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Thompkins, W. T., Jr.

Publications and source records attributed to Thompkins, W. T., Jr..

15 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

Giles, M. B.↗
NASA NTRS1984

Conservative streamtube solution of steady-state Euler equations

This paper presents a new method for solving the steady state Euler equations. The method is similar to streamline curvature methods but has a conserative finite volume formulation which ensures correct shock capturing. Either wall position or wall pressure may be prescribed as boundary conditions, permitting both direct and inverse calculations. In supersonic applications the solution is obtained by space-marching while in subsonic and transonic applications iterative relaxation methods are used. Numerical results are given for: (1) supersonic diffuser with oblique shocks (direct calculation); (2) supersonic jet entering still reservoir (inverse calculation); (3) subsonic bump in a channel with 25 percent blockage (direct and inverse); (4) subsonic high-work turbine cascade (direct); and (5) transonic bump in a channel with 12 percent blockage (direct calculation).

Drela, M.↗
NASA NTRS1983

Asymptotic analysis of numerical wave propagation in finite difference equations

An asymptotic technique is developed for analyzing the propagation and dissipation of wave-like solutions to finite difference equations. It is shown that for each fixed complex frequency there are usually several wave solutions with different wavenumbers and the slowly varying amplitude of each satisfies an asymptotic amplitude equation which includes the effects of smoothly varying coefficients in the finite difference equations. The local group velocity appears in this equation as the velocity of convection of the amplitude. Asymptotic boundary conditions coupling the amplitudes of the different wave solutions are also derived. A wavepacket theory is developed which predicts the motion, and interaction at boundaries, of wavepackets, wave-like disturbances of finite length. Comparison with numerical experiments demonstrates the success and limitations of the theory. Finally an asymptotic global stability analysis is developed.

Giles, M.↗
NASA NTRS1983

A study of non-unique solutions of the two-dimensional boundary layer equations at laminar separation and reattachment points

Nonunique laminar boundary layer equation solutions in direct problem calculations are identified for the case of accelerating flow. As a separation or reattachment point is approached, the multiple solutions approach each other and become identical. The computer code used to generate these results was developed for the solution of compressible, laminar or turbulent boundary layer, and free wake problems, in either direct or inverse mode. Similarity solutions in either a primitive variable or a stream function form are possible, and the resulting equations are solved by means of a modified Keller's Box scheme in which the energy equation and turbulence modeling equations are solved simultaneously with the continuity and momentum equations. Examples illustrating the nature of the solutions at the separation and reattachment points are presented.

Drela, M.↗
NASA NTRS1982

A FORTRAN program for calculating three dimensional, inviscid and rotational flows with shock waves in axial compressor blade rows: User's manual

A FORTRAN-IV computer program was developed for the calculation of the inviscid transonic/supersonic flow field in a fully three dimensional blade passage of an axial compressor rotor or stator. Rotors may have dampers (part span shrouds). MacCormack's explicit time marching method is used to solve the unsteady Euler equations on a finite difference mesh. This technique captures shocks and smears them over several grid points. Input quantities are blade row geometry, operating conditions and thermodynamic quanities. Output quantities are three velocity components, density and internal energy at each mesh point. Other flow quanities are calculated from these variables. A short graphics package is included with the code, and may be used to display the finite difference grid, blade geometry and static pressure contour plots on blade to blade calculation surfaces or blade suction and pressure surfaces. The flow in a low aspect ratio transonic compressor was analyzed and compared with high response total pressure probe measurements and gas fluorescence static density measurements made in the MIT blowdown wind tunnel. These comparisons show that the computed flow fields accurately model the measured shock wave locations and overall aerodynamic performance.

Thompkins, W. T., Jr.↗
NASA NTRS1982

Time resolved measurements in a low aspect ratio transonic compressor stage

The time resolved flowfield in a low aspect ratio transonic compressor stage has been studied using a high frequency response sphere probe with a bandpass of D.C. to 20 kHz in a blowdown compressor facility. Averaged over the compressor annulus, the data agree well with those measured with standard pitot type probes on the same stage in a conventional test rig. Not all the spanwise distributions agree, however. These differences are explained as errors in the pitot probe readings due to fluctuations in the flow. The experimental data are compared to the results of a three-dimensional inviscid Euler calculation.

Epstein, A. H.↗
NASA NTRS1981

Boundary treatments for implicit solutions to Euler and Navier-Stokes equations

It seems apparent that for inviscid calculations the differences between the explicit and implicit boundary formulations tested are far smaller than anticipated. New work should focus on understanding of how the convergence rate is limited or affected by boundary formulations. Since the inflow/outflow boundary treatments tested were simple extrapolations, it may be the case that treatments more closely representing the differential equations will prove to have superior convergence properties. However, several such improved boundary treatments were attempted with disappointing results.

Thompkins, W. T., Jr.↗
NASA NTRS1981

A quasi-three-dimensional blade surface boundary layer analysis for rotating blade rows

A quasi-three-dimensional approximation has been developed for a blade boundary layer which involves the calculation of the effect of nonzero pressure gradients, turbulent flow, and blade twist, but includes only a simple coupling between streamlines. The resulting set of equations is solved using Keller's box scheme. The solution scheme is checked against available incompressible flow solutions and then applied to a NASA low aspect ratio transonic compressor stage for which extensive experimental and computational data are available. It is found that the three-dimensional boundary layer separates significantly sooner and has a much larger influence on rotor performance than would be expected from a two-dimensional analysis.

Thompkins, W. T., Jr.↗
NASA NTRS1980

Comparison of experimental and computational shock structure in a transonic compressor rotor

Measurement of passage shock strength in a transonic compressor rotor using a gas fluorescent technique revealed an unexpected variation in shock strength in the radial direction. An axisymmetric idealization would normally predict that the passage shock strength would gradually weaken when moving radially inward until disappearing at the sonic radius. However, the measurements indicated a sharp peak in strength at the nominal sonic radius. Blade boundary layer separation originating at this point accounts for about one half of the total rotor losses. A numerical computation of the three-dimensional inviscid flow, using time-marching techniques, has accurately predicted in general the radial and tangential variations in passage shock strength and in particular the sharp pressure peak at the nominal sonic radius. The overall shock strength was somewhat overpredicted, but this overprediction may be the result of boundary layer separation in the experiment. This paper presents comparisons between the optical density measurements and computational results and in addition a short analytical discussion which demonstrates that the sharp shock strength rise may occur in many transonic compressor rotors.

Haymann-Haber, G.↗
NASA NTRS1980

A miniature high frequency sphere probe

A spherical probe having five surface mounted silicon pressure sensors is described. The probe is 0.2 inches in diameter yielding a frequency response above 30 kHz. A scheme is described for retrieving from the five pressure signals the stagnation and static pressures, Mach number and flow angles in two planes. The calibrations forming the base for this procedure, obtained from steady state tests, are given in the form of polynomials in the two flow angles. A method for compensating the silicon pressure sensors for thermal effects is given. Typical data obtained in the MIT Blowdown Compressor are presented in raw form and after reduction to flow angles, Mach number and stagnation pressure.

Kerrebrock, J. L.↗
NASA NTRS1979

Shock structure in transonic compressor rotors

The inadequacy of axisymmetric theory in modeling the structure of the shock system in a transonic compressor rotor is shown with a simple model. A more accurate model for the flow near the sonic radius is proposed, which is supported by some flow visualization data and three-dimensional computations.

Epstein, A. H.↗
NASA NTRS1976

Three-dimensional flow calculation for a transonic compressor rotor

A numerical calculation of the steady, inviscid, three dimensional flow in a isolated transonic compressor rotor has been completed using MacCormack's second order accurate time-marching scheme. This rotor has a tip Mach number of 1.2, an overall diameter of 2 feet, and inlet hub/tip ratio of 0.5. The computed rotor total pressure ratio is 1.82. Comparisons between the numerical solution, measurements of the intra-blade static density field obtained by gas fluorescence, and time resolved exit flow measurements showed that the inviscid computation accurately models transonic rotor aerodynamics and rotor blade pressure distributions in the upstream portions of the blade passages, the viscous effects influencing mainly the downstream flow.

Thompkins, W. T., Jr.↗
NASA NTRS1976

A comparison of the computed and experimental three dimensional flow in a transonic compressor rotor

The three dimensional inviscid flow in a transonic compressor rotor; total pressure ratio of 1.65, has been numerically computed using MacCormack's time-marching method. This solution is compared to intra-blade static density measurements obtained by gas fluorescence. These results and comparisons illustrate the importance of three dimensional flow phenomena in determining the rotor flow field and show that while the viscous phenomena have an important influence, particularly on the outflow, the inviscid computation properly models the flow in the inlet portion of the rotor passages.

Thompkins, W. T., Jr.↗
NASA NTRS1976

Exit flow from a transonic compressor rotor

The three dimensional unsteady flow field behind a transonic compressor rotor with a design pressure ratio of 1.6 at a tip Mach number of 1.2 has been resolved on the blade passing time scale. Quantities determined were total and static pressures, tangential flow angle, and radial flow angle. The spatial and temporal resolution achieved was sufficient to determine velocity components inside individual blade wakes and in the surrounding flow. From these measurements the flow structure is described at stations immediately behind the rotor and one chord downstream. Some dominant features of the flow just behind the rotor are large radial velocity components, large static pressure fluctuations near the blade wakes, and definite unsteadiness (in rotor coordinates) of the wakes. The wake behavior one chord downstream is described in terms of the effect of the strong mean swirl on the behavior of shear disturbances. In the outer portion of the annulus, where the mean flow approximates a solid body rotation, a strong, persistent oscillatory flow is found with 16 periods in the circumference as roughly predicted by theory. In the inner portion of the annulus the disturbances attenuate axially.

Thompkins, W. T., Jr.↗