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At least 37 records · Page 2

Flow of Gas Through Turbine Lattices

This report is concerned with fluid mechanics of two-dimensional cascades, particularly turbine cascades. Methods of solving the incompressible ideal flow in cascades are presented. The causes and the order of magnitude of the two-dimensional losses at subsonic velocities are discussed. Methods are presented for estimating the flow and losses at high subsonic velocities. Transonic and supersonic flows in lattices are then analyzed. Some three-dimensional features of the flow in turbines are noted.

BOUNDARY LAYER - AIRFOILS - CASCADES

The "limiting line" in mixed subsonic and supersonic flow of compressible fluids

It is well known that the vorticity for any fluid element is constant if the fluid is non-viscous and the change of state of the fluid is isentropic. When a solid body is placed in a uniform stream, the flow far ahead of the body is irrotational. Then if the flow is further assumed to be isentropic, the vorticity will be zero over the whole filed of flow. In other words, the flow is irrotational. For such flow over a solid body, it is shown by Theodorsen that the solid body experiences no resistance. If the fluid has a small viscosity, its effect will be limited in the boundary layer over the solid body and the body will have a drag due to the skin friction. This type of essentially isentropic irrotational flow is generally observed for a streamlined body placed in a uniform stream, if the velocity of the stream is kept below the so-called "critical speed." At the critical speed or rather at a certain value of the ratio of the velocity of the undisturbed flow and the corresponding velocity of sound, shock waves appear. This phenomenon is called the "compressibility bubble." Along a shock wave, the change of state of the fluid is no longer isentropic, although still adiabatic. This results in an increase in entropy of the fluid and generally introduces vorticity in an originally irrotational flow. The increase in entropy of the fluid is, of course, the consequence of changing part of the mechanical energy into heat energy. In other words, the part of fluid affected by the shock wave has a reduced mechanical energy. Therefore, with the appearance of shock waves, the wake of the streamline body is very much widened, and the drag increases drastically. Furthermore, the accompanying change in the pressure distribution over the body changes the aerodynamic moment acting on it and in the case of an airfoil decreases the lift force. All these consequences of the breakdown of isentropic irrotational flow are generally undesirable in applied aerodynamics. Its occurrence should be delayed as much as possible by modifying the shape or contour of the body. However, such endeavor will be very much facilitated if the cause or the criterion for the breakdown can be found first.

MACH NUMBER

On rotational conical flow

Some general properties of isoenergetic rotational conical fields are determined. For such fields, provided the physical parameters of the fluid flow are known on a conical reference surface, it being understood that they satisfy certain imposed conditions, it is shown how to construct the hodographs in the various meridional semiplanes, as the envelope of either the tangents to the hodographs or of the osculatory circles.

BODIES - AERODYNAMIC THEORY

Two-dimensional symmetrical inlets with external compression

The purpose of inlets like, for instance, those of air-cooled radiators and scoops is to take a certain air quantity out of the free stream and to partly convert the free-stream velocity into pressure. In the extreme case this pressure conversion may occur either entirely in the interior of the inlet (inlet with internal compression) or entirely in the free stream ahead of the inlet (inlet with external compression). In this report a theory for two-dimensional inlets with external compression is developed and illustrated by numerical examples. Intermediary forms between inlets with internal and external compression which can be derived from the latter are briefly discussed.

FLOW - DIFFUSERS

Theory of plane, symmetrical intake diffusers

The present report ties in with the investigations on the inlet diffusers by P. Ruden. The theory developed by Ruden had produced results which found excellent confirmation in wind-tunnel tests and in spite of certain still-existing defects, are technically very promising. The reasons for the new theory of the diffuser forms indicated by Ruden are twofold: first, the arguments adduced in Ruden's theory deal only with one specific operating condition, that is, a certain ratio of mean velocity within the diffuser to flying speed, while in the present report any desired velocity ratios are involved; second, a different choice of parameters and the increased possibilities of variation result in diffuser forms which cannot be reconciled at once with Ruden's theory. The first enables a theoretical check of the measurements made with Ruden's diffusers at variable velocity ratio, the second permits the calculation of diffuser types which in many respects are superior to Ruden's diffusers.

FLOW - CONFORMAL TRANSFORMATION - HODOGRAPH METHOD

Theoretical and computational dynamics of a compressible flow

An introduction to the theoretical and computational fluid dynamics of a compressible fluid is presented. The general topics addressed include: thermodynamics and physical properties of compressible fluids; 1D flow of an inviscid compressible fluid; shock waves; fundamental equations of the dynamics of a compressible inviscid non-heat-conducting and radiating fluid, method of small perturbations, linearized theory; 2D subsonic steady potential flow; hodograph and rheograph methods, exact solutions of 2D insentropic steady flow equations, 2D steady transonic and hypersonic flows, method of characteristics, linearized theory of 3D potential flow, nonlinear theory of 3D compressibe flow, anisentropic (rotational) flow of inviscid compressible fluid, electromagnetogasdynamics, multiphase flows, flows of a compressible fluid with transport phenomena.

Pai, Shih-I

Design of supercritical cascades with high solidity

The method of complex characteristics of Garabedian and Korn was successfully used to design shockless cascades with solidities of up to one. A code was developed using this method and a new hodograph transformation of the flow onto an ellipse. This code allows the design of cascades with solidities of up to two and larger turning angles. The equations of potential flow are solved in a complex hodograph like domain by setting a characteristic initial value problem and integrating along suitable paths. The topology that the new mapping introduces permits a simpler construction of these paths of integration.

Sanz, J. M.

Design of supercritical cascades with high solidity

The method of complex characteristics of Garabedian and Korn has been successfully used to design shockless cascades with solidities of up to one. A new code has been developed using this method and a new hodograph transformation of the flow onto an ellipse. This new code allows the design of cascades with solidities of up to two and larger turning angles. The equations of potential flow are solved in a complex hodograph-like domain by setting a characteristic initial value problem and integrating along suitable paths. The topology that the new mapping introduces permits a simpler construction of these paths of integration.

Sanz, J. M.

Improved design of subcritical and supercritical cascades using complex characteristics and boundary layer correction

The method of complex characteristics and hodograph transformation for the design of shockless airfoils was extended to design supercritical cascades with high solidities and large inlet angles. This capability was achieved by introducing a conformal mapping of the hodograph domain onto an ellipse and expanding the solution in terms of Tchebycheff polynomials. A computer code was developd based on this idea. A number of airfoils designed with the code are presented. Various supercritical and subcritical compressor, turbine and propeller sections are shown. The lag-entrainment method for the calculation of a turbulent boundary layer was incorporated to the inviscid design code. The results of this calculation are shown for the airfoils described. The elliptic conformal transformation developed to map the hodograph domain onto an ellipse can be used to generate a conformal grid in the physical domain of a cascade of airfoils with open trailing edges with a single transformation. A grid generated with this transformation is shown for the Korn airfoil.

Sanz, J. M.