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.

scholarly journals Compressible Flow Pressure Losses in Wye-Junctions

1992 ◽  
Author(s):  
N. I. Abou-Haidar ◽  
S. L. Dixon
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Incompressible Flows ◽  
Separate Flow ◽  
Working Fluid ◽  
Flow Visualisation ◽  
Vena Contracta ◽  
Pressure Losses ◽  
Flow Pressure ◽  
Limiting Condition

This paper considers the compressible flow pressure losses in sharp cornered wye-junctions with symmetrical branches under dividing and combining flow conditions. Determination of the additional total pressure losses occurring in flow through several three-leg junctions, using dry air as the working fluid, has been made experimentally. Results covering a wide speed range up to choking are presented for three different wye-junction geometries. Separate flow visualisation Schlieren tests detected the presence of normal shock waves, located at up to one duct diameter downstream of the junction, and therefore confirmed the choking of the flow at the vena contracta. The highest attainable Mach number (M3) of the averaged whole flow was 0.9 for one of the dividing flow geometries and 0.65 for several of the combining flow cases. These values of M3 were the maximum possible and hence represent a limiting condition dictated by choking. In general, the compressible flow loss coefficients, caused by the presence of the wye-junctions, can be expected to be higher for dividing flows and lower for combining flows than would be the case for incompressible flows because of the influence of Mach number (M3) on the magnitude of the denominator.

Measurement of Compressible Flow Pressure Losses in Wye-Junctions

1994 ◽  
Vol 116 (3) ◽  
pp. 535-541 ◽  
Author(s):  
N. I. Abou-Haidar ◽  
S. L. Dixon
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Incompressible Flows ◽  
Separate Flow ◽  
Working Fluid ◽  
Vena Contracta ◽  
Pressure Losses ◽  
Flow Loss ◽  
Flow Pressure ◽  
Limiting Condition

This paper considers the compressible flow pressure losses in sharp-cornered wye-junctions with symmetric branches under dividing and combining flow conditions. Determination of the additional total pressure losses occurring in flow through several three-leg junctions, using dry air as the working fluid, has been made experimentally. Results covering a wide speed range up to choking are presented for 30, 60, and 90 deg wye-junctions. Separate flow visualization schlieren tests detected the presence of normal shock waves, located at up to one duct diameter downstream of the junction, and therefore confirmed the choking of the flow at the vena contracta. The highest attainable Mach number (M3) of the averaged whole flow was 0.9 for one of the dividing flow geometries and 0.65 for several of the combining flow cases. These values of M3 were the maximum possible and hence represent a limiting condition dictated by choking. In general, the compressible flow loss coefficients, caused by the presence of the wye-junctions, can be expected to be higher for dividing flows and lower for combining flows than would be the case for incompressible flows because of the influence of Mach number, M3.

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 weakly compressible flow model for the restart of thixotropic drilling fluids

2011 ◽  
Vol 166 (23-24) ◽  
pp. 1369-1381 ◽  
Author(s):  
Cezar O.R. Negrão ◽  
Admilson T. Franco ◽  
Leandro L.V. Rocha
Keyword(s):  
Compressible Flow ◽  
Flow Model ◽  
Drilling Fluids ◽  
Weakly Compressible

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.

The flow of a jet from a body opposing a supersonic free stream

1966 ◽  
Vol 26 (2) ◽  
pp. 337-368 ◽  
Author(s):  
P. J. Finley
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Steady Flow ◽  
Flow Model ◽  
Free Stream ◽  
Sufficient Condition ◽  
Exit Plane ◽  
Force Coefficient ◽  
Short Account ◽  
Series Of Experiments

A series of experiments is described in which a jet issues from an orifice at the nose of a body in supersonic flow to oppose the mainstream. An analytical model of the flow is developed which suggests that the aerodynamic features of a steady flow depend primarily on a jet flow-force coefficient, and the Mach number of the jet in its exit plane. A sufficient condition for steady flow is developed. The experiments are found to agree well with predictions based on the flow model. A short account is presented of some previous investigations, and some of their conclusions are re-examined in the light of the present study.

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.

500 An in vitro steady flow model of mitral regurgitation by three-dimensional Doppler

1999 ◽  
Vol 1 ◽  
pp. S86-S86
Author(s):  
R DESIMONE ◽  
G GLOMBITZA ◽  
C VAHL ◽  
H MEINZER ◽  
S HAGL
Keyword(s):  
Mitral Regurgitation ◽  
Steady Flow ◽  
Flow Model ◽  
Three Dimensional
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