Wanyr Romero Ferreira

Final Drying of Whole Milk Powder in Vibrated-Fluidized Beds

Abstract Vibro-fluidized beds are widely used in drying sticky powders and agglomerated materials as milk powder. Using a vibro-fluidized laboratory scale dryer, this work is aiming at analyzing preliminarily the effect of its operational variables on the drying kinetics and characteristics of whole milk powder. The full-factorial design technique with three replications at the central point has been employed to generate data and correlations to quantify the effect of inlet air temperature, air flow rate, and vibration bed amplitude on the drying curves and the milk powder properties related to its faster reconstitution in water (as tapped density, Hausner cohesion ratio, agglomerate size distribution, and internal pore concentration). Results obtained are analyzed and discussed to identify the adequate operation condition for final drying whole milk powder in vibro-fluidized beds, assuring a high product quality.

Modelagem de um condicionador de ar de alta precisão para uso em processamento agrícola

In this work, a detailed procedure for the analysis of an accurately controlled air conditioner is presented. A computer program, that allows predicting the behavior of the system under different psychrometric conditions and different input air mass flow rates, was developed. The global physical-mathematical model includes mass and energy conservation equations for three different control volumes that compose the conditioner. Thus, the processes of mixture of air, simultaneous evaporation (or condensation) from a water surface and from a drop, and the air-stream heating are modeled separately. Simple semi-empiric expressions for heat and mass coefficients inherent to the evaporation process on a water surface are proposed as well a simplified model for the spray system. Experimental tests made on an air-conditioner allowed to obtain the constants that appear in the expressions for the heat and mass transfer coefficients and to validate the global model, within an engineering acceptable precision level.

Numerical Simulation Techniques for Optimizing Thermodynamic Efficiencies of Cereal Grain Dryers

As a first objective, this study addresses a novel approach to drying efficiency analysis through transient models based on both the first and second laws of thermodynamics. As a second objective, we developed a numerical meshless scheme based on cubic radial basis functions to solve the associated nonlinear coupled advection-dominated set of partial differential equations. The simulated results showed excellent accuracy when compared with available literature data on drying. Finally, and most significantly, this study presents an original methodology for optimizing dryers based on energy and exergy efficiencies and the associated controllable operational parameters: drying air velocity (flowrate) and temperature.

The one-dimensional transient diffusional method: finite element adaptive solutions to convection-diffusion problems

Abstract The diffusional method, a new, simple and natural concept, is introduced for solving convection-diffusion equations. The inherent formulation leads to the variational scheme for one-dimensional steady-state problems; however, the formulation is general and can be directly used in multidimensional analysis. Additionally, a lumped capacitance (mass) matrix first-order time integration technique is presented that is unconditionally stable in its implicit form and conditionally stable for Courant numbers less than one in its explicit form. The explicit form is shown, by comparison with a two-step Taylor-Galerkin scheme, to present an excellent performance for solving transient boundary layer problems and Burgers non-linear equation. Because of dampening due to first order accuracy of the time integrator, the method is not well suited to solve advection dominated problems involving travelling waves at high Peclet numbers; in this respect, a brief analysis is made on the explicit form of the Taylor-Galerkin scheme. This work also presents a performance analysis of the method when used in conjunction with adaptive time stepping procedures. The resulting adaptive PMGV scheme works very well for boundary layer problems and for solving Burgers non-linear viscous and non-viscous equations.

Energy and exergy efficiencies as design criteria for grain dryers

ABSTRACT We devised a novel methodology for optimizing cereal grain dryers grounded on the transient spatial–temporal first and second laws of thermodynamics and associated balance equations. Model equations were solved using a special time-adaptive radial basis function. Comprehensive sensitivity tests show the quantitative effects of initial moisture content, air velocity, and drying air temperature on the temporal profiles of outlet air temperature and moisture content and temporally integrated energy and exergy efficiencies. Drying temperature is the most efficacious parameter in the drying range of 50–90°C. Finally, selected examples show optimized dryer operation points under unrestrained and restrained conditions. Second law efficiency is well suited for expressing drying performance, portraying time, noble energy expenditure, and intrinsic sustainability. Three decision tables, based on simulation results, can be used to define dryer design under normal technical choice. First law efficiency and the specific moisture extraction rate are concepts more adequate for designing in-bin low-temperature dryers. Second law efficiency is indicated when exergy recuperation is at stake: higher drying temperatures, shorter drying times, recirculation drying, and other processes.

Optimization Aspects of Dryeration Based on Drying Simulation Analysis of a Single Corn Kernel

Dryeration consists of three basic steps. Initially, the grain mass is fast dried at a high temperature. Drying is interrupted when the grain mass presumably reaches an acceptable moisture content level. In the second step, called tempering, the grain mass is allowed to rest for a few hours. Finally, the grain mass is cooled slowly so as to remove the residual water while letting the drying process to continue. Up to present time, in the reviewed literature, there is no modeling work of dryeration that could cast light to some crucial questions. This work presents a systematic analysis of a single kernel drying and dryeration, by making use of Fortes and Okos´ irreversible thermodynamics models, which have been applied successfully to model drying of several products. The nonlinear coupled system of energy and mass transport of benchmark solutions were used to warrantee the accuracy of the numerical solutions. Simulation results include a simulation study with drying temperature of 75° C, two tempering periods (4 and 8 h) and a high temperature drying at 97°C, followed by cooling, with variable boundary conditions. The kernel moisture content, as well its mass flux and temperature during dryeration process were evaluated. Numerical data were compared with experimental ones, mutatis mutandis. The comparison led to confirmation of the usefulness of the drying models and techniques presented. Thus, the result herein presented should be of value to researchers and engineers interested in optimizing drying procedures.

Transient and Spatial Energy and Exergy Analysis of Deep-bed Corn Drying A paper from the State-of-the-Art in Application of Finite Element Numerical Solutions to Engineering Problems: A Session Honoring Pioneering Contributions of Professor Kamyar Haghig

This paper addresses the use of the first and second laws of thermodynamics to analyzing food and cereal grain drying processes, as a means to assure full sustainable compatibility between drying speed and energy source. Energy and exergy procedures are applied to the analysis of deep-bed grain drying, with a model consisting of four non-linear advection-dominated partial differential equations (PDE). The numerical solutions involved the use of the recent radial basis function (RBF) method, with excellent accuracy. The simulated results were compared against experimental available data for deep-bed corn grain drying, without loss of generality. A parametric study was carried on by spanning air temperature and interstitial velocity in the ranges of 30-70 oC and 0.2-0.6 m/s, respectively, and initial bulk grain moisture contents ranging from 0.25 to 0.33 db.The analyses were based on numerical time and spatial profiles for air and corn temperatures, bed moisture ratios, corn moisture content and first and second law efficiencies. Therefore, this work should be of value to dryer designers and for drying research objective.

Transport coefficients for low and high-rate mass transfer along a biological horizontal cylinder

O conhecimento dos coeficientes de transferencia de calor e massa e essencial para o estudo de simulacao de secagem e para o projeto de processamento termico de graos e alimentos, inclusive secagem. Este trabalho apresenta o desenvolvimento completo de um metodo de elementos finitos segregado para resolver problemas de conveccao-difusao. O esquema desenvolvido permite que se resolvam as equacoes de Navier-Stokes incompressiveis em regime permanente, alem de problemas convectivos-difusivos com propriedades dependentes da temperatura e da umidade. Apresenta-se o problema de transferencia simultânea de energia, momentum e especies ao longo de um cilindro horizontal, infinito sob condicoes de secagem em conveccao forcada, considerando-se condicoes normalmente encontradas em tratamento termico ou secagem de material biologico. Compararam-se resultados numericos para Nusselt e Sherwood com expressoes empiricas disponiveis; os resultados concordaram dentro dos erros experimentais associados. Para processos com altas taxas de transporte de massa, a metodologia proposta permite simular condicoes de secagem envolvendo fluxo convectivo de massa na parede, por meio de uma simples inclusao de condicoes de contorno apropriadas.

Equivalence of finite element, volume and difference methods used to solve one-dimensional convectiondiffusion problems – Application to a solute transport process

This work shows that, by adequately rewriting the one-dimensional convection-diffusion equation in a diffusional form, all the usual numerical procedures, that is, the finite element, finite volume and finite difference procedures, lead to the same and optimal steady-state stencil for numerical solutions. Additionally, a lumped capacitance (mass) matrix first-order time integration technique is presented. The resulting scheme, expressed with a transient, special lumped capacitance matrix (PMGV or prevailing main grid value method), was used to solve the problem of onedimensional transient saturated soil solute transport. A benchmark problem with analytical solution, representing a moving concentration front in a saturated soil was solved by both the diffusional method and by the Two-Step Taylor-Galerkin (TSTG) finite element method. The diffusional (PMGV) method proved itself to be an excellent option for solving advection dominated problems such as soil solute transport problems. The simulation results showed that the explicit PMGV scheme leads to the same accuracy as the TSTG scheme. The TSTG scheme shows numerical dispersion while the diffusional method showed false diffusion. However, the stability region for the PMGV is broader. The PMGV scheme is more effective than the TSTG in problems involving either low Pe numbers or high Pe numbers, if mesh refinement is made.

Heat and Mass Transfer Coefficients for Natural and Mixed Convection Drying of a Horizontal Cylinder

This work presents a finite element methodology for solving convection-diffusion problems; the method is a modification of its original version and includes a streamline upwind technique so that false diffusion numerical errors can be decreased. The problem of simultaneous heat, mass and momentum transfer around a horizontal infinite cylinder was solved for natural, mixed and forced convection conditions, as specified by the following conditions: Reynolds numbers less than 10, ambient temperature and cylinder wall temperature in the range from 25 to 60 0C and from 30 to 80 0C, respectively; cylinder wall humidity ratio ranged from 0.0198 to 0.1330 kg-vapor/kg-dry air while the ambient humidity ratio was kept at 0.0099 kg-vapor/kg-dry air . The simulated data agreed with the available experimental data and regression equation within the associated experimental errors. A large number of simulations involving benchmark problems allow inferring that the present method can be applied to anomalously shaped bodies and other conditions.