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At least 253 records · Page 14

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NASA NTRS1981

An assessment of theoretical models for viscous and transonic flow

Topics discussed include shear flow models, simplified models for treating separation, classical linear theory, a local linearization theory, a transonic linear theory, a transonic nonlinear theory, the experiment of Davis, and the experiment of Tijdeman. It is concluded that shear flow models, which have proven very accurate in taking into account boundary layer effects for panel flutter, are likely to be less so for lifting surface flutter. For many applications in transonic flow, transonic linear theory will be adequate.

Dowell, E. H.↗

NASA NTRS1979

Experiments in unsteady transonic flow

The static and dynamic response of a 0.5-m-chord airfoil were measured in the NASA-Ames 11- by 11-Foot Transonic Wind Tunnel. The effects of mean angle of attack, Reynolds number, oscillation mode, and frequency were investigated over a range of subsonic and transonic Mach numbers. Unsteady pressure distributions and loads on an oscillating NACA 64A010 airfoil are discussed. The unsteady pressure distributions are compared with classical subsonic theory and with newer unsteady aerodynamic codes. The experimental data are also used to assess the validity of linearity and modal superposition in the transonic-flow regime.

Davis, S. S.↗

NASA NTRS1987

Numerical simulations of unsteady, viscous, transonic flow over isolated and cascaded airfoils using a deforming grid

A compressible, unsteady, full Navier-Stokes, finite difference code was developed for modeling transonic flow through two-dimensional, oscillating cascades. The procedure introduces a deforming grid technique to capture the motion of the airfoils. Results using a deforming grid are presented for both isolated and cascaded airfoils. The load histories and unsteady pressure distributions are predicted for the NASA 64A010 isolated airfoil and compared with existing experimental data. Results show that the deforming grid technique can be used to successfully predict the unsteady flow properties around an oscillating airfoil. The deforming grid technique was extended for modeling unsteady flow in a cascade. The use of a deforming grid simplifies the specification of boundary conditions. Unsteady flow solutions similar to the isolated airfoil predictions are found for a NACA 0012 cascade with zero interblade phase angle and zero stagger. Experimental data for these cases are not available for code validation, but computational results are presented to show sample predictions from the code. Applications of the code to typical turbomachinery flow conditions will be presented in future work.

Huff, Dennis L.↗

NASA NTRS1987

Numerical simulations of unsteady, viscous, transonic flow over isolated and cascaded airfoils using a deforming grid

Huff, Dennis L.↗

NASA NTRS1989

Unsteady transonic flow using Euler equations

An implicit, two factor, split flux, finite volume Euler equations solution algorithms is applied to the time accurate solution of transonic flow about an NACA 0012 airfoil and a rectangular planform supercritical wing undergoing pitch oscillations. Accuracy for Courant numbers greater than one is analyzed. Freezing the flux Jacobians can result in significant savings for steady state solutions; the accuracy of freezing flux Jacobians for unsteady results is investigated. The Euler algorithm results are compared with experimental results for an NACA 0012 and a rectangular planform supercritical wing.

Belk, Dave M.↗

NASA NTRS1985

Application of Runge Kutta time marching scheme for the computation of transonic flows in turbomachines

Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The present study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions, and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in the solution procedure.

Subramanian, S. V.↗

NASA NTRS1987

Application of Runge Kutta time marching scheme for the computation of transonic flows in turbomachines

Numerical solutions of the unsteady Euler equations are obtained using the classical fourth order Runge Kutta time marching scheme. This method is fully explicit and is applied to the governing equations in the finite volume, conservation law form. In order to determine the efficiency of this scheme for solving turbomachinery flows, steady blade-to-blade solutions are obtained for compressor and turbine cascades under subsonic and transonic flow conditions. Computed results are compared with other numerical methods and wind tunnel measurements. The study also focuses on other important numerical aspects influencing the performance of the algorithm and the solution accuracy such as grid types, boundary conditions and artificial viscosity. For this purpose, H, O, and C type computational grids as well as characteristic and extrapolation type boundary conditions are included in solution procedures.

Subramanian, S. V.↗

NASA NTRS1953

On transonic flow past a wave-shaped wall

This report is an extension of a previous investigation (described in NACA rep. 1069) concerned with the solution of the nonlinear differential equation for transonic flow past a wavy wall. In the present work several new notions are introduced which permit the solution of the recursion formulas arising from the method of integration in series. In addition, a novel numerical tests of convergence, applied to the power series (in transonic similarity parameter) representing the local Mach number distribution at the boundary, indicates that smooth symmetrical potential flow past the wavy wall is no longer possible once the critical value of the stream Mach number has been exceeded.

Kaplan, Carl↗

NASA NTRS1978

Conservative implicit schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) were investigated for the solution of matrix equations resulting from finite difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, was introduced by an upwind bias of the density. Two implicit AF procedures are presented and their convergence performance is compared with that of the standard transonic solution procedure, successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. The results indicate that the AF schemes are substantially faster than SLOR.

Holst, T. L.↗

NASA NTRS1982

Procedures for the computation of unsteady transonic flows including viscous effects

Modifications of the code LTRAN2, developed by Ballhaus and Goorjian, which account for viscous effects in the computation of planar unsteady transonic flows are presented. Two models are considered and their theoretical development and numerical implementation is discussed. Computational examples employing both models are compared with inviscid solutions and with experimental data. Use of the modified code is described.

Rizzetta, D. P.↗

NASA NTRS1990

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

Chang, I-Chung↗

NASA NTRS1979

Fast, conservative schemes for the full potential equation applied to transonic flows

Implicit approximate factorization techniques (AF) are investigated for the solution of matrix equations resulting from finite-difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, is introduced by an upwind bias of the density. Two implicit AF procedures are presented, and their convergence performance is compared with that of the standard transonic solution procedure: successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. Results indicate a substantial improvement in convergence rate for AF schemes relative to SLOR.

Holst, T. L.↗

NASA NTRS1977

Implicit finite-difference computations of unsteady transonic flows about airfoils, including the treatment of irregular shock-wave motions

A computer code, LTRAN2, has been constructed that efficiently computes low-frequency unsteady transonic flows about airfoils in motion. The code solves the two-dimensional, nonlinear, low-frequency, small-disturbance equation by an alternating-direction implicit (ADI) algorithm. First, as a check on the code, LTRAN2 is used to solve the linear, low-frequency, small-disturbance equation. The results are compared with known answers from linear theory. Then nonlinear results are presented. Tijdeman's experimental observations of shock wave motions resulting from airfoil flap oscillations are qualitatively reproduced by LTRAN2. These computations compare favorably with those of Magnus and Yoshihara and are obtained in substantially less computer time. Also the underlying theory of the governing equation and the construction of the algorithm are discussed.

Ballhaus, W. F.↗

NASA NTRS1985

Transonic flow analysis for rotors. Part 2: Three-dimensional, unsteady, full-potential calculation

A numerical method is presented for calculating the three-dimensional unsteady, transonic flow past a helicopter rotor blade of arbitrary geometry. The method solves the full-potential equations in a blade-fixed frame of reference by a time-marching implicit scheme. At the far-field, a set of first-order radiation conditions is imposed, thus minimizing the reflection of outgoing wavelets from computational boundaries. Computed results are presented to highlight radial flow effects in three dimensions, to compare surface pressure distributions to quasi-steady predictions, and to predict the flow field on a swept-tip blade. The results agree well with experimental data for both straight- and swept-tip blade geometries.

Chang, I. C.↗

NASA NTRS1973

Relaxation methods for transonic flow about wing-cylinder combinations and lifting swept wings

The mixed elliptic-hyperbolic relaxation method for obtaining steady-state solutions to two-dimensional transonic potential equations is extended to the transonic small disturbance equation in three dimensions. In particular, transonic flow is considered both about nonlifting wing-cylinder combinations and over thin lifting wings with sweep and taper. The treatment is restricted to freestream Mach numbers less than one and to wings with subsonic trailing edges.

Bailey, F. R.↗

NASA NTRS1977

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Butler, T. D.↗

NASA NTRS1980

An approximate factorization solution of the Navier-Stokes equations for transonic flow using body-fitted coordinates with application to NACA 64A010 airfoils

The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.

Copper, G. K.↗

NASA NTRS1981

Predicted and experimental steady and unsteady transonic flows about a biconvex airfoil

Results of computer code time dependent solutions of the two dimensional compressible Navier-Stokes equations and the results of independent experiments are compared to verify the Mach number range for instabilities in the transonic flow field about a 14 percent thick biconvex airfoil at an angle of attack of 0 deg and a Reynolds number of 7 million. The experiments were conducted in a transonic, slotted wall wind tunnel. The computer code included an algebraic eddy viscosity turbulence model developed for steady flows, and all computations were made using free flight boundary conditions. All of the features documented experimentally for both steady and unsteady flows were predicted qualitatively; even with the above simplifications, the predictions were, on the whole, in good quantitative agreement with experiment. In particular, predicted time histories of shock wave position, surface pressures, lift, and pitching moment were found to be in very good agreement with experiment for an unsteady flow. Depending upon the free stream Mach number for steady flows, the surface pressure downstream of the shock wave or the shock wave location was not well predicted.

Levy, L. L., Jr.↗