CFD MODELLING OF LIQUID JET AND CASCADE BREAKUP IN CROSSFLOWS

Transcription

1 Seventh International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia 9-11 December 2009 CFD MODELLING OF LIQUID JET AND CASCADE BREAKUP IN CROSSFLOWS Benny KUAN Process Science and Engineering, Commonwealth Scientific and Industrial Research Organisation Box 312, Clayton South, VIC 3169, AUSTRALIA ABSTRACT Formation and breaku of liquid drolets lay key roles in a wide range of chemical rocesses, most of which are concerned with atomising the liquid into fine drolet srays in a co-flow environment where the liquid jet is sandwiched between high-velocity air streams to roduce a drolet cloud. The resent work deals with drolet breaku in a cross-flow environment where the air stream directly imacts onto a liquid jet or column. A CFD model has been develoed for the breaku of this liquid jet and subsequent formation of drolets. The model has been tested for liquid jets in a crossflow that are documented in the ublished literature. Both the shae of the liquid column and disersion attern of the drolets as redicted by the model agree well with the ublished data. NOMENCLATURE C model constant C D drag coefficient d drolet diameter F momentum source k turbulence kinetic energy M Mach number n drolet number density On Ohnesorge number P ressure q liquid/air momentum flux ratio, ρ lv f ρ av r volume fraction T characteristic timescale for drolet breakage U mean velocity vector u fluctuating velocity vector V sli sli velocity w cascade width We Weber number ε ρ σ μ hase turbulence dissiation rate density Prandtl number dynamic molecular viscosity 2 / a 2 INTRODUCTION Formation and breaku of liquid drolets lay key roles in a wide range of chemical rocesses, including fuel sray in combustors, sray coating, owder formation, and gas scrubbing. Most of these rocesses are concerned with atomising the liquid into fine drolet srays in a co-flow environment in which the liquid jet is sandwiched between high-velocity air streams to roduce a drolet cloud. There is a large body of scientific knowledge addressing this toic (Varga et. al., 2003; Inamura and Daikoku, 2002; Park et. al, 2002) in the ublished literature. By comarison, liquid drolets used in some industrial rocesses, such as sray cooling towers, need to be introduced in such a way that facilitates maximum contact between a large body of gas and the liquid. In cases where the gas temerature is considerably less than boiling oint of the liquid, liquid drolets can be srayed directly onto the gas to stri the solids off the articleladen gas stream. However, for rocesses where the liquid also lays a significant role in cooling the gas through vaorisation, it is not aroriate to sray fine liquid drolets onto the hot gas streams. Liquid drolets thus need to be generated using an oosing- or crossflow arrangement with resect to the gas stream. Wu et. al. (1995, 1997, 1998) have erformed a series of exeriments to examine the atomisation of an uflowing liquid jet injected into a strong crossflow. Parameters investigated include liquid injection velocity, gas velocity and liquid surface tension. Their flow visualisation study has revealed a series of events taking lace during the liquid jet breaku rocess. Breaku first starts at the liquid jet surface from which some liquid fragments are stried and drolets form. This causes instability to the jet surface in the form of acceleration waves which deform and flatten the liquid column. The liquid column eventually disintegrates into ligaments and drolets. The resent aer outlines the develoment of a drolet breaku model that is suitable for Eulerian-Eulerian twohase flow alications where the article hase is solved as a continuum fluid. The model is based on a oulationbalance aroach with one governing equation reresenting the transort of drolet number density. Drolet breaku is evaluated based on local drolet Weber number and reflected as a source term to the oulationbalance equation. The model is validated using exerimental data rovided in Wu et. al. (1997) and Lim et. al. (2006). Model develoment and results of model validation are resented in this aer. MODEL DESCRIPTION Gas and liquid flow models were develoed using a commercial CFD code ANSYS CFX-11 and are based on a two-fluid aroach. The flow field is assumed to be in a steady-state throughout the flow domain. Two-Fluid Model Gas and liquid flow roerties are calculated by numerically solving the following set of Reynoldsaveraged Navier-Stokes equations for each hase ( ρ U ) = 0 r (1) Coyright 2009 CSIRO Australia 1

2 ( r ρ U U ) = r P + ( r ( r μ U ρ u ) ' u ') + F h (2) u' u' is Reynolds stresses. The momentum source where term, F h, takes into account hydrodynamic forces acting on the disersed hase and the resulting interfacial forces on the continuous hase. A k-ε turbulence model, modified to account for two hase flow, is used in this study to account for the effect of turbulence in both the gas and liquid flow field. Eddy viscosity μ t for hase is defined as μ t 2 C μ ρ k / ε, = ρ μ t, gas, ρ gas σ = gas = liquid Solution of the governing equations is based on a finite volume aroach with the advection terms aroximated using a High Resolution Scheme which is second order accurate. Further details of the solution rocess are available in Ansys Inc. (2007). Drolet Motion Hydrodynamic Forces In a two hase flow system consisting of a continuous gas hase and a disersed liquid hase, the hydrodynamic force acting on the disersed hase and its back-influence on the continuous hase can also critically affect gas and drolet motion. Such a deendency is modelled through F h which reresents the combined effect of inter-hase drag, lift force, virtual mass force, gravity, and turbulent disersion. Of all the hydrodynamic forces considered in the simulation, the inter-hase drag is the most imortant. The resent simulation makes use of a drag model of Clift et al. (1978) which considers the effect of fluid drolet shae transition from a shere at low drolet Reynolds number Re to an ellisoid at high Re. In the model, drolet shae is characterised by Eotvos number Eo which, like Re, is also a function of the drolet size d. However, the drolet size d is not a constant and varies satially throughout the flow domain. A reliable drolet size model is thus necessary to ensure the effect of interhase drag is adequately accounted for in the model. Drolet Breaku A drolet size model which reflects the formation and breaku of liquid drolets has been develoed and it rovides an estimate of the local liquid drolet size everywhere within the flow domain. In our model, the timescale of liquid drolet formation and breaku is determined from a breaku model which was originally roosed by Pilch and Erdman (1987) and later reviewed by Gelfand (1996). In their studies, the drolet breaku rocess is categorised into different regimes by drolet Weber number. Based on time history data collected from ublished exeriments, such as Hassler (1970) and Li and Fogler (1978), Pilch and Erdman ostulated the following correlations for total breaku time, ΔT * (3) ΔT = β T (4) T * d = V sli ρ ρ f ( We Wecrit ), Wecrit < We ( We Wecrit ), 18 < We β = 14.1( We Wecrit ), 45 < We ( We Wecrit ), 351 < We , 2670 < We (6) with We crit being the critical Weber number. Drolet size after total breaku is determined from a model of Schmehl et al. (2000) where d (1) (0) br (5) = d f (7) (0) (1) with d and d resectively denote drolet diameter before and after drolet breaku; br = 1.5On Wecorr f (8) μ On = (9) 0 ρ d σ 2 0 ρ f Vslid We = (10) σ We We corr = (11) On V sli refers to sli velocity between gas and the drolets and σ is drolet surface tension coefficient. Drolet Weber number, as defined in equation (10), is recognised as the single most imortant arameter that characterises drolet breaku in the literature (Wu et. al., 1995 & 1997). It is a measure of disrutive hydrodynamic forces with resect to the stabilising surface tension force. Being a dimensionless arameter, one can exect a breaku model that is develoed based on the drolet Weber number to be alicable to a wide range of gasliquid flow systems. In order to redict the variation of drolet size due to breaku within the flow domain, equations (4) and (7) are alied to construct a simlified oulation balance equation to model local growth of drolet oulation due to drolet breaku. The model tracks the drolet number density, n, using the equation ( rl ρ l l n) = rl ρl Sbr U (12) The source term S br for equation (12) reresents the time rate of change in drolet oulation er unit volume, i.e. S br n = C (1) n ΔT (0) (13) with C being a model constant. Liquid drolets are assumed to remain intact where We < We crit. The Coyright 2009 CSIRO Australia 2

3 associated S br is thus set to zero to reflect negligible growth in local drolet numbers. Drolet size is determined from drolet number density n through the following exression n = (14) π 3 d 6 r where r is volume occuied by the liquid hase in a control volume. Boundary Conditions Equation (12) allows one to control drolet breaku/growth through the definition of the source term S br. The resent study assumes that all wall surfaces are wetted and are covered by an established thin liquid film. Following the exerimental observation of Pan and Law (2005) who have categorised tyical regimes in which drolet-film absortion occurs, drolets that collide with a liquid film on to of a solid surface will either be deflected away or absorbed into the film deending on the normalised film thickness and drolet collision Weber number We collision which is calculated as a function of drolet imact velocity and liquid density. Where the drolet-film collision results in drolet absortion into the film, the source term S br at the wall is set to zero. The drolet number density is arbitrarily set to unity at all walls. Free-sli condition is assumed for the liquid hase at the wall surfaces and hence the effect of wall friction which acts to slow down liquid movement on the wall is not considered in the model. At the liquid inlet, an initial drolet size is estimated from hydraulic diameter of the discharge slots. Following equation (14), this then leads to an aroximated inlet drolet number density. For the gas inlet, the drolet number density is zero corresonding to zero liquid volume fraction. For the liquid jet breaku, the comuted flow domain covers a 3D region that is 40d tall, 50d long and 20d wide (ref. Figure 1). All faces of the flow domain are assumed to be free boundaries, excet the bottom one which is a wall with a jet inlet. More than 270,000 elements were used. For the liquid cascade breaku, the flow domain is 1w wide and stretches 4w and 2.4w in the streamwise and vertical directions (ref. Figure 5). All domain faces are set u as free boundaries, excet the back face which is a solid wall and the front face through which the swirling jet enters the flow domain. More than 670,000 elements were used in the simulation. MODEL VALIDATION 0.4. Shadowgrahs of the water jets under the influence of the crossflow were generated from the exeriment based on which Wu et al. (1997) roosed a correlation for the liquid column trajectories: y dq n x π C D (15) = / dq where d is jet diameter; q is liquid/air momentum flux ratio; (x, y) is the coordinate of the liquid column trajectory as sketched in Figure 1. Their trajectory analysis for the water jet indicated a mean C D value of 1.5 with standard deviation of 0.45, and n = 0.5. Water jet trajectories based on the numerical simulation for crossflow velocities of M = 0.2, 0.3 and 0.4 are comared against the exerimental rofiles in Figure 2. The CFD results resented in the figure are based on a critical Weber number of 80 and C = The critical Weber number is set on the basis of Wu et al. s exerimental observation. The redicted water jet trajectories for all crossflow velocities fall within one standard variation of the mean rofile. Success of the resent modelling aroach lies in the fact that the drolet Weber number is high at the base of the liquid column (We = 77 for M = 0.2) such that the breaku is dominated by a rocess similar to that of the secondary breaku of a sherical drolet. The model, however, is unable to cature fracture of the liquid column as observed in the exeriment. According to Wu et. al., uon introduction of the liquid jet into the air crossflow, the liquid column first undergoes surface breaku in which some drolets are stried from the column surfaces. The remainder of the liquid column then deforms under the action of aerodynamic forces and eventually disintegrates into ligaments and drolets. Air Figure 1: Sketch of the liquid column trajectory. x d y Liquid jet Liquid Jet Breaku in Crossflows Exerimental data obtained for the breaku of a vertically uward water jet as studied in Wu et. al. (1997) has been alied to validate the CFD model. In the exeriment, a water jet with a diameter of 0.5 mm is injected uwards at 28 m/s into an air flow field which is dominated by a horizontal crossflow at Mach number M = 0.2, 0.3 and Coyright 2009 CSIRO Australia 3

4 y/dq 1.0 M=0.4 (CFD) 0.5 M=0.3 (CFD) M=0.2 (CFD) Eqn (15) for CD= Eqn (15) for CD=1.5 Eqn (15) for CD= x/dq Figure 2: Comarison of water jet trajectories. Figure 4: Three-dimensional structure of the water jet at M = 0.4. A shadow grah extracted from Wu et. al. (1997) for water jet in air crossflow at M = 0.4 is comared against the redicted centre-lane distribution of water volume fraction in Figure 3. In the exeriment, column fracture location is identified by a discontinuity in the water column. This oint is marked in Figure 3a). By comarison, the rediction indicates a gradual decay of water volume fraction as a direct result of drolet breaku. a) Fracture oint Desite the above weakness, the model does rovide a realistic reresentation on water column breaku. Isosurface lots for water volume fraction over 1.0E-4 are resented in Figure 4. Cross-section of the water column is found to be in the shae of a horseshoe. This correlates well with the findings of Cavaliere et al. (2003) who utilised a laser light scattering technique to reconstruct the cross-sectional shae of a liquid jet sray at high ressure. A kidney shaed sray cross-section was observed. One can thus exect the side view of the water column in Figure 4 to match with the shae of the deformed water column as seen in the shadowgrah (Figure 3a). Breaku of Liquid Cascade Lim et. al. (2006) has erformed a flow visualisation study on the breaku of liquid cascading from the edge of a steel roof. This is sketched in Figure 5. As shown in the figure, a swirling nozzle is laced at a horizontal distance L and vertical distance H from the edge of the roof. The nozzle is directed at the water cascade running from the edge of the roof. b) Figure 3: Comarison of water column rofiles distribution. a) shadow grah extracted from Wu et. al. (1997); b) redicted water volume fraction on centrelane. It is hyothesised in the resent study that an infinite number of liquid columns form the liquid cascade which disintegrates into drolets. The CFD model as develoed reviously has been alied to simulate the breaku of the liquid cascade. Comutations were erformed for air jet velocity ranging between 0 and 30 m/s. Some of the modelling results are resented in Figure 6. Figure 6 lots the redicted centre-lane distribution of water volume fraction at increasing gas jet velocities. At Coyright 2009 CSIRO Australia 4

5 0 m/s, water cascades from leading and trailing edges of the roof under the influence of gravity (Figure 6a). An increase in the air jet velocity brings distortion to the water columns through the action of gas-liquid entrainment. At 30 m/s (Figure 6d), the gas jet is strong enough to comletely entrain the water columns, thus w Liquid feeder L roducing a longer and more visible water trail in the downstream direction. As shown in Figure 6b and 6c, drolet breaku is more ronounced underneath the trailing edge. This is due to gas jet sreading under the influence of swirl such that the jet entrains a larger body of air further away from the nozzle. Therefore, whilst the sli between the two hases is very strong but localised in the leading columns, the gas-liquid sli in the trailing columns is weaker but more extensive and yet sufficient to cause drolet breaku. At 30 m/s (Figure 6d), the air jet essentially blows all liquid columns in the direction of the jet. Distribution and movement of the water columns are found to match well with the exerimental observation. Roof Swirling jet Nozzle H Water streamlines are lotted in FIGURE 7. The water streamlines serve to reresent water columns cascading down the roof at gas jet velocities of 10 and 30 m/s. FIGURE 7a indicates local enetration of the gas jet through the water columns (10 m/s case) while the gas jet ertaining to the 30 m/s case has lifted both the front and rear water columns (FIGURE 7b). Aart from entraining the liquid columns in the direction of the gas jet, the gas jet also imarts swirling motion onto the liquid columns. Subsequently, centre-lane liquid columns are forced to veer away from the centre lane by the swirling gas jet, leading to seemingly weaker and shorter liquid streams at the trailing edge as seen in Figure 6b and c. Figure 5: Sketch of the liquid cascade test rig a) b) c) d) Figure 6: Predicted centre-lane distributions of water volume fraction at increasing jet velocity U. a) U = 0 m/s; b) U = 5 m/s; c) U = 10 m/s; d) U = 30 m/s. Coyright 2009 CSIRO Australia 5

6 Figure 7: Predicted water streamlines under the influence of the gas jet (uer: u = 10 m/s; lower: u = 30 m/s) CONCLUSION An Eulerian-Eulerian two-hase model has been develoed in an effort to cature the breaku rocess of liquid jets or columns. The model makes use of a modified scalar transort equation to account for drolet breaku as well as transort of drolets. Model validation has been erformed for two crossflow cases where either a liquid jet or a liquid cascade is interruted by a high seed air jet. The model is able to realistically redict the deformation of both a liquid jet and cascade under the influence of a strong air jet in a crossflow arrangement. Further, the model has demonstrated its ability to cature the henomenon of surface breaku reasonably well. A major weakness of the model, however, lies in its oor reresentation of the free surface interfaces such that the shae of the liquid column is not well reserved in areas where drolet breaku is minimal, e.g. at the base of the column, or in areas where the column has terminated comletely, e.g. column fracture. Owing to a lack of article size distribution data, size of the drolets roduced during the modelled breaku rocess can not be directly verified. REFERENCES VARGA, C.M., LASHERAS, J.C. and HOPFINGER, E. J., (2003), Initial breaku of a small-diameter liquid jet by a high-seed gas stream, J. Fluid Mech., 497, INAMURA, T. and DAIKOKU M., (2002), Numerical simulation of drolet formation from coaxial twin-fluid atomizer, Atomization and Srays, 12, PARK, J.W., HUH, K.Y., LI, X., and RENKSIZBULUT, M., (2002), Exerimental study on the breaku mechanism of a thin liquid sheet from an airassisted lanar nozzle, J. Flow Visualization & Image Processing, 9, WU, P.K., MIRANDA, R.F., and FAETH, G.M., (1995), Effects of initial flow conditions on rimary breaku of nonturbulent and turbulent round liquid jets, Atomization and Srays, 5, WU, P.K., KIRKENDALL, K.A., FULLER, R.P., and NEJAD, A.S., (1997), Breaku rocesses of liquid jets in subsonic crossflows, J. Proulsion and Power, 13, WU, P.K., KIRKENDALL, K.A., FULLER, R.P. and NEJAD, A.S., (1998), Sray structures of liquid jets atomized in subsonic crossflows, J. of Proulsion and Power, 14, LIM, S., SANDERSON, J., DENKE, R., JOYCE, T., and SANETSIS, S., (2006), Visualisation of Liquid Break-U by Swirling Gas Jet from a Cyclone Gas Outlet Snout, CSIRO Minerals DMR-3013, Australia. ANSYS INC, A., (2007), ANSYS-CFX Version 11.0 Documentation. Pittsburgh, Pennsylvania, United States of America. CLIFT, R., GRACE, J.R., and WEBER M.E., (1978), Bubbles, Dros and Particles, Academic Press, New York, United States of America. PILCH, M. and ERDMAN, C.A., (1987), Use of Breaku time data and velocity history data to redict the maximum size of stable fragments for accelerationinduced breaku of a liquid dro, Int. J. Multihase Flow, 13(6), GELFAND, B.E., (1996), Drolet breaku henomena in flows with velocity lag, Progress in Energy and Combustion Science, 22, HASSLER, G., (1970), Breaku of large water dros under the influence of aerodynamic forces in a steady stream of stream and stream at subsonic velocities, Proceedings of the 3 rd International Conference on Rain Erosion and Related Phenomena, Hamshire, England. LI, M.K. and FOGLER, H.S., (1978), Acoustic emulsification. Part 2. breaku of the large rimary oil drolets in water medium, J. Fluid Mechanics, 88, SCHMEHL, R., MAIER, G., and WITTIG, S., (2000), CFD analysis of fuel atomization, secondary drolet breaku and sray disersion in the remix duct of a LPP combustor, Proceedings of 8th International Conference on Liquid Atomization and Sray Systems, Pasadena, California, United States of America. PAN, K.L. and LAW, C.K., (2005), Dynamics of drolet film collision, 43rd AIAA Aerosace Science Meeting & Exhibition, Reno, USA, Paer Number AIAA CAVALIERE, A., RAGUCCI, R., and NOVIELLO, C., (2003), Bending and break-u of a liquid jet in a high ressure airflow, Exerimental Thermal and Fluid Science, 27, Coyright 2009 CSIRO Australia 6