A Numerical Study of The Flow Inside Annular Jet pump

M .El Gazzar , AIAA-2004-2359 , TP-10

Helwan Eng. Industries Co.( MF 99 ) Cairo Egypt . Gazzar327@hotmail.com

Dr . Tarek Meakhail

Lecturer at the High Institute of Energy Aswan Egypt Mina_tarek@Hotmail.com

Dr . Samy Mikhail

Professor . Cairo University Giza Egypt . Mouraddahab@minanet.com

Computational fluid dynamics ( CFD ) simulations are carried out for the fluid flow inside an annular jet pump .There is no published work as far as the authors know, which deals with the numerical simulation of this type of flow pumps. In this study, simulation of the flow inside a water water annular jet pump is carried out to predict the performance and characteristics of this type of pumps, using CFX-TASCflow code. The numerical results are compared with the experimental results, obtained by other authors data for different cases of geometric configurations and fluid flow conditions as; head ratio versus mass flow ratio, mass flow ratio versus overall efficiency, and wall static pressure distributions. A good agreement between experimental and numerical results is found. The experimental results in the previous literature, have not included velocity distributions or static pressure distributions inside the pump, which are necessary to understand the mechanism of mixing between the primary and secondary streams. Thus, the details of velocity vector distributions, and static pressure contours of the flow are predicted for the mixing process between the two streams in each of the convergent nozzle and the mixing chamber .The details of the fluid flow give us a complete picture of the mixing process inside the pump, and proves the validity of using this code when properly applied.

Introduction

he pumping action of the jet pump results from transfer of energy from a high velocity jet to a

low velocity stream. The pump consists mainly of a jet nozzle ,a convergent nozzle, a mixing chamber , and an outlet diffuser, as shown in Fig. (1) . In general, there are two types of this pump: a jet pump with the primary jet nozzle placed along the center line of the pump and the second stream around it (namely, the central type) , and the other type has the suction stream in center and the annular driving jet on the outside

(namely, the annular jet type) . The primary power is provided by a high pressure stream of fluid directed through the nozzle to produce the highest possible velocity. Due to the high velocity of the primary fluid , a low pressure in the suction chamber created suction of the secondary stream. Consequently, turbulent mixing between the two streams (with two different velocities) occurs, with increased pressure due to change of momentum, then the pressure of the combined flow is increased further in the outlet diffuser. Even through its efficiency is low, such pumps are widely used because of their simplicity and high reliability (as a consequence of no moving parts). The jet pump have a very wide range of application , such as in deep well pumping, booster pumping , dredging , priming devices , and slurry pump . The one dimensional jet pump theory was first

who established the governing equations representing the processes inside jet pumps . This theory (for central jet pump type) supported by extensive experimental data , was later

T

Fig . ( 1 ) Schimatic Diagram of Annular Jet Pump

Mixing Chamber

Convergent Nozzle

Annular Jet Nozzle

Suction Nozzle

Annular Jet Nozzle

Outlet Flow

Diffuser

37th AIAA Thermophysics Conference28 June - 1 July 2004, Portland, Oregon

AIAA 2004-2389

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

improved to include the friction losses by Cunningham and River 1957 [2] , Mueller 1964 [3] , Vogel 1956 [4] , Reddy and Kar 1968 [5] , Sanger 1970 [6] , and many others .In contrast , for annular jet pump type the experimental information is limited since only few studies were carried out such as ; Shimizu 1986 [7 , 8] , and Yokota , A. 1974 [ 9 ] . Numerical Technique In this study, the numerical computational carried out by using CFX-TASCflow [10]. This code solves Reynolds average Navier - Stokes equations in primitive variable form. The standard K- � turbulence model is used to study the effect of turbulence of fluid flow. Also, in order to study the flow near wall; wall function is used to resolve the wall flows. This code uses a finite element based finite volume method. Finite difference, finite element and finite volume methods can all be shown to belong to a broader class called the method of weighted residuals, as presented in [11]. To achieve a numerical solution that is convergent, consistent and stable, various numerical schemes have been implemented in CFX-TASCflow code . Boundary conditions To get an accurate simulation, the same dimensions of the design test rig of Shimizu [ 8 ] were set . Also, the boundary conditions of fluid flow were the same which set at carry out the experimental results .The mass flow rate of each primary and secondary that gives the correct mass flow ratio and the outlet static pressure were applied in the code .The turbulent intensity and the eddy length were 0.03, 0.03 respectively, while the average Reynolds number was 7.0 E+05. The maximum residuals were less than E-04.To reach a good convergent , the number of iterations were 120 for a time of calculation about 5.5 hours , for each condition of the fluid flow . Grid Generation A high quality mesh is produced using multi

block [ H ] grid inside the jet pump . This type of grid , for this problem , gives better minimum skew angle, which should not be less than 20 degrees , and better maximum aspect ratio , which should not be more than 100 . Fig. ( 2 )

shows the grid nodes of the whole pump . The total number of grid nodes is about 430,000 .

Fig. (2) The grid nodes of the whole jet pump . Results and discussion 1.Characteristic Curves The main characteristics curves , showing the performance of a jet pump are the M- N , and M - ηo curves . The optimum efficiency in the experimental results of Shimizu [ 8 ] , is at At / Ao = 0.48 , Aso / Ao = 0.61 , R = 0.57. Thus the prediction of the characteristic curves are carried out with these ratios . The main variables are the ration of mixing chamber length to inner diameter of suction line (Lt / Do ) , and convergent nozzle angle (

�) .Figure ( 3.a )

shows the relation between head ratio ( N ) versus mass flow ratio ( M ) at constant value of ( Lt / Do = 1.86 ) , and for different convergent nozzle angle (

� = 18 , 30 ) , while M - ηo

curves for the same configuration is illustrated in figure ( 3.b ) . Figures ( 4 . a ) , ( 4 . b ) show M- N , and M - ηo curves for another value of ( Lt / Do = 3.26 ) , for the same values of convergent nozzle angle (

� = 18 , 30 ) .The previous curves

( 3.a 4.b ) exhibit the effect of the convergent nozzle angle on the performance of the annular jet pump . To show the effect of the mixing chamber length on the performance curves , Figs . ( 5.a ) , ( 5.b ) show this effect at constant at constant convergent nozzle angle (

� = 18) ,

while Figs . ( 6.a ) , ( 6.b ) show the same effect at (

� = 30 ) .

2. Static wall Pressure distribution in the flow direction . The static wall pressure distribution inside the convergent nozzle , the mixing chamber , and the diffuser is a good pointer to know what occurs inside the jet pump . Fig. ( 7 a , b ) ,

shows the pressure coefficient Cp versus dimensionless axial position ( X / Do ) from the jet exit . These results are a sample of the experimental results for various values of the convergent angle � = 18 o , At / Ao = 0.48 , and L ' / Do = 4.24 . Fig. ( 7.a ) , shows the static wall pressure coefficient for an area ratio ( R = 0.57 ) , and ( Aso / Ao = 0.61 ) , for mass flow ratios ( M = 0.3 , 0.58 ) . While Fig . ( 7.b ) shows the pressure coefficient ( Cp ) for an area ratio ( R = 0.82 ) , and ( Aso / Ao = 0.5 ) , and mass flow ratios ( M = 0.19 , 0.34 ) . In every case , the static pressure distribution in the mixing chamber drops at ( X / Do ) = 0 to 3.8 and then recovers in the diffuser ( X / Do ) = 3.8 to 6.9 until it becomes almost constant . 3. Velocity Distribution The prediction of velocity distribution inside the convergent nozzle and the mixing chamber are carried out . These are at R = 0.57 , (Aso / Ao = 0.61) , (At / Ao = 0.48) , and ( L '/Do = 4.24 ) , � = 18 o and at mass flow ratio 0.58 . Fig . ( 8 ) shows the prediction of the dimensionless velocity distributions at six sections from X / Do = 0.018 to 1 , along the axis of convergent nozzle . The velocity distributions are referred to the velocity at the exit of annular jet nozzle ( V / VJ ) .The dimensionless velocity distribution along the mixing chamber at six sections from X / Dt = 0.075 to 4.72 is shown in Fig . ( 9 ). In this figure , the velocity distributions are referred to the average velocity at inlet of mixing chamber ( V / Vt ). 4. Velocity vector and pressure contours

The velocity vector contours in both the convergent nozzle and the mixing chamber are shown in Fig . (10 ) . The prediction was for the same data of the velocity distribution in Figs . (8 , 9 ) . Examining Fig ( 10 ) , in the convergent nozzle , the two streams , the high velocity stream jet ( in the outer diameter , region ) , and the low velocity stream suction ( in the inner diameter region ) , start to mix directly at the exit of the jet nozzle . Then the momentum transfer gradually from high momentum region to low momentum region . Thus the stream of jet velocity decreases as the stream of suction velocity increases . On the other hand , Fig . ( 11 ) shows the difference in static pressure of the different stream , at inlet of the mixing chamber but equalize gradually until it is almost constant at the end of the mixing chamber .

5. Turbulent kinetic energy contours The contours of Turbulent kinetic energy the inside convergent nozzle and the mixing chamber are

shown in Fig . ( 12 ) . While the contours illustrating the dissipation of the turbulent kinetic energy are shown in Fig . ( 13 ) .It clear from two Figs., that the maximum turbulent kinetic energy occurs at the edge of jet nozzle ( the thickness of material of jet nozzle ) , then decreases gradually .The contours of dissipation of turbulent kinetic energy show the same trend . Also the two Figs. , show that , the minimum turbulent kinetic energy at the layer adjacent the wall.

Conclusions In this study the simulation of the flow inside annular jet pumps are carried out using CFX-TASCflow code . The experimental data were obtained from the extensive results obtained of Shimizu [ 8 ] . The comparison between the experimental results and prediction results are carried out , for the characteristics and performance curves of jet pump at At / Ao = 0.48 , Aso / Ao = 0.61 , R = 0.57 , for two convergent nozzle angles ( � = 18 , 30 ) , and for two configurations ( Lt / Do = 18 , 3.26 ) . The static wall pressure distribution in pressure coefficient form (Cp ) are calculated for two area ratios ( R = 0.57 , 0.82 ) mass flow rate were ranging ( M = 0.19 0.58 ) . A good agreement between them is found . Further , the dimensionless velocity distribution at various sections carried out for R = 0.57 , ( Lt / Do = 3.26 ) along the axis . The pressure contours are obtained for the same configuration and condition of flow . Finally , the turbulent kinetic energy and the dissipation of turbulent kinetic energy are calculated . The numerical results illustrate the mechanism of the mixing process inside both the convergent nozzle and the mixing chamber. The comparison proves the validity of the used code, when properly applied, and open the possibility for extensive study of the effect of the various kinematic and geometric ratios of the pump, without the need for resort to the more expensive and time consuming experimental research.

Nomenclature

Ao area of suction and delivery lines . Aso area of central suction nozzle At area of mixing chamber .

AJ sectional area of annular jet . Cp pressure coefficient = [ ( Px - Ps ) ] / [0.5 � VJ

2 ] Do inner diameter of suction line . Dt diameter of mixing chamber

Lt length of mixing chamber . L` total length of the convergent nozzle and the mixing chamber .

M mass flow ratio = [ � s Qs / � J QJ ] . N head ratio = [ ( Pd Ps ) / ( PJ Pd ) ] . QJ jet flow rate . Qs suction flow rate . Pd delivery total pressure . PJ jet total pressure . Ps suction total pressure Px total pressure at location ( X ) . r the distance from center line along the radius . R area ratio of jet and mixing chamber = [ AJ / At ]. VJ mean axial velocity of the jet nozzle . Vt mean axial velocity of the mixing chamber . X axial position from the jet exit . � angle of convergent nozzle . � efficiency = [ M , N ] .

REFERENCES 1 . Gosline , J . E . , and O' Brine , M.P., " The Water

in Engineering , Vol. 3 , No.3 , PP. 167 190 , 1934 . 2 . Cunningham, R . G . , River . W .," Jet Pump Theory and Performance with fluids of High

Mechanical Engineers .Vol. 79 , PP. 1807 , 1957 . 3 . Mueller ,N . G . H. " Water Jet Pump. " Journal of the Hydraulics Division, HY3 , PP. 83 113, May 1964 .

-

-chnik , Berlin . 5 , pp. 619 637, 1956 . 5 . Reddy , Y . R . , Kar , S . " Theory And Performance of Water Jet Pump . " Journal of the Hydraulics Division , HY5 , PP. 1261 1281, Sep. 1968 . 6. Sanger , N . L . " An Experimental Investigation of Several Low Area Water Jet Pumps . " , Transaction of the ASME , Journal of Basic Engineering , PP. 11 20 , Mar. 1970 7 . Shimizu , Y . ,et al .," Studies of the configuration and performance of annular jet type pumps ", Journal Of Fluids Engineering , Vol. 109 , PP 205-212 , September 1987. 8 . Shimizu , Y. , et al. , " Studies on the Annular Jet Pump with Swirling Components in Driving Jet Flow ," Trans JSME . Vol. 49-448 , PP. 2746 , 1983 . 9. Yokota , A. , et al . , " On the Annular Ring Type Jet Pump ." Japan Miner . Engrs . Soc. , No . 90- 1038 , PP 539 , 1974 .

10 . ASC , -TASCflow Documentation Version

Waterloo , Ontario , Canada 1999 . 11 .

Conference paper, Canadian Congress of Applied Mechanics (CANCAM), Winnipeg, Manitoba , Canada, June 1991 .

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Fig . ( 12 ) Contours of turbulent kinetic energy Fig . ( 13 ) Contours of dissipation of turbulent kinetic inside convergent nozzle and mixing energy inside convergent nozzle and mixing

chamber . chamber .