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Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                 Applications (IJERA)...
Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                  Applications (IJERA...
Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                 Applications (IJERA)...
Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                                  App...
Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                 Applications (IJERA)...
Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                                 Appl...
Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and                 Applications (IJERA)...
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  1. 1. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-763Flow of Single-Phase Water and Two-Phase Air-Water Mixtures through Sudden Contractions in Mini Channels *Manmatha K. Roula,*Sukanta K. Dash *Department of Mechanical Engineering, Bhadrak Institute of Engg & Tech, Bhadrak(India) 756113 **Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur (India) 721302Abstract Pressure drop through sudden contraction pressure drop across sudden contractions. Theyin small circular pipes have been numerically assumed the occurrence of the vena-contractainvestigated, using air and water as the working phenomenon and a dispersed droplet flow patternfluids at room temperature and near atmospheric downstream of the vena-contracta point. However,pressure. Two-phase computational fluid Schmidt and Friedel [1], based on their experimentaldynamics (CFD) calculations, using Eulerian– results indicated that the vena-contracta phenomenonEulerian model with the air phase being did not occur in their system at all. Applications ofcompressible, are employed to calculate the mini and micro channels in advanced and highpressure drop across sudden contraction. The performance systems have been rapidly increasing inpressure drop is determined by extrapolating the recent years. Some two-phase hydrodynamics andcomputed pressure profiles upstream and heat transfer processes in mini and micro channelsdownstream of the contraction. The larger and are different from larger channels [5-7], indicatingsmaller tube diameters are 1.6 mm and 0.84 mm, that the available vast literature associated with flowrespectively. Computations have been performed and heat transfer in larger channels may not bewith single-phase water and air, and two-phase directly applicable to micro channels. Significantmixtures in a range of Reynolds number velocity slip occurs at the vicinity of the flow(considering all-liquid flow) from 1000 to 12000 disturbance in case of mini and micro channelsand flow quality from 1.9 103 to 1.6 102 . The (Abdelall et al. [7]). They observed that homogeneous flow model over predicts the datacontraction loss coefficients are found to be monotonically and significantly and with the slipdifferent for single-phase flow of air and water. ratio expression of Zivi [8], on the other hand, theirThe numerical results are validated against experimental data and theory were in relatively goodexperimental data from the literature and are agreement. Pressure drops associated with single-found to be in good agreement. Based on the phase flow through abrupt flow area changes innumerical results as well as experimental data, a commonly-applied large systems have beencorrelation is developed for two-phase flow extensively studied in the past. But little has beenpressure drop caused by the flow area reported with respect to two-phase flow through minicontraction. and micro channels. In the present work, an attempt has been made to simulate the flow through suddenKeywords: Two-phase flow; pressure drop; loss contraction in mini channels using two phase flowcoefficients; flow quality; two-phase multiplier. models in an Eulerian scheme. The flow field is assumed to be axisymmetric and solved in two1. Introduction dimensions. Before, we can rely on CFD models to In the recent years, several papers have been study the two-phase pressure drop through suchpublished on flow of two-phase gas/liquid mixtures sections; we need to establish whether the modelthrough pipe fittings. Schmidt and Friedel [1] studied yields valid results. For the validation of results, weexperimentally two-phase pressure drop across have referred to the experimental studies conductedsudden contractions using mixtures of air and liquids, by Abdelall et al. [7], who measured pressure dropssuch as water, aqueous glycerol, calcium nitrate resulting from an abrupt flow area changes insolution and Freon 12 for a wide range of conditions. horizontal pipes.Salcudean et al. [2] studied the effect of various flowobstructions on pressure drops in horizontal air-water 2. Mathematical formulationflow and derived pressure loss coefficients and two- The Eulerian-Eulerian mixture model hasphase multipliers. Many of the published studies have been used as the mathematical basis for the two phaseassumed the occurrence of the vena-contracta simulation through sudden contraction. The volumephenomenon in analogy with single-phase flow and fractions  q and  p for a control volume canhave assumed that dissipation occurs downstream ofthe vena-contracta point [3-4]. Al’Ferov and therefore be equal to any value between 0 and 1,Shul’zhenko [3], Attou and Bolle [4] have attempted depending on the space occupied by phase q andto develop mechanistic models for two-phase 757 | P a g e
  2. 2. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-763phase p . The mixture model allows the phases to p 2 vq Eq  hq   (9)move at different velocities, using the concept of slip q 2velocities. and E p  hp for the incompressible phase, where hqContinuity Equation: is the sensible enthalpy for phase q .Continuity equation for the mixture is given by: Relative (Slip) Velocity and the Drift Velocity:    m   .  m vm   0 (1) The slip velocity is defined as the velocity of a t secondary phase p relative to the velocity of the where, vm is the mass averaged velocity: primary phase q :    v pq  v p  vq (10)     q q vq   p  p v p The mass fraction for any phase p is defined as vm  (2) m ppand  m is the mixture density: cp  (11) m  The drift velocity and the relative velocity ( v pq ) are m   q q   p  p (3) connected by the following expression:and  q is the volume fraction of phase q .    vdr , p  v pq  c p vqp (12) The basic assumption of the algebraic slip mixtureMomentum Equation: model is to prescribe an algebraic relation for theThe momentum equation for the mixture can be relative velocity so that a local equilibrium betweenobtained by summing the individual momentum the phases should be reached over short spatial length  p   p  m  equations for all phases. It can be expressed as (Drew[9]; Wallis[10])  scale. v pq  a (13) f drag p  mvm   . mvmvm   p  .  m vm  vm      T where  p is the particle relaxation time and is givent   (4)     by:  m g  F  .  q  q vdr , q vdr , q    p  p vdr , pvdr , p      pdp2where, m is the viscosity of the mixture: p  (14) 18 p where d p is the diameter of the particles (or droplets  m   q q   p  p (5)  or bubbles) of secondary phase p , a is thevdr , p is the drift velocity for the secondary phase p :    secondary-phase particle’s acceleration. The drag vdr , p  v p  vm (6) function f drag is taken from Schiller and Naumann: 1  0.15Re0.687 Re  1000Energy Equation: f drag   (15)The energy equation for the mixture takes the 0.0183Re Re  1000following form:  and the acceleration a is of the form:      v a  g   vm .  vm  mt   q q Eq   p  p E p   .  q vq  q Eq  p   (7)  t (16) In turbulent flows the relative velocity should contain  .  p v p   p E p  p   .  keff T   S E  a diffusion term due to the dispersion appearing in the momentum equation for the dispersed phase.where keff is the effective conductivity:   p  m  d p2 a  m  (17)  keff   q  kq  kt    p  k p  kt   (8)  v pq  18q f drag   p D qand kt is the turbulent thermal conductivity. The where ( m ) is the mixture turbulentfirst term on the right hand side of Equation (7) viscosity and (  D ) is a Prandtl dispersion coefficient.represents energy transfer due to conduction. S E It may be noted that, if the slip velocity is not solved,includes any other volumetric heat sources. For the the mixture model is reduced to a homogeneouscompressible phase, multiphase model. Volume Fraction Equation for the Secondary Phase: 758 | P a g e
  3. 3. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-763From the continuity equation for the secondary phase p , the volume fraction equation for the secondaryphase p can be obtained:  t  p  p   . p  p vm   . p  p vdr , p  (18)  Turbulence modeling:The k and  equations used in this model are asfollows (FLUENT 6.2 Manual [11]):     mk      mvmk      t , m k   Gk , m  m (19)t  k and      m      mvm      t ,m    C1 Gk ,m  C2 m  (20)t    k where the mixture density and velocity  m and vm ,are computed from m   p  p   q q (21)     p  p v p   q  q vq vm  (22) Fig. 1: (a) Idealized course of boundary stream lines  p  p   q q and (b) pressure profile for a sudden contraction.The turbulent viscosity t , m is computed from k2 t , m  m C (23)  r Walland the production of turbulent kinetic energy, Gk , m Mass flow Inlet Wallis computed from 0.8 mm   Outflow 0.42mm   T  Gk , m  t , m vm   vm  : vm (24)The constants in the above equations are z Axis of symmetryC1  1.44; C2  1.92; C  0.09;  k  1.0;    1.3 0.4 m3. Results and discussion Fig. 2: Computational domain for contraction section3.1. Single phase flow pressure drop Idealized course of boundary stream linesand pressure profile for single phase flow of waterthrough sudden contraction is shown in Fig. 1. 10000Computational domain with boundary conditions is 0shown in Fig. 2. The flow field is assumed to beaxisymmetric and solved in two dimensions. The -10000 ReferencePressure profiles for the single-phase flow of water -20000 Pressureand air through sudden contraction is depicted in Pc (Pa) -30000Figs. 3 and 4 respectively, for different mass flow Waterrates. It can be seen that the pressure profiles are -40000 m = 0.69 g/snearly linear up to 5 pipe diameters, both upstream -50000 m = 1.36 g/sand downstream from the contraction plane. Because m = 2.31 g/sthere is a change in pipe cross-section and hence a -60000 m = 2.58 g/schange in mean velocity, the slopes of the pressure m = 2.98 g/s -70000 m = 3.69 g/sprofiles before and after contraction are different. The -80000gradients are greater in the smaller diameter pipe. It -25 -20 -15 -10 -5 0 5 10 15 20 25can be observed from figs.3 and 4 that very close to Fig. 3: Pressure profiles for single-phase water L/Dthe contraction plane the static pressure in the inlet flow through sudden contractionline decreases more rapidly than in fully developedflow region. It attains the (locally) smallest value at a 759 | P a g e
  4. 4. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-763 4000 1.0 Air 0.9 Computation,---Kc=0.5 0 Theory, kd1=1.33, =2 m = 0.0234 g/s 0.8 Theory, kd1==1 Contraction Coefficient, Kc -4000 m = 0.0245 g/s Ref 0.7 Experiment[7] m = 0.0255 g/s pr -8000 m = 0.0356 g/s 0.6Pc (Pa) m = 0.0365 g/s -12000 m = 0.0373 g/s 0.5 m = 0.0524 g/s m = 0.0574 g/s 0.4 -16000 m = 0.0625 g/s m = 0.0681 g/s 0.3 -20000 m = 0.11 g/s 0.2 Laminar Turbulent m = 0.116 g/s -24000 m = 0.122 g/s 0.1 m = 0.142 g/s -28000 0.0 0 1000 2000 3000 4000 5000 6000 -25 -20 -15 -10 -5 0 5 10 15 20 25 L/D Reynolds Number, Re1 Fig. 4: Pressure profiles for single-phase air Fig. 6: Contraction loss coefficient for flow through sudden contraction single phase water flow 1.0 Computation 0.9 Theory, kd1==1 0.8 Theory, kd1=1.33, =2 Contraction Coefficient, Kc Experiment[7] 0.7 0.6 0.5 0.4 0.3 0.2 Laminar Turbulent 0.1 0.0 0 2000 4000 6000 8000 10000 12000 14000 (a) Reynolds Number, Re1 Fig. 7: Contraction loss coefficient for single phase air flow 0 Reference -10 pressure Pc (kPa) -20  mL= 2.578 g/s mG = 0.00493 g/s -30 mG = 0.00624 g/s mG = 0.00777 g/s mG = 0.00931 g/s (b) -40 mG = 0.0122 g/s mG = 0.015 g/s Fig. 5: (a) Velocity vectors & (b) Stream lines for single- phase flow through sudden contraction ( mL  3.69 g/s )  -20 -15 -10 -5 0 5 10 15 20 L/D Fig. 8: Pressure profiles for flow of two-phase air-water through sudden contraction 760 | P a g e
  5. 5. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-763distance of about L/D = 0.5 after the contraction mass flow rates of either water or air. The velocitysection and depends only slightly on the mass flow vectors and stream lines for a particular mass flowrates. The same is also demonstrated by the velocity rate of water and air are illustrated in Fig.9. It clearlyvectors and streamline contours in fig. 5, which demonstrates that unlike single phase flow, the two-shows that the flow has minimum cross-sectional phase flow does not contract behind the edge ofarea at about 0.5D downstream of pipe contraction, D transition and there is no change in the flow directionbeing the diameter of the smaller pipe. Then, the i.e; a zone of recirculation is not observed. Thuspressure gradually increases and, after reaching its vena-contracta is not a relevant term in two-phasemaximum, it merges into the curve of the pipe flow through sudden contractions. The computedfrictional pressure drop downstream of contraction. two-phase flow pressure drops caused by flow areaThis local minimum value of pressure corresponds to contractions are displayed in Figs. 10 (a) and (b) asthe vena-contracta position. So, it can be concluded functions of Reynolds number ( Re L 0,1 ).that vena-contracta is always obtained in the single-phase flow of water and air through sudden Where ReL 0,1   GD 1 L , (26)contraction at a distance of 0.5D from the contractionplane in the downstream direction. Simulatedvelocity vectors are shown in fig. 5(a), which clearly Here G1 is the total mass fluxshows that eddy zones are formed in the separated corresponding to the smaller diameter pipe. Theflow region. The pressure change at the contraction computed as well as the experimental data areplane  Pc  is obtained by extrapolating the compared with analytical model calculations assuming homogeneous flow, and slip flow (Abdelallcomputed pressure profiles upstream and downstream et al.[7]) with the aforementioned slip ratio ofof the pipe contraction (in the region of fully 1developed flow) to the contraction plane. It is S    L G  3 . The homogeneous flow and the slipobserved that the pressure drop increases with the flow models are considered assuming a vena-mass flow rates for single phase flow of both water contracta, and no vena-contracta (i.e., C c=l). It isand air through sudden contraction. observed that calculations with the homogeneous Assuming uniform velocity profiles at cross- flow assumption over predict the data monotonicallysection 1 and 3, the contraction loss coefficient can be and significantly. The computational and thefound by applying one-dimensional momentum and experimental data ([7]) are found to be in relativelymechanical energy conservation equations (Abdelall good agreement with the predictions of slip flowet al.[7]; Kays [12]): model.. An attempt is made to correlate the two-phase pressure 1 2Kc   u1    P2,3  P2,1    u1 2  1 2 2 1    (25) 2 change data in terms of the Martinelli factor: 0.1 0.5    1  x   G  0.9 Where ( P2,3  P2,1 ) is obtained numerically. XM   L      , (27)  G   x   L The contraction loss coefficients for single-phase Fig. 11 shows the graph  L 0,c X M verseswater and air flows are depicted in Figs. 6 and 7,respectively, where the experimental data [7] and X M ReL 0,1 considering both computational as well astheoretical predictions are also shown. The data the experimental data for sudden contraction. Thepoints for water, although few and scattered, are resulting correlation for two-phase multiplier forhigher than that of the theoretical predictions and sudden contraction is given by:in relatively close agreement with the  L 0,c  160  X M Re L 0,1  0.6877experimental data. For turbulent flow in the smaller (28)channel, contraction loss coefficient for single XMphase water flow (Kc ) is found to be 0.5 (Fig. 6).The contraction loss coefficient obtained for The comparison between the predictedsingle phase air flow (depicted in Fig. 7), on the values of the two-phase pressure drops (calculatedother hand, agree with the aforementioned theoretical from Eq. 28) with the computed as well aspredictions as well as experimental data [7] well. experimental data [7] are depicted in Fig. 12. The agreement is found to be quite good. It is notable that3.2 Two-phase flow pressure drop the correlation can predict the two-phase pressure Fig. 8 depicts the two-phase pressure drop drop quite well within 16% error. The correlation isthrough sudden contraction for different mass flow valid in the range of 1000 < ReL0,1 < 12000.rates of air keeping the mass flow rate of waterconstant. Similarly for different mass flow rates ofwater several numerical experiments are performedand it is observed that the pressure drop throughsudden contractions increases with increasing the 761 | P a g e
  6. 6. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-763 100000 Computation (Homogeneous flow model with vena-contracta) 90000 (Homogeneous flow model, no vena-contracta) (Slip flow model with vena-contracta) 80000 (Slip flow model, no vena-contracta) 70000 Experiment[7] Pc (Pa) 60000 50000 40000 30000 20000 10000 0 3512 3516 3520 3524 3528 3532 3536 3540 3544 (a) Reynolds Number, ReL0,1 (b) Fig. 10(b): Two-phase flow pressure drop caused by flow area contraction 0.6 Experiment[7] 0.5 Computation Eq.(28) 0.4 L0,c/XM 0.3 0.2 (b) Fig. 9: (a) Velocity vectors and (b) Stream lines for  mL  2.319 g/s and mG  0.0203 g/s    0.1 0.0 0 20000 40000 60000 80000 100000 120000 80000 Computation XMReL0,1 (Homogeneous flow model with vena-contracta) 70000 (Homogeneous flow model, no vena-contracta) Fig. 11: Correlation for two-phase multiplier (Slip flow model with vena-contracta) through sudden contraction 60000 (Slip flow model, no vena-contracta) Experiment[7] 25 50000 Computation +16%Pc (Pa) Experiment[7] 40000 20 -16% Predicted Pc(kPa) 30000 20000 15 10000 10 0 2576 2580 2584 2588 2592 2596 2600 2604 Reynolds Number, ReL0,1 5 (a) Fig. 10(a): Two-phase flow pressure drop caused by flow area contraction 0 0 5 10 15 20 25 Measured Pc(kPa) Fig. 12: Comparison between predicted and measured P c 762 | P a g e
  7. 7. Manmatha K. Roul, Sukanta K. Dash / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.757-7634. Conclusions channels, Exp. Thermal Fluid science, Vol. Pressure drops caused by abrupt flow area 26, (2002), pp. 389-407.contraction in mini channels using water and air [7] F. F. Abdelall, G. Hann, S. M. Ghiaasiaan,mixtures have been numerically investigated by using S. I. Abdel-Khalik, S. S. Jeter, M. Yoda, andtwo-phase flow model in an Eulerian scheme. For D. L. Sadowski, Pressure drop caused bysingle phase flow of water and air through sudden abrupt flow area changes in small channels,contraction, the vena contracta is always established Exp. Thermal and Fluid Sc, Vol. 29, (2005),at a distance of L/D = 0.5 after the contraction section pp. 425-434.and its position depends only slightly on mass flow [8] S. M. Zivi, Estimation of steady state steamrates. With turbulent flow in the smaller channel, void-fraction by means of principle ofapproximately constant contraction loss coefficients are minimum entropy production, ASME Trans.obtained for single phase flow of water and air. The Series C 86, (1964), pp. 237–252.contraction loss coefficients for water are found to be [9] D. A. Drew, Mathematical Modeling ofslightly larger than the theoretical predictions and that for Two-Phase Flows, Ann. Rev. Fluid Mech,air is in good agreement with the theoretical Vol. 15, (1983), pp. 261-291predictions. The computed values of two-phase flowpressure drops caused by sudden flow area contraction [10] G. B. Wallis, One-dimensional two-phase flow, McGraw Hill, New York, (1969).are found to be significantly lower than the predictionsof the homogeneous flow model and are in relatively [11] FLUENT’s User Guide. Version 6.2.16,close agreement with the predictions of slip flow Fluent Inc., Lebanon, New Hampshiremodel. It is observed that there is significant velocity 03766, (2005).slip in the vicinity of the flow area change. The data [12] W. M. Kays, Loss coefficients for abruptsuggest that widely-applied methods for pressure drops in flow cross section with lowdrops due to flow area changes, particularly for Reynolds number flow in single andtwo-phase flow is not applicable to mini and micro multiple-tube systems, Trans. ASME 73channels. It is also observed that unlike single phase (1950), pp. 1068-1074.flow, the two-phase flow does not contract behind theedge of transition and there is no change in the flowdirection i.e; a zone of recirculation is not observed.Thus vena-contracta is not a relevant term in two-phase flow through sudden contractions. Based on thecomputational as well as the experimental data,correlations have been developed (Eq.28) for two-phase flow pressure drop caused by the flow areacontraction.References [1] J. Schmidt and L. Friedel, Two-phase pressure drop across sudden contractions in duct areas, Int. J. Multiphase Flow; Vol. 23, (1997), pp. 283–299. [2] M. Salcudean, D. C. Groeneveld, and L. Leung, Effect of flow obstruction geometry on pressure drops in horizontal air-water flow, Int. J. Multiphase Flow, Vol. 9/1, (1983), pp. 73-85. [3] N. S. Al’Ferov, and Ye. N. Shul’Zhenko, Pressure drops in two-phase flows through local resistances, Fluid Mech.-Sov. Res, Vol. 6, (1977), pp. 20–33. [4] A. Attou and L. Bolle, Evaluation of the two-phase pressure loss across singularities, ASME FED, Vol. 210 (1995), pp. 121–127. [5] S. M. Ghiaasiaan and S. I. Abdel-Khalik, Two-phase flow in micro-channels, Adv. Heat Transfer, Vol. 34, (2001), pp. 145-254 [6] S. G. Kandlikar, Fundamental issues related to flow boiling in mini channels and micro 763 | P a g e