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The prediction of boundary layer deceleration and separation in regions of adverse pressure gradients are discussed as an unsolved problem of fundamental practical importance in aerodynamics. A three layered theoretical flow model of boundary layer separation including viscous-inviscid interaction was conceived for the case of subsonic two dimensional steady laminar flow.
The objective of the investigation reported in this thesis is to study the characteristics of a turbomachinery rotor wake, both analytically and experimentally. The constitutive equations for the rotor wake are developed using generalized tensors and a non-inertial frame of reference. Analytical and experimental investigation is carried out in two phases; the first phase involved the study of a cascade wake in the absence of rotation and three dimensionality. In the second phase the wake of a rotor is studied. Simplified two- and three-dimensional models are developed for the prediction of the mean velocity profile of the cascade and the rotor wake, respectively, using the principle of self-similarity. The effect of various major parameters of the rotor and the flow geometry is studied on the development of a rotor wake. Laws governing the decay of the wake velocity defect in a cascade and rotor wake as a function of downstream distance from the trailing edge, pressure gradient and other parameters are derived.
A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on the method of feasible directions coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full potential equation. Results are presented for airfoils designed to have small adverse pressure gradients, high maximum lift, and low pitching moment.
Heat transfer data measured in gaps representative of those being employed for joints in the space shuttle reusable surface insulation (RSI) thermal protection systems (TPS) were assimilated, analyzed, and correlated. Several types of gap were investigated with emphasis on simple butt joints. Gap widths ranged from 0.0 to 0.76 cm and depths ranged from 1 to 6 cm. Laminar, transitional, and turbulent boundary layer flows over the gap opening were investigated. The angle between gap axis and external flow was varied between 0 and pi/2 radians. The contoured cross section gap performed significantly better than all other wide gaps and slightly better than all other narrow gap geometries. Three dimensional heating variations were observed within gaps in the absence of external flow pressure gradients. Interactions between heating within gaps and heating of adjacent top tile surfaces were observed. Gaps aligned with the flow were observed to promote boundary layer transition. Heat transfer correlation equations were obtained for many of the tests. The TPS thickness requirements with and without gaps were computed for a current shuttle entry trajectory. Experimental data employed in the study are summarized. A description of each test facility, run schedule and test conditions, model descriptive information, and heat flux data are included.
A heated-element, skin-friction gage employing a very low thermal conductivity support is described. It is shown that the effective dimension of the gage in the stream direction in only 0.06 mm, including the effects of heat conduction in the supporting material. Because of its small size, the calibration of the gage is independent of the kind of boundary-layer flow (whether laminar or turbulent) and is insensitive to pressure gradients. Construction tolerances can be maintained so that a single universal calibration can be applied. Multiple gages, sufficiently closely spaced so as to interfere with each other, are shown to provide accurate determinations of the locations of the points of boundary-layer separation and reattachment.
A multifluids model to investigate ionospheric dynamics was established on kinetic theory. Its resultant equations are used to examine the following dynamic problems in the gamma region of 80-2000 Km of the ionosphere: (1) propagation of acoustic modes in the 500-2,000 Km of the ionosphere (two fluid model); (2) the relation between the cross field plasma drift instabilities and type I and type II ionospheric irregularities; and (3) time dependent neutral wind structure and horizontal pressure gradient.
Two methods for determining the virtual origin of turbulent boundary layers in hypersonic flow are evaluated. The results of the analyses are restricted to wind-tunnel models having sharp-edged surfaces with zero or small pressure gradients. Virtual origin and skin friction estimates from these two methods are compared with values from a base method for which the virtual origin is calculated from the measured momentum thickness at a station downstream of boundary layer transition.
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.
A detailed experimental study of three-dimensional separation in supersonic flow is described. Three-dimensional wedges affixed to flat plates were used to generate the flow fields that were used to examine the relationship of cross flow to the extent of separation. Models with strong transverse pressure gradients resulted in a diminished extent of separation about the model plane of symmetry but demonstrated expansive growth of separation to a limit with distance from the plane of symmetry. A secondary flow region was found embedded in the separated flow.
Electric fields in the earth's upper atmosphere are capable of setting the neutral atmosphere in motion via ion-neutral collisions as well as pressure gradients from resultant Joule heating. By means of simple models for the high-latitude thermosphere and electric fields a simplified set of coupled equations is solved which show that moderate electric fields, when present for a period of several hours, are capable of displacing the neutral atmosphere of the order of 50 km in the vertical, a few hundred kilometers in the north-south direction and over 1000 km in the east-west direction.
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.
Diffuser is inserted into inlet manifold, producing smooth transition of flow from pipe diameter to manifold diameter. Expected pressure gradient and resulting cell-to-cell temperature gradient are reduced. Outlet manifold has nozzle insert that reduces exit losses.
Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.
An experiment designed to test and guide computations of the interaction of an impinging shock wave with a turbulent boundary layer is described. Detailed mean flow-field and surface data are presented for two shock strengths which resulted in attached and separated flows, respectively. Numerical computations, employing the complete time-averaged Navier-Stokes equations along with algebraic eddy-viscosity and turbulent Prandtl number models to describe shear stress and heat flux, are used to illustrate the dependence of the computations on the particulars of the turbulence models. Models appropriate for zero-pressure-gradient flows predicted the overall features of the flow fields, but were deficient in predicting many of the details of the interaction regions. Improvements to the turbulence model parameters were sought through a combination of detailed data analysis and computer simulations which tested the sensitivity of the solutions to model parameter changes. Computer simulations using these improvements are presented and discussed.
Traction measurements under starved elastohydrodynamic conditions were obtained for a point-contact geometry. Simultaneous measurements of the film thickness and the location of the inlet lubricant boundary were made. Optical interferometry was used to measure film thickness. The thickness of a starved film for combined rolling and sliding conditions varies with the location of the inlet boundary in the same way as previously found for pure rolling conditions. When the fluid velocity distribution is calculated in the inlet region by a Reynolds lubrication analysis, backflow is seen to occur over a portion of the inlet region. Backflow is essential for the establishment of a flooded condition. The location of certain fluid velocity conditions within the inlet region, as suggested in the literature, does not adequately describe the onset of starvation. For the same slide-roll ratio a starved film was observed to possess greater traction than a flooded film. Traction measurements under starved conditions were also compared with those under flooded conditions for equivalent shear rates in the Hertzian region. When the shear rates within the Hertzian region were low and the film was severely starved, the measured tractions were lower than expected. This may be due to large shear stresses developed by the large pressure gradients that are generated in the inlet region when it is severely starved.
The transmission of acoustic disturbances from the interior of a jet into the ambient air is studied. The jet is assumed infinitely long with mean velocity profile independent of streamwise location. The noise generator is a sequence of transient sources drifting with the local fluid and confined to a short length of the jet. In Part 1, supersonic jets are considered. Numerical results for mean-square pressure versus angle in the far-field show unexpected peaks which are very sharp. Analysis of simplified models indicates that these are complex quasi-resonant effects which appear to the stationary observer in a high frequency range. The peaks are real for the idealized model, but would be smoothed by mathematical integration over source position, velocity, and frequency. Subsonic jets were considered in part 2, and a preliminary study of the near-field was attempted. Mean-square radial displacements (or mean radial energy flow or space-time correlations of radial pressure gradient) are first found for very simple cases. The most difficult case studied is a sequence of transient sources at the center of a uniform-velocity circular cylindrical jet. Here a numerical triple integration is required and seems feasible although only preliminary results for mean square radial displacement are now available. These preliminary results show disturbances decreasing with increasing radial distance, and with increasing distance upstream and downstream from the source. A trend towards greater downstream disturbances appears even in the near field.
A thoroughly documented experiment is reported that was specifically designed to test and guide computations of the interaction of an impinging shock wave with a turbulent boundary layer. Detailed mean flow field and surface data are presented for two shock strengths which resulted in attached and separated flows, respectively. Numerical computations are used to illustrate the dependence of the computations on the particulars of the turbulence models. Models appropriate for zero pressure gradient flows predicted the overall features of the flow fields, but were deficient in predicting many of the details of the interaction regions. Improvements to the turbulence model parameters were sought through a combination of detailed data analysis and computer simulations which tested the sensitivity of the solutions to model parameter changes. Computer simulations using these improvements are presented and discussed.
Plug nozzle film cooling data were obtained downstream of a slot located at 42 percent of the total plug length on a J-85 engine. Film cooling reduced the aft end wall temperature as much as 150 K, reduced total pressure loss in the upstream convection cooling passages by 50 percent, and reduced estimated compressor bleed flow requirement by 14 percent compared to an all convectively cooled nozzle. Shock waves along the plug surface strongly influenced temperature distributions on both convection and film cooled portions. The effect was most severe at nozzle pressure ratios below 10 where adverse pressure gradients were most severe.