Turbulent Flow Simulation of a Runner for Francis Hydraulic Turbines Using Pseudo-Compressibility

1996 ◽  
Vol 118 (2) ◽  
pp. 285-291 ◽  
Author(s):  
Chuichi Arakawa ◽  
Yi Qian ◽  
Takashi Kubota
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Leading Edge ◽  
Design Tool ◽  
Design Flow ◽  
Navier Stokes ◽  
Small Computer ◽  
Strong Vortex

A three-dimensional Navier-Stokes code with pseudo-compressibility, an implicit formulation of finite difference, and a k – ε two-equation turbulence model has been developed for the Francis hydraulic runner. The viscous flow in the rotating field can be simulated well in the design flow operating condition as well as in the off-design conditions in which a strong vortex occurs due to the separation near the leading edge. Because the code employs an implicit algorithm and a wall function near the wall, it does not require a large CPU time. It can therefore be used on a small computer such as the desk-top workstation, and is available for use as a design tool. The same kind of algorithm that is used for compressible flows has been found to be appropriate for the simulation of complex incompressible flows in the field of turbomachinery.

scholarly journals Numerical Flow Simulation in a Centrifugal Pump at Design and Off-Design Conditions

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
K. W. Cheah ◽  
T. S. Lee ◽  
S. H. Winoto ◽  
Z. M. Zhao
Keyword(s):  
Centrifugal Pump ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Internal Flow ◽  
Leading Edge ◽  
Design Flow ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Pump Impeller ◽  
Rate Condition

The current investigation is aimed to simulate the complex internal flow in a centrifugal pump impeller with six twisted blades by using a three-dimensional Navier-Stokes code with a standardk-εtwo-equation turbulence model. Different flow rates were specified at inlet boundary to predict the characteristics of the pump. A detailed analysis of the results at design load,Qdesign, and off-design conditions, Q = 0.43Qdesignand Q = 1.45Qdesign, is presented. From the numerical simulation, it shows that the impeller passage flow at design point is quite smooth and follows the curvature of the blade. However, flow separation is observed at the leading edge due to nontangential inflow condition. The flow pattern changed significantly inside the volute as well, with double vortical flow structures formed at cutwater and slowly evolved into a single vortical structure at the volute diffuser. For the pressure distribution, the pressure increases gradually along streamwise direction in the impeller passages. When the centrifugal pump is operating under off-design flow rate condition, unsteady flow developed in the impeller passage and the volute casing.

Simulation of the subsonic flow in a high-speed centrifugal compressor impeller by the pressure-based method

1998 ◽  
Vol 212 (4) ◽  
pp. 269-287 ◽  
Author(s):  
Y Wang ◽  
S Komori
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equations ◽  
Compressor Impeller ◽  
Collocated Grid

A pressure-based finite volume procedure developed previously for incompressible flows is extended to predict the three-dimensional compressible flow within a centrifugal impeller. In this procedure, the general curvilinear coordinate system is used and the collocated grid arrangement is adopted. Mass-averaging is used to close the instantaneous Navier-Stokes equations. The covariant velocity components are used as the main variables for the momentum equations, making the pressure-velocity coupling easier. The procedure is successfully applied to predict various compressible flows from subsonic to supersonic. With the aid of the k-ɛ turbulence model, the flow details within a centrifugal impeller are obtained using the present procedure. Predicted distributions of the meridional velocity and the static pressure are reasonable. Calculated radial velocities and flow angles are favourably compared with the measurements at the exit of the impeller.

Influence of Surface Roughness on Three-Dimensional Separation in Axial Compressors

2004 ◽  
Vol 126 (4) ◽  
pp. 455-463 ◽  
Author(s):  
Semiu A. Gbadebo ◽  
Tom P. Hynes ◽  
Nicholas A. Cumpsty
Keyword(s):  
Surface Roughness ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Leading Edge ◽  
Major Effect ◽  
Surface Flow ◽  
Design Flow ◽  
Flow Coefficient ◽  
Navier Stokes ◽  
Suction Surface

Surface roughness on a stator blade was found to have a major effect on the three-dimensional (3D) separation at the hub of a single-stage low-speed axial compressor. The change in the separation with roughness worsened performance of the stage. A preliminary study was carried out to ascertain which part of the stator suction surface and at what operating condition the flow is most sensitive to roughness. The results show that stage performance is extremely sensitive to surface roughness around the leading edge and peak-suction regions, particularly for flow rates corresponding to design and lower values. Surface flow visualization and exit loss measurements show that the size of the separation, in terms of spanwise and chordwise extent, is increased with roughness present. Roughness produced the large 3D separation at design flow coefficient that is found for smooth blades nearer to stall. A simple model to simulate the effect of roughness was developed and, when included in a 3D Navier–Stokes calculation method, was shown to give good qualitative agreement with measurements.

Influence of Surface Roughness on Three-Dimensional Separation in Axial Compressors

2004 ◽  
Author(s):  
Semiu A. Gbadebo ◽  
Tom P. Hynes ◽  
Nicholas A. Cumpsty
Keyword(s):  
Surface Roughness ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Leading Edge ◽  
Major Effect ◽  
Surface Flow ◽  
Design Flow ◽  
Flow Coefficient ◽  
Navier Stokes ◽  
Suction Surface

Surface roughness on a stator blade was found to have a major effect on the three-dimensional (3D) separation at the hub of a single-stage low-speed axial compressor. The change in the separation with roughness worsened performance of the stage. A preliminary study was carried out to ascertain which part of the stator suction surface and at what operating condition the flow is most sensitive to roughness. The results show that stage performance is extremely sensitive to surface roughness around the leading edge and peak-suction regions, particularly for flow rates corresponding to design and lower values. Surface flow visualization and exit loss measurements show that the size of the separation, in terms of spanwise and chordwise extent, is increased with roughness present. Roughness produced the large 3D separation at design flow coefficient that is found for smooth blades nearer to stall. A simple model to simulate the effect of roughness was developed and, when included in a 3D Navier-Stokes calculation method, was shown to give good qualitative agreement with measurements.

Numerical Simulation of Unsteady Viscous Compressible Flows Applied to Blade Flutter Analysis

1991 ◽  
Author(s):  
L. D. Gunnar Sidén
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Flutter Analysis ◽  
Blade Flutter ◽  
Viscous Compressible Flow

A numerical method for simulating quasi three-dimensional unsteady viscous compressible flow is developed and applied to blade flutter analysis. The Reynolds-averaged Navier-Stokes equations are solved in a time accurate manner on a continuously deforming computational mesh. Turbulence is accounted for by the inclusion of a two-layer algebraic turbulence model. This method is compared with measurements and a full velocity potential solver for two different subsonic compressor cascades and a range of flow conditions. Both methods are found to predict unsteady attached flows reasonably well. However, the Navier-Stokes solver picks up the pressure fluctuations associated with the unsteady leading edge separation bubble. These types of fluctuations have large amplitudes and tend to dominate the cascade’s aerodynamic damping behavior.

Numerical Simulation of Clocking Effect on Wake Transportation and Interaction in a 1.5-Stage Axial Turbine

2010 ◽  
Author(s):  
Wei Li ◽  
Hua Ouyang ◽  
Zhao-hui Du
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Pressure Surface ◽  
Turbine Efficiency ◽  
Small Influence

To give insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has a very small influence on the turbine efficiency in this investigation. The efficiency difference between the maximum and minimum configuration is nearly 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passed through the mid-channel in the 2nd stator.

scholarly journals Heat Transfer on a Film-Cooled Rotating Blade

1999 ◽  
Author(s):  
Vijay K. Garg
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Three Dimensional ◽  
Leading Edge ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Film Cooling Effectiveness ◽  
Film Cooling Holes

A multi-block, three-dimensional Navier-Stokes code has been used to compute heat transfer coefficient on the blade, hub and shroud for a rotating high-pressure turbine blade with 172 film-cooling holes in eight rows. Film cooling effectiveness is also computed on the adiabatic blade. Wilcox’s k-ω model is used for modeling the turbulence. Of the eight rows of holes, three are staggered on the shower-head with compound-angled holes. With so many holes on the blade it was somewhat of a challenge to get a good quality grid on and around the blade and in the tip clearance region. The final multi-block grid consists of 4784 elementary blocks which were merged into 276 super blocks. The viscous grid has over 2.2 million cells. Each hole exit, in its true oval shape, has 80 cells within it so that coolant velocity, temperature, k and ω distributions can be specified at these hole exits. It is found that for the given parameters, heat transfer coefficient on the cooled, isothermal blade is highest in the leading edge region and in the tip region. Also, the effectiveness over the cooled, adiabatic blade is the lowest in these regions. Results for an uncooled blade are also shown, providing a direct comparison with those for the cooled blade. Also, the heat transfer coefficient is much higher on the shroud as compared to that on the hub for both the cooled and the uncooled cases.

scholarly journals Numerical simulation of complex 3D compressible viscous flows through rotating blade passage

2003 ◽  
pp. 55-82
Author(s):  
M. Despotovic ◽  
Milun Babic ◽  
D. Milovanovic ◽  
Vanja Sustersic
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Convergence Acceleration ◽  
Design Tool ◽  
Navier Stokes ◽  
Internal Flows ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Compressible Viscous Flows

This paper describes a three-dimensional compressible Navier-Stokes code, which has been developed for analysis of turbocompressor blade rows and other internal flows. Despite numerous numerical techniques and statement that Computational Fluid Dynamics has reached state of the art, issues related to successful simulations represent valuable database of how particular tech?nique behave for a specifie problem. This paper deals with rapid numerical method accurate enough to be used as a design tool. The mathematical model is based on System of Favre averaged Navier-Stokes equations that are written in relative frame of reference, which rotates with constant angular velocity around axis of rotation. The governing equations are solved using finite vol?ume method applied on structured grids. The numerical procedure is based on the explicit multistage Runge-Kutta scheme that is coupled with modem numerical procedures for convergence acceleration. To demonstrate the accuracy of the described numer?ical method developed software is applied to numerical analysis of flow through impeller of axial turbocompressor, and obtained results are compared with available experimental data.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

Shroud Leakage Modeling of the Flow in a Two Stage Axial Test Turbine

2008 ◽  
Author(s):  
M. Pau ◽  
F. Cambuli ◽  
N. Mandas
Keyword(s):  
Three Dimensional ◽  
Design Tool ◽  
Navier Stokes ◽  
Computational Time ◽  
Leakage Flow ◽  
Two Stage ◽  
Flow Paths ◽  
Flow Interaction ◽  
Full Calculation ◽  
Mainstream Flow

Three dimensional steady multistage calculations, using mixing plane approach, are presented for two different blade geometries in a two stage axial test turbine with shrouded blades. A 3D multiblock Navier-Stokes finite volume solver (TBLOCK) has been used in all the simulations. In order to study shroud leakage flow effects the whole shroud cavity geometry has been modeled, overcoming most of the limitations of simple shroud leakage model in calculating fluid flow over complex geometries. Numerical investigations are mainly focused on assessing the ability of the solver to be used as multistage design tool for modeling leakage-mainstream flow interaction. Several calculations are compared. The first computes the main blade flow path with no modeling of the shroud cavities. The second includes the modeling of the shroud cavities for a zero leakage mass flow rate. Finally a multiblock calculation which models all the leakage flow paths and shroud cavities has been carried out for two different levels of shroud seal clearance. It is found that neglecting shroud leakage significantly alters the computed velocity profiles and loss distributions, for both the computed blade geometries. A numerically predicted shroud leakage offset loss is presented for the two considered blade geometries, focusing on the relative importance of the leakage flow, re-entry mixing losses, and inlet and exit shroud cavity effect. Results demonstrates that full calculation of leakage flow paths and cavities is required to obtain reliable results, indicating the different effects of the leakage-to-mainstream flow interaction on the blade geometries computed. Despite a slight increase in the computational time, multiblock approach in handling leakage flow problem can now-days be used as a practical tool in the blade design process and routine shroud leakage calculations.

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