Three-Dimensional Calculation of Flow in Turbomachines With the Aid of Singularities

1968 ◽  
Vol 90 (3) ◽  
pp. 258-264 ◽  
Author(s):  
M. Ribaut
Keyword(s):  
Numerical Calculation ◽  
Calculation Method ◽  
Arbitrary Shape ◽  
Linear Equations ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
System Of Linear Equations ◽  
Simplifying Assumptions ◽  
Suitable Form ◽  
Flow Through

An analysis is presented which applies to the flow through a three-dimensional cascade of arbitrary shape using potential theory. It is shown that without simplifying assumptions a calculation method can be developed, which avoids numerical calculation of derivatives and leads for incompressible and inviscid flow to a system of linear equations. The different possibilities for the boundary vortex vector are discussed and the most suitable form for the components of velocity derived.

Status of Centrifugal Impeller Internal Aerodynamics—Part I: Inviscid Flow Prediction Methods

1980 ◽  
Vol 102 (3) ◽  
pp. 728-737 ◽  
Author(s):  
D. Adler
Keyword(s):  
Three Dimensional ◽  
Internal Flow ◽  
Inviscid Flow ◽  
Centrifugal Impeller ◽  
Future Research ◽  
Prediction Methods ◽  
Inviscid Flows ◽  
Recent Developments ◽  
Simplifying Assumptions ◽  
Internal Aerodynamics

Recent developments in inviscid prediction methods of internal flow fields of centrifugal impellers and related flows are critically reviewed. The overall picture which emerges provides the reader with a state-of-the-art perspective on the subject. Restricting simplifying assumptions of the various methods are identified to stimulate future research. Topics included in this review are: two-dimensional subsonic and transonic inviscid flows as well as three-dimensional inviscid flows.

Three Dimensional Thermoacoustic Oscillation in a Premix Combustor

2001 ◽  
Author(s):  
S. Akamatsu ◽  
A. P. Dowling
Keyword(s):  
Boundary Conditions ◽  
Acoustic Waves ◽  
Linear Equations ◽  
Three Dimensional ◽  
Total System ◽  
Mean Flow ◽  
Modal Coupling ◽  
Rate Of Heat Release ◽  
Flow Through ◽  
Combustion Processes

A theory is developed to describe high frequency three-dimensional thermoacoustic waves in a simplified geometry representing a typical premix combustor. The theory considers linear modes of frequency ω and circumferential mode number m i.e. proportional to eiωt+imθ. The radial and axial dependence is determined for a cylindrical combustor. Simple geometries are investigated systematically to analyze the effect of different inlet boundary conditions to the combustion chamber on the frequency of oscillation and on the susceptibility to instability, both near and away from the cut-off frequencies. The model includes a one-dimensional mean flow, radial mode coupling and idealized combustion processes, which are added in stages to build up an understanding of the complicated acoustics of the premix combustor geometry. It is demonstrated that the flow through the premix ducts provides a frequency-dependent boundary condition at combustor inlet and causes modal coupling. Generalized linear equations of conservation of mass, momentum and energy, together with boundary conditions, are solved to identify the eigenfrequencies, ω, of the total system. Then Real ω determines the frequency of the oscillation, while Imaginary ω indicates the growth rate of the disturbance. It is found that strong resonant peaks in the pressure waves exist close to the cut-off condition for acoustic waves and that the relationship between the unsteady rate of heat release and the flow significantly influences the instability of oscillation.

Wavelet based method for solving generalized Burger’s type equations

2019 ◽  
Vol 08 (04) ◽  
pp. 1950020
Author(s):  
Inderdeep Singh
Keyword(s):  
Differential Equations ◽  
Algebraic System ◽  
Numerical Experiments ◽  
Nonlinear Differential Equations ◽  
Linear Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Haar Wavelet ◽  
Nonlinear Ordinary Differential Equation ◽  
System Of Linear Equations

In this work, an efficient numerical method is proposed for solving generalized Burger’s type equations. The generalized Burger’s type equations are first converted into a nonlinear ordinary differential equation by choosing some suitable wave variable transformation. Linearize such nonlinear differential equations by using quasilinearization technique. For solving algebraic system of linear equations Haar wavelet-based collocation method is used. A distinct feature of the proposed method is their simple applicability in a variety of two- and three- dimensional nonlinear partial differential equations. Numerical experiments are performed to illustrate the accuracy and efficiency of the proposed method.

scholarly journals An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Vladimir Kisil
Keyword(s):  
Continued Fractions ◽  
Linear Equations ◽  
Three Dimensional ◽  
Conformal Invariant ◽  
System Of Linear Equations ◽  
Quadratic Relation ◽  
Conformally Invariant ◽  
Lie Geometry ◽  
Symbolic Data

We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. ``to be orthogonal'', ``to be tangent'', etc.), as new objects in an extended M\"obius--Lie geometry. It was recently demonstrated in several related papers, that such ensembles of cycles naturally parameterize many other conformally-invariant families of objects, e.g. loxodromes or continued fractions. The paper describes a method, which reduces a collection of conformally in\-vari\-ant geometric relations to a system of linear equations, which may be accompanied by one fixed quadratic relation. To show its usefulness, the method is implemented as a {\CPP} library. It operates with numeric and symbolic data of cycles in spaces of arbitrary dimensionality and metrics with any signatures. Numeric calculations can be done in exact or approximate arithmetic. In the two- and three-dimensional cases illustrations and animations can be produced. An interactive {\Python} wrapper of the library is provided as well.

The Calculation of Three Dimensional Viscous Flow Through Multistage Turbomachines

1990 ◽  
Author(s):  
J. D. Denton
Keyword(s):  
Boundary Conditions ◽  
Unsteady Flow ◽  
Viscous Flow ◽  
Calculation Method ◽  
Three Dimensional ◽  
Mixing Process ◽  
Three Dimensional Flow ◽  
Flow Calculation ◽  
Dimensional Flow ◽  
Flow Through

The extension of a well established three dimensional flow calculation method to calculate the flow through multiple turbomachinery blade rows is described in this paper. To avoid calculating the unsteady flow, which is inherent in any machine containing both rotating and stationary blade rows, a mixing process is modelled at a calculating station between adjacent blade rows. The effects of this mixing on the flow within the blade rows may be minimised by using extrapolated boundary conditions at the mixing plane.

The effects of trailing vorticity on the flow through highly loaded cascades

1976 ◽  
Vol 74 (4) ◽  
pp. 721-740 ◽  
Author(s):  
James E. Mccune ◽  
William R. Hawthorne
Keyword(s):  
Incompressible Flow ◽  
Design Problem ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Dimensional Theory ◽  
Blade Loading ◽  
Large Pressure ◽  
Flow Through ◽  
The Mean ◽  
Highly Loaded

This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem, i.e. given blade loading. Formulae are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined.

Dissertation on “The Rank Technique” and its Application

1965 ◽  
Vol 69 (652) ◽  
pp. 280-283 ◽  
Author(s):  
John Robinson
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Attractive Feature ◽  
System Of Linear Equations ◽  
Initial Development ◽  
The Matrix ◽  
Plane Frames ◽  
General Plane ◽  
Basic Characteristics ◽  
Selection Of

Summary“The Rank Technique” is a method for automatic selection of redundancies in the Matrix Force Method. The method was developed for the complete linear analysis of general plane frames, but is equally applicable to other forms of two- and three-dimensional configurations whose state can be expressed as a system of linear equations. An attractive feature of the method is that the structure is systematically and automatically investigated to determine its basic characteristics. The first point considered is whether the structure is stable or unstable for the prescribed load conditions; if stable, whether determinate or redundant and if redundant, the degree of redundancy. A consistent set of redundants is automatically isolated. For general structures the technique automatically generates the basic and redundant load systems in an indirect manner which can be made readily available, if required. The initial development of “The Rank Technique” was carried out in collaboration with Robert R. Regl and is given in reference 1.

Three-Dimensional Theory of Incompressible and Inviscid Flow Through Mixed Flow Turbomachines

1965 ◽  
Vol 87 (4) ◽  
pp. 361-372
Author(s):  
M. J. Schilhansl
Keyword(s):  
Radial Flow ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Surfaces Of Revolution ◽  
Dimensional Theory ◽  
Mixed Flow ◽  
Three Dimensional Flow ◽  
Flow Through ◽  
Flow Study

In this paper the author presents a three-dimensional flow study for mixed (axial and radial) flow rotors. In order to make the analysis manageable the actual stream surfaces are assumed to coincide with surfaces of revolution. The intersections of the blade surfaces with these surfaces of revolution are mapped onto planes normal to the axis of the rotor. The investigation of the flow in the “picture” planes is based on available two-dimensional cascade theories. Position and shape of the surfaces depend upon the equilibrium of the flow in the direction perpendicular to the surfaces of revolution. The flow in each individual surface of revolution is found by remapping from the planes. Improved position and shape of the surfaces of revolution can be derived from the equilibrium condition. This procedure must be iterated until two consecutive iterations lead to the same result.

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