STUDY OF A HYDROFLUIDIZATION SYSTEM USING COMPUTATIONAL FLUID DYNAMICS AND A DISCRETE ELEMENT METHOD I : FLOW FIELD AND VELOCITY PROFILES

Hydrofluidization (HF) is a method of chilling and freezing of foods that pumps a refrigerating liquid upwards through orifices into a vessel creating submerged jets and thus results in extremely high surface transfer phenomena. The objective was to model the flow field and the velocity profiles of spheres in a HF system using computational fluid dynamics and a discrete element method. The HF system consisted in a cylindrical vessel of 100‒mm diameter and 100‒mm height and a perforated plate with orifices of 3‒mm diameter. The samples were 13 potato spheres of 10‒mm diameter. The operative variables were temperature (‒5°C, ‒10°C), distance among the orifices (10 mm, 20 mm) and average velocity of the fluid at the orifices (0.59 m/s, 1.18 m/s). The results are promising to obtain relevant information about the momentum transfer and the dynamics of samples being processed within a HF system.


INTRODUCTION
Hydrofluidization (HF) is a method of chilling and freezing of foods that pumps a refrigerating liquid upwards through orifices into a vessel creating submerged jets and thus results in extremely high surface transfer phenomena (Fikiin, 1992;Peralta et al., 2012).Under controlled conditions, it represents an attractive industrial method with advantages related to the small equipment used and the improvement of the freezing of individual pieces of food, besides the advantages related to the immersion chilling and freezing process (ICF).
Several experimental (Verboven et al., 2003;Peralta et al., 2009) and theoretical (Peralta et al., 2010;2012;Belis et al., 2012;2013;2014) studies on HF were conducted using different operative and geometric configurations.Those studies showed the effects of flow rate, refrigerant temperature, number of orifices, orifice arrangement, orifice-sample distance, orifice-orifice distance and sample-sample distance (Peralta et al., 2012;Belis et al., 2012;2013;2014) on the heat, momentum and mass transfer within the system.As a result, a better understanding of the relationship between the operative variables and the transport phenomena in simple HF configurations was obtained.However, in most of these studies, food samples were static single spheres impinged by single jets.Although those studies are useful as a first approach, their simplified nature limited the description capability of the methods used and consequently, the information of the transport phenomena involved.Thus, studies with several food samples are necessary.the orifices (V = 0.59 m s -1 and V = 1.18 m s -1 ).A total of 8 conditions were used.These conditions were codified as follows: TxxVyyySz, where xx are the digits of T (absolute value), yyy are the digits of V (multiplied by 100) and z is the digit of S. For example: the code T10V059S2 means T = -10°C, V = 0.59 m s -1 and S = 2 cm.

Mathematical Modeling
The flow field was modeled by solving mass (continuity) and momentum (Navier-Stokes) balances.The turbulence effect was estimated by the two parameter κ-ω Shear Stress Transport (SST) model (Fluent, 2011).
The relative movement of the spheres was considered taking into account the interactions between the fluid and the spheres, among spheres and between spheres and solid walls.These interactions were estimated through momentum balances for each sphere and structural data of the food.The sphere-fluid interactions were calculated by using a discrete phase method (DPM) and the sphere-sphere and sphere-wall interactions were estimated by using a discrete element method (DEM) (Fluent, 2011).The collisions were estimated taking into account elastic, viscous and friction effects (Fluent, 2011).A default set of the mechanical properties needed for the collisions of the spheres were used (Fluent, 2011).

Computational Domain and Analyzed Variables
The computational domain was similar to the physical domain.The main assumptions were those proposed by Peralta et al. (2010).A 6-mm slit at the top of the cylindrical wall was used as a fluid exit (Figure 1).Solid walls were assumed to be adiabatic and the system pressure was 0.1 MPa.A 1/7th power velocity profile was used in the round orifice because a fully turbulent liquid-jet with a turbulence intensity of 5% was assumed.
A mesh composed by tetrahedral elements was used to discretize the computational domain.This mesh was denser near the orifices.
Each condition was simulated up to 8 s.In the first 3 s, only the momentum and mass balances in the fluid were simulated to reach steady state conditions in the flow field.After t = 3 s, the spheres were injected and the following 5 s were used to simulate their movements and interactions inside the domain.
The momentum and mass balances for the fluid and the spheres (Navier-Stokes, continuity, DPM and DEM) were solved using the commercial CFD software ANSYS-ICEM-CFD 14.1 and ANSYS-FLUENT 14.1 (ANSYS Inc., Canonsburg, USA).The simulations were carried out using a PC with an Intel core i7 3930 processor of 3.2 GHz with 16 GB of RAM (DDR3 1600 MHz).Each simulation took approximately 90 h to converge.
Representative variables were used to study the flow field and spheres velocities.These variables were the volume-averaged sphere velocity v p  (Equation ( 1)) and the volume-averaged slip velocity v slip  (Equation ( 2)).
where p v is the magnitude of the velocity vector of an sphere p v [m s -1 ], slip v is the magnitude of the relative velocity to the fluid of an sphere is the velocity vector of the fluid at the center position of an sphere [m s -1 ] and T V is the domain volume.

Model Validation
The mathematical model was partially validated using heat transfer data from Belis et al. (2012) for a similar HF configuration but using static spheres.This validation is shown in Part II (Oroná et al., 2014).

Independence Test
A mesh independence test was carried out testing 6 different mesh compositions (from 86296 to 170770 tetrahedra) using profiles of v p  and v f  (i.e.area-averaged fluid velocity) at t = 3 s for the condition T5V118S1.Based on this procedure and taking into account heat transfer and turbulence intensity variables checked in Part II (Oroná et al., 2014), a mesh composed by 170770 tetrahedra was used for the simulations.It is important to mention that to minimize convergence problems, a mesh with elements of the same or greater size than the spheres were considered in the selection procedure (Fluent, 2011).Figure 2 shows the velocity profiles for the meshes checked.

Velocity Contours and Streamlines
Velocity contours with their respective streamlines for half of the conditions studied are shown in Figure 3.Only conditions with T = -5ºC are presented due to their similarity with     5b due to the time discretization used to show the results.Then, a second maximum value is observed when (and where) a maximum value of v p  is obtained.Later, a plateau or a slight decrease is observed similarly to the v p  profiles (Figure 5a) due to the small values of v f .Finally, a value of v slip  equal to v f  is obtained due to the spheres reached the liquid-air interface and v p  = 0.For cases with V = 1.18 m s -1 and S = 1 cm, higher final values of v slip  are obtained, possibly due to the synergic effect of V and S on v f .Finally, the effect of the operational variables on v slip  was similar to that observed for v p  (Figure 5a).In general, an increment in S and a decrease in V and T (marginal effect), produced a decrease in v slip .

CONCLUSIONS
A study of the effect of operational variables (flow rate and temperature) and the number of orifices, on transfer of and mass that occur between moving spheres and the refrigerant in a HF system was performed.It was out using a mathematical model that solved Navier-Stokes and continuity with CFD and the mobility of spheres using discrete phase (DPM) and discrete element methods (DEM).Representative variables such as velocity contours and streamlines for the fluid and absolute and relative velocity profiles for the spheres were used to study the transfers.In general, S was the most significant parameter followed by V.The refrigerant temperature had a marginal effect on the studied transfers.
This study, along with Part II, shows that the combination of CFD with DPM and DEM can be a powerful tool to simulate and study real HF systems with a minimum computational requirement compared to other approaches such as solid-fluid interaction studies.

Figure 2 -
Figure 2 -Mesh independence.Local values of (a) v p  as a function of time and (b) v f  as a function of axial position for different mesh compositions. Figu

Figure 5 -
Figure 5 -Profiles of (a) v p  and (b) v slip  as a function of time for the studied conditions.