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At least 235 records · Page 13

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NASA NTRS1978

Numerical solution of a three-dimensional shock wave and turbulent boundary-layer interaction

A rapid numerical scheme is used to solve the complete mass-averaged Navier-Stokes equations for supersonic turbulent flow over a three-dimensional compression corner. A simple eddy viscosity model is developed, and the interaction of a swept shock wave and a three-dimensional turbulent boundary layer is studied. Good agreement is obtained between the present results and experimental measurements for the case of a wedge with an angle of 6 deg on a flat-plate sidewall. For the case of a 12-deg wedge angle, the computed results do not show the existence of a peak pressure found experimentally. However, the range of interaction, the plateau pressure, and the peak heat transfer are closely predicted for all cases. The high heat transfer near the axial corner is due to the thinning of the boundary layer and inflow of fresh high-momentum fluid. The heat transfer is relieved through pressure reduction and boundary-layer thickening.

Hung, C. M.↗

NASA NTRS1977

Interacting turbulent boundary layer over a wavy wall

This paper is concerned with the two-dimensional supersonic flow of a thick turbulent boundary layer over a train of relatively small wave-like protuberances. The flow conditions and the geometry are such that there exists a strong interaction between the viscous and inviscid flow. The problem cannot be solved without inclusion of interaction effects due to the occurrence of the separation singularity in classical boundary layer methods. Here the interacting boundary layer equations are solved numerically using a time-like relaxation method with turbulence effects represented by the inclusion of the eddy viscosity model of Cebeci and Smith. Results are presented for flow over a train of up to six waves for Mach numbers of 2.5 and 3.5, Reynolds numbers of 10,000,000/m and 32,000,000/m, and wall temperature ratios of 0.4 and 0.8. Limited comparisons with independent experimental and analytical results are also given.

Polak, A.↗

NASA NTRS1977

Navier-Stokes solution for the laminar and turbulent supersonic flow near the trailing edge of a flat plate

The present paper deals with problems of two-dimensional laminar and turbulent flow of a viscous incompressible fluid near the trailing edge of a thin flat plate. The complete system of Navier-Stokes equations is solved by means of MacCormack's finite-difference scheme. In the laminar case, the results are compared with the triple deck solution of Daniels (1973). The comparisons indicate that the asymptotic triple deck theory for supersonic trailing-edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clausner algebraic eddy viscosity model is used, showing that the region of upstream influence is roughly of the order of the boundary layer thickness.

Hussaini, M. Y.↗

NASA NTRS1978

Effect of wall temperature on a supersonic turbulent boundary layer

Measurement of mean flow profiles in a fully developed Mach 3 turbulent boundary layer with negligible pressure gradient is reported. Data were acquired at several streamwise locations for wall-to-total temperature ratios of 0.94, 0.71, and 0.54. The results demonstrate that the velocity defect formulation of the law-of-the-wake, which successfully correlates compressible, adiabatic boundary layers, is also valid for nonadiabatic flows. It is also shown that for adiabatic walls, the linear Crocco relation between total temperature and velocity does not provide a valid test of the nature of the boundary-layer flow for practical cases where the Prandtl number departs from unity. Finally, the turbulent shear stress, mixing length, and eddy viscosity were extracted from the 'time-averaged' conservation equations using the measured mean flow profiles and found to be insensitive to wall temperature. In particular, the latter properties are in good agreement with earlier compressible, adiabatic correlations of turbulent transport properties.

Laderman, A. J.↗

NASA NTRS1978

An evaluation of several compressible turbulent boundary-layer models Effects of pressure gradient and Reynolds number

Computations, employing several turbulence models, are compared with a series of attached supersonic turbulent boundary-layer experiments over an extensive range of Reynolds numbers (11.7 x 10 to the 6th to 314 x 10 to the 6th). These experiments included measurements of surface pressure and skin friction for adverse pressure gradients ranging in magnitude from those of previous investigations to an order of magnitude greater. The turbulence models evaluated include algebraic and two-equation eddy-viscosity models and two full Reynolds stress models. In general all the models tested performed well independently of the magnitude of the pressure gradient or Reynolds number and could predict the measured skin friction for most cases with sufficient accuracy for engineering purposes.

Horstman, C. C.↗

NASA NTRS1978

Comparison of multiequation turbulence models for several shock-separated boundary-layer interaction flows

Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows. The types of flow studied are: (1) a normal shock at transonic speeds in both a circular duct and a two-dimensional channel; (2) an incident oblique shock at supersonic speeds on a flat surface; and (3) a two-dimensional compression corner at supersonic speeds. Established zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence models are each utilized to describe the Reynolds shear stress for the three classes of flows. These models are assessed by comparing the calculated values of skin friction, wall pressure distribution, velocity, Mach number, and turbulent kinetic energy profiles with experimental measurements. Of the models tested the two-equation model results gave the best overall agreement with the data.

Viegas, J. R.↗

NASA NTRS1978

Numerical solution of two-dimensional turbulent blunt body flows with an impinging shock

An implicit finite-difference method has been developed to compute two-dimensional, turbulent, blunt body flows with an impinging shock wave. The full time-averaged Navier-Stokes equations are solved with algebraic eddy viscosity and turbulent Prandtl number models employed for shear stress and heat flux. The irregular-shaped bow shock is treated as a discontinuity across which the Rankine-Hugoniot equations are applied. A Type III turbulent shock interference flow field has been computed and the numerical results compare favorably with existing experimental data. In addition, comparisons are made between the present implicit code and a previous explicit code.

Tannehill, J. C.↗

NASA NTRS1978

Theoretical and experimental study of the drag of multielement airfoils

The viscous/potential flow past single-element and multielement airfoils is studied theoretically and experimentally. A computerized analysis, based on iteratively coupled potential-flow and boundary-layer analysis, is used to predict the flow field of the airfoil. The method yields detailed characteristics of conventional laminar and turbulent boundary layers, turbulent wakes, and confluent boundary layers. The viscous flows are analyzed with a method that uses finite-difference solutions of the boundary-layer equations. Reynolds stress in the boundary layers and wakes is simulated with eddy viscosity models for the various flow zones. The viscous calculations are carried into the wake of the airfoil where the drag is found from the defect in the wake momentum.

Olson, L. E.↗

NASA NTRS1978

A vortex model for transport in the polar stratosphere

A semi-empirical model based on a Gaussian vorticity distribution was developed for determining eddy diffusivity and wind transport distributions in the polar stratosphere. The model uses as input data pressure surface heights measured at periods of the year when the stratospheric polar vortex exhibits nearly circular patterns around the pole. The components of the polar wind velocities that result from a Prandtl eddy viscosity distribution are found to be in general agreement with those obtained by other investigators.

Eberstein, I. J.↗

NASA NTRS1979

Numerical solution of the Navier-Stokes equations for arbitrary two-dimensional multi-element airfoils

The development of a numerical simulation of time dependent, turbulent, compressible flow about two dimensional multi-element airfoils of arbitrary shape is described. The basis of this simulation is a technique of automatic numerical generation of coordinate systems fitted to the multiple bodies regardless of their number or shape. Procedures developed whereby the coordinate lines are automatically concentrated in the boundary layer at any Reynolds number are discussed. The compressible turbulent solution involves an algebraic eddy viscosity turbulence model. The laminar version was run for transonic flow at free stream Mach numbers up to 0.9.

Thompson, J. F.↗

NASA NTRS1979

Computation of turbulent near wake for asymmetric airfoils

A numerical procedure for studying the turbulent near wake of two dimensional airfoil sections is presented. The Reynolds Navier-Stokes equations were written for flow about bodies of arbitrary geometry and solved on an arbitrary nonuniform curvilinear computational mesh. Eddy viscosity and Reynolds stress turbulence transport models are considered. Specific examples are shown for airfoil section by using an algebraic viscosity model with streamwise relaxation and the interactive Reynolds stress model.

Deiwert, G. S.↗

NASA NTRS1979

Mesospheric heating due to intense tropospheric convection

A series of rocket measurements made twice daily at Wallops Island, Va., revealed a rapid heating of the mesosphere on the order of 10 K on days when thunderstorms or squall lines were in the area. This heating is explained as the result of frictional dissipation of vertically propagating internal gravity waves generated by intense tropospheric convection. Ray-tracing theory is used to determine the spectrum of gravity wave groups that actually reach mesospheric heights. This knowledge is used in an equation describing the spectral energy density of a penetrative convective element to calculate the fraction of the total energy initially available to excite those waves that do reach the level of heating. This value, converted into a vertical velocity, is used as the lower boundary condition for a multilayer model used to determine the detailed structure of the vertically propagating waves. The amount of frictional dissipation produced by the waves is calculated from the solutions of the frictionless model by use of a vertically varying eddy viscosity coefficient. The heating produced by the dissipation is then calculated from the thermodynamic equation.

Taylor, L. L.↗

NASA NTRS1978

Wind Field and Trajectory Models for Tornado-Propelled Objects

A mathematical model to predict the trajectory of tornado born objects postulated to be in the vicinity of nuclear power plants is developed. An improved tornado wind field model satisfied the no slip ground boundary condition of fluid mechanics and includes the functional dependence of eddy viscosity with altitude. Subscale wind tunnel data are obtained for all of the missiles currently specified for nuclear plant design. Confirmatory full-scale data are obtained for a 12 inch pipe and automobile. The original six degree of freedom trajectory model is modified to include the improved wind field and increased capability as to body shapes and inertial characteristics that can be handled. The improved trajectory model is used to calculate maximum credible speeds, which for all of the heavy missiles are considerably less than those currently specified for design. Equivalent coefficients for use in three degree of freedom models are developed and the sensitivity of range and speed to various trajectory parameters for the 12 inch diameter pipe are examined.

Redmann, G. H.↗

NASA NTRS1979

Large eddy simulation of turbulent channel flow: ILLIAC 4 calculation

The three-dimensional time dependent equations of motion were numerically integrated for fully-developed turbulent channel flow. A large scale flow field was obtained directly from the solution of these equations, and small scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC 4 computer. The computed flow patterns show that the wall layer consists of coherent structures of low speed and high speed streaks alternating in the spanwise direction. These structures were absent in the regions away from the wall. Hot spots, small localized regions of very large turbulent shear stress, were frequently observed. The profiles of the pressure velocity-gradient correlations show a significant transfer of energy from the normal to the spanwise component of turbulent kinetic energy in the immediate neighborhood of the wall ('the splatting effect').

Kim, J.↗

NASA NTRS1978

Kinetic model of turbulence in an incompressible fluid

A statistical description of turbulence in an incompressible fluid obeying the Navier-Stokes equations is proposed, where pressure is regarded as a potential for the interaction between fluid elements. A scaling procedure divides a fluctuation into three ranks representing the three transport processes of macroscopic evolution, transport property, and relaxation. Closure is obtained by relaxation, and a kinetic equation is obtained for the fluctuation of the macroscopic rank of the distribution function. The solution gives the transfer function and eddy viscosity. When applied to the inertia subrange of the energy spectrum the analysis recovers the Kolmogorov law and its numerical coefficient.

Tchen, C. M.↗

NASA NTRS1979

Computation of three-dimensional turbulent separated flows at supersonic speeds

Numerical solutions of the time-averaged Navier-Stokes equations employing a simple eddy-viscosity model have been obtained for three dimensional turbulent flow fields at supersonic speeds. The computer results are compared with a series of experimental test flows describing the interaction of a swept shock wave with a turbulent boundary layer for various shock-wave strengths. Very good agreement is obtained between the computed and experimental surface and flow-field results. The computed flow fields are examined in detail to investigate the physics of this type of flow field. Questions concerning the existence of a vortex and the relationship between converging surface oil streaks and the resulting flow field are addressed.

Horstman, C. C.↗

NASA NTRS1979

Calculation of transonic aileron buzz

An implicit finite-difference computer code that uses a two-layer algebraic eddy viscosity model and exact geometric specification of the airfoil has been used to simulate transonic aileron buzz. The calculated results, which were performed on both the Illiac IV parallel computer processor and the Control Data 7600 computer, are in essential agreement with the original expository wind-tunnel data taken in the Ames 16-Foot Wind Tunnel just after World War II. These results and a description of the pertinent numerical techniques are included.

Steger, J. L.↗

NASA NTRS1979

Computation of supersonic viscous flows over ogive-cylinders at angle of attack

The parabolic Navier-Stokes (PNS) marching finite-difference method is applied to 3-D viscous flow over pointed ogive-cylinders, and to turbulent flow over a cone. Ogive computations were performed using the new technique recently reported by Vigneron, Rakich, and Tannehill. Comparison is made with experiment and inviscid computations. The present results show that this method, which neglects part of the pressure gradient in the x-momentum equation, is nevertheless valid for flows with a strong favorable pressure gradient. In addition, turbulent separated flow over a cone has been computed using the older PNS code due to Lubard and Helliwell. It is found that one must freeze the turbulent eddy-viscosity model upstream of 3-D separation to get agreement with experiment.

Rakich, J. V.↗