A 3D Compressible Flow Model for Weak Rotating Waves in Vaneless Diffusers—Part I: The Model and Mach Number Effects

2011 ◽  
Vol 134 (4) ◽  
Author(s):  
Hua Chen ◽  
Feng Shen ◽  
Xiao-Cheng Zhu ◽  
Zhao-Hui Du
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Wave Speed ◽  
Flow Model ◽  
Radius Ratio ◽  
Rotating Waves ◽  
Flow Angle ◽  
Rotating Wave ◽  
Vaneless Diffusers ◽  
Undisturbed Flow

A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. Linearized 3D compressible Euler equations were casted on a rotating coordinate system traveling at the same angular speed as the wave cells. A uniform static pressure at the outlet of the diffuser was imposed. Complex functions of the solutions to the equations were obtained by a second-order finite difference method and the singular value decomposition technique. The influences of the inlet Mach number of undisturbed flow, inlet spanwise distribution of undisturbed radial velocity, and diffuser radius ratio on the rotating waves were studied and results show that (1) the critical flow angle and rotating wave speed are both affected by the Mach number. However, the angle only increases slightly with the Mach number while the wave speed increases rapidly with the Mach number; (2) inlet distribution has minor influences on diffuser instability but the wave speed increases with the inlet distortion; (3) diffuser instability increases rapidly and the wave speed decreases quickly with the diffuser radius ratio; and (4) backward traveling rotating wave may occur if diffuser is sufficiently long and the inlet Mach number is sufficiently small.

A 3D Compressible Flow Model for Weak Rotating Waves in Vaneless Diffusers—Part II: Detailed Results

2011 ◽  
Vol 134 (4) ◽  
Author(s):  
Feng Sheng ◽  
Hua Chen ◽  
Xiao-cheng Zhu ◽  
Zhao-hui Du
Keyword(s):  
Mach Number ◽  
Radial Velocity ◽  
Compressible Flow ◽  
Wave Speed ◽  
Flow Model ◽  
Radius Ratio ◽  
Wave Number ◽  
Rotating Waves ◽  
Inlet Distortion ◽  
Vaneless Diffusers

A 3D compressible flow model was presented in Part I of the paper to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. In this paper, detailed results on the influences of flow and diffuser geometry parameters, including inlet Mach number, inlet distortion, wave number, diffuser outlet-to-inlet radius ratio, diffuser width to inlet radius ratio, and impeller backswept angle, on the rotating waves are presented. It was found that inlet spanwise distortion of radial velocity has little effects on diffuser stability, but rotating wave speed increases with the distortion. The speed also increases with inlet Mach number, so does diffuser instability. Impeller backswept improves diffuser stability and this effect increases with diffuser radius ratio. Multiple resonances were found when impeller backswept is coupled to inlet distortion of radial velocity. These resonances may have similar stabilities but with different wave speeds, suggesting that two rotating waves with different rotating speeds may occur at the same time. Diffuser width was found to have little effects on stability and on wave speed if the same maximum and same minimum values of inlet distortion of radial velocity are kept, but have some effects if the values are not kept. A comparison was also made between the present model predictions and results in open literatures, and good agreement with the experimental results than previous 2D models was achieved.

A 3-D Compressible Flow Model for Weak Rotating Waves in Vaneless Diffusers: Part I—The Model

2010 ◽  
Author(s):  
Hua Chen ◽  
Fen Shen ◽  
Xiao-cheng Zhu ◽  
Zhao-hui Du
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Wave Speed ◽  
Flow Model ◽  
Three Dimensional ◽  
Angular Speed ◽  
Rotating Waves ◽  
Flow Angle ◽  
Vaneless Diffusers ◽  
Value Decomposition

A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic and to have no axial velocity. Linearised 3D compressible Euler eqns. were casted on a rotating coordinate system traveling at the same angular speed as the wave cells. A disturbance of radial velocity at the inlet and a uniform static pressure at the outlet of the diffuser were imposed. Complex functions of the solutions to the eqns. were obtained by a second order finite difference method and the Singular Value Decomposition technique. The influences of the inlet Mach number on the rotating waves were studied and preliminary results show that the critical flow angle and rotating wave speed are both affected by the Mach number. However, the angle only increases slightly with the Mach number while the wave speed increases rapidly with the Mach number.

A three-dimensional compressible flow model for rotating waves in vaneless diffusers with unparallel walls

2012 ◽  
Vol 226 (9) ◽  
pp. 2230-2249 ◽  
Author(s):  
Feng Sheng ◽  
Hua Chen ◽  
Xiao-cheng Zhu ◽  
Zhao-hui Du
Keyword(s):  
Compressible Flow ◽  
Euler Equations ◽  
Flow Model ◽  
Three Dimensional ◽  
Rotating Stall ◽  
Experimental Result ◽  
Viscous Effects ◽  
Rotating Waves ◽  
Vaneless Diffusers ◽  
Suppression Effects

A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in unparallel wall vaneless diffusers in centrifugal compressors. The model extends the three-dimensional compressible flow model for parallel wall diffusers recently developed by present authors. Linearised three-dimensional compressible Euler equations casted on a rotating frame of reference travelling at the same speeds as the waves are employed and the viscous effects are ignored. Complex functions of the solutions to the linearised Euler equations are then obtained by a second-order finite difference method and the singular value decomposition technique. Undisturbed flow is assumed potential and first solved by numerical method of strongly implicit procedure. Critical inlet flow rate and rotating wave speed of diffusers of three different shroud wall shapes, namely, convergent, convergent then divergent and constant area tapered, are studied for three different diffuser outlet-to-inlet radius ratios and for different inlet Mach numbers, and results compared with those from diffusers with parallel walls. The results show suppression effects on rotating stall by the contracting walls and the suppression effects vary with wall contraction rate, wall shape, inlet Mach number and the diffuser radius ratio. Further, the effects of diffuser inlet contraction are studied and prediction of the model is compared with experimental result.

A Weakly Compressible Flow Model and Rapid Convergence Methods

1988 ◽  
Vol 110 (4) ◽  
pp. 441-445 ◽  
Author(s):  
Charles C. S. Song ◽  
Mingshun Yuan
Keyword(s):  
Mach Number ◽  
Steady Flow ◽  
Compressible Flow ◽  
Flow Model ◽  
Incompressible Flows ◽  
Acoustic Noise ◽  
Hydraulic Transients ◽  
Flow Solution ◽  
Weakly Compressible ◽  
Speed Up

A weakly compressible flow model for small Mach number flows is applied to the computation of steady and unsteady inviscid flows. The equations of continuity and motion are decoupled from the energy equation, but, unlike the equations for incompressible fluids, these equations retain the ability to represent rapidly changing flows such as hydraulic transients and hydroacoustics. Two methods to speed up the process of convergence when an explicit method is used to calculate steady incompressible flows are proposed. The first method which is quite similar to the artificial compressiblity method is to assume an arbitrarily small sound speed (equivalent to large Mach number) to speed up the convergence. Any positive finite number may be used for M. One disadvantage of this method is the contamination of the steady flow solution by acoustic noise that may reverberate in the flow field for some time after the steady flow has been essentially established. The second method is based on the concept of valve stroking or boundary control. Certain boundary stroking functions that will unify the hydroacoustic and hydrodynamic processes can be found by using the inverse method of classical hydraulic transients. This method yields uncontaminated steady flow solution very rapidly independent of the Mach number.

Flow Investigations on Swirling Compressible Flow Through a Vaneless Radial Diffuser

1987 ◽  
Author(s):  
D. P. Agrawal ◽  
S. M. Yahya ◽  
D. N. Reddy
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Performance Parameters ◽  
Flow Angle ◽  
Swirl Generator ◽  
Swirl Angle ◽  
Inlet Swirl ◽  
Flow Through ◽  
Swirl Vane ◽  
Nozzle Type

The present study deals with the experimental investigation of Swirling compressible flow through a parallel walled vaneless radial diffuser. Swirl generator of vortex nozzle type is used for supplying swirling compressible flow at the diffuser inlet up to a Mach number of 0.8. The desired flow angles are achieved by adjusting inlet swirl vane setting angles from 2.5° to 12.5°. The results are presented in terms of performance parameters such as pressure recovery and loss coefficient for various diffuser inlet Mach numbers from 0.3 to 0.8 and flow angle range from 20° to 35°. The effect of Mach number and swirl angle on the performance of the vaneless radial diffuser are discussed.

Assessment of the Loss Map of a Centrifugal Compressor’s External Volute

2020 ◽  
Author(s):  
Thomas Ceyrowsky ◽  
Andre Hildebrandt ◽  
Martin Heinrich ◽  
Rüdiger Schwarze
Keyword(s):  
Mach Number ◽  
Flow Rate ◽  
Numerical Approach ◽  
Operating Conditions ◽  
Circumferential Velocity ◽  
Flow Angle ◽  
Absolute Flow ◽  
Highly Sensitive ◽  
Geometrical Features ◽  
Comparison With Experimental Data

Abstract A volute’s loss coefficient is highly sensitive to Mach number, circumferential velocity and flow rate at volute inlet. In case of a backswept impeller, these parameters are coupled to each other. An increased flowrate leads to a steeper absolute flow angle at impeller exit and hence to a decrease of circumferential velocity. The absolute Mach number is also altered. Therefore, in order to investigate the effects of flowrate and flow angle separately, one would have to vary the diffuser width together with the flowrate, keeping the flow angle constant. This corresponds to coupling the volute with aerodynamically similar impellers, designed for higher and lower flowrates. Since this is elaborate, there is no adequate study available in open literature, assessing a volute’s global loss map. In this work, a new numerical approach for the prediction of a volute’s representative loss map is presented: The volute is calculated by means of steady CFD as a standalone component. The inlet boundary conditions are carefully selected by means of 1D and applied together with different diffuser widths. This allows for separate investigation of the impacts of flow angle, flow rate and Mach number. Validation against full stage CFD confirms the applicability of the standalone model. The results exhibit that minimum losses do not necessarily occur at the theoretical matching point but either when the volute is smaller or bigger, depending on the inlet flow angle. Investigations of the loss mechanisms at different operating conditions provide useful guidelines for volute design. Finally, the validity of these study’s findings for volutes with different geometrical features is examined by comparison with experimental data as well as with fullstage CFD.

On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2161-2175 ◽  
Author(s):  
M Parmar ◽  
A Haselbacher ◽  
S Balachandar
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Propagation Speed ◽  
Added Mass ◽  
The Body ◽  
Mass Force ◽  
Unsteady Force ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
Cylinders And Spheres

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c ∞ t / R ≳10, where c ∞ is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.

Sign in / Sign up

Export Citation Format

Share Document