Inviscid Flow Through a Cascade of Thick, Cambered Airfoils: Part 2—Compressible Flow

1973 ◽  
Vol 95 (3) ◽  
pp. 227-232 ◽  
Author(s):  
D. A. Frith
Keyword(s):  
Numerical Methods ◽  
Compressible Flow ◽  
Stream Function ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Regular Array ◽  
Unique Method ◽  
Flow Through ◽  
Grid Points ◽  
Inviscid Compressible Flow

Evaluation of two-dimensional, inviscid, compressible flow through a cascade of airfoils must involve numerical methods. Some of the associated problems are avoided if the flow field is mapped to the interior of a unit circle as the airfoil boundaries become grid points of the regular array in this domain. Further, far upstream and far downstream map to points in this circle so the uniform inlet and outlet flows are simply defined. For a solution obtained in terms of a stream function the compressible flow may be derived as a numerical perturbation from an analytical, incompressible stream function. A method incorporating these features is described in detail and some results for thick, cambered airfoils in cascade are presented. As supersonic patches can exist on the airfoils for high subsonic inlet Mach numbers, a unique method of relating the density to the stream function is employed in order to enable such flows to be calculated.

A Calculation Procedure for Three-Dimensional, Time-Dependent, Inviscid, Compressible Flow through Turbomachine Blades of any Geometry

1979 ◽  
Vol 21 (1) ◽  
pp. 39-49 ◽  
Author(s):  
C. Bosman ◽  
J. Highton
Keyword(s):  
Secondary Flow ◽  
Compressible Flow ◽  
Subsonic Flow ◽  
Three Dimensional ◽  
Experimental Results ◽  
Time Dependent ◽  
Two Dimensional ◽  
Through Flow ◽  
Flow Through ◽  
Inviscid Compressible Flow

A method for calculating three-dimensional, time-dependent, inviscid, subsonic flow is presented. Application is made to flow through the rotor of a small radial inflow turbine and comparison with conventional through-flow calculations and experimental results is made. The nature of the strong secondary flow in this rotor indicates the probable inadequacy of the two-dimensional calculations which is confirmed by the comparison.

Nonlinear dynamics of a two dimensional airfoil with freeplay in an inviscid compressible flow

2000 ◽  
Vol 4 (2) ◽  
pp. 125-133 ◽  
Author(s):  
Zoran Dimitrijević ◽  
Guy Daniel Mortchéléwicz ◽  
Fabrice Poirion
Keyword(s):  
Nonlinear Dynamics ◽  
Compressible Flow ◽  
Two Dimensional ◽  
Inviscid Compressible Flow

The Compressible Flow Through Cascade Actuator Discs

1958 ◽  
Vol 9 (2) ◽  
pp. 110-130 ◽  
Author(s):  
J. H. Horlock
Keyword(s):  
Shear Flow ◽  
Compressible Flow ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Guide Vanes ◽  
The Past ◽  
Flow Through ◽  
Annular Cascade

SummaryA theory of the incompressible flow through two- and three-dimensional cascade actuator discs has been developed by several workers over the past ten years, and its accuracy has been confirmed in several experiments. This theory is briefly reviewed, and a parallel theory for subsonic compressible flow through actuator discs is developed. Approximate solutions for several examples are considered, including a compressible shear flow through a two-dimensional cascade, and a compressible flow through an annular cascade of guide vanes.

scholarly journals On the Kutta Condition in Compressible Flow over Isolated Airfoils

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 102 ◽  
Author(s):  
Farzad Mohebbi ◽  
Ben Evans ◽  
Mathieu Sellier
Keyword(s):  
Numerical Methods ◽  
Finite Difference Method ◽  
Compressible Flow ◽  
Stream Function ◽  
Compressible Flows ◽  
Accurate Method ◽  
Computational Domain ◽  
Kutta Condition ◽  
Trailing Edges ◽  
Comparison Of The Results

This paper presents a novel and accurate method to implement the Kutta condition in solving subsonic (subcritical) inviscid isentropic compressible flow over isolated airfoils using the stream function equation. The proposed method relies on body-fitted grid generation and solving the stream function equation for compressible flows in computational domain using finite-difference method. An expression is derived for implementing the Kutta condition for the airfoils with both finite angles and cusped trailing edges. A comparison of the results obtained from the proposed numerical method and the results from experimental and other numerical methods reveals that they are in excellent agreement, which confirms the accuracy and correctness of the proposed method.

On an Approximation to the Flow Through Axi-Symmetric Contracting Ducts

1981 ◽  
Vol 32 (1) ◽  
pp. 72-81
Author(s):  
R. Jordinson ◽  
J.G. Rodger
Keyword(s):  
Inviscid Flow ◽  
Area Ratio ◽  
Small Scale ◽  
Two Dimensional ◽  
Qualitative Explanation ◽  
Pressure Coefficients ◽  
Original Proposal ◽  
Two Dimensional Flow ◽  
Flow Through ◽  
Overshoot And Undershoot

SummaryA method is given for the calculation of incompressible, inviscid flow through an axi-symmetric contracting duct for which the two dimensional flow with the same meridianal boundaries is known. The method, which is based on Whitehead, Wu and Waters original proposal, assumes that the contraction consists of two separate portions, upstream and downstream respectively. The flow in each portion is calculated and the two portions matched to produce a contraction of given area ratio with preassigned values of the two dimensional ‘overshoot’ and ‘undershoot’ parameters. It is worth emphasizing that in practice it is only necessary to do the calculations once to predict wall velocities for a family of contraction shapes with different area ratios provided they share a common upstream or downstream portion. The results given here show reasonable agreement with the pressure coefficients obtained in experiment for the upstream end of a small scale contraction of area ratio 16:1. There is however a discrepancy between theory and experiment at the downstream end and a qualitative explanation is advanced for this.

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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