The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines

1992 ◽  
Vol 114 (1) ◽  
pp. 18-26 ◽  
Author(s):  
J. D. Denton
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
High Pressure Ratio ◽  
Machine Performance ◽  
Multistage Turbine ◽  
Flow Through

The extension of a well-established three-dimensional flow calculation method to calculate the flow through multiple turbomachinery blade rows is described in this paper. To avoid calculating the unsteady flow, which is inherent in any machine containing both rotating and stationary blade rows, a mixing process is modeled at a calculating station between adjacent blade rows. The effects of this mixing on the flow within the blade rows may be minimized by using extrapolated boundary conditions at the mixing plane. Inviscid calculations are not realistic for multistage machines and so the method includes a range of options for the inclusion of viscous effects. At the simplest level such effects may be included by prescribing the spanwise variation of polytropic efficiency for each blade row. At the most sophisticated level viscous effects and machine performance can be predicted by using a thin shear layer approximation to the Navier–Stokes equations and an eddy viscosity turbulence model. For high-pressure-ratio compressors there is a strong tendency for the calculation to surge during the transient part of the flow. This is overcome by the use of a new technique, which enables the calculation to be run to a prescribed mass flow. Use of the method is illustrated by applying it to a multistage turbine of simple geometry, a two-stage low-speed experimental turbine, and two multistage axial compressors.

A Reynolds-Averaged Navier-Stokes Solver in a Turbomachinery Design System

2007 ◽  
Author(s):  
Fahua Gu ◽  
Mark R. Anderson
Keyword(s):  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Integrated Design ◽  
Navier Stokes ◽  
Design System ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Machine Performance ◽  
Reynolds Averaged Navier Stokes

The design of turbomachinery has been focusing on the improvement of the machine efficiency and the reduction of the design cost. This paper presents an integrated design system to create the machine geometry and to predict the machine performance at different levels of approximation, including one-dimensional design and analysis, quasi-three-dimensional-(blade-to-blade, throughflow) and full-three-dimensional-steady-state CFD analysis. One of the most important components, the Reynolds-averaged Navier-Stokes solver, is described in detail. It originated from the Dawes solver with numerous enhancements. They include the use of the low speed pre-conditioned full Navier-Stokes equations, the addition of the Spalart-Allmaras turbulence model and an improvement of wall functions related with the turbulence model. The latest upwind scheme, AUSM, has been implemented too. The Dawes code has been rewritten into a multi-block solver for O, C, and H grids. This paper provides some examples to evaluate the effect of grid topology on the machine performance prediction.

Design and Experimental Study on the Surge Performance Improvement by the Effects of Bleed Slot Casing of a Centrifugal Compressor

2014 ◽  
Author(s):  
Hong Won Kim ◽  
Jae Hoon Chung ◽  
Hyo Seong Lee ◽  
Min Ouk Choi
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Operating Range ◽  
Surge Margin ◽  
Commercial Code

The primary design goal of a compressor is focused on improving efficiency. Secondary objective is to widen the compressor’s operating range. This paper presents a numerical and experimental investigation of the influence of the bleed slot to enlarge operating range for the 1.2MW class centrifugal compressor installed in a turbocharger. The main design parameters of the bleed slot casing are upstream slot position, inlet pipe slope, downstream slot position and width. The DOE (design of experiment) method was carried out to optimize the casing design. Numerical analyses were done by the commercial code ANSYS-CFX based on the three dimensional Reynolds-averaged Navier-Stokes equations. From the analysis, as the downstream slot position and width are smaller and upstream position is located away from impeller inlet, efficiency and pressure ratio are increased. Experimental works were done with and without the bleed slot casing. The simulation results were in good agreement with the test data. In case without the bleed slot casing, the surge margin value came out to be only 11.8% but with the optimized bleed slot design, the surge margin reached 23%. Therefore, the surge margin increase of 11.2% was achieved.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

Study of Supersonic Flowfield With Secondary Injection

2004 ◽  
Author(s):  
D. Sun ◽  
R. S. Amano
Keyword(s):  
Total Pressure ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Weighted Essentially Nonoscillatory ◽  
Secondary Injection ◽  
Total Pressure Ratio

Two and three-dimensional steady flowfields generated by transverse secondary injection into a supersonic flow, was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory (WENO) schemes. Both the two-dimensional and three-dimensional results are given. Some parameters affecting the penetration height and separation length of the interactive flowfield, including the total pressure ratio of the jet to the freestream, the boundary layer thickness, slot width, the Mach number of the freestream and injection, the jet angle, and the shape of the injection orifice in the 3D flowfield, were calculated in more detail.

Simulation of Fluid Flow Through a Granular Bed

2006 ◽  
Author(s):  
Arezou Jafari ◽  
S. Mohammad Mousavi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Packed Bed ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Duct Geometry ◽  
Flow Through

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.

Investigation of Vortex Structures for Supersonic Jet Interaction Flowfield

2015 ◽  
Vol 798 ◽  
pp. 546-550 ◽  
Author(s):  
Asel Beketaeva ◽  
Amr H. Abdalla ◽  
Yekaterina Moisseyeva
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Supersonic Jet ◽  
Three Dimensional ◽  
Horseshoe Vortex ◽  
Bow Shock ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Trailing Vortices ◽  
Barrel Shock

The three-dimensional supersonic turbulent flow in presence of symmetric transverse injection of round jet is simulated numerically. The simulation is based on the Favre-averaged Navier-Stokes equations coupled with Wilcox’s turbulence model. The numerical solution is performed using ENO scheme and is validated with the experimental data that include the pressure distribution on the wall in front of the jet in the plane symmetry. The numerical simulation is used to investigate in detail the flow physics for a range of the pressure ratio . The well-known primary shock formations are observed (a barrel shock, a bow shock, and the system of λ-shock waves), and the vortices are identified (horseshoe vortex, an upper vortex, two trailing vortices formed in the separation region and aft of the bow shock wave, two trailing vortices that merge together into one single rotational motion). During the experiment the presence of the new vortices near the wall behind the jet for the pressure ratio is revealed.

scholarly journals Design Optimization of a Transonic-Fan Rotor Using Numerical Computations of the Full Compressible Navier-Stokes Equations and Simplex Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
M. A. Aziz ◽  
Farouk M. Owis ◽  
M. M. Abdelrahman
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Simplex Algorithm ◽  
Navier Stokes ◽  
Numerical Computations ◽  
Navier Stokes Equations ◽  
Pressure Losses ◽  
Optimization Parameters ◽  
Transonic Fan

The design of a transonic-fan rotor is optimized using numerical computations of the full three-dimensional Navier-Stokes equations. The CFDRC-ACE multiphysics module, which is a pressure-based solver, is used for the numerical simulation. The code is coupled with simplex optimization algorithm. The optimization process is started from a suitable design point obtained using low fidelity analytical methods that is based on experimental correlations for the pressure losses and blade deviation angle. The fan blade shape is defined by its stacking line and airfoil shape which are considered the optimization parameters. The stacking line is defined by lean, sweep, and skews, while blade airfoil shape is modified considering the thickness and camber distributions. The optimization has been performed to maximize the rotor total pressure ratio while keeping the rotor efficiency and surge margin above certain required values. The results obtained are verified with the experimental data of Rotor 67. In addition, the results of the optimized fan indicate that the optimum design is found to be leaned in the direction of rotation and has a forward sweep from the hub to mean section and backward sweep to the tip. The pressure ratio increases from 1.427 to 1.627 at the design speed and mass flow rate.

Three-dimensional transverse instabilities in detached boundary layers

2007 ◽  
Vol 571 ◽  
pp. 221-233 ◽  
Author(s):  
FRANÇOIS GALLAIRE ◽  
MATTHIEU MARQUILLIE ◽  
UWE EHRENSTEIN
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Linear Analysis ◽  
Navier Stokes ◽  
Physical Origin ◽  
Viscous Effects ◽  
Global Mode ◽  
Navier Stokes Equations ◽  
Recirculation Bubble

A direct numerical simulation of the incompressible Navier–Stokes equations of the flow over a bump shows a stationary longitudinal instability at a Reynolds number of Re = 400. A three-dimensional global mode linear analysis is used to interpret these results and shows that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximately ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.

scholarly journals Детально-сравнительный анализ взаимодействия сверхзвукового потока с поперечной газовой струей при больших параметрах нерасчетности

2019 ◽  
Vol 89 (10) ◽  
pp. 1513
Author(s):  
А.О. Бекетаева ◽  
P. Bruel ◽  
А.Ж. Найманова
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Mach Disk ◽  
Navier Stokes ◽  
Third Order ◽  
Navier Stokes Equations ◽  
The Third ◽  
Eno Scheme

The interaction of the spatial supersonic turbulent gas flow with a sound jet injected perpendicularly was widely studied both numerically and experimentally. However, there are only a few studies of the detail analysis of the formation and distribution of vortex structures from moderate till high pressure ratio (the ratio of pressure in the jet to pressure in the main flow).The aim of this paper is the study and identify the system of the vortex forming behind the injected sound jet in a transverse supersonic flow from the point of view of the mixing efficiency. For that the three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The presence of well known vortex structures are shown: two oppositely rotating vortices in front of the jet; horseshoe vortex; two pairs of the vortex in the mixing zone of the jet and the main flow, where one of them is located in the wake behind the jet and other in the lateral line of the jet. Also, the pressure ratio parameters are determined at which the additional pairs of vortices appear. Where, the first of them is formed on the edge of the Mach disk as a result of the interaction of the decelerated jet flow behind the Mach disk with the high-speed ascending flow behind the barrel. And, the second is due to the interaction of the ascending jet flow with the main gas flow. As a result of comparative analysis the criterion of the pressure ratio parameters are found under which a clear picture of additional horn vortices is observed near the wall in the region behind the jet. The graph of the dependence of the angle of inclination of the bow shock wave on the parameter of pressure ratio is obtained. Satisfactory agreement of the pressure distribution on the wall in front of the jet in the symmetry plane with experimental data is established.

Numerical Study of the Pulsating Flow at the Tongue Region of a Centrifugal Pump for Several Flow Rates

2008 ◽  
Author(s):  
Rau´l Barrio ◽  
Jorge Parrondo ◽  
Eduardo Blanco ◽  
Joaqui´n Ferna´ndez
Keyword(s):  
Unsteady Flow ◽  
Centrifugal Pump ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
Partial Load ◽  
Flow Through

A numerical study is presented on the unsteady flow at the tongue region of a single suction volute-type centrifugal pump with a specific speed of 0.46. The flow through the pump, available at laboratory, was simulated by means of a commercial CFD software that solved the Reynolds averaged Navier-Stokes equations for three-dimensional unsteady flow (3D-URANS). A sensitivity analysis of the numerical model was carried out and the numerical predictions were compared with previous experimental results of both global and unsteady variables. Once validated, the model was used to study the flow pulsations associated to the interaction between the impeller blades and the volute tongue as a function of the flow rate, from partial load to overload. The study allowed relating the passage of the impeller blades with the tangential and radial velocity pulsations at some reference positions and with the pressure pulsations at the tongue region.

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