Calculation of the Quasi Three-Dimensional Flow in a Turbomachine Blade Row

1977 ◽  
Vol 99 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Jean-Pierre Veuillot
Keyword(s):  
Finite Difference ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Through Flow ◽  
Blade Row ◽  
Time Marching ◽  
Space Discretization ◽  
Finite Volume Approach ◽  
Marching Method ◽  
Finite Difference Techniques

The equations of the through flow are obtained by an asymptotic theory valid when the blade pitch is small. An iterative method determines the meridian stream function, the circulation, and the density. The various equations are discretized in an orthogonal mesh and solved by classical finite difference techniques. The calculation of the steady transonic blade-to-blade flow is achieved by a time marching method using the MacCormack scheme. The space discretization is obtained either by a finite difference approach or by a finite volume approach. Numerical applications are presented.

Numerical Analysis of Internal Flow Field in an Impeller with the Time Marching Method

2011 ◽  
Vol 94-96 ◽  
pp. 1476-1480
Author(s):  
Cai Hua Wang
Keyword(s):  
Flow Field ◽  
High Speed ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Internal Flow ◽  
Centrifugal Impeller ◽  
Three Dimensional Flow ◽  
Vector Distribution ◽  
Time Marching ◽  
Marching Method

Centrifugal compressors are power machineries used widely. Fully understanding of the complex three-dimensional flow field is very important to design higher pressure ratio, higher efficiency centrifugal compressor. In this paper, time marching method is adopted to solve the three-dimensional viscous N-S equations under the relative coordinate system. The internal flow field of the “full controllable vortex” high speed centrifugal impeller is analyzed and the medial velocity vector distribution and the development of the velocity of each section in the impeller are showed. From the figures, it can be seen that the “wake” phenomenon, such as Ecckart described, caused by the curvature, Coriolis force and the boundary layer is exist

Computation of Three-Dimensional Flow Fields Through Rotating Blade Rows and Comparison With Experiment

1982 ◽  
Vol 104 (2) ◽  
pp. 394-400 ◽  
Author(s):  
K. P. Sarathy
Keyword(s):  
Pressure Ratio ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Peak Efficiency ◽  
Three Dimensional Flow ◽  
Flow Solver ◽  
Rotating Blade ◽  
Blade Row ◽  
Time Marching ◽  
Design Speed

A three-dimensional inviscid time-marching calculation solving the unsteady Euler equations in a coordinate system rotating with the blade row has been developed, based on the Denton flow solver. This calculation was used to compute the flow field through the rotor of a transonic axial compressor and compared to measurements made with an advanced laser velocimeter at DFVLR. The comparison is made at design speed at pressure ratio corresponding to peak efficiency. Comparisons of the calculated and experimentally determined Mach number contours indicate excellent agreement in the entrance region where the viscous blockage effects are small. The methodology of the analysis is also described in this paper.

Calculation of the Three-Dimensional, Steady, Inviscid Flow in a Transonic Axial Turbine Stage

1985 ◽  
Vol 107 (2) ◽  
pp. 286-292 ◽  
Author(s):  
T. Arts
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Stage ◽  
Axial Turbine ◽  
Absolute Flow ◽  
Cylindrical Coordinate ◽  
Blade Row ◽  
Time Marching ◽  
Finite Volume Approach ◽  
Blade Row Interaction

The aim of this paper is to develop an approach to compute the three-dimensional, rotational, adiabatic, inviscid flow of a perfect gas in a transonic axial turbine stage. The time-dependent Euler equations, expressed in a cylindrical coordinate system, are solved using a time-marching method and a finite volume approach. The absolute flow is calculated in the stator, whereas the relative flow is computed in the rotor. A time-averaged blade row interaction is assumed. The method is applied to a transonic single-stage turbine. The calculated results agree well with the measured performance and three-dimensional aspects of the flow appear clearly.

scholarly journals Numerical Calculation of the Three-Dimensional Swirling Flow Inside the Centrifugal Pump Volutes

2003 ◽  
Vol 9 (4) ◽  
pp. 247-253 ◽  
Author(s):  
E. Cezmi Nursen ◽  
Erkan Ayder
Keyword(s):  
Centrifugal Pump ◽  
Cross Sections ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Flow Solver ◽  
Through Flow ◽  
Measured Flow ◽  
Space Discretization ◽  
The Cross ◽  
Finite Volume Approach

The flow inside the volute of a centrifugal pump is threedimensional and, depending upon the position of the inlet relative to the cross-section center line, a single or double swirling flow occurs. The purpose of this study was the calculation of the three-dimensional swirling flow inside the centrifugal pump volute.The developed flow solver provides detailed pressure and velocity distribution information inside the volute, and the calculated results are verified by means of the experimental results presented in the literature.Three-dimensional continuity and momentum equations are solved by means of an artificial compressibility technique. The finite volume approach is applied for space discretization, and an explicit fourth-order modified Runge-Kutta scheme is used for time discretizetion.Calculations are performed at three different mass flows, one of which corresponds to the design's point mass flow. The calculated volute flow conditions—namely, the variation in static pressure and total pressure and the through-flow and swirling component of the flow velocity over the cross-sections, which are located at various circumferential positions—are compared with the experimental data in detail, and they exhibit a good agreement with the measured flow field.

scholarly journals Through-Flow Analysis for Axial-Stage Design Including Streamline-Slope Effects

1993 ◽  
Author(s):  
Theodosios Korakianitis ◽  
Dequan Zou
Keyword(s):  
Mass Flow ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Total Enthalpy ◽  
Streamline Curvature ◽  
Flow Balance ◽  
Through Flow ◽  
Blade Row ◽  
Iteration Loop ◽  
Predictor Corrector

This paper presents a new method to design (or analyze) subsonic or supersonic axial compressor and turbine stages and their three-dimensional velocity diagrams from hub to tip by solving the three-dimensional radial-momentum equation. Some previous methods (matrix through-flow based on the streamfunction approach) can not handle locally supersonic flows, and they are computationally intensive when they require the inversion of large matrices. Other previous methods (streamline curvature) require two nested iteration loops to provide a converged solution: an outside iteration loop for the mass-flow balance; and an inside iteration loop to solve the radial momentum equation at each flow station. The present method is of the streamline-curvature category. It still requires the iteration loop for the mass-flow balance, but the radial momentum equation at each flow station is solved using a one-pass numerical predictor-corrector technique, thus reducing the computational effort substantially. The method takes into account the axial slope of the streamlines. Main design characteristics such as the mass-flow rate, total properties at component inlet, hub-to-tip ratio at component inlet, total enthalpy change for each stage, and the expected efficiency of each streamline at each stage are inputs to the method. Other inputs are the radial position and axial velocity component at one surface of revolution through the axial stages. These can be provided for either the hub, or the mean, or the tip location of the blading. In addition the user specifies the azimuthal deflection of the flow from the axial direction at each radius (or as a function of radius) at each blade row inlet and outlet. By construction the method eliminates radial variations of total enthalpy (work) and entropy at each blade row inlet and outlet. In an alternative formulation enthalpy variations across radial positions at each axial station are included in the analysis. The remaining three-dimensional velocity diagrams from hub to tip, and the radial location of the remaining streamlines, are obtained by solving the momentum equation using a predictor-corrector method. Examples for one turbine and one compressor design are included.

Excess Streamwise Vorticity and Its Role in Secondary Flow

1987 ◽  
Vol 201 (6) ◽  
pp. 413-420 ◽  
Author(s):  
P W James
Keyword(s):  
Secondary Flow ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Point Of View ◽  
Streamwise Vorticity ◽  
Three Dimensional Flow ◽  
Approximate Methods ◽  
Blade Row ◽  
Flow Through ◽  
Loss Term

The purpose of this paper is, firstly, to show how the concept of excess secondary vorticity arises naturally from attempts to recover three-dimensional flow details lost in passage-averaging the equations governing the flow through gas turbines. An equation for the growth of excess streamwise vorticity is then derived. This equation, which allows for streamwise entropy gradients through a prescribed loss term, could be integrated numerically through a blade-row to provide the excess vorticity at the exit to a blade-row. The second part of the paper concentrates on the approximate methods of Smith (1) and Came and Marsh (2) for estimating this quantity and demonstrates their relationship to each other and to the concept of excess streamwise vorticity. Finally the relevance of the results to the design of blading for gas turbines, from the point of view of secondary flow, is discussed.

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