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It is shown that, in a time-dependent nonequilibrium flow analysis, erroneous and unstable solutions can result from the use of temperature equations and flow variables other than pressure in fitting the bow shock. A formulation is presented that has been critically evaluated by comparison with a previous one and found to yield steady and more accurate solutions in conserving total enthalpy.
Rudy and Bushnell's (1972) mixing length theory for the prediction of mean velocity fields in turbulent shear layers is extended to include supersonic free turbulent mixing. The normal momentum equation is coupled with the conventional equations of motion and is solved iteratively. Results show that transverse static pressure variation has very little effect on the mean flow variables in compressible free turbulent shear layers.
We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.
A detailed analysis of steady normal shock waves in a layer of lunar ash by the theory of two phase flow of a mixture of a gas and small solid particles is presented. New terms of pressure gradient and virtual mass forces in the particle momentum equation and the particle kinetic energy and work done in the particle energy equation are included in the fundamental equations and their influences are investigated. The flow variables as functions of the free stream Mach number, initial particle volume fraction and the density ratio G are presented. The thickness of the relaxation zone is found to increase with decreasing initial particle volume fraction and almost independent of G for any given values of free stream Mach number. A new empirical relation of the drag coefficient for the spherical particles in the mixture is proposed to fit experimental data.
A wind-tunnel experiment was performed to examine the effect of turbulence enhancers on the growth of a flat-plate turbulent boundary layer. The free-stream Mach number was varied from 0.6 to 0.9 with unit Reynolds numbers of 6.56 million/m and 13.12 million/m. Several configurations of high-drag objects were mounted near the leading edge of a long flat plate to introduce momentum losses. Measurements of both mean and time-variable flow parameters were made at downstream locations to quantify the influence of the turbulence enhancers. A configuration consisting of two rows of alternately spaced, vertical, 0.317-cm-diameter cylinders of 16 and 12 diameters length produced 1/9to 1/7-power velocity profiles. Unsteady total-temperature and static-pressure profiles were found to be similar to natural turbulent boundary-layer profiles. The techniques presented can be useful whenever thick turbulent boundary layers are required, but the natural growth of the layer is limited by the test facility.
A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable. To close the system, a formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer. The model is tested in simplified versions which depend only on roughness, surface buoyancy, and Coriolis effects by comparison with planetary-boundary-layer wind- and temperature-profile observations, measurements of flat-plate boundary layers in a thermally stratified wind tunnel and observations of profiles of terms in the turbulent kinetic-energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.
Comparisons with experimental data and the results of other computational methods demonstrated that very accurate solutions can be obtained by using relatively few lines with the method of lines approach. This method is semidiscrete and has relatively low core storage requirements as compared with fully discrete methods since very little data were stored across the shock layer. This feature is very attractive for three dimensional problems because it enables computer storage requirements to be reduced by approximately an order of magnitude. In the present study it was found that nine lines was a practical upper limit for two dimensional and axisymmetric problems. This condition limits application of the method to smooth body geometries where relatively few lines would be adequate to describe changes in the flow variables around the body. Extension of the method to three dimensions was conceptually straightforward; however, three dimensional applications would also be limited to smooth body geometries although not necessarily to total of nine lines.
A self-synchronizing schlieren flow visualization technique has been developed to study unsteady periodic flows which may result from aeroelastic effects. The technique allows the experimentalist to stroboscopically 'freeze' the streak line pattern at any phase in one period of the motion by driving the schlieren light source with an electronically processed synchronizing signal that is derived by measuring a periodic flow variable with a convenient sensor. Results for the visualization of the near-wake behind an oscillating airfoil at low speeds which show an ordered series of discrete vortices and a curious short-wave-length wake disturbance are examined. Results are also presented for edge tone sound generation.
A steady-state analysis is conducted to examine the basic flow structure of a non-Newtonian fluid in a domain including an inflow region, a contraction region, and an outflow region. A Cartesian grid system is used throughout the entire flow domain, including the contraction region, thus creating an irregular grid cell structure adjacent to the curved boundary. At node points adjacent to the curved boundary symmetry conditions are derived for the different flow variables in order to solve the governing difference equations. Attention is given to the motion and non-Newtonian constitutive equations, the boundary conditions, the numerical modeling of the non-Newtonian equations, the stream function contour lines for the non-Newtonian fluid, the vorticity contour lines for the non-Newtonian fluid, the velocity profile across the contraction, and the shear stress contour lines for the non-Newtonian fluid.
The indicial method for calculating flutter derivatives for two-dimensional airfoils at transonic speeds is discussed, with particular attention given to the effect of a moving shock on the flow variables in the indicial method. An expression for the pressure coefficient is developed on the basis of an explicit treatment of the shock motion; the pressure distribution may then be calculated for general oscillations through use of the indicial method. Explicit inclusion of the shock motion is not necessary if only the lift and pitching moment coefficients are desired.
Solutions to the one-fluid solar-wind equations that include pressure and heating due to outwardly propagating Alfven waves are presented. The solutions are given for two forms of the heat flux: the classical Spitzer (1962) formula and a 'collisional' heat flux. Both high-speed and low-speed solar-wind streams are considered. A comparison of solutions with and without waves shows that the solutions without waves cannot come close to reproducing observations of total mass and energy flux at 1 AU, while those with waves are capable of bringing nearly all flow variables into reasonable agreement with the observations. The required wave flux is found to be about 100,000 erg/sq cm per sec for the high-speed streams and an order of magnitude less for the low-speed streams. It is concluded that the pressure and heating due to outwardly propagating Alfven waves are important elements of solar-wind dynamics that cannot be neglected and that wave heating is especially important for the protons in high-speed streams.
The aeronautical R & D effort in NASA is discussed with emphasis on those areas where major needs and opportunities exist. In aerodynamics, areas selected for discussion include computational aerodynamics, transonic test techniques, high Reynolds number research, skin friction drag reduction, and propulsive lift. In propulsion, consideration is given to the areas of fuel-efficient subsonic propulsion, variable-flow engines, hypersonic propulsion, alternate fuels, and aircraft noise reduction. Consideration is also given to the utilization of advanced composites and integrated avionic systems.
The acoustic pressure fluctuations due to large-scale finite amplitude disturbances in a free turbulent shear flow are calculated. The flow is decomposed into three component scales; the mean motion, the large-scale wave-like disturbance, and the small-scale random turbulence. The effect of the large-scale structure on the flow is isolated by applying both a spatial and phase average on the governing differential equations and by initially taking the small-scale turbulence to be in energetic equilibrium with the mean flow. The subsequent temporal evolution of the flow is computed from global energetic rate equations for the different component scales. Lighthill's theory is then applied to the region with the flowfield as the source and an observer located outside the flowfield in a region of uniform velocity. Since the time history of all flow variables is known, a minimum of simplifying assumptions for the Lighthill stress tensor is required, including no far-field approximations. A phase average is used to isolate the pressure fluctuations due to the large-scale structure, and also to isolate the dynamic process responsible. Variation of mean square pressure with distance from the source is computed to determine the acoustic far-field location and decay rate, and, in addition, spectra at various acoustic field locations are computed and analyzed. Also included are the effects of varying the growth and decay of the large-scale disturbance on the sound produced.
Detailed parametric studies of the effect of grid system on finite element calculation for potential flows were made. These studies led to the formulation of a design criteria for optimum mesh system and the development of two methods to generate the optimum mesh system. The guidelines for optimum mesh system are: (1) the mesh structure should be regular; (2) the element should be as regular and equilateral as possible; (3) the distribution of size of element should be consistent with that of flow variables to insure maximum uniformity in error distribution; (4) for non-Dirichlet boundary conditions, smaller boundary elements or higher order interpolation functions should be used; and (5) the mesh should accommodate the boundary geometry as accurately as possible. The results of the parametric studies are presented.
A users manual is presented for a computer program that prepares the bulk of the input data set required for the Denton three dimensional turbomachine blade row analysis code. The Denton input is generated from a minimum of geometry and flow variable information by using cubic spline curve fitting procedures. The features of the program are discussed. The input is described and special instructions are included to assist in its preparation. Sample input and output are included.
A three-level, time-split, mixed spectral/finite difference method for the numerical solution of the three-dimensional, compressible Navier-Stokes equations has been developed and implemented on the Control Data Corporation (CDC) CYBER-203. This method uses a spectral representation for the flow variables in the streamwise and spanwise coordinates, and central differences in the normal direction. The five dependent variables are interleaved one horizontal plane at a time and the array of their values at the grid points of each horizontal plane is a typical vector in the computation. The code is organized so as to require, per time step, a single forward-backward pass through the entire data base. The one-and two-dimensional Fast Fourier Transforms are performed using software especially developed for the CYBER-203.
Computer program (MERNEW3D) developed that prepares bulk of input data set required for Denton three-dimensional inviscid turbomachine-blade-row analysis code. Denton input generated from minimum of geometry and flow-variable information by using cubic spline curve fits for interpolation and extrapolation. Curve-fitting procedures taken from previously developed and widely used NASA computer program (MERIDL), which performs meridional streamsurface analysis.
Numerical and experimental simulation of unsteady airflow through the control valve and slotted air duct of a circulation control rotor is described. The numerical analysis involves the solution of the quasi-one-dimensional compressible fluid-dynamic equations in the blade air duct together with the coupled isentropic flow equations for flow into the blade through the valve and out of the blade through the Coanda slot. Numerical solutions are compared with basic experimental results obtained for a mockup of a circulation control rotor and its pneumatic valving system. The pneumodynamic phenomena that were observed are discussed with particular emphasis on the characteristic system time lags associated with the response of the flow variables to transient and periodic control valve inputs.