Sound radiation from a turbulent boundary layer.
Acoustic radiation from supersonic compressible turbulent boundary layer calculated from space- time correlation tensors for sound field
ACOUSTIC RADIATION↗
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Hypersonic laminar boundary layers around slender bodies.
Nonsimilar compressible laminar boundary layer equations for hypersonic flow around slender bodies solved by integration based on steepest descent method
Jeng, D. R.↗
Computation of unsteady flows over airfoils
Two methods are described for calculating unsteady flows over rapidly pitching airfoils. The first method is based on an interactive scheme in which the inviscid flow is obtained by a panel method. The boundary layer flow is computed by an interactive method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier-Stokes equations. The solution of these equations is obtained with an approximately factorized numerical algorithm, and with single block or multiple grids which enable grid embedding to enhance the resolution at isolated flow regions. In addition, the attached flow region can be computed by the numerical solution of compressible boundary layer equations. Unsteady pressure distributions obtained with both methods are compared with available experimental data.
Ekaterinaris, J. A.↗
Thermal response behavior of boundary-layer flows
This paper presents an approximate, but general, analysis for the thermal response behavior of incompressible, constant property, laminar boundary layer flow over a smooth object of arbitrary shape. It encompasses the classic time-dependent Leveque problem as its special case. Comparisons with available data show that, for fluids with Prandtl number of the order of unity or larger, this analytical solution is able to provide reasonably accurate results for most engineering applications. Under certain restrictive conditions, it can also be used to predict the thermal response of a compressible boundary layer flow.
Lin, F. N.↗
Turbulence measurements in axisymmetric supersonic boundary layer flow in adverse pressure gradients
Measurements have been made of the mean-flow and turbulence properties in adiabatic turbulent boundary layer flows subjected to adverse pressure gradients. In the freestream region upstream of the adverse pressure gradient the Mach number was 3.86, the unit Reynolds number 5.3 million per foot. The boundary layer developed on the wall of an axisymmetric nozzle and straight test section. The pressure gradients at the test section wall were induced by contoured centerbodies mounted on the wind tunnel centerline. The flow under study simulated that which might be found in an axially symmetric engine inlet of a supersonic aircraft. The results obtained have shown good agreement to exist between the measured normalized turbulent velocity fluctuations and the results from other recent investigations of compressible boundary layers.
Gootzait, E.↗
Design optimization of natural laminar flow fuselages in compressible flow
An optimization method has been developed to design axisymmetric body shapes such as fuselages, nacelles, and external fuel tanks with increased transition Reynolds numbers in subsonic compressible flow. The new design method involves a constraint minimization procedure coupled with analysis of the inviscid and viscous flow regions, and linear stability analysis of the compressible boundary layer. Boundary-layer transition is predicted by a 'hybrid' transition criterion based on Granville's transition criterion and a criterion using linear stability theory coupled with the e(n)-method. A tiptank of a business-jet is used as an example to illustrate that the method can be utilized to design an axisymmetric body shape with extensive natural laminar flow. Boundary layer transition is predicted to occur at a transition Reynolds number of 6.04 x 10 to the 6th on the original tiptank. On the designed body shape, a transition Reynolds number of 7.22 x 10 to the 6th is predicted using compressible linear stability theory coupled with e(n)-method.
Dodbele, Simha S.↗
Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow
We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.
Choudhari, Meelan↗
Computer program for solving compressible nonsimilar-boundary-layer equations for laminar, transitional, or turbulent flows of a perfect gas
A computer program is described which solves the compressible laminar, transitional, or turbulent boundary-layer equations for planar or axisymmetric flows. Three-point implicit difference relations are used to reduce the momentum and energy equations to finite-difference form. These equations are solved simultaneously without iteration. Turbulent flow is treated by the inclusion of either a two-layer eddy-viscosity model or a mixing-length formulation. The eddy conductivity is related to the eddy viscosity through a static turbulent Prandtl number which may be an arbitrary function of the distance from the wall boundary. The transitional boundary layer is treated by the inclusion of an intermittency function which modifies the fully turbulent model. The laminar-boundary-layer equations are recovered when the intermittency is zero, and the fully turbulent equations are solved when the intermittency is unity.
Price, J. M.↗
Some similar laminar flows obtained by quasilinearization.
Laminar compressible boundary layer equations solved by quasi-linearization, considering pressure gradients and hypersonic layers
Libby, P. A.↗
Lee surface flow phenomena over space shuttle at large angles of attack at M sub infinity equal 6
Surface pressure and heat transfer, flow separation, flow field, and oil flow patterns on the leeward side of a space shuttle orbiter model are investigated at a free stream Mach number of 6. The free stream Reynolds numbers are between 1.64 times 10 to the 7th power and 1.31 times 10 to the 8th power per meter, and the angle of attack is varied between 0 deg and 40 deg for the present experiments. The stagnation temperatures for the tests are approximately 500 K and the wall temperature is maintained at 290 K. Existing numerical methods of three-dimensional inviscid supersonic flow theory and compressible boundary layer theory are used to predict the present experimental measurements. Results of the present tests indicate two distinct types of flow separation and surface peak heating depending on the angle of attack.
Zakkay, V.↗
On the calculation of supersonic separating and reattaching flows
A method is developed for solving the laminar and turbulent compressible boundary layer equations for separating and reattaching flows. Results of this method are compared with experimental data for two laminar and three turbulent layer, shock wave interactions. Several Navier-Stokes solutions are obtained for each of the laminar boundary layer, shock wave interactions considered. Comparison of these solutions indicates a first order sensitivity in C sub f to the computational mesh selected in both the viscous and inviscid portions of the flow. Comparison of the present boundary layer solutions with the Navier-Stokes solutions and with data for a given Mach number indicates that as long as the separation bubble is small, the boundary layer approximation yields solutions whose accuracy is comparable to the Navier-Stokes solutions.
Murphy, J. D.↗
Accurate numerical solution of compressible, linear stability equations
The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.
Malik, M. R.↗
Theoretical investigations, and correlative studies for NLF, HLFC, and LFC swept wings at subsonic, transonic and supersonic speeds
Attention is given to the results of theory/experiment-correlation studies for natural laminar flow, LFC, and hybrid-LFC airfoils at subsonic and supersonic Mach numbers. The method of characteristics, integral compressible boundary layer methods for infinitely swept wings, and a method for prediction of separating turbulent boundary layer characteristics. The integral boundary layer methods are found to be successful at predicting both transonic and supersonic transition phenomena. Computations for wings with 0-50 deg sweep angle, Reynolds number range of 1-30 million, and with and without LFC, are in good agreement with experimental data.
Goradia, S. H.↗
Comparisons of TVD schemes applied to the Navier-Stokes equations
In this study, the following total variation diminishing (TVD) schemes for solving the Navier-Stokes equations have been tested: the Chakravarthy and Szema (1985) upwind biased TVD scheme, the Harten's upwind TVD scheme described by Yee et al. (1983), and the Yee's (1985) symmetric TVD scheme. The schemes have been compared using three test cases. The first case was the one-dimensional shock tube problem which tested the shock-capturing abilities of the schemes. Chakravarthy's and Harten's schemes gave similar results which were found to be more accurate than the results from Yee's scheme. The second case was a compressible boundary layer which tested the schemes's abilities to solve fiscous flows. In this case, the three schemes yielded almost identical results. Finally, the shock/boundary-layer interaction case studied experimentally by Hakkinen et al. (1959) was computed. Here, Chakravarthy's and Yee's schemes compared most favorably with the published data, with Yee's scheme giving slightly better results.
Buelow, Philip E.↗
Theory of instability and transition
The strongly nonlinear area of theory is discussed, as well as linear and weakly nonlinear (i.e., perturbation) theories, and it is noted that the weaknesses of the weakly nonlinear theory are essentially the inappropriate formulation in earlier works and the lack of guidance for the choice of the lowest-order basis. Attention is focused on the areas of theoretical/numerical development contributing to understanding the transition mechanism and new means for analyzing and predicting transition quantitatively. The nonlinear stability of nonparallel flows, linear secondary instability, and nonlinear wave interaction are analyzed. The incompressible flow over a flat plate with zero-pressure gradient is chosen as an example, while applications range to other shear flows including three-dimensional and compressible boundary layers.
Herbert, Thorwald↗
LDA measurements in a Mach 2 flow over a rearward facing step with staged transverse injection
Measurements of the mean velocity field and selected turbulence statistics have been obtained via 2D LDA in a Mach 2 flow over a rearward facing step with downstream transverse injection. Axial mean velocity profiles, profiles of the axial and normal RMS levels, and the correlation coefficient between the axial and normal fluctuating components are presented for locations upstream of the step. These data, through comparison with other reported measurements in zero pressure gradient compressible boundary layers indicate that the boundary layers upstream of the step are consistent with 'quasi-equilibrium' turbulent boundary layers with the adiabatic wall boundary condition. Mean velocity field measurements on the symmetry plane of the tunnel are compared to laser induced iodine fluorescence measurements reported in the literature and obtained in the same facility. This comparison demonstrates the quality of the present LDA data set and shows that particle lag is not significant in the LDA measurements despite the complex nature of the downstream flow.
Wang, J.-A.↗
High speed transition prediction
The main objective of this work period was to develop, maintain and exercise state-of-the-art methods for transition prediction in supersonic flow fields. Basic state and stability codes, acquired during the last work period, were exercised and applied to calculate the properties of various flowfields. The development of a code for the prediction of transition location using a currently novel method (the PSE or Parabolized Stability Equation method), initiated during the last work period and continued during the present work period, was cancelled at mid-year for budgetary reasons. Other activities during this period included the presentation of a paper at the APS meeting in Tallahassee, Florida entitled 'Stability of Two-Dimensional Compressible Boundary Layers', as well as the initiation of a paper co-authored with H. Reed of the Arizona State University entitled 'Stability of Boundary Layers'.
Gasperas, Gediminis↗
Computation of selected eigenvalues of generalized eigenvalue problems
The Arnoldi (1951) and Lanczos (1950) iterative algorithms are used to obtain a few selected eigenvalues of the generalized eigenvalue problem A(x) = lambdaB(x), where A and B are n x n nonsymmetric banded complex matrices. A shift-and-invert strategy is used to increase the rate of convergence toward the desired eigenvalues, and the two approaches are evaluated in view of their performance in a model problem concerning the linear stability of compressible boundary layers. A general scheme for computing the eigenvalues that lie within a 'box' in the complex plane is presented.
Nayar, Narinder↗