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Publications and source records attributed to Baldwin, B. S..
One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.
A semi-implicit method is applied to solve the Navier-Stokes equations numerically and to evaluate the features of the free-interaction phenomenon that occurs when a shock wave impinges on a Blasius boundary layer. Comparisons are made with predictions of the triple-deck theory and experiment. Results include pressure and skin-friction distribution in the free-interaction region for various values of Reynolds number.
In the present study, problems of laminar and turbulent two-dimensional flow of a viscous compressible fluid near the trailing edge of a thin flat plate are considered. The complete set of Navier-Stokes equations is solved by the finite-difference method of MacCormack (MacCormack and Baldwin, 1975). It is an explicit, predictor-corrector, time-splitting method of second order acuracy. The computational mesh employed has sufficient resolution for all the characteristic lengths suggested by theory. In the laminar case, the present results are compared with the triple deck solution of Daniels (1974). This comparison indicates 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-Clauser algebraic eddy viscosity model is used. The numerical results show that the region of upstream influence is approximately of the order of the boundary layer thickness. The solutions for skin-friction, pressure and wake center-line velocity are presented.
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.
Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.
The time-splitting explicit numerical method of MacCormack is applied to separated turbulent boundary layer flow problems. Modifications of this basic method are developed to counter difficulties associated with complicated geometry and severe numerical resolution requirements of turbulence model equations. The accuracy of solutions is investigated by comparison with exact solutions for several simple cases. Procedures are developed for modifying the basic method to improve the accuracy. Numerical solutions of high-Reynolds-number separated flows over an airfoil and shock-separated flows over a flat plate are obtained. A simple mixing length model of turbulence is used for the transonic flow past an airfoil. A nonorthogonal mesh of arbitrary configuration facilitates the description of the flow field. For the simpler geometry associated with the flat plate, a rectangular mesh is used, and solutions are obtained based on a two-equation differential model of turbulence.
A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.
The reported investigation represents an extension of the time-dependent solution of separated laminar flows based on the complete Navier-Stokes equations reported by MacCormack (1971) and Carter (1973). The current study includes turbulence models in conjunction with the compressible flow equations. The calculations start with a uniform flow except for values imposed along the upstream and outer boundaries. The basic numerical method is discussed along with questions concerning the exponential accuracy and the resolution of the viscous sublayer in a compressed region.
Numerical solutions of the complete, time-averaged conservation equations using several eddy-viscosity models for the Reynolds shear stress to close the equations are compared with experimental measurements in a compressible, turbulent separated flow. An efficient time-splitting, explicit difference scheme was used to solve the two-dimensional conservation equations. The experiment used for comparison was a turbulent boundary layer that was separated by an incident shock wave in a Mach 2.93 flow with a unit Reynolds number of 5.7 x 10 to the seventh power m. Comparisons of predicted and experimental values of surface pressure, shear stress along the wall, and velocity profiles are shown. One of the tested eddy-viscosity models which allows the shear stress to be out of equilibrium with the mean flow produces substantially better agreement with the experimental measurements than the simpler models. A tool is thereby provided for inferring additional information about the flow, such as static pressures in the stream, which might not be directly obtainable from experiments.
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A finite difference machine code is used in the wake vortex problems in the quasi-cylindrical boundary layer approximation. A turbulent energy model containing new features is developed that accounts for the major effects disclosed by more advanced models in which the parameters are not yet established. Several puzzles that arose in previous theoretical investigations of wake vortices are resolved.
Methods for reduction of velocities in trailing vortices of large aircraft are of current interest for the purpose of shortening the waiting time between landings at central airports. We have made finite-difference calculations of the flow in turbulent wake vortices as an aid to interpretation of wind-tunnel and flight experiments directed toward that end. Finite-difference solutions are capable of adding flexibility to such investigations if they are based on an adequate model of turbulence. Interesting developments have been taking place in the knowledge of turbulence that may lead to a complete theory in the future. In the meantime, approximate methods that yield reasonable agreement with experiment are appropriate. The simplified turbulence model we have selected contains features that account for the major effects disclosed by more sophisticated models in which the parameters are not yet established. Several puzzles are thereby resolved that arose in previous theoretical investigations of wake vortices.
A finite-difference machine code is brought to bear on the wake-vortex problem in the quasi-cylindrical boundary-layer approxmation. A turbulent-energy model containing new features is developed that accounts for the major effects disclosed by more advanced models in which the parameters are not yet established. Several puzzles are resolved that arose in previous theoretical investigations of wake vortices.
For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.
Properties of the shock relations for steady, irrotational, transonic flow are discussed and compared for the full and approximate governing potential in common use. Results from numerical experiments are presented to show that the use of proper finite difference schemes provide realistic solutions and do not introduce spurious shock waves. Analysis also shows that realistic drags can be computed from shock waves that occur in isentropic flow. In analogy to the Oswatitsch drag equation, which relates the drag to entropy production in shock waves, a formula is derived for isentropic flow that relates drag to the momentum gain through an isentropic shock. A more accurate formula for drag, based on entropy production, is also derived, and examples of wave drag evaluation based on these formulas are given and comparisons are made with experimental results.
A finite-difference machine code is brought to bear on the wake-vortex problem in the quasi-cylindrical boundary-layer approximation. A turbulent-energy model containing new features is developed. Parameters of the model are evaluated by comparison of calculated velocities and turbulent intensities with measurements in an axisymmetric wake. Comparisons are made with a previous calculation of the decay of an isolated vortex and with wind tunnel and flight measurements in trailing vortices. A self-similar solution develops at large axial distance that decays with the square root of distance. A slower decay occurs in the preceding transition region.
Application of the continuum, inviscid-flow equations of gas dynamics to predict the effect of thermal radiation on the internal structure of a shock wave