CFD simulation of coupled heat and mass transfer through porous foods during vacuum cooling process

A numerical simulation by using a computational fluid dynamics (CFD) code is carried out to predict heat and mass transfer during vacuum cooling of porous foods on the basis of mathematical models of unsteady heat and mass transfer. The simulations allow the simultaneous prediction of temperature distribution, weight loss and moisture content of the meats at low saturation pressure throughout the chilling process. The simulations are also capable of accounting for the effects of the dependent variables such as pressure, temperature, density and water content, thermal shrinkage, and anisotropy of the food. The model is verified by vacuum cooling of cooked meats with cylindrical shape within an experimental vacuum cooler. A data file for pressure history was created from the experimental pressure values, which were applied in the simulations as the boundary condition of the surface temperature.     

A computational fluid dynamic model of the heat and moisture transfer during beef chilling

The unsteady heat and mass transfer process during beef carcass chilling was modelled for a three-dimensional beef carcass geometry. A three-step method was used to simulate the simultaneous heat and mass transfer process in order to reduce the computational time. In the first step, a steady state simulation of the flow field was conducted. In the second step, the local heat and mass transfer coefficients were calculated. Finally, the third step consists of the simultaneous heat and mass transfer process simulation on the meat carcass only. A separate 1-D grid was used to calculate the moisture diffusion in the meat. The simulation of a 20-h chilling run takes 5 days on a 2.5 GHz Pentium 4 computer. The model allows calculating and predicting the heat load, temperatures, weight loss and water activity. Local variations in the heat and mass transfer coefficients, temperature and water activity were found around the beef carcass. The CFD model gives temperature predictions that agree with experimental data better than any previous model. The weight loss tends to be over-predicted probably due to neglecting the resistance caused by the fat cover.     

Mathematical model of heat and mass transfer processes in evaporative condensers

This study presents a new mathematical model of heat and mass transfer processes in evaporative condensers. The model consists of four ordinary differential equations with their boundary conditions and some associated algebraic equations. The model was formulated for steady-state heat and mass transfer conditions. A simulation computer program based on the model was written. It was devised for heat calculations in condensers built from bare tubes. The quality of the model was calculated by comparing the results obtained by running the program with experimental results achieved by other authors. The computed results show a good degree of conformity with experimental results. The differences are less than 20% (but in one case, 30%). The computer program may be used to determine heat performance of evaporative condensers of horizontal in-line and staggered bundle systems (if S_q > 2d_z).     

The reliable simple one-dimensional 64-CPWTR model applied to the two-dimensional heat transfer problem of an insulated rectangular duct in an air conditioning or refrigeration system

The heat-transfer characteristics of an insulated long rectangular or square duct are analyzed by using the one-dimensional plane wedge thermal resistance (PWTR) model and plate thermal resistance (PTR) model in this study. It is found that the errors generated by the PWTR model are all positive and the errors generated by the PTR model are all negative. Thus, the combined plate wedge thermal resistance (CPWTR) model generated by paralleling PWTR and PTR models with the proportion factors of α=0.6 vs. β=0.4 (64-CPWTR model) can neutralize the positive and negative errors and obtain very accurate results in comparison with the two-dimensional numerical solutions analyzed by the CFD software. The errors generated by the one-dimensional 64-CPWTR model are within 1% for practical sizes and practical insulated thickness in air conditioning and refrigeration systems. Thus, the engineer can obtain very reliable heat transfer results when applying the one-dimensional 64-CPWTR model to an insulated rectangular duct.     

Assessment of boiling heat transfer correlations in the modelling of fin and tube heat exchangers

A new way to assess the performance of refrigeration system models is presented in this paper, based on the estimation of cycle parameters, such as the evaporation temperature which will determine the validity of the method. This paper is the first of a series which will also study the influence of the heat transfer coefficient models on the estimation of the refrigeration cycle parameters. It focuses on fin and tube evaporators and includes the dehumidification process of humid air. The flow through the heat exchanger is considered to be steady and the refrigerant flow inside the tubes is considered one-dimensional. The evaporator model is discretised in cells where 1D mass, momentum and energy conservation equations are solved by using an iterative procedure called SEWTLE. This procedure is based on decoupling the calculation of the fluid flows from each other assuming that the tube temperature field is known at each fluid iteration. Special attention is paid to the correlations utilised for the evaluation of heat transfer coefficients as well as the friction factor on the air and on the refrigerant side. A comparison between calculated values and measured results is made on the basis of the evaporation temperature. The experimental results used in this work correspond to an air-to-water heat pump and have been obtained by using R-22 and R-290 as refrigerants.     

Numerical investigation of three-dimensional turbulent flow and endwall heat transfer in a large-scale cascade of turbine blades

Numerical simulation is performed of three-dimensional turbulent flow and heat transfer in a cascade of turbine blades (Langston cascade), for which numerous data are available in the literature. For closing the system of Reynolds-averaged Navier-Stokes equations, use is made of two-parameter models of turbulence of the k-ω family, low-Reynolds version of the Wilcox model, and the SST model of Menter. Numerical solutions are obtained in detailed grids (over a million cells) using the finite-volume code of second-order accuracy. It is demonstrated that the predicted structure of flow and local heat transfer on the end wall are very sensitive to the choice of model of turbulence, especially in the case of a thick boundary layer at the cascade inlet. By and large, the use of the Menter model enables one to well reproduce the complex vortex structures of flow in the cascade, as well as the local and integral characteristics of loss of total pressure. The local endwall heat transfer is predicted adequately.     

Steady state CFD modeling of airflow, heat transfer and moisture loss in a commercial potato cold store

Storage loss beyond permissible limit is one of the most important problems in Indian potato cold stores, which has been hindering further growth of this industry. The losses in the stored potatoes have a direct relation to the intricate coupled transport phenomena of heat, mass and momentum transfer therein. Therefore, airflow, heat transfer and moisture loss was investigated in a potato cold store of commercial scale under steady state condition using the computational fluid dynamics technique. The developed CFD model was a two-dimensional simplification of the cold store. Heat and mass transfer at the cooling coils were not modeled, instead temperature and relative humidity in the air space were specified based on measured values. The model was validated in a commercial scale cold store and was found to be capable of predicting the air velocity as well as product temperature with an average accuracy of 19.5% and 0.5 °C, respectively and also the simulated average total moisture loss was found to be only 0.61% water (w.b.) higher than the experimental one for a storage period of 6 months. The main deficiencies of the airflow pattern which resulted in wide variations in temperature and moisture loss within the stored commodity can be investigated. The model located the probable zones of hot and cold spots, excessive product dehydration and moisture condensation within the storage facility, which might lead to qualitative and quantitative deterioration in stored product. This modeling tool could very well be applied to incorporate necessary design improvements with a view to improve the airflow distribution and heat transfer in order to limit the storage losses within the permissible limit.     

Heat transfer enhancement by winglet-type vortex generator arrays in compact plain-fin-and-tube heat exchangers

The potential of winglet type vortex generator (VG) arrays for air-side heat transfer enhancement is experimentally evaluated by full-scale wind-tunnel testing of a compact plain-fin-and-tube heat exchanger. The effectiveness of a 3VG alternate-tube inline array of vortex generators is compared to a single-row vortex generator design and the baseline configuration. The winglets are placed in a common-flow-up orientation for improved tube wake management. The overall heat transfer and pressure drop performance are assessed under dry-surface conditions over a Reynolds number range based on hydraulic diameter of 220 ≤ Re ≤ 960. It is found that the air-side heat transfer coefficient increases from 16.5% to 44% for the single-row winglet arrangement with an increase in pressure drop of less than 12%. For the three-row vortex generator array, the enhancement in heat transfer coefficient increases with Reynolds number from 29.9% to 68.8% with a pressure drop penalty from 26% at Re = 960 to 87.5% at Re = 220. The results indicate that vortex generator arrays can significantly enhance the performance of fin-tube heat exchangers with flow depths and fin densities typical to those used in air-cooling and refrigeration applications.     

Heat transfer characteristics of cooked meats using different cooling methodsCaractéristiques du transfert de chaleur de viandes cuites réfrigérées par des méthodes différentes

Cooling rate and heat transfer characteristics of cooked meats using four different cooling systems of vacuum cooling, air blast cooling, water immersion cooling and slow air cooling were investigated. The experimental results show that only the vacuum cooling can achieve the requirement of cooling the cooked meats from about 74 to 10°C within 2.5 h. The vacuum cooling shows different heat transfer characteristics during the cooling process, as compared with other cooling methods. Vacuum cooling rate is controlled by the evaporation rate of water from the cooked meats, while the cooling rates of the other three cooling methods are governed by the thermal conductivity of the cooked meats. Therefore, it is impossible for air blast, water immersion and slow air cooling to obtain high cooling rates since these three methods are different only in the convective heat transfer from the surface of the cooked meat to the cooling medium.     

Assessment of condensation heat transfer correlations in the modelling of fin and tube heat exchangers

This is the second paper of a series that assesses the performance of a refrigeration system model by means of cycle parameters. In this case, the condensation temperature is the parameter to study and it is focused on fin and tube condensers. It also studies the influence of the heat transfer models on the estimation of this refrigeration cycle parameter and different correlations for the heat transfer coefficients have been implemented in order to characterise the heat transfer in the heat exchangers. The flow inside the heat exchangers is considered one-dimensional as in previous works. In the cycle definition, other submodels for all the cycle component have been taken into account to complete the system of equations that characterises the behaviour of the refrigeration cycle. This global system is solved by means of a Newton–Raphson algorithm and a known technique called SEWTLE is used to model the heat exchangers. Some experimental results are employed to compare the condensation temperatures provided by the numerical procedure and to evaluate the performance of each heat transfer coefficient. These experimental results correspond to an air-to-water heat pump and are obtained by using R-22 and R-290 as refrigerants.     

Experimental correlation of pool boiling heat transfer for HFC134a on enhanced tubes: Turbo-E

The objectives of this paper are to study the heat transfer characteristics for enhanced surface tubes in the pool boiling and to provide a guideline for the design conditions for the evaporator using HFC134a. The shape of tube surfaces, the wall superheat, and the saturation temperature are considered as the key parameters. Copper tubes (d_o = 19.05 mm) are treated with different helix angles and the saturation temperatures are controlled from 3 to 16 °C. It is found that the pool boiling heat transfer coefficient decreases with increasing the wall superheat. It is also found that boiling heat transfer coefficients for Turbo-II and Turbo-III are 1.5–3.0 times and 1.2–2.0 times higher than that for Turbo-I without the helix angle, respectively. The higher heat transfer performance from Turbo-II and Turbo-III can be explained by the “bubble detention” phenomenon on the surface without the helix angle for the Turbo-I. The experimental correlations for the pool boiling heat transfer on the present enhanced tubes without (Type I) and with the helix angle (Type II and Type III) are developed with the error bands of ±30%, respectively.     

Experimental study of turbulent single-phase flow and heat transfer inside a micro-finned tube

Single-phase heat transfer and pressure drop characteristics of a commercially available internally micro-finned tube with a nominal outside diameter of 7.94 mm were studied. Experiments were conducted in a double pipe heat exchanger with water as the cooling as well as the heating fluid for six sets of runs. The pressure drop data were collected under isothermal conditions. Data were taken for turbulent flow with 3300 ≤ Re ≤ 22,500 and 2.9 ≤ Pr ≤ 4.7. The heat transfer data were correlated by a Dittus–Boelter type correlation, while the pressure drop data were correlated by a Blasius type correlation. The correlation predicted values for both the Nusselt number and the friction factors were compared with other studies. It was found that the Nusselt numbers obtained from the present correlation fall in the middle region between the Copetti et al. and the Gnielinski smooth tube correlation predicted Nusselt number values. For pressure drop results, the present correlation predicted friction factors values were nearly double that of the Blasius smooth tube correlation predicted friction factors. It was also found that the rough tube Gnielinski and Haaland correlations can be used as a good approximation to predict the finned tube Nusselt number and ffriction factor, respectively, in the tested Reynolds number range.     

Flow boiling heat transfer characteristics of CO2 at low temperatures

This paper presents an overview of the flow boiling heat transfer characteristics and the special thermo-physical properties of CO₂ at low temperatures (down to −30 °C). Subsequently, the boiling heat transfer of CO₂ at low temperatures is experimentally investigated in a horizontal tube with inner diameter of 4.57 mm. Due to the large surface tension, the boiling heat transfer coefficient of CO₂ is found to be much lower at low temperatures but it increases with vapour quality (until dryout), which is contrary to the trend at high temperatures around 0 °C. None of the empirical correlations from open literature were able to predict the boiling heat transfer coefficient for CO₂ in good agreement with the experimental data, suggesting the need for further research in this area.     

A semi-theoretical model for predicting refrigerant/lubricant mixture pool boiling heat transfer

This paper outlines the framework of a semi-theoretical model for predicting the pool boiling heat transfer of refrigerant/lubricant mixtures on a roughened, horizontal, flat pool-boiling surface. The predictive model is based on the mechanisms involved in the formation of the lubricant excess layer that exists on the heat transfer surface. The lubricant accumulates on the surface in excess of the bulk concentration via preferential evaporation of the refrigerant from the bulk refrigerant/lubricant mixture. As a result, excess lubricant resides in a thin layer on the surface and influences the boiling performance, giving either an enhancement or degradation in heat transfer. A dimensionless excess layer parameter and a thermal boundary layer constant were derived and fitted to data in an attempt to generalize the model to other refrigerant/lubricant mixtures. The model inputs include transport and thermodynamic refrigerant properties and the lubricant composition, viscosity, and critical solution temperature with the refrigerant. The model predicts the boiling heat transfer coefficient of three different mixtures of R123 and lubricant to within ±10%. Comparisons of heat transfer predictions to measurements for 13 different refrigerant/lubricant mixtures were made, including two different refrigerants and three different lubricants.     

Experimental investigation of ice slurry heat transfer in horizontal tube

Heat transfer of ice slurry flow based on ethanol–water mixture in a circular horizontal tube has been experimentally investigated. The secondary fluid was prepared by mixing ethanol and water to obtain initial alcohol concentration of 10.3% (initial freezing temperature -4.4 °C). The heat transfer tests were conducted to cover laminar and slightly turbulent flow with ice mass fraction varying from 0% to 22% depending on test performed. Measured heat transfer coefficients of ice slurry are found to be higher than those for single phase fluid, especially for laminar flow conditions and high ice mass fractions where the heat transfer is increased with a factor 2 in comparison to the single phase flow. In addition, experimentally determined heat transfer coefficients of ice slurry flow were compared to the analytical results, based on the correlation by Sieder and Tate for laminar single phase regime, by Dittus–Boelter for turbulent single phase regime and empirical correlation by Christensen and Kauffeld derived for laminar/turbulent ice slurry flow in circular horizontal tubes. It was found that the classical correlation proposed by Sieder and Tate for laminar forced convection in smooth straight circular ducts cannot be used for heat transfer prediction of ice slurry flow since it strongly underestimates measured values, while, for the turbulent flow regime the simple Dittus–Boelter relation predicts the heat transfer coefficient of ice slurry flow with high accuracy but only up to an ice mass fraction of 10% and Re_cf > 2300 regardless of imposed heat flux. For higher ice mass fractions and regardless of the flow regime, the correlation proposed by Christensen and Kauffeld gives good agreement with experimental results.     

Finite element model for beef chilling using CFD-generated heat transfer coefficients

A combined model of the beef chilling process is presented, in which computational fluid dynamics (CFD) was used to estimate the local heat and mass transfer coefficients, assuming uniform surface temperatures, and a set of 2-D finite element grids was used to solve the heat transfer equation in the product, which has an elongated shape. Another set of 1-D grids was used to solve the water transport equation near the surface of the meat. The surface transfer coefficients were calculated for various combinations of air orientations and speeds, and summarised in a set of regression equations. The model was verified by existing and new data on heat load, temperatures, weight loss and surface water activity.     

Airside heat transfer and friction characteristics for enhanced fin-and-tube heat exchanger with hydrophilic coating under wet conditions

The airside heat transfer and friction characteristics of 14 enhanced fin-and-tube heat exchangers with hydrophilic coating under wet conditions are experimented. The effects of number of tube rows, fin pitch and inlet relative humidity on airside performance are analyzed. The test results show that the influences of the fin pitch and the number of tube rows on the friction characteristic under wet conditions are similar to that under dry surface owing to the existence of the hydrophilic coating. The Colburn j factors decrease as the fin pitch and the number of tube rows increase. For wavy fin, the Colburn j factors increase with the increase of the inlet relative humidity, but for interrupted fin, the Colburn j factors are relatively insensitive to the change of the inlet relative humidity. The friction characteristic is independent of the inlet relative humidity. Based on the test results, heat transfer and friction correlations, in terms of the Colburn j factor and Fanning f factor, are proposed to describe the airside performance of the enhanced fin geometry with hydrophilic coating under wet conditions. For wavy fin, the correlation of the Colburn j factor gives a mean deviation of 7.6%, while the correlation of Fanning f factor shows a mean deviation of 9.1%. For interrupted fin, the correlation of the Colburn j factor gives a mean deviation of 9.7%, while the correlation of Fanning f factor shows a mean deviation of 7.3%.