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One dimensional compound compressible nozzle flow solution dependence on initial conditions and nozzle geometry, discussing applications to bypass turbojets and solid propellant motors
By use of the assumption that the pressure-volume relation is linear, a solution to the problem of designing a cascade for a given turning and with a prescribed velocity distribution along the blade in a potential flow of a compressible perfect fluid was obtained by a method of correspondence between potential flows of compressible and incompressible fluids. The designing of an isolated airfoil with a prescribed velocity distribution along the airfoil is considered as a special case of cascade. If the prescribed velocity distribution is not theoretically attainable, the method provides a means of modifying the distribution so as to obtain a physically significant blade shape. Numerical examples are included.
Equations of motion for flutter and stability of coaxial elastic circular cylindrical shells between which flows compressible fluid
Compressible linear boundary-layer stability analyses of two representative axisymmetric fuselage geometries indicate that a favorable effect will be exerted on the characteristics of a fuselage's axisymmetric boundary layer by compressibility. A freestream Mach number increase from 0.6 to 0.8 significantly reduces TS wave growth rates in the laminar boundary layer of the fuselages analyzed. The generally destabilizing effect of increasing length Re number on boundary layer stability can be overpowered by the favorable effects of compressibility on the fluid.
A near-wall two-equation model for compressible flows is proposed. The model is formulated by relaxing the assumption of dynamic field similarity between compressible and incompressible flows. A postulate is made to justify the extension of incompressible models to ammount for compressibility effects. This requires formulation the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilatational part, which is directly affected by these changes. A model with an explicit dependence on the turbulent Mach number is proposed for the dilatational dissipation rate.
An analytical solution for the compressible one-dimensional flow in convergent and divergent ducts with friction is obtained. It is found that a nondimensional parameter, N, can be formed using the friction factor, duct half-angle and the ratio of specific heats of the gas. Seven flow regimes are describable with the solution, based on certain bounds on the magnitude of N. The regimes are discussed and corollary data are presented graphically.
The theory of the hydraulic analogy -- that is, the analogy between water flow with a free surface and two-dimensional compressible gas flow -- and the limitations and conditions of the analogy are discussed. A test was run using the hydraulic analogy as applied to the flow about circular cylinders of various diameters at subsonic velocities extending into the supercritical range. The apparatus and techniques used in this application are described and criticized. Reasonably satisfactory agreement of pressure distributions and flow fields existed between water and air flow about corresponding bodies. This agreement indicated the possibility of extending experimental compressibility research by new methods.
The theory of hydraulic analogy, that is, the analogy between water flow with a free surface and two-dimensional compressible gas flow and the limitations and conditions of the analogy are discussed. A test run was made using the hydraulic analogy as applied to the flow about circular cylinders at various diameters at subsonic velocities extending to the super critical range. The apparatus and techniques used in this application are described and criticized. Reasonably satisfactory agreement of pressure distributions and flow fields existed between water and airflow about corresponding bodies. This agreement indicated the possibility of extending experimental compressibility research by new methods.
Steady, diabatic (nonadiabatic), frictional, variable-area flow of a compressible fluid is treated in differential form on the basis of the one-dimensional approximation. The basic equations are first stated in terms of pressure, temperature, density, and velocity of the fluid. Considerable simplification and unification of the equations are then achieved by choosing the square of the local Mach number as one of the variables to describe the flow. The transformed system of equations thus obtained is first examined with regard to the existence of a solution. It is shown that, in general, a solution exists whose calculation requires knowledge only of the variation with position of any three of the dependent variables of the system. The direction of change of the flow variables can be obtained directly from the transformed equations without integration. As examples of this application of the equations, the direction of change of the flow variables is determined for two special flows. In the particular case when the local Mach number m = 1, a special condition must be satisfied by the flow if a solution is to exist. This condition restricts the joint rate of variation of heating, friction, and area at m = 1. Further analysis indicates that when a solution exists at this point it is not necessarily unique. Finally it is shown that the physical phenomenon of choking, which is known to occur in certain simple flow situations, is related to restrictions imposed on the variables by the form of the transformed equations. The phenomenon of choking is thus given a more general significance in that the transformed equations apply to a more general type of flow than has hitherto been treated. (author)
A two-equation k-epsilon turbulence model is presently modified for applicability to compressible flows by adapting a compressibility correction model. Compressible mixing layer computations show that the reduced growth rate of the mixing layer with increasing convective Mach number is accurately predicted by these means. Preliminary studies of reacting mixing problems involving dissimilar gases show the model's suitability for application to such flows.
Numerical calculation of viscous compressible flow around harmonic oscillating rigid cylinder
The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.
The first application of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The solution scheme can be adapted to the particular requirement in each subdomain. To illustrate these advantages, a Mach 11 shock calculation is presented to study the chemical kinetics initiated as air passes through a fully resolved shock wave.
Turbulent, nonisothermal, viscous, compressible flow in inlet sections of axisymmetric flat channels
A detailed step-by-step computational outline is presented for the design of two-dimensional cascade blades having a prescribed velocity distribution on the blade in a potential flow of the usual compressible fluid. The outline is based on the assumption that the magnitude of the velocity in the flow of the usual compressible nonviscous fluid is proportional to the magnitude of the velocity in the flow of a compressible nonviscous fluid with linear pressure-volume relation.
A multiple-scale model for compressible turbulent flows is proposed. It is assumed that turbulent eddy shocklets are formed primarily by the 'collisions' of large energetic eddies. The extra straining of the large eddy, due to their interactions with shocklets, enhances the energy cascade to smaller eddies. Model transport equations are developed for the turbulent kinetic energies and the energy transfer rates of the different scale. The turbulent eddy viscosity is determined by the total turbulent kinetic energy and the rate of energy transfer from the large scale to the small scale, which is different from the energy dissipation rate. The model coefficients in the modeled turbulent transport equations depend on the ratio of the turbulent kinetic energy of the large scale to that of the small scale, which renders the model more adaptive to the characteristics of individual flow. The model is tested against compressible free shear layers. The results agree satisfactorily with measurements.
Physical properties and rotational effects on isothermal compressible flow across shaft seals
Work was carried out to extend the near-wall models formulated for the incompressible Reynolds stress equations to compressible flows. The idea of splitting the compressible dissipation function into a solenoidal part that is not sensitive to changes of compressibility indicators and a compressible part that is directly affected by these changes is adopted. This means that all models involving the dissipation rate could be expressed in terms of the solenoidal dissipation rate and an equation governing its transport could be formulated to close the set of compressible Reynolds stress equations. The near-wall modelling of the dissipation rate equation is investigated and its behavior near a wall is studied in detail using k-epsilon closure. It is found that all existing modelled equations give the wrong behavior for the dissipation rate near a wall. Improvements are suggested and the resultant behavior is found to be in good agreement with near-wall data. Furthermore, the present modified k-epsilon closure is used too calculate a flat plate boundary layer and the results are compared with four existing k-epsilon closures. These comparisons show that all closures tested give essentially the same flow properties, except in a region very close to the wall. In this region, the present k-epsilon closure calculations are in better agreement with measurements and direct simulation data; in particular, the behavior of the dissipation rate.