis have increased rapidly over the past decade, and these applications offer significant benefits to aeroelasticians. The past developments are traced by means of a number of specific examples, and the trends are projected over the next several years. The crucial factors that limit the present capabilities for unsteady analyses are identified; they include computer speed and memory, algorithm and solution methods, grid generation, turbulence modeling, vortex modeling, data processing, and coupling of the aerodynamic and structural dynamic analyses. The prospects for overcoming these limitations are presented, and many improvements appear to be readily attainable. If so, a complete and reliable numerical simulation of the unsteady, transonic viscous flow around a realistic fighter aircraft configuration could become possible within the next decade. The possibilities of using artificial intelligence concepts to hasten the achievement of this goal are also discussed.

Mccroskey, W. J.↗

NASA NTRS1983

Numerical computation of transonic flow about wing-fuselage configurations on a vector computer

The transonic wing analysis code TWING, which uses the AF2 relaxation algorithm, has been vectorized to run on the Cray-1S computer. Vectorization of this code improved computational efficiency over that of the CDC 7600 computer by factors of 11 to 13. The improvement compares favorably with the prediction of a theoretical performance model. A convenient generalization now permits the treatment of rudimentary wing-fuselage combinations. Flow predictions for a transport configuration in both isolated-wing and wing-fuselage modes show the expected trends in shock strength and position when compared with wind-tunnel results. An isolated fighter wing is examined in terms of execution time on three different computers and in comparison with experimental data. The computational fluid dynamics code produced during this study is a careful union of an efficient three-dimensional, transonic, numerical algorithm and the vector features presently available on modern computers.

Thomas, S. D.↗

NASA NTRS1989

A vapor generator for transonic flow visualization

A vapor generator was developed for use in the NASA Langley Transonic Dynamics Tunnel (TDT). Propylene glycol was used as the vapor material. The vapor generator system was evaluated in a laboratory setting and then used in the TDT as part of a laser light sheet flow visualization system. The vapor generator provided satisfactory seeding of the air flow with visible condensate particles, smoke, for tests ranging from low subsonic through transonic speeds for tunnel total pressures from atmospheric pressure down to less than 0.1 atmospheric pressure.

Bruce, Robert A.↗

NASA NTRS1971

Numerical calculation of transonic flow about slender bodies of revolution

A relaxation method is described for the numerical solution of the transonic small disturbance equation for flow about a slender body of revolution. Results for parabolic arc bodies, both with and without an attached sting, are compared with wind-tunnel measurements for a free-stream Mach number range from 0.90 to 1.20. The method is also used to show the effects of wind-tunnel wall interference by including boundary conditions representing porous-wall and open-jet wind-tunnel test sections.

Bailey, F. R.↗

NASA NTRS1978

A uniqueness proof for a transonic flow problem

The uniqueness of the first-order lifting-line correction to the two-dimensional transonic small disturbance potential for the flow past a lifting, three-dimensional, large-aspect-ratio wing is proved. The correction is the solution of a linear equation of mixed type in the plane slit along the positive x-axis. The boundary data consist of Neumann data, continuity restrictions, the Kutta condition, and the form of the asymptotic behavior at infinity. The zeroth-order flow is assumed to be shock-free, and hence the correction is shock-free.

Cook, L. P.↗

NASA NTRS1979

Vector processor algorithms for transonic flow calculations

This paper discusses a number of algorithms for solving the transonic full-potential equation in conservative form on a vector computer, such as the CDC STAR-100 or the CRAY-1. Recent research with the 'artificial density' method for transonics has led to development of some new iteration schemes which take advantage of vector-computer architecture without suffering significant loss of convergence rate. Several of these more promising schemes are described and 2-D and 3-D results are shown comparing the computational rates on the STAR and CRAY vector computers, and the CYBER-175 serial computer. Schemes included are: (1) Checkerboard SOR, (2) Checkerboard Leapfrog, (3) odd-even vertical line SOR, and (4) odd-even horizontal line SOR.

South, J. C., Jr.↗

NASA NTRS1983

A fast viscous correction method for unsteady transonic flow about airfoils

This study modified the inviscid, small-disturbances, unsteady, transonic code, LTRAN2, so that the viscous effect could be considered for the purpose of improving the code's accuracy without substantially increasing the computational time. By using a conventional integral boundary layer method to determine the displacement thickness and an empirical model of viscous wedge to simulate the suddenly thickened boundary layer behind a shock, it resulted in better agreement with experimental data for both the shock position and the pressure coefficient. Aerodynamic performances were calculated for two supercritical airfoils. When the unsteady procedure was used to obtain steady state results as the initial condition, the unsteady viscous solution for the RAE 2822 airfoil required 100.5% of the computational time of the inviscid solution. When an iterative scheme was used to obtain the steady state results as the initial condition, the unsteady viscous solution for the NLR 7301 airfoil required 88% of the computational time of the inviscid solution.

Lee, S. C.↗

NASA NTRS1988

Navier-Stokes calculations of transonic flows past open and transitional cavities

Computational simulations of deep and transitional cavities at transonic regimes were performed. The three-dimensional unsteady separation on the cavity floor was analyzed, and computational flow visualization inside the cavity was done. A parametric study was performed to investigate the effects of varying Mach number and the ratio delta/D, where delta is the instantaneous boundary layer thickness at the upstream lip and D is the depth. Both time-averaged and instantaneous solutions were obtained. Comparison of the solutions with experimental data were generally favorable; some discrepancies are explained.

Srinivasan, S.↗

NASA NTRS1984

Unsteady transonic flow in cascades

There is a need for methods to predict the unsteady air loads associated with flutter of turbomachinery blading at transonic speeds. The results of such an analysis in which the steady relative flow approaching a cascade of thin airfoils is assumed to be transonic, irrotational, and isentropic is presented. The blades in the cascade are allowed to undergo a small amplitude harmonic oscillation which generates a small unsteady flow superimposed on the existing steady flow. The blades are assumed to oscillate with a prescribed motion of constant amplitude and interblade phase angle. The equations of motion are obtained by linearizing about a uniform flow the inviscid nonheat conducting continuity and momentum equations. The resulting equations are solved by employing the Weiner Hopf technique. The solution yields the unsteady aerodynamic forces acting on the cascade at Mach number equal to 1. Making use of an unsteady transonic similarity law, these results are compared with the results obtained from linear unsteady subsonic and supersonic cascade theories. A parametric study is conducted to find the effects of reduced frequency, solidity, stagger angle, and position of pitching axis on the flutter.

Surampudi, S. P.↗

NASA NTRS1984

Unsteady transonic flow in cascades

There is a need for methods to predict the unsteady air loads associated with flutter of turbomachinery blading at transonic speeds. The results of such an analysis in which the steady relative flow approaching a cascade of thin airfoils is assumed to be transonic, irrotational, and isentropic is presented. The blades in the cascade are allowed to undergo a small amplitude harmonic oscillation which generates a small unsteady flow superimposed on the existing steady flow. The blades are assumed to oscillate with a prescribed motion of constant amplitude and interblade phase angle. The equations of motion are obtained by linearizing about a uniform flow the inviscid nonheat conducting continuity and momentum equations. The resulting equations are solved by employing the Weiner Hopf technique. The solution yields the unsteady aerodynamic forces acting on the cascade at Mach number equal to 1. Making use of an unsteady transonic similarity law, these results are compared with the results obtained from linear unsteady subsonic and supersonic cascade theories. A parametric study is conducted to find the effects of reduced frequency, solidity, stagger angle, and position of pitching axis on the flutter.

Surampudi, S. P.↗

NASA NTRS1997

Computation of Transonic Flows Using Potential Methods

The proposed paper will describe the state of the art associated with numerical solution of the full or exact velocity potential equation for solving transonic, external-aerodynamic flows. The presentation will begin with a review of the literature emphasizing research activities of the past decade. Next, the various forms of the full or exact velocity potential equation, the equation's corresponding mathematical characteristics, and the derivation assumptions will be presented and described in detail. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, will be presented and discussed relative to the more complete Euler or Navier-Stokes formulations. The technical presentation will continue with a description of recently developed full potential numerical approach characteristics. This description will include governing equation nondimensionalization, physical-to-computational-domain mapping procedures, a limited description of grid generation requirements, the spatial discretization scheme, numerical implementation of boundary conditions, and the iteration scheme. The next portion of the presentation will present and discuss numerical results for several two- and three-dimensional aerodynamic applications. Included in the results section will be a discussion and demonstration of a typical grid refinement analysis for determining spatial convergence of the numerical solution and level of solution accuracy. Computer timings for a variety of full potential applications will be compared and contrasted with similar results for the Euler equation formulation. Finally. the presentation will end with concluding remarks and recommendations for future work.

Hoist, Terry L.↗

NASA NTRS1981

Numerical simulation of steady transonic flow about airfoils

A computer code has been developed that couples a fast transonic full-potential AF2 solver with both an efficient integral boundary-layer method and a viscous wedge approximation of the shock/boundary-layer interaction. The efficiency of the coupled analysis methods and the method of coupling has resulted in a uniquely efficient analysis tool. The airfoil geometry is modified by the displacement thickness before the shock and the displacement thickness plus the viscous wedge thickness after the shock by considering the viscous effects as an equivalent transpiration boundary condition. The flow about conventional and supercritical airfoils under moderately strong shock situations has been calculated. Comparisons with experimental data indicate that this viscous correction method has improved the accuracy of the full-potential analysis. Furthermore, the computer time required to obtain a converged solution has been reduced.

Lee, S. C.↗

NASA NTRS1978

Performance of single-stage axial-flow transonic compressor with rotor and stator aspect ratios of 1.19 and 1.26, respectively, and with design pressure ratio of 1.82

The overall and blade-element performance of a low-aspect-ratio transonic compressor stage is presented over the stable operating flow range at 70, 90, and 100 percent design speeds. At design speed the rotor and stage achieved peak efficiencies of 0.872 and 0.845 at pressure ratios of 1.875 and 1.842, respectively. The stage stall margin at design speed was 21.8 percent.

Reid, L.↗

NASA NTRS1979

Computations of unsteady transonic flow governed by the conservative full potential equation using an alternating direction implicit algorithm

A development was the time linearization of the density function. This linearization reduces the solution process from solving just a single equation. Two sample cases were computed. First, a one dimensional traveling shock wave was computed and compared with the analytic solution. Second, a two dimensional case was calculated for a flow field which resulted from a thickening and subsequently, thinning airfoil. The resulting flow field, which included a traveling shock wave, was compared to the flow field obtained from the low frequency, small disturbance, transonic equation.

Goorjian, P. M.↗

NASA NTRS1980

Performance of single-stage axial-flow transonic compressor with rotor and stator aspect ratios of 1.19 and 1.26 respectively, and with design pressure ratio of 2.05

The overall and blade-element performances of a low-aspect-ratio transonic compressor stage are presented over the stable operating flow range for speeds from 50 to 100 percent of design. At design speed the rotor and stage achieved peak efficiencies of 0.876 and 0.840 at pressure ratios of 2.056 and 2.000, respectively. The stage stall margin at design speed was 10 percent.

Moore, R. D.↗