Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices

In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can be satisfied for the rectangular D2Q9 lattice for only fluid flow in the weakly compressible regime. The analysis of source terms shows that fluxes are really defined on the boundaries of the Wigner-Seitz cells, and not on the lattice sites where the densities are defined¿which is quite similar to the staggered grid finite-volume schemes. Our theoretical findings are confirmed by numerical solutions of benchmark problems for convection diffusion and natural convection. The lattice Boltzmann scheme shows remarkably good performance for convection diffusion, showing little to non-numerical diffusion or numerical dispersion, even at high grid Peclet number

Lattice Boltzmann schemes for convection-diffusion phenomena : application to packages of agricultural products

Packaging is crucial for the control of quality of fresh agricultural products. How to optimise the packaging design for a particular product and distribution chain, is still not fully understood. Various empirical studies have shown that existing packaging designs can still be improved significantly. The packaging design process can be greatly enhanced by the use of computer models, describing the physical and physiological processes.In transport packaging systems with vent holes, the dominant physical processes are convection-diffusion of heat and water vapour. The numerical solution of convection-diffusion problems is a complex matter. Traditionally, solutions are obtained with specific Finite Element or Finite Difference schemes, which require a highly-specialised knowledge of numerical mathematics. /P>In this thesis, the Lattice Boltzmann method is investigated as an alternative numerical method to solve the convection-diffusion problems in packaging systems. It simulates physical transport phenomena with quasi-particles, which move and collide on a lattice. Space, time and particle speed are discrete.The dynamics of the quasi-particles are governed by a discretised Boltzmann equation. Since the Lattice Boltzmann method has shown to be able to model Navier-Stokes flow, it has recieved a rapidly growing interest from the scientific community. This interest can be attributed to the simplicity and the appeal to physical intuition of the Lattice Boltzmann method.In the first part of this thesis several test case problems, taken from the practice of packing agricultural products, are solved with the Lattice Boltzmann method. Accurate and efficient schemes have been developed for the following applications: the cooling of cut flowers, the natural convection in a potato container, and the water vapour transfer in a potato container with vent holes.In order to solve these test case problems, the Lattice Boltzmann method has been extended with:a scheme for convection-diffusion on an orthorhombic lattice,a scheme for porous media flow as described by Darcy's law,interactions modelling heat and mass transfer between solid and fluid phase of a porous medium,boundary conditions for heat conducting and water permeating packaging material, andboundary conditions for vent holes.Despite the successful solution of the test case problems, the Lattice Boltzmann schemes have up to now have had drawbacks, which make them difficult to compete with Finite Element and Finite Difference schemes.Because the lack of a clear theoretical foundation, and the inability to Support grid refinements, it is difficult for the Lattice Boltzmann method to compete with the Finite Element and Finite Difference method in solving convection-diffusion problems. Hence, in the latter part of the thesis we investigate whether these drawbacks of the Lattice Boltzmann scheme can be resolved.Theoretical analysis shows that the diffusion Lattice Boltzmann scheme can be derived from the basic principle that the hydrodynamic moments of the equilibrium particle distribution must equal those of the Maxwell-Boltzmann distribution up to second order.By extending this theoretical framework to convection-diffusion, LB schemes are developed for orthorhombic lattices and irregular grids. These new Lattice Boltzmann schemes are compared to several Finite Difference and Finite Element schemes by solving benchmark problems. Analysis of the numerical solutions shows that the accuracy of the Lattice Boltzmann schemes is comparable to high-order Finite Element schemes, but can be achieved with much less computer resources, i.e., memory and computing time. Its good performance, the existence of a theoretical framework clearly linked with physics, and the algorithmic simplicity, make the Lattice Boltzmann method a strong competitor for conventional numerical schemes.From the results of this thesis it can be concluded that the Lattice Boltzmann method is a very suitable framework for modelling convection-diffusion phenomena and can be applied to packaging systems. It has attractive properties in simplicity, efficiency, and accuracy. Thereby, it can greatly contribute to better quality management of packed, fresh agricultural products.</p

Analysis of mixed motion in deterministic ratchets via experiment and particle simulation

Deterministic lateral displacement (DLD) ratchets are microfluidic devices, which are used for size-based sorting of cells or DNA. Based on their size, particles are showing different kinds of motion, leading to their fractionation. In earlier studies, so-called zigzag and displacement motions are observed, and in recent study by our group (Kulrattanarak et al., Meas Sci Technol, 2010a; J Colloid Interface Sci, 2010b), we have shown that also mixed motion occurs, which is an irregular alternation of zigzag and displacement motion. We have shown that the mixed motion is due to asymmetry of the flow lane distribution, induced by the symmetry breaking of the oblique primitive lattice cell (Kulrattanarak et al. 2010b). In this study, we investigate mixed motion in depth by numerical and experimental analysis. Via 3D simulations, we have computed explicit particle trajectories in DLD, and are able to show that there are two critical length scales determining the type of motion. The first length scale d f,1 is the first flow lane width, which determines the transition between zigzag motion and mixed motion. The other length scale, d f,c , determines the transition between mixed motion and displacement motion. Based on our experimental and numerical results we have been able to correlate the migration angle of particles showing mixed motion to the particle size, relative to the two critical length scales d f,1 and d f,

Model predictions and control of conditions in a CA-reefer container

In this paper a concept for energy saving for refrigerated container transport is presented. The concept is based on model-predictive control of the set points of the cooling unit. These models predict energy consumption of the cooling unit, climatic conditions inside the cargo space, and the change in product quality. The objective of the control is to minimize energy consumption while retaining a certain level of product quality. After presenting the concept of the model-predictive control the predictive power of the models used are shown. These models show that we are able to predict energy consumption, temperature, humidity and gas conditions quite accurately. Furthermore, an indication is given for the quality change model to be employed. The impact of the novel control is shown by simulation of a transport of apple

Rheology of paste-like food inks for 3D printing:Effects of nutrient and water content

This research delves into understanding the effects of composition on the rheological response of multi-component food inks for 3D food printing. Accordingly, the motivation is to decouple the nutrient and water content effects on the rheology. We formulated inks by combining pea fractions with water and employing a water-holding-capacity based hydration method. Rheology is characterized by steady shear rate and oscillatory strain amplitude sweeps. Strain sweep curves infer that the deformation response of all inks follows a similar trend, and samples sharing the same macronutrient formulation are mapped to a master curve after scaling with the elastic plateau modulus. Samples sharing the same macronutrient formulation mapped to a master curve after scaling with the elastic modulus. Shear rate testing showed that the inks were shear thinning yield stress materials. Shear rate sweeps also collapsed on a master curve scaled by the yield stress and critical shear rate on the y and x axes. The yield stress and the plateau modulus appeared to be controlled by the water content, while the shear and strain thinning exponents were independent of the formulations, inferring that the rheology is scaled by the water content while preserving the shear thinning response. Observing the independence of the rheological properties from the nutrient composition and scalability of the rheology by the water content provided a step forward in developing formulations with various nutrient content at desired ow properties, which promises personalized nutrition. Furthermore, the study shows the applicability of various rheological techniques, which are expected to contribute to the literature on the rheology of granular pastes.</p

Shear-induced self-diffusion and microstructure in non-brownian suspensions at non-zero Reynolds numbers

This paper addresses shear-induced self-diffusion in a monodisperse suspension of non-Brownian particles in Couette flow by two-dimensional computer simulations following the lattice-Boltzmann method. This method is suited for the study of (many-particle) particulate suspensions and can not only be applied for Stokes flow, but also for flow with finite Reynolds number. At relatively low shear particle Reynolds numbers (up to 0.023), shear-induced diffusivity exhibited a linear dependence on the shear rate, as expected from theoretical considerations. Simulations at shear particle Reynolds numbers between 0.023 and 0.35, however, revealed that in this regime, shear-induced diffusivity did not show this linear dependence anymore. Instead, the diffusivity was found to increase more than linearly with the shear rate, an effect that was most pronounced at lower area fractions of 0.10 and 0.25. In the same shear regime, major changes were found in the flow trajectories of two interacting particles in shear flow (longer and closer approach) and in the viscosity of the suspension (shear thickening). Moreover, the suspended particles exhibited particle clustering. The increase of shear-induced diffusivity is shown to be directly correlated with this particle clustering. As for shear-induced diffusivity, the effect of increasing shear rates on particle clustering was the most intensive at low area fractions of 0.10 and 0.25, where the radius of the clusters increased from about 4 to about 7 particle radii with an increase of the shear Reynolds number from 0.023 to 0.35. The importance of particle clustering to shear-induced diffusion might also indicate the importance of other factors that can induce particle clustering, such as, for example, colloidal instability

Investigation on the influence of pre-treatments on drying behaviour of broccoli by MRI experiments

Abstract: Magnetic Resonance Imaging (MRI) allows the monitoring of internal moisture content of food products during drying non-destructively. In an experimental set-up with continuous and controlled hot air supply, the internal moisture distribution of broccoli with different pre-treatments are measured during drying. Moisture distribution, drying rate and shrinkage are compared and analyzed quantitatively. MRI results indicated that for fresh broccoli stalks the moisture content in the core of the sample increased after some hours of drying. With pre-treatments as peeling, blanching or freezing the moisture transport barrier in the skin of the broccoli sample was reduced. Shrinkage was uniform for most of the pre-treated samples and the moisture increment in the core did not occur. It was also found that with these pre-treatments progress of drying enhanced significantly. Therefore, from an drying efficiency and economic point of view, pre-treatments prior to drying offer important opportunities. Keywords: MRI, hot air drying, broccoli stalk, increased moisture content, pre-treatment