The Extension and Application of Three-Dimensional Time-Marching Analyses to Incompressible Turbomachinery Flows

1990 ◽  
Vol 112 (3) ◽  
pp. 385-390 ◽  
Author(s):  
P. J. Walker ◽  
W. N. Dawes
Keyword(s):  
Mach Number ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Rotor ◽  
Navier Stokes ◽  
Flow Solver ◽  
Flow Equations ◽  
Long Wavelength ◽  
Time Marching ◽  
Wave Boundary

Conventional time-marching flow solvers perform poorly when integrating compressible flow equations at low Mach number levels. This is shown to be due to unfavorable interaction between long-wavelength errors and the inflow and outflow boundaries. Chorin’s method of artificial compressibility is adopted to extend the range of Denton’s inviscid flow solver and Dawes’ three-dimensional Navier–Stokes solver to zero Mach number flows. The paper makes a new contribution by showing how to choose the artificial acoustic speed systematically to optimize convergence rate with regard to the error wave–boundary interactions. Applications to a turbine rotor and generic water pump geometry are presented.

scholarly journals The Extension and Application of Three-Dimensional Time Marching Analyses to Incompressible Turbomachinery Flows

1989 ◽  
Author(s):  
P. J. Walker ◽  
W. N. Dawes
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Rotor ◽  
Navier Stokes ◽  
Flow Solver ◽  
Artificial Compressibility ◽  
Flow Equations ◽  
Long Wavelength ◽  
Time Marching ◽  
Wave Boundary

Conventional time marching flow solvers perform poorly when integrating compressible flow equations at low Mach numbers levels. This is shown to be due to unfavourable interaction between long wavelength errors and the inflow and outflow boundaries. Chorin’s method of artificial compressibility is adopted to extend the range of Denton’s inviscid flow solver and Dawes’ three-dimensional Navier-Stokes solver to zero Mach number flows. The paper makes a new contribution by showing how to systematically choose the artificial acoustic speed to optimize convergence rate with regard to the error wave-boundary interactions. Applications to a turbine rotor and generic water pump geometry are presented.

Aerodynamic Design of Turbomachinery Blading in Three-Dimensional Flow: An Application to Radial Inflow Turbines

1993 ◽  
Vol 115 (3) ◽  
pp. 602-613 ◽  
Author(s):  
Y. L. Yang ◽  
C. S. Tan ◽  
W. R. Hawthorne
Keyword(s):  
Parametric Design ◽  
Design Method ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Rotor ◽  
Computational Method ◽  
Navier Stokes ◽  
Design Calculation ◽  
Analysis Tool ◽  
Turbine Wheel

A computational method based on a theory for turbomachinery blading design in three-dimensional inviscid flow is applied to a parametric design study of a radial inflow turbine wheel. As the method requires the specification of swirl distribution, a technique for its smooth generation within the blade region is proposed. Excellent agreements have been obtained between the computed results from this design method and those from direct Euler computations, demonstrating the correspondence and consistency between the two. The computed results indicate the sensitivity of the pressure distribution to a lean in the stacking axis and a minor alteration in the hub/shroud profiles. Analysis based on a Navier–Stokes solver shows no breakdown of flow within the designed blade passage and agreement with that from a design calculation; thus the flow in the designed turbine rotor closely approximates that of an inviscid one. These calculations illustrate the use of a design method coupled to an analysis tool for establishing guidelines and criteria for designing turbomachinery blading.

Aerodynamic Design of Turbomachinery Blading in Three-Dimensional Flow: An Application to Radial Inflow Turbines

1992 ◽  
Author(s):  
Y. L. Yang ◽  
C. S. Tan ◽  
W. R. Hawthorne
Keyword(s):  
Parametric Design ◽  
Design Method ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Rotor ◽  
Computational Method ◽  
Navier Stokes ◽  
Design Calculation ◽  
Analysis Tool ◽  
Turbine Wheel

A computational method, based on a theory for turbomachinery blading design in three-dimensional inviscid flow, is applied to a parametric design study of a radial inflow turbine wheel. As the method requires the specification of swirl distribution, a technique for its smooth generation within the blade region is proposed. Excellent agreements have been obtained between the computed results from this design method and those from direct Euler computations, demonstrating the correspondence and consistency between the two. The computed results indicate the sensitivity of the pressure distribution to a lean in the stacking axis and a minor alteration in the hub/shroud profiles. Analysis based on Navier-Stokes solver shows no breakdown of flow within the designed blade passage and agreement with that from design calculation; thus the flow in the designed turbine rotor closely approximates that of an inviscid one. These calculations illustrates the use of a design method coupled to an analysis tool for establishing guidelines and criteria for designing turbomachinery blading.

Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

scholarly journals Numerical Simulation of Cascade Flow: Vortex Element Method for Inviscid Flow Analysis and Axial Turbine Blade Design

2021 ◽  
Vol 85 (2) ◽  
pp. 14-23
Author(s):  
Nono Suprayetno ◽  
Priyono Sutikno ◽  
Nathanael P. Tandian ◽  
Firman Hartono
Keyword(s):  
Best Practice ◽  
Lift Coefficient ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Turbine Rotor ◽  
Design Stage ◽  
Outer Diameter ◽  
Axial Turbine ◽  
Cascade Flow

This study aims to design an axial turbine rotor blade and predict the turbine performance at preliminary design stage. Quasi three dimensional method was applied to design including blade to blade flow analysis. The blade profile uses a NACA 0015 airfoil by varying the profile thickness from hub to tip. The profile is divided into eleven segments which has different parameters. The profile was analysed using blade to blade flow/cascade flow analysis called vortex panel method to obtain lift coefficient. The analysis of cascade flow was performed in potential flow and prediction of turbine perfomance is carried out involving common best practice to give drag effect on the blade. The design of the turbine was applied on three different rotors, which also have a different discharge, head, and design rotation. The outer diameter of turbine 1 is 0.65 m, while turbine 2 and turbine 3 have an outer diameter of 0,60 m. The calculation result show that the efficiency of turbines 1, 2, and 3 were 88,32%, 89,67%, and 89,04%, respectively.

scholarly journals Vibration Performance of a Flow Energy Converter behind Two Side-by-Side Cylinders

2019 ◽  
Vol 7 (12) ◽  
pp. 435
Author(s):  
Mohammad Rasidi Rasani ◽  
Hazim Moria ◽  
Michael Beer ◽  
Ahmad Kamal Ariffin
Keyword(s):  
Three Dimensional ◽  
Reynold Number ◽  
Mean Amplitude ◽  
Navier Stokes ◽  
Cantilever Plate ◽  
Arbitrary Lagrangian Eulerian ◽  
Flow Solver ◽  
Energy Harvesters ◽  
Flow Energy ◽  
Flexible Plates

Flow-induced vibrations of a flexible cantilever plate, placed in various positions behind two side-by-side cylinders, were computationally investigated to determine optimal location for wake-excited energy harvesters. In the present study, the cylinders of equal diameter D were fixed at center-to-center gap ratio of T / D = 1 . 7 and immersed in sub-critical flow of Reynold number R e D = 10 , 000 . A three-dimensional Navier–Stokes flow solver in an Arbitrary Lagrangian–Eulerian (ALE) description was closely coupled to a non-linear finite element structural solver that was used to model the dynamics of a composite piezoelectric plate. The cantilever plate was fixed at several positions between 0 . 5 < x / D < 1 . 5 and - 0 . 85 < y / D < 0 . 85 measured from the center gap between cylinders, and their flow-induced oscillations were compiled and analyzed. The results indicate that flexible plates located at the centerline between the cylinder pairs experience the lowest mean amplitude of oscillation. Maximum overall amplitude in oscillation is predicted when flexible plates are located in the intermediate off-center region downstream of both cylinders. Present findings indicate potential to further maximize wake-induced energy harvesting plates by exploiting their favorable positioning in the wake region behind two side-by-side cylinders.

Three-Dimensional Navier-Stokes Analysis of Turbine Rotor and Tip-Leakage Flowfield

1997 ◽  
Author(s):  
J. Luo ◽  
B. Lakshminarayana
Keyword(s):  
Three Dimensional ◽  
Turbine Rotor ◽  
Secondary Flows ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Tip Leakage ◽  
Blade Tip

The 3-D viscous flowfield in the rotor passage of a single-stage turbine, including the tip-leakage flow, is computed using a Navier-Stokes procedure. A grid-generation code has been developed to obtain embedded H grids inside the rotor tip gap. The blade tip geometry is accurately modeled without any “pinching”. Chien’s low-Reynolds-number k-ε model is employed for turbulence closure. Both the mean-flow and turbulence transport equations are integrated in time using a four-stage Runge-Kutta scheme. The computational results for the entire turbine rotor flow, particularly the tip-leakage flow and the secondary flows, are interpreted and compared with available data. The predictions for major features of the flowfield are found to be in good agreement with the data. Complicated interactions between the tip-clearance flows and the secondary flows are examined in detail. The effects of endwall rotation on the development and interaction of secondary and tip-leakage vortices are also analyzed.

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