Session 12

Chairman: P. Heggs

LATTICE BOLTZMANN MODEL OF THE HEAT AND MASS TRANSFER OF PACKED MATERIAL IN BULK CONTAINERS WITH VENT HOLES

R.G.M. van der Sman
Agrotechnological Research Institute
p.o. box 17, Wageningen, the Netherlands
April 11,1997

INTRODUCTION

In this paper we present a numerical study on the effects of vent holes on the heat and mass transfer in bulk containers of packed material with vent holes. The aim of this study is to provide guide lines for the design of vent holes in bulk packaging systems of agricultural products.

The model we use is based on the novel technique of the Lattice Boltzmann schemes [l]. LB-schemes are able to reproduce various complex physical phenomena such as hydrodynamics, natural convection and multi-phase flow. [2, 3, 4]. The basic idea behind LB-schemes is to model physical phenomena with quasiparticles, representing packets of matter or energy, moving over a discrete regular lattice and colliding according to simple rules.

Due to its simple nature LB-schemes are also very suitable for modelling the strongly coupled heat and mass transfer phenomena as occur in packaging systems [5, 6]. Furthermore the implementation of complex boundary conditions such as vent holes in heat conducting and vapour permeating walls is straightforward.

Numerical simulations are performed for various containers with different vent hole designs. The model is tested with available experimental data of heat and mass transfer in bulk packagings of potatoes. From the simulation results the guide lines for vent hole design are deduced.

PROBLEM DESCRIPTION

The ojective of vent hole design in packaging of agricultural products is to prevent quality loss due to weight loss, condensation and heat accumulation. This demands a careful design of vent holes: large holes prevent condensation, but pro- mote weight loss, and at the other hand small holes promote heat accumulation and possible condensation.

In the model we have to incooperate the various heat and mass transfer pro- cesses as occur in bulk packagings of agricultural products. These processes are:

1. convection of heat and water vapour by air flow in the voids between the packed products,
2. heat conduction through the products, air and packaging material,
3. water vapour diffusion through the packaging material,
4. vaporation of water from the product,
5. condensation of water vapour on the product,
6. the ventilation of heat and water vapour through the vent holes in the container [7, 8, 9].

In this model we assume the air flow is driven by natural convection.

LATTICE BOLTZMANN SCHEME

For the numerical simulation of the heat and mass transfer in bulk containers we consider a Lattice Boltzmann scheme with three lattice gasses modelling the heat and mass transport and fluid flow respectively, The water content of the packed material and the condensed moisture are modelled with stagnant particles. The LB scheme is an extension of the scheme modeling the heat transfer by natural convection in closed potato packagings. We have incorporated the mass transfer and the boundary conditions necessary for the heat and mass transfer through the vent holes.

NUMERICAL SIMULATIONS

Numerical simulations are performed with several container designs varying in size and location of ventholes. The questions which we try to solve are:

1. what is the ef£ect of vent holes when located in a single plane,
2. what is the effect of the combination of several planes with vent holes,
3. what is the effect of the distribution of holes in a plane.

The model will first be tested with experimental data available on the heat and mass transfer from bulk packagings of potatoes. With the validated model we do calculations for various new designs. All designs are evaluated on their performance on condensation, weight loss and heat transfer.

CONCLUSIONS

A Lattice Boltzmann model for the heat and mass transfer for bulk containers of packed material with vent holes is developed. Qualitatively good agreement with experiments is found when comparing the simulation results with experimental data for potato containers. Further calculations are performed for containers with new vent hole designs. After evaluation of the simulation results guide lines are deduced for the design of vent holes in bulk containers.

REFERENCES

1. R. Benzi et.al., Phgs. Rep. 222 (3), 145 (1992).
2. J.M.V.A. Koelman, Europhys. Lett.15, 603 (1991).
3. J.G.M. Eggels, and J.A. Somers, Int. J. Heat and Fluid Flow 16, 357-365, 1995
4. E.G. Flekkoy, Phgs. Rev. E 47, 4247 (1993).
5. R.G.M. van der Sman, and M.F.M. Janssens, Proc. Eur. Simulation MultiConference'94, (Barcelona,l994).
6. R.G.M. van der Sman, and M.H. Ernst, Int. J. of Heat and Mass Transfer, submitted (1996).
7. F.W. Bakker-Arkema et.al., J. Agr. Eng. Research 12 (4), 297 (1967).
8. K.J. Beukema, Ph. D. 'rhesis, Agr. Univ., Wageningen, the Netherlands, 1980.
9. K.K. Khankari et.al, ASEA paper no. 93-6017, 1993.

The permeability of porous media has long been a focus of interest in many fields ranging in diversity from underground water filtration to composites manufacturing processes. Permeability is a measure of how permitting a medium is to an oncoming flow and can play a crucial role in many applications. This parameter is a mathematical variable as well as a physical term and can easily be defined as the proportionality constant K in Darcy’s Equation

where V is the superficial velocity of the fluid flowing through the porous medium, m the viscosity of the fluid and dP/ds the negative pressure gradient in the direction of the flow.

All the parameters in eqn. (1) are measurable through proper techniques except permeability which can only be determined indirectly through this equation. Since many applications benefit from prediction of flow properties such as pressure and velocity, the characterization of permeability through analytical means has been a topic of numerous studies. Permeability is a strong function of porous medium architecture and given the many configurations of porosity, it is a challenging and yet popular problem with continuous demand arising from such fields as the increasingly complex geometric and performance requirements of composites processing.

The porous media can generally be classified as being either granular or fibrous. In the case of granular media, the porous structure is formed by groups of grains bound together with networks of constrictions in between (which form the porous phase). The fibrous media on the otherhand, can be formed by tightly woven continuous fibers as well as packs of loose short fibers oriented randomly. The present paper focuses on permeabilities of continuous fiber-reinforced composites during the processing stage where the porous medium is formed by fibrous preforms impregnated by the injected resin. This is a typical description of resin transfer molding, one of many liquid molding processing techniques for manufacturing primarily polymer composites.

There have been numerous studies on prediction of permeability in fibrous porous structure. These studies have expanded to include three-dimensionality and anisotropy of loose and woven fibrous media. The current work takes into consideration the additional complexity of two-phase (solid-liquid) flow in which solid particles are introduced to the flow penetrating the porous medium. As a consequence of the resulting filtration, the medium permeability is no longer a function of the porous structure alone, but is influenced by the filtered particles as well. The particle phase now becomes part of the porous structure and must be included in the characterization of permeability.

This paper presents a two-dimensional permeability model for non-woven continuous fiber porous media undergoing filtration based on a mesoscale analysis coupled with macroscale flow. The flow is incompressible and slow enough to justify creeping flow assumption. As a first approximation to the problem, two configurations are investigated for the fiber architecture: flow along bundles of fibers and flow perpendicular to bundles of fibers. In each case, the filtered particle sizes are approximated as being much smaller than the fiber diameter. In addition, the filtered particles are assumed to be evenly deposited around the fibers and instead of fractal geometries, they form ring-like crusts. As a result, an effective diameter is defined for the fibers deposited with particles, however this diameter varies spatially and temporally within the medium due to changing particle content along the fibers. The resulting permeability is a function of fiber volume fraction, diameter and architecture as well as the filtered particle content.

The results are tested on a two-dimensional mold filling simulation which depicts the injection of particle-filled resin into an irregular-shaped, thin mold cavity with a pre-placed continuous fiber preform. A previously developed filtration model is used in conjunction with Darcy’s Law to model the filtering flow. It is observed that permeability, like the rest of the process parameters, varies spatially and temporally within the mold domain due to continuous filtration. The results also indicate that in a filtering medium, the permeability indirectly becomes a function of flow properties as well as porous structure and filtrate characteristics.