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  • 1
    Publication Date: 2013-08-31
    Description: For many internal transonic flows of practical interest, some of the relevant nondimensional parameters typically are small enough that a perturbation scheme can be expected to give a useful level of numerical accuracy. A variety of steady and unsteady transonic channel and cascade flows is studied with the help of systematic perturbation methods which take advantage of this fact. Asymptotic representations are constructed for small changes in channel cross-section area, small flow deflection angles, small differences between the flow velocity and the sound speed, small amplitudes of imposed oscillations, and small reduced frequencies. Inside a channel the flow is nearly one-dimensional except in thin regions immediately downstream of a shock wave, at the channel entrance and exit, and near the channel throat. A study of two-dimensional cascade flow is extended to include a description of three-dimensional compressor-rotor flow which leads to analytical results except in thin edge regions which require numerical solution. For unsteady flow the qualitative nature of the shock-wave motion in a channel depends strongly on the orders of magnitude of the frequency and amplitude of impressed wall oscillations or fluctuations in back pressure. One example of supersonic flow is considered, for a channel with length large compared to its width, including the effect of separation bubbles and the possibility of self-sustained oscillations. The effect of viscosity on a weak shock wave in a channel is discussed.
    Keywords: AERODYNAMICS
    Type: NASA, Langley Research Center, Transonic Symposium: Theory, Application, and Experiment, Volume 1, Part 1; p 261-291
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  • 2
    Publication Date: 2019-06-27
    Description: An asymptotic description is derived for the interaction between a shock wave and a turbulent boundary layer in transonic flow, for a particular limiting case. The dimensionless difference between the external flow velocity and critical sound speed is taken to be much smaller than one, but large in comparison with the dimensionless friction velocity. The basic results are derived for a flat plate, and corrections for longitudinal wall curvature and for flow in a circular pipe are also shown. Solutions are given for the wall pressure distribution and the shape of the shock wave. Solutions for the wall shear stress are obtained, and a criterion for incipient separation is derived. Simplified solutions for both the wall pressure and skin friction distributions in the interaction region are given. These results are presented in a form suitable for use in computer programs.
    Keywords: AERONAUTICS (GENERAL)
    Type: NASA-CR-3194
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  • 3
    Publication Date: 2019-06-28
    Description: The asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer is reviewed. The layers necessary in a rational analysis of the interaction are discussed with emphasis on the differences from an interaction with a laminar boundary layer, the uncoupling of solutions for the distribution of pressure and skin friction at the wall, and the role of the Reynolds shear stress in these solutions. The accuracy of asymptotic solutions in flows at Reynolds numbers of technical interest is discussed. Solutions for the distribution of pressure and skin friction at the wall and the shape of the shock are considered for the case where the flow is near separation. For the pressure and skin friction, it is possible to write two simplified partial solutions, one valid at the beginning of the interaction and one valid somewhat downstream of the shock wave. A solution composed of these two parts and a linear interpolation between them appears to give good comparison with experiment; one unknown constant, independent of the parameters of the interaction, must be found from experiment. The simplified relations are presented. Comparison of numerical computations with experimental data indicates a possible value for the constant and shows quite satisfactory results.
    Keywords: AERODYNAMICS
    Type: AGARD Computation of Viscous-Inviscid Interactions; 14 p
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  • 4
    Publication Date: 2019-06-27
    Description: A nonlinear analysis to study tangential mode shock instabilities in a thin annular chamber is carried out by employing a one dimensional two phase detonation wave as a reaction model. It is assumed that phase change and reaction take place only within the wave, which is treated as a discontinuity. The annulus is unrolled and the flow is considered as two dimensional with the coordinate system fixed on the wave front. Between waves, the flow is assumed to be isentropic with no interaction between droplets and burned gases. Jump conditions across the wave are solved for two phase flow. The average pressure along the injection plate is related to the design chamber pressure by the use of overall conservation equations. The wave strength is written in terms of the design parameters of the chamber. The results compare favorably with existing experiments. Finally, the effects of drop size on the wave strength are discussed and a simple criterion which sets the lower limit of validity for this strong wave analysis, is presented.
    Keywords: PROPULSION SYSTEMS
    Format: text
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  • 5
    Publication Date: 2019-06-27
    Description: Interaction between a shock wave and an unseparated turbulent boundary layer is considered. The method of matched asymptotic expansions is used, with solutions valid in the double limit as Reynolds number tends to infinity and Mach number tends to unity. The shock is weak enough that interaction effects can be considered as perturbations to the undisturbed flow; the case considered is that where the sonic line is near the outer edge of the boundary layer. It is shown that, with order estimates for Reynolds stress perturbations, the induced wall pressure distribution can be calculated using only the two outer interaction regions, independent of a specific closure condition and that this solution is in fact a turbulent free interaction solution. A detailed analysis of the inner regions, for which an eddy viscosity model for the Reynolds shear stress is used, provides a description of the variations in velocity, temperature and density near and at the wall.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: SIAM Journal on Applied Mathematics; 29; July 197
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  • 6
    Publication Date: 2019-06-27
    Description: Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.
    Keywords: AERODYNAMICS
    Type: Zeitschrift fuer angewandte Mathematik und Physik; 31; Mar. 25
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  • 7
    Publication Date: 2019-06-27
    Description: An analysis is presented of the flow in the two inner layers, the Reynolds stress sublayer and the wall layer. Included is the calculation of the shear stress at the wall in the interaction region. The limit processes considered are those used for an inviscid flow.
    Keywords: AERODYNAMICS
    Type: NASA-CR-158542
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  • 8
    Publication Date: 2019-06-27
    Description: The method of matched asymptotic expansions is used in analyzing the structure of the interaction region formed when a shock wave impinges on a turbulent flat plate boundary layer in transonic flow. Solutions in outer regions, governed by inviscid flow equations, lead to relations for the wall pressure distribution. Solutions in the inner regions, governed by equations in which Reynolds and/or viscous stresses are included, lead to a relation for the wall shear stress. Solutions for the wall pressure distribution are reviewed for both oblique and normal incoming shock waves. Solutions for the wall shear stress are discussed.
    Keywords: AERODYNAMICS
    Type: NASA. Langley Res. Center Advan. in Eng. Sci., Vol. 4; p 1425-1435
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  • 9
    Publication Date: 2019-07-13
    Description: The structure of transonic shock wave-boundary layer interactions is studied using asymptotic analyses, for an oblique shock impinging on a flat plate boundary layer. Solutions for unseparated laminar and turbulent boundary layers are reviewed, and incipient separation of a turbulent boundary layer is considered.
    Keywords: AERODYNAMICS
    Type: Symposium Transsonicum II; Sep 08, 1975 - Sep 13, 1975; Goettingen
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  • 10
    Publication Date: 2019-06-27
    Description: Tangential mode, non-linear wave motion in a liquid propellant rocket engine is studied, using a two phase detonation wave as the reaction model. Because the detonation wave is followed immediately by expansion waves, due to the side relief in the axial direction, it is a Chapman-Jouguet wave. The strength of this wave, which may be characterized by the pressure ratio across the wave, as well as the wave speed and the local wave Mach number, are related to design parameters such as the contraction ratio, chamber speed of sound, chamber diameter, propellant injection density and velocity, and the specific heat ratio of the burned gases. In addition, the distribution of flow properties along the injector face can be computed. Numerical calculations show favorable comparison with experimental findings. Finally, the effects of drop size are discussed and a simple criterion is found to set the lower limit of validity of this strong wave analysis.
    Keywords: THERMODYNAMICS AND COMBUSTION
    Type: NASA-CR-121194
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