Modeling and Simulation of an Air-Assist Atomizer for Food Sprays

ILASS Americas, 21 st Annual Conference on Liquid Atomization and Spray Systems, Orlando FL, May 18 21 28 Modeling and Simulation of an Air-Assist Atomizer for Food Sprays Franz X. Tanner 1, Kathleen A. Feigl 1, Tim O. Althaus 2 and Erich J. Windhab 2 1 Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931-1295, U.S.A. 2 Laboratory of Food Process Engineering, Swiss Federal Institute of Technology (ETH), CH-892 Zurich, Switzerland ABSTRACT An air-assist atomization model for food sprays has been developed and validated. The model is based on the Cascade Atomization and Drop Breakup (CAB) model. The modifications include a change in the product drop distributions, namely, instead of a uniform distribution, as used in the original CAB model, a χ-squared distribution with the same average drop size has been assumed. The second modification addresses the air-assist atomization process. This process has been modeled by estimating the Weber number due to the increased relative velocity caused by the air jet. This leads to exactly one breakup depending on whether the Weber number is in the catastrophic, stripping or bag breakup regime. The model changes have been validated with a low-pressure atomizer for a cocoa butter melt spray, and for an air-assist atomizer using a highly viscous nutrious liquid. The simulations were performed with a modified version of the KIVA-3 CFD code and they showed good agreement with the experimental data. Corresponding author: phone: (96) 487 219, fax: (96) 487 3133, e-mail: tanner@mtu.edu

Average Diameter [µm] 7 6 5 4 3 2 p inj =6 bar p inj =12 bar Experiment Average Diameter [µm] 7 6 5 4 3 2 d noz =267 µm d noz =4 µm d noz =6 µm 1 1 2 4 6 8 1 12 14 16 18 2 Time [ms] Figure 1. Average drop diameter of the entire spray for different injection pressures. 2 4 6 8 1 12 14 16 18 2 Time [ms] Figure 2. Average drop diameter of the entire spray for different nozzle orifice diameters. INTRODUCTION Sprays in food processing are used to produce a powdered substance via spray-drying or spray-freezing. Depending on the application, this powder is required to have specific macroscopic properties such as a desired drop size distribution, and microscopic structures which enclose exact amounts of different substances in each of the powder particles. The liquids involved in food sprays can be very complex, typically consisting of multi-phase/multi-component suspensions or emulsions, which have anisotropic structure and can exhibit non-newtonian and even viscoelastic behavior. Therefore, high-pressure atomizers are not suited for food sprays because the high pressures needed in this process could alter the complex material structures and thus change taste, shelf life and other essential food properties. Using pressure atomizers at relatively low injection pressures is not an option either, as a computational investigation of a highly viscous nutriose liquid spray revealed. In fact, as is seen in Fig. 1, an injection pressure increase from 6 bar to 12 bar had almost no influence on the average drop sizes. The reason for this behavior lies in the fact that the drop Weber numbers 1 were mainly subcritical, i.e., for p inj = 6 bar, We 5.5 < We crit = 12 and therefore, there is only insignificant breakup activity, if there is breakup at all. In addition, the average drop sizes are considerably larger than the ones obtained from the experiment. Moreover, the drop sizes are determined by the nozzle diameters, as is illustrated in the nozzle orifice variation simulations in Fig. 2. 1 The Weber number is defined as We = ρ g Dv 2 r /σ, where ρ g is the gas density, D the drop diameter, v r the relative gas-drop velocity, and σ is the surface tension. These findings support the fact that in food-related sprays air-assist atomizers are mainly used. In airassist atomizers, the liquid exiting the nozzle interacts with air jets which leads to the liquid breakup. The interaction between the air and the liquid jets is a complex multi-scale problem which cannot be resolved for a realistic spray by present-day computers. Therefore, the simulation of an air-assist atomizer poses a modeling challenge which is the subject of this study. The starting point of this modeling approach is the Cascade Atomization and Drop Breakup (CAB) model developed in previous studies [1] to describe the atomization process of pressure atomizers. In the CAB model, large droplets of orifice size are injected which subsequently break up into tiny droplets via a cascade of drop decays until the droplets reach a stable condition. Each individual breakup event is caused by aerodynamic instabilities and its nature depends on the drop Weber number. More precisely, the breakups are modeled after the experimentally observed bag, stripping, and catastrophic breakup regimes. In an air-assist nozzle, the interaction of the air streams with the liquid jets increases the relative velocity between the gas and the liquid. This increases the Weber number and hence determines the liquid breakup. This liquid-gas interaction occurs only within a short distance near the nozzle exit, and therefore, the air-assisted breakup occurs exactly once. In the air-assist breakup model introduced in this study, this first breakup is modeled using the breakup criteria of the CAB model, taking the increased Weber number into account. After the initial breakup, the droplets are subject to the usual air-droplet interaction described by the standard CAB model. In addition to the air-assist modeling, since the pri-

mary breakup occurs only once, the uniform product droplet assumption results in unrealistic product drop size distributions. Therefore, the product droplets are equipped with a χ-squared distribution which has the same mean value as the uniform distribution. This air-assist breakup model has been validated with experimental drop size distributions obtained from sprays of a cocoa butter melt and a highly viscous nutriose liquid. Both substances were injected into a freezing environment at ambient pressure which resulted in a powder. The corresponding simulations have been performed with a modified version of a Kiva-3-based CFD code. It should be noted that in the simulation results presented in this study, the phase change due to freezing has been neglected. This phenomenon will be considered in a future investigation. BREAKUP MODELING The modeling of the air-assist atomization process is based on the Cascade Atomization and Drop Breakup (CAB) model [1]. A summary of the CAB model is given below, followed by a detailed description of the low-pressure atomization and the air-assist atomization modeling. The CAB Drop Breakup Model The basic idea of the CAB model is the simulation of individual breakup events which are modeled after the experimentally observed bag, stripping or catastrophic breakup mechanism, as reported by Liu and Reitz [3]. The actual breakup criterion of a single drop is determined from the Taylor drop oscillator [4] as introduced by O Rourke and Amsden [5] in the context of spray simulations. In this approach, the drop distortion is described by a forced, damped, harmonic oscillator where the forcing term is given by the aerodynamic droplet-gas interaction, the damping is due to the liquid viscosity and the restoring force is supplied by the surface tension. Breakup occurs when the normalized drop distortion, y(t), exceeds the critical value of one. The behavior of the product droplets is derived from a drop creation rate equation, which, in conjunction with mass conservation and a uniform product drop size distribution assumption, leads to the relation r a = e K but bu, (1) where a and r are the radii of the parent and product drops, respectively, t bu is the breakup time, and K bu is the breakup frequency which depends on the breakup regime. These breakup regimes are classified with respect to increasing gas Weber num- Table 1. Constants used in the CAB model. C λ jet breakup length coefficient 5.5 θ spray angle [deg] 8 & Ref. [2] k 1 breakup regime constant.5 n exponent in IDSD.5 bers into bag breakup (We crit < We We b,s ), stripping breakup (We b,s < We We s,c ) and catastrophic breakup (We > We s,c ), where the regime-dividing Weber numbers are taken to be We crit = 12, We b,s = 8 and We s,c = 35, as suggested in Liu and Reitz [3]. More formally, the breakup frequency can be expressed as k 1 ω if We crit < We We b,s K bu = k 2 ω We if We b,s < We We s,c k 3 ωwe 3/4 if We s,c < We where, according to [5], the drop oscillation frequency, ω, is given by ω 2 = 8σ ρ l a 3 25µ2 l 4ρ 2 l a4. In this equation, σ denotes the surface tension, ρ l the liquid density, a the drop radius and µ l the liquid viscosity. As a consequence of continuity considerations of K bu at the regime-dividing Weber numbers, only one model constant, k 1, is required to characterize the different breakup regimes; its value has been determined to be k 1 =.5 (cf. [1]). An additional property of the product droplets are their initial velocities. The axial velocity is inherited from the parent drop, whereas the transversal (radial) velocity, which is responsible for the radial expansion of the spray, is derived from an energy conservation argument involving the surface, kinetic and deformation energies of the parent and product drops. Jet Breakup Modeling The simulation of a fragmented liquid core at the nozzle exit is achieved by injecting large drops of the size of the nozzle orifice. These drops eventually break up into smaller product droplets until they reach a stable condition, thus forming a breakup cascade where each breakup event is governed by the cascade breakup law given in Eq. (1). In order to avoid the almost immediate breakup of the highly unstable initial drops, each (2)

Table 2. Data used in the model validations for the cocoa butter (CB) melt and the nutriose liquid (NL). Parameter CB NL Atomization type pressure air-assist Gas type air air Gas temperature [K] 253 253 Gas pressure [bar] 1 1 Liquid temperature [K] 318 363 Liquid density [g/cm 3 ].894 1.256 Orifice diameter [mm].5.4 Injection duration [ms] 1 1 Injection pressure [bar] 6 6 Injected fuel mass [mg].5284.47 drop is equipped with a drop deformation velocity to prolong its lifetime such that the jet breakup length matches experimentally determined correlations. In order to account for the droplet surface stripping near the nozzle exit, the initially injected drops have been equipped with an initial drop size distribution (IDSD) such that the small droplets reflect the surface stripping and the large drops yield good penetration and simulate the fragmented liquid core. For highpressure sprays, this (integral) drop size distribution is formally given by the power law H(d) = ( d do ) n+1 if < d < d otherwise where d and d o are the drop and nozzle radii, respectively. The model tuning described in [1] has resulted in a value of n =.5. The initial value of the normalized rate of drop deformation, ẏ o = ẏ(), is chosen such that the first (and only the first) droplet breakup time is considerably delayed, while keeping the initial drop deformation y o = y() =. With this choice of initial conditions, the injected drops have an extended life span; in fact, ẏ o is determined numerically as the largest negative root of the equation y(t bu ;, ẏ o ) = 1, (3) where y(t;, ẏ o ) is the solution of the Taylor drop oscillator with initial conditions (, ẏ o ), and the value 1 is the critical deformation. More specifically, for an inviscid fluid, the largest negative root of Eq. (3) is given by ẏ o /ω o = [1 We 12 (1 cos ω ot bu )]/ sin ω o t bu, (4) where ω 2 o = 8σ/(ρ l a 3 ). The value of the breakup time, t bu, of a high velocity liquid jet injected into a gas is determined from the experimental jet breakup length correlation due to Levich [6] L = v inj t bu = C λ ρl ρ g d, (5) where d is the nozzle diameter and v inj the jet exit velocity. The constant C λ is nozzle dependent and for the computations considered in this study, a value of C λ =5.5 has been used. This value gave good comparisons with the experimental jet breakup lengths. In the CAB model, the spray angle, θ, is prescribed as an initial condition. This approach requires a correction to the radial drop velocity at the first breakup, as described in [1]. The spray angle for the lowpressure cocoa butter sprays were taken to be 8 degrees, and the one for the air-assisted nutriose liquid sprays were determined automatically from the correlation of Naber and Siebers [2]. The CAB model constants are summarized in Table 1. The constants θ and C λ depend on the nozzle and on the injection system specific properties and, in general, need to be adjusted in order to compensate for such influences. Low-Pressure Atomization Modeling In the original CAB model, the product droplet distribution was taken to be uniform, i.e., after a breakup all product droplets have the same diameter determined by the breakup frequency K bu in Eq. (2). The uniform product drop size distribution assumption works well for high-pressure sprays because the initially injected large drops fall into the catastrophic breakup regime and therefore, they undergo several breakups (in different breakup regimes) until they reach a stable condition. Also, it should be noted that the uniform product drop size assumption is realistic for the stripping breakup regime. For low-pressure sprays, however, the initially injected droplets are either stable or they fall into the bag breakup regime, which means that the product droplets are not uniform. Consequently, the assumption of a uniform product drop size distribution leads to unrealistic drop sizes. This is also the case for airassist atomizers, because the air jet causes only one drop breakup at high Weber numbers (usually in the catastrophic regime), whose product droplets are in general not uniform. To describe a more realistic non-uniform product drop behavior, the product droplets are assumed to follow a χ-squared distribution whose mean value corresponds to the product droplet radius determined

.1 χ 2 : f(r)=e -r/1 /1 Vol-weighted χ 2 : g(r)= (r/1) 3 e -r/1 /6 5 4 Air jet exit velocity Speed of sound [1/µm].5 Velocity [m/s] 3 2 1. 2 4 6 8 1 Drop Radius [µm]..2.4.6.8 1. Gas Pressure Ratio [p /p] Figure 3. χ-squared and volume-weighted χ-squared distributions for a hypothetical case with r = 1 µm. via Eq. (1). More precisely, the χ-squared droplet distribution is given by f (r) = exp( r/ r), 1 r where r is the mean drop size determined by Eq. (1). Observe that r = r f (r)dr, i.e., r is also the mean value of the χ-squared distribution. Consequently, Eq. (1) is to be interpreted as determining the mean values of the product droplet distributions. In the actual program implementation, the drop distributions are discretized into parcels, where each parcel is a collection of droplets of equivalent states [7]. In particular, each parcel contains drops of identical mass, and therefore, the χ-squared distribution for the drop radii becomes the volume-weighted density distribution for the parcels g(r) = 1 A r3 f (r). The normalization g(r)dr = 1 yields A = 6 r 3 and, therefore, the χ-squared parcel distribution becomes g(r) = 1 6 ( r r ) 3 1 exp( r/ r). (6) r Eq. (6) is the actual distribution used in the modeling of the product drop sizes. The difference between the χ-squared distribution and the volume-weighted χ-squared distribution is illustrated in Fig. 3 for a hypothetical case with r = 1 µm. Air-Assist Atomization Modeling In the air-assist atomizer used in this study, there are six air jets which intersect the liquid jet transversally Figure 4. Air jet exit velocity as a function of the gas pressure ratio for ambient gas conditions of 1 bar and 273 K. near the nozzle exit. These air jets increase the relative gas-liquid velocity, which increases the Weber number of the liquid, and consequently, leads to the liquid breakup. This air-liquid interaction occurs only on a small region of the liquid jet which determines the primary jet breakup. The air jet exit velocity is obtained from the compressible Bernoulli equation γ p γ 1 ρ + gz + u2 2 = const along streamlines, where γ is the isentropic coefficient, p is the pressure, ρ the density, g the gravitation constant, z the height, and u is the velocity. Note that γ = c p /c v 1.4 for an ideal gas, where c p and c v are the specific heat capacities at constant pressure and constant volume, respectively. Solving this expression for the air exit velocity, assuming an isentropic process (p ρ γ ), neglecting height differences and using the ideal gas law, one obtains 2γ u = γ 1 RT 1 ( p p ) γ 1 γ, (7) where R is the specific gas constant and the subscript indicates the conditions at the nozzle exit. It is interesting to note that for a pressure ratio p /p =.5 and a gas jet temperature of T = 333.15 K, one obtains an air exit velocity of u = 347.5 m/s, which is very close to the speed of sound. Since the air jet exit velocity cannot exceed the speed of sound, u sound = γrt, the air jet exit velocity is taken to be u exit = min{u, u sound }, a relationship which is illustrated in Fig. 4 for the ambient gas at 1 bar and

6 5 5 4 Standard mesh: 5'5 cells Fine mesh: 167'97 cells Weber Number 4 3 2 1 Catastrophic breakup Stripping breakup Bag breakup Nozzle Distance [mm] 3 2 1..2.4.6.8 1. Gas Pressure Ratio [p /p] Figure 5. Liquid jet Weber number as a function of the gas pressure ratio, and the associated breakup regimes. 273 K. The effect of the air jet on the liquid jet Weber number as a function of the gas pressure ratio p /p is illustrated in Fig. 5 for the injection configuration whose data are listed in Table 2. This figure also relates the gas pressure ratio to the respective breakup regimes; for instance, if p /p =.5 then the resulting liquid jet breakup lies in the catastrophic regime. COMPUTATIONAL DETAILS The computations presented in this study have been performed with a modified version of the KIVA-3 code [7] equipped with many new or improved models. As described above, the CAB atomization and drop breakup model [1] has been utilized. The turbulence has been accounted for via the RNG k-ε turbulence model as implemented by Han and Reitz [8]. Unless stated otherwise, all the standard values of the model parameters, as reported in the respective citations, have been used. The liquid was injected axially downward along the centerline of the cylindrical spray tower by means of a single orifice nozzle. The air in the spray tower was cooled by spraying liquid nitrogen into the chamber via several nozzles located near the top of the tower. Simulations were performed for a cocoa butter melt and a nutriose liquid. More details are given in Table 2. The mesh dependence of the air-assist model has been investigated in terms of the spray penetration for nutriose liquid sprays. The results are presented in Fig. 6, which shows that the penetrations are virtually mesh independent, and the choice of the standard mesh is justified. The meshes used are structured, hexahedral, polar meshes whose cells are concentrated 5 1 15 2 Time [ms] Figure 6. Mesh dependence of the spray penetration for the standard and the fine mesh. radially and vertically around the nozzle exit in the top center of the cylindrical geometry, as can be seen in the vertical cut plane in Fig. 9. The cylinder part of the standard mesh has 35 2 75 cells (a total of 5 5 cells) in radial, azimuthal and axial directions. The smallest cell is at the nozzle exit measuring approximately 1.5 mm by 1.5 mm in radial and axial direction. Resolution changes in all directions by a factor of 1.5 have resulted in the fine mesh with 52 3 112 (167 97) cells. MODEL VALIDATIONS The two modifications of the CAB model, the volume-weighted χ-squared distribution of the product droplets and the air-assisted primary breakup, have been validated separately. The χ-squared distributions have been compared with experimental data of a cocoa butter melt for a pressure atomizer, and the air-assisted primary breakup has been investigated for a nutriose liquid in a second step. The experimental data have been obtained in the Laboratory of Food Process Engineering at the Swiss Federal Institute of Technology (ETH) Zurich. A summary of the validation conditions is given in Table 2, and the model parameters used are listed in Table 1. Low-Pressure Atomization Model Validation The χ-squared drop size distribution introduced into the breakup model has been validated with experimental data of a cocoa butter melt spray for a simple, solid-cone, pressure atomizer with a nominal spray angle of 8 degrees. The computed volume-weighted drop size distributions of the entire sprays are compared with experimental data in Fig. 7 for the liquid

q3(x) [1/µm].1.5 Experiment: p inj =4 bar (subcritical) Experiment: p inj =6 bar Experiment: p inj =8 bar Average Diameter [µm] 7 6 5 4 3 2 p /p=1 (no air jet) p /p=.91 (bag BU) p /p=.67 (stripping BU) p /p=.5 (catastrophic BU) Experiment 1. 2 4 6 8 1 Drop Diameter [µm] Figure 7. Volume-weighted χ-squared drop size distributions for various injection pressures. The filled symbols denote the experiments and the open symbols the simulations. 2 4 6 8 1 12 14 16 18 2 Time [ms] Figure 8. Average drop diameter of the entire spray for different air jet pressure ratios of an air-assist atomization process of a nutriose liquid. injection pressures of 4 bar, 6 bar and 8 bar. As seen in Table 3 the injection pressure of 4 bar leads to drop Weber numbers of around 12 which is the critical bag breakup limit. Therefore, the breakup activity is very low, which is reflected in the relatively large drop size distribution in Fig. 7. Note that the agreement between simulation and experiment is reasonably good. The two higher injection pressures of 6 bar and 8 bar lead to droplets at the nozzle exit whose Weber numbers are supercritical; in fact, they are in the bag breakup regime. Here, the breakup activity is large which results in smaller droplets. Again, as is seen in Fig. 7, the agreement between the experimental and simulated drop size distributions are again in good agreement. Air-Assist Atomization Model Validation The air-assist modeling has been investigated for different air jet pressure ratios of nutriose liquid sprays (cf. Table 2). The pressure ratios determine the air jet Table 3. Jet exit velocities and Weber numbers for different injection pressures of the cocoa butter melt at 318 K. p inj [bar] v inj [m/s] We 4 25.9 12.6 6 33.4 21. 8 39.5 29.4 exit velocities according to Eq. (7). The pressure ratio p /p = 1 indicates that there is no air-assist atomization, and the ratios of p /p =.91,.67,.5 result in an air jet-induced bag breakup, stripping breakup or catastrophic breakup, respectively. The average drop sizes of the total sprays, as a function of the injection time, are shown in Fig. 8. This figure shows that the increased air jet pressures, which lead to the different breakup regime of the primary breakup, result in smaller drop sizes. In fact, the average drop sizes obtained with the pressure ratio p /p =.5 are in very good agreement with the experimental results. A comparison between a pure pressure atomization (p /p = 1) and an air-assist atomization in the catastrophic regime (p /p =.5) is shown in Fig. 9 in a vertical cut plane at an injection time of 2 ms. These pictures show that the pure pressure atomizer, apart from larger drop sizes, leads to a narrower spray and deeper penetration. For the air-assist atomizer, the drop sizes do not change much after the primary breakup at the nozzle exit. Both atomization cases show increased drop sizes near the tip of the spray. This phenomenon has been called the tip-clustering effect in a previous computational study by Tanner and Boulouchos [9]; it has been explained in terms of tail wind interactions between successively injected drops. Experimental evidence of this phenomenon has been obtain by means of X-ray measurements and is discussed in [1].

although, the actual freezing process has not been taken into account. The phase change due to freezing is the subject of a future investigation. REFERENCES [1] F. X. Tanner, Development and Validation of a Cascade Atomization and Drop Breakup Model for High-Velocity Dense Sprays, Atomization and Sprays, vol. 14, no. 3, pp. 211 242, 24. [2] J. Naber and D. Siebers, Effects of Gas Density and Vaporization on Penetration and Dispersion of Diesel Sprays, SAE Transactions: Journal of Engines, vol. 15, no. 3, 1997. [3] A. B. Liu and R. D. Reitz, Mechanisms of Air- Assisted Liquid Atomization, Atomization and Sprays, vol. 3, pp. 55 75, 1993. Figure 9. Pure pressure atomization (left) and airassist atomization (right) of a nutriose liquid spray at the end of the injection cycle. (The colors represent the drop sizes.) SUMMARY AND CONCLUSIONS The CAB model has been modified to accommodate atomization processes for low-pressure, air-assist atomizers. The modifications include a change in the product drop distributions. Instead of a uniform distribution, as used in the original CAB model, a χ- squared distribution with the same average drop size has been utilized. In the actual implementation, a volume-weighted distribution has been used in order to account for the parcel discretization of the spray probability distribution function. The second modification addresses the air-assist atomization process. This process has been modeled by estimating the Weber number due to the increased relative velocity caused by the air jet. More precisely, the air jet exit velocity has been estimated by means of the compressible Bernoulli equation, assuming an isentropic process. The interaction between the liquid and the air jets leads to exactly one breakup whose characteristics depend on whether the Weber number is in the catastrophic, stripping or bag breakup regime. The model changes have been validated with a low-pressure atomizer for a cocoa butter melt spray, and for an air-assist atomizer using a highly viscous nutriose liquid. The simulations were performed with a KIVA-3-based code which is equipped with well-established spray models. The validations showed good agreement with the experimental data, [4] G. I. Taylor, The Shape and Acceleration of a Drop in a High Speed Air Stream, The Scientific Papers of Sir Geoffrey Ingram Taylor (G. K. Batchelor, ed.), vol. 3, pp. 457 464, Cambridge University Press, 1963. [5] P. J. O Rourke and A. A. Amsden, The TAB Method for Numerical Calculation of Spray Droplet Breakup, SAE Paper 87289, 1987. [6] V. G. Levich, Physicochemical Hydrodynamics, Prentice Hall, Englewood Cliffs, N.J., pp. 639 65, 1962. [7] A. A. Amsden, P. J. O Rourke, and T. D. Butler, KIVA II: A Computer Program for Chemically Reactive Flows with Sprays, Tech. Rep. LA- 1156-MS, Los Alamos National Laboratory, May 1989. [8] Z. Y. Han and R. D. Reitz, Turbulence Modeling of Internal Combustion Engines Using RNG k-ε Models, Combust. Sci. and Tech., vol. 16, pp. 267 295, 1995. [9] F. X. Tanner and K. Boulouchos, A Computational Investigation of the Spray-Induced Flow and Its Influence on the Fuel Distribution for Continuous and Intermittent DI-Diesel Sprays, SAE Paper 96631, 1996. [1] F. Tanner, K. Feigl, S. Ciatti, C. Powell, S.-K. Cheong, J. Liu, and J. Wang, Structure of High- Velocity Dense Sprays in the Near-Nozzle Region, Atomization and Sprays, vol. 16, pp. 579 597, 26.