Attenuation of sinusoidal disturbances in nonviscous liquid flowing in a long line with distributed leakage
Attenuation of sinusoidal disturbances in nonviscous liquid flowing in long line with distributed leakage
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Attenuation of sinusoidal disturbances in nonviscous liquid flowing in long line with distributed leakage
A method for the solution of the incompressible nonviscous flow through a centrifugal impeller, including the inlet region, is presented. Several numerical solutions are obtained for four weight flows through an impeller at one operating speed. These solutions are refined in the leading-edge region. The results are presented in a series of figures showing streamlines and relative velocity contours. A comparison is made with the results obtained by using a rapid approximate method of analysis.
The boundary layer calculation program (BLAY) is a program code which accurately analyzes the three-dimensional boundary layer of a wing with an undefined plane. In comparison with other preexisting programs, the BLAY is characterized by the following: (1) the time required for computation is shorter than any other; (2) the program is adaptable to a parallel processing computer; and (3) the program is associated with a secondary accuracy in the z-direction. As a boundary layer modification to transonic nonviscous flow analysis programs, it is used to adjust viscous and nonviscous interference problems repeatedly. Its efficiency is an important factor in cost reduction in aircraft designing.
A numerical study of the nonviscous flow characteristics in the cross-sectional planes of a radial inflow turbine scroll is presented. The velocity potential is used in the formulation to determine the flow velocity in these planes resulting from the continuous mass discharge. The effect of the through flow velocity is simulated by a continuous distribution of source/sink in the cross-section. A special iterative procedure is devised to handle the solution of the resulting Poisson's differential equation with Neumann boundary conditions in a domain with generally curved boundaries. The analysis is used to determine the effects of the radius of curvature, the location of the scroll section and its geometry on the flow characteristics in the turbine scroll.
Turbulent flow within turbomachines having arbitrary blade geometries is examined. Effects of turbulence are modeled using two equations, one expressing the development of the turbulence kinetic energy and the other its dissipation rate. To account for complicated blade geometries, the flow equations are formulated in terms of a nonorthogonal boundary fitted coordinate system. The analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between the different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.
A method for analyzing the viscous nonadiabatic flow within turbomachine rotors is presented. The field analysis is based upon the numerical integration of the incompressible Navier-Stokes equations together with the energy equation over the rotors blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. Effects of turbulence are modeled with two equations; one expressing the development of the turbulence kinetic energy and the other its dissipation rate. The method of analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.
A computer program has been developed to obtain subsonic or shockfree transonic, nonviscous flow analysis on the hub-shroud mid-channel flow surface of a turbomachine. The analysis may be for any annular passage, with or without blades. The blades may be fixed or rotating and may be twisted and leaned. The flow may be axial, radial or mixed. Blade surface velocities over the entire blade are approximated based on the rate of change of angular momentum. This gives a 3-D flow picture based on a 2-D analysis. The paper discusses the method used for the program and shows examples of the type of passages and blade rows which can be analyzed. Also, some numerical examples are given to show how the program can be used for practical assistance in design of blading, annular passages, and annular diffusers.
Six numerical examples are presented for steady, two-dimensional, compressible, nonviscous flow in centrifugal compressors with thin straight blades, the center lines of which generate the surface of a right circular cone when rotated about the axis of the compressor. A seventh example is presented for incompressible flow. The solutions were obtained in a region of the compressors, including the impeller tip, that was considered to be unaffected by the diffuser vanes or by the impeller-inlet configuration. Each solution applies to radial and mixed flow compressors with various cone angles but with the same angle between blades on the conic flow surface. The solution also apply to radial and mixed flow turbines with the rotation and the flow direction reversed. The effects of variations in the following parameters were investigated: (1) flow rate, (2) impeller-tip speed, (3) variation of passage height with radius, and (4) angle between blades on conic flow surface. The numerical results are presented in plots of the streamlines and constant Mach number lines. Correlation equations are developed whereby the flow conditions in any impeller with straight blades can be determined (in the region investigated by this analysis) for all operating conditions.
A computer program has been developed to obtain subsonic or shock-free transonic, nonviscous flow analysis on the hub-shroud midchannel flow surface of a turbomachine. The analysis may be for any annular passage, with or without blades. The blades may be fixed or rotating and may be twisted and leaned. The flow may be axial, radial, or mixed. Blade surface velocities over the entire blade are approximated, based on the rate of change of angular momentum. This gives a three-dimensional flow picture based on a two-dimensional analysis. This paper discusses the method used for the program and shows examples of the type of passages and blade rows which can be analyzed. Also, some numerical examples are given to show how the program can be used for practical assistance in design of blading, annular passages, and annular diffusers.
Equations of motion were derived, and a computational procedure is presented, for determining the nonviscous flow characteristics in the cross-sectional planes of a curved channel due to continuous mass discharge or mass addition. An analysis was applied to the radial inflow turbine scroll to study the effects of scroll geometry and the through flow velocity profile on the flow behavior. The computed flow velocity component in the scroll cross-sectional plane, together with the through flow velocity profile which can be determined in a separate analysis, provide a complete description of the three dimensional flow in the scroll.
A method is described for determining the "displacement surface" of known three-dimensional compressible boundary-layer flow in terms of the mass-flow defects associated with the profiles of the two velocity components parallel to the surface. The result is a generalization of the plane flow concept of displacement thickness introduced in order to describe how a thin boundary layer distorts the outer nonviscous flow. Numerical values are found for the known three-dimensional boundary-layer flow about a cone at a small angle of attack to a supersonic stream.
An investigation is conducted concerning the validity of analytical methods which are based on deriving an integral equation, taking into account small perturbations in the case of a nonuniform but irrotational flow. The results obtained apply to a wide Mach number range, but are restricted to small amplitude motions and to nonviscous flows. It is shown that the integral equation relating the unknown velocity potential to the known normal flow velocity can be derived from the appropriate Green's identity.
A procedure is presented for obtaining the pressure distribution on an arbitrary airfoil section in cascade in a two-dimensional, incompressible, and nonviscous flow. The method considers directly the influence on a given airfoil of the rest of the cascade and evaluates this interference by an iterative process, which appeared to converge rapidly in the cases tried (about unit solidity, stagger angles of 0 degree and 45 degrees). Two variations of the basic interference calculations are described. One, which is accurate enough for most purposes, involves the substitution of sources, sinks, and vortices for the interfering airfoils; the other, which may be desirable for the final approximation, involves a contour integration. The computations are simplified by the use of a chart presented by Betz in a related paper. Illustrated examples are included.
Computer program calculates the velocity distribution and streamlines over widely separated blades of turbomachines. It gives the solutions of a two dimensional, subsonic, compressible nonviscous flow problem for a rotating or stationary circular cascade of blades on a blade-to-blade surface of revolution.
Computer program gives blade-to-blade solution of the two-dimensional, subsonic, compressible, nonviscous flow problem for a circular or straight infinite cascade of tandem or slotted turbomachine blades. The method of solution is based on the stream function using iterative solution of nonlinear finite-difference equations.
FORTRAN computer program for detailed solution of compressible, subsonic, nonviscous flow at leading or trailing edges of blade surface
Two modeling areas, the development of a mesoscale chemistry-meteorology interaction model, and the development of a combined urban chemical kinetics-transport model are examined. The problems associated with developing a three dimensional combined meteorological-chemical kinetics computer program package are defined. A similar three dimensional hydrostatic real time model which solves the fundamental Navier-Stokes equations for nonviscous flow is described. An urban air quality simulation model, developed to predict the temporal and spatial distribution of reactive and nonreactive gases in and around an urban area and to support a remote sensor evaluation program is reported.
A general method of design is developed for two-dimensional unbranched channels with prescribed velocities as a function of arc length along the channel walls. The method is developed for both compressible and incompressible, irrotational, nonviscous flow and applies to the design of elbows, diffusers, nozzles, and so forth. In part I solutions are obtained by relaxation methods; in part II solutions are obtained by a Green's function. Five numerical examples are given in part I including three elbow designs with the same prescribed velocity as a function of arc length along the channel walls but with incompressible, linearized compressible, and compressible flow. One numerical example is presented in part II for an accelerating elbow with linearized compressible flow, and the time required for the solution by a Green's function in part II was considerably less than the time required for the same solution by relaxation methods in part I.