scholarly journals Transonic Flow Along Arbitrary Stream Filament of Revolution Solved by Separate Computations With Shock Fitting

1986 ◽  
Author(s):  
Wang Baoguo ◽  
Hua Yaonan ◽  
Huang Xiaoyan ◽  
Wu Chung-Hua
Keyword(s):  
Flow Field ◽  
Stream Function ◽  
Transonic Flow ◽  
Matrix Method ◽  
Axial Compressor ◽  
Iteration Scheme ◽  
Curvilinear Coordinates ◽  
Algebraic Equations ◽  
Compressor Rotor ◽  
Orthogonal Curvilinear Coordinates

The transonic flow field in a cascade of blades lying on an S1 stream surface of revolution is solved by separate computations in the supersonic and the transonic region. The characteristics method is used to solve the supersonic flow upstream of the passage shock and the direct matrix method is used to solve the transonic flow downstream of the passage shock. The transonic stream-function equation in weak conservative form was discretized with respect to general non-orthogonal curvilinear coordinates. Using the artificial density technique and a new iteration scheme between the stream function and the density, the set of algebraic equations was solved by the direct matrix method. A computer program has been developed and is applied to compute the flow field on several S1 stream surfaces of revolution for the DFVLR transonic axial compressor rotor. It is found that the thickness of the S1 stream filament and the variation of entropy along the streamlines have strong influence on calculation. The calculated result agrees with the experimental data fairly well.

Numerical Solution of Transonic Stream Function Equation on S1 Stream Surface in Cascade

1986 ◽  
Author(s):  
Hua Yaonan ◽  
Wu Wenquan
Keyword(s):  
Stream Function ◽  
Transonic Flow ◽  
Momentum Equation ◽  
Curvilinear Coordinates ◽  
Algebraic Equations ◽  
Central Difference ◽  
Linear Algebraic Equations ◽  
Difference Formula ◽  
Grid Nodes ◽  
Transonic Cascade

A method is presented in this paper for calculating transonic flow field in turbomachinery cascades. With respect to non-orthogoanl curvilinear coordinates, the stream function equation governing fluid flow was established. Using the Artificial Compressibility Method, the discretization of the partial differential equation was carried out by use of the standard central difference formula. The set of linear algebraic equations obtained is solved by means of the Direct Matrix Method. In order to overcome the non-uniqueness of density in transonic flow in the stream function method, the velocities at grid nodes are first obtained by integrating the momentum equation and then the densities are determined from the energy equation. Application of this method to some transonic cascade-flow with supersonic or subsonic inlet velocity shows that the solution obtained is in fair agreement with experimental data.

Stream Function Solution of Transonic Flow Along S2 Streamsurface of Axial Turbomachines

1986 ◽  
Vol 108 (1) ◽  
pp. 138-143 ◽  
Author(s):  
Xiaolu Zhao
Keyword(s):  
Stream Function ◽  
Transonic Flow ◽  
Fluid Velocity ◽  
Measurement Data ◽  
Curvilinear Coordinates ◽  
Design Problems ◽  
Artificial Compressibility ◽  
Function Solution ◽  
Compressor Rotor ◽  
Design Speed

Based on Wu’s general equations of 3-D turbomachine flow, expressed with respect to nonorthogonal curvilinear coordinates, the conservative stream-function formulations of transonic flow along S2 streamsurface have been discussed. The problem of mixed flow can be solved by the use of the artificial compressibility method, and the passage shock on the S2 streamsurface can be captured. The distribution of the fluid velocity from hub to shroud can be obtained directly by integrating the velocity gradient equation, after the principal equation has been solved, so that the difficulty of the nonuniqueness of density-mass flux relation is avoided. The density is determined after the velocity has been obtained. Two computer programs have been coded; one can be used to compute the hybrid or design problems, the other is suitable to compute the analysis problem. The former has been used to compute the transonic flow field along a mean S2 streamsurface in the DFLVR compressor rotor at design speed. The numerical results agree well with L2F measurement data.

3D Transonic Potential Flow Computation in an Axial-Flow Compressor Rotor by an Approximate Factorization Scheme

1986 ◽  
Vol 108 (1) ◽  
pp. 112-117
Author(s):  
Jialin Zhang
Keyword(s):  
Flow Field ◽  
Transonic Flow ◽  
Axial Flow ◽  
Curvilinear Coordinates ◽  
Full Potential ◽  
Approximate Factorization ◽  
Factorization Scheme ◽  
Compressor Rotor ◽  
Fully Implicit ◽  
Flow Compressor

A conservative full-potential equation of 3D transonic flow in a turbomachine has been derived with the tensor method and expressed with respect to nonorthogonal curvilinear coordinates, and a fully implicit approximate factorization scheme to calculate the flow field has been developed in this paper. The new algorithm has been used to compute the 3D transonic flow field within an axial-flow single-stage compressor rotor tested by DFVLR. Comparisons between the computed flow field and the DFVLR data have been made. Results demonstrate that fast convergence can be achieved by the presented algorithm and that the agreement with the measurements obtained with an advanced laser velocimeter is quite good.

Study of the Standard k-ε Model for Tip Leakage Flow in an Axial Compressor Rotor

2016 ◽  
Vol 33 (4) ◽  
Author(s):  
Yanfei Gao ◽  
Yangwei Liu ◽  
Luyang Zhong ◽  
Jiexuan Hou ◽  
Lipeng Lu
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Axial Compressor ◽  
Leakage Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Compressor Rotor

AbstractThe standard k-ε model (SKE) and the Reynolds stress model (RSM) are employed to predict the tip leakage flow (TLF) in a low-speed large-scale axial compressor rotor. Then, a new research method is adopted to “freeze” the turbulent kinetic energy and dissipation rate of the flow field derived from the RSM, and obtain the turbulent viscosity using the Boussinesq hypothesis. The Reynolds stresses and mean flow field computed on the basis of the frozen viscosity are compared with the results of the SKE and the RSM. The flow field in the tip region based on the frozen viscosity is more similar to the results of the RSM than those of the SKE, although certain differences can be observed. This finding indicates that the non-equilibrium turbulence transport nature plays an important role in predicting the TLF, as well as the turbulence anisotropy.

The Impact of Manufacturing Variations on Performance of a Transonic Axial Compressor Rotor

2018 ◽  
Author(s):  
Marcus Lejon ◽  
Niklas Andersson ◽  
Lars Ellbrant ◽  
Hans Mårtensson
Keyword(s):  
Flow Field ◽  
Geometric Mean ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Mean Deviation ◽  
Design Intent ◽  
Compressor Rotor ◽  
Measuring Machine ◽  
The Mean ◽  
The Impact

In this paper, the impact of manufacturing variations on performance of an axial compressor rotor are evaluated at design rotational speed. The geometric variations from the design intent were obtained from an optical coordinate measuring machine and used to evaluate the impact of manufacturing variations on performance and the flow field in the rotor. The complete blisk is simulated using 3D CFD calculations, allowing for a detailed analysis of the impact of geometric variations on the flow. It is shown that the mean shift of the geometry from the design intent is responsible for the majority of the change in performance in terms of mass flow and total pressure ratio for this specific blisk. In terms of polytropic efficiency, the measured geometric scatter is shown to have a higher influence than the geometric mean deviation. The geometric scatter around the mean is shown to impact the pressure distribution along the leading edge and the shock position. Furthermore, a blisk is analyzed with one blade deviating substantially from the design intent, denoted as blade 0. It is shown that the impact of blade 0 on the flow is largely limited to the blade passages that it is directly a part of. The results presented in this paper also show that the impact of this blade on the flow field can be represented by a simulation including 3 blade passages. In terms of loss, using 5 blade passages is shown to give a close estimate for the relative change in loss for blade 0 and neighboring blades.

scholarly journals A Stream Function Relaxation Method for Solving Transonic S1 Stream Surface With Pre-Determination of the Density

1985 ◽  
Author(s):  
Ge Manchu
Keyword(s):  
Difference Scheme ◽  
Stream Function ◽  
Flow Theory ◽  
Relaxation Method ◽  
Curvilinear Coordinates ◽  
Transonic Flows ◽  
Stream Surface ◽  
Numerical Examples ◽  
Orthogonal Curvilinear Coordinates

On the basis of Prof. Wu’s 3-D flow theory (ref.1, 2, 3, 4, 5), a general streamfunction equation in non-orthogonal curvilinear coordinates is developed. The equation can be used to calculate subsonic or transonic flows on S1 or S2 stream surfaces of turbomachinery. In this paper streamlines coordinates and a mixed difference scheme are adopted in solving the stream function equation. A procedure for pre-determination of the density is developed and used to determine the unique-value of density from the known value of the stream function. Numerical examples are given.

Impact of Sweep on Part Speed Performance of an Axial Compressor Rotor With Circumferential Casing Grooves

2019 ◽  
Author(s):  
Shraman Goswami ◽  
M. Govardhan
Keyword(s):  
Flow Field ◽  
High Performance ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Field Investigation ◽  
Performance Comparison ◽  
Rotor Blades ◽  
Stall Margin ◽  
Compressor Rotor ◽  
Design Speed

Abstract High performance and increased operating range of an axial compressor is obtained by employing three-dimensional design features, such as sweep, as well as shroud casing treatments, such as circumferential casing grooves. A number of different rotor blades with different amounts of sweeps and different sweep starting spans are studied at design speed. Different swept rotors, including zero sweep, are derived from Rotor37 rotor geometry. In the current study the best performing rotor with sweep is analyzed at part speed. The analyses were done for baseline rotor, devoid of any sweep, and with and without circumferential casing grooves. A detailed flow field investigation and performance comparison is presented to understand the changes in flow field at part speed. It is found that that at 100% design speed, stall margin improvement is achived by both sweep and casing grooves, but at 90% speed improvement in stall margin due to sacing groove is very minimal over and above the gain due to sweep. It is also noticed that due to reduced shock loss efficiency is higher at 90% speed than at 100% speed.

scholarly journals A high-precision algorithm for axisymmetric flow

1995 ◽  
Vol 1 (1) ◽  
pp. 11-25
Author(s):  
A. Gokhman ◽  
D. Gokhman
Keyword(s):  
Velocity Field ◽  
Boundary Conditions ◽  
Stream Function ◽  
Potential Flow ◽  
Axisymmetric Flow ◽  
Curvilinear Coordinates ◽  
Shape Functions ◽  
Quadrilateral Elements ◽  
Orthogonal Curvilinear Coordinates ◽  
Double Integrals

We present a new algorithm for highly accurate computation of axisymmetric potential flow. The principal feature of the algorithm is the use of orthogonal curvilinear coordinates. These coordinates are used to write down the equations and to specify quadrilateral elements following the boundary. In particular, boundary conditions for the Stokes' stream-function are satisfied exactly. The velocity field is determined by differentiating the stream-function. We avoid the use of quadratures in the evaluation of Galerkin integrals, and instead use splining of the boundaries of elements to take the double integrals of the shape functions in closed form. This is very accurate and not time consuming.

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