A careful review of the literature reveals that extensive research has been done on the hydrodynamics in packed bed columns using turbulence models. It can be noted that the choice of turbulence model is influenced by the number of phases, type of fluid, Reynolds number range and the type of packing. Thus, comparison of turbulence models for the selection of a suitable model assumes great importance for the better prediction of flow pattern. This is due to the fact that poor prediction of the flow pattern can lead to a limited heat and mass transfer model as the rate of transfer processes in packed bed is governed by the hydrodynamics of the packed bed. The aim of this paper is to give a review of the computational fluid dynamics (CFD)-based hydrodynamics studies of packed bed columns with the primary interest of studying pressure drop and drag coefficient in packed beds. From the literature survey in Science Direct database, more than 48,000 papers related to packed bed columns have been published with more than 3,000 papers focused on the hydrodynamic studies of the bed to date. Unfortunately, there are only a few studies reported on the hydrodynamics of packed columns under supercritical fluid condition. Therefore, it is imperative that the future work has to focus on the hydrodynamics of supercritical packed column and particularly on the selection of suitable turbulence model.

Soft sensors are becoming increasingly important in our world today as tools for inferring difficult-to-measure process variables to achieve good operational performance and economic benefits. Recent advancement in machine learning provides an opportunity to integrate machine learning models for soft sensing applications, such as Least Square Support Vector Regression (LSSVR) which copes well with nonlinear process data. However, the LSSVR model usually uses the radial basis function (RBF) kernel function for prediction, which has demonstrated its usefulness in numerous applications. Thus, this study extends the use of non-conventional kernel functions in the LSSVR model with a comparative study against widely used partial least square (PLS) and principal component regression (PCR) models, measured with root mean square error (RMSE), mean absolute error (MAE) and error of approximation (Ea) as the performance benchmark. Based on the empirical result from the case study of the penicillin fermentation process, the Ea of the multiquadric kernel (MQ) is lowered by 63.44% as compared to the RBF kernel for the prediction of penicillin concentration. Hence, the MQ kernel LSSVR has outperformed the RBF kernel LSSVR. The study serves as empirical evidence of LSSVR performance as a machine learning model in soft sensing applications and as reference material for further development of non-conventional kernels in LSSVR-based models because many other functions can be used as well in the hope to increase the prediction accuracy.

In this paper, the comparison of turbulence models for fluid flow past single sphere under supercritical conditions is reported. Firstly, Dixon et al.’s models [1], which are under non-supercritical conditions, were used as benchmarks to validate the simulated results. Two turbulence models namely RNGk-εand SSTk-ωmodels parameters were fine-tuned accordingly in order to obtain almost comparable results generated by Dixon et al.’s models [1]. The simulation works were then extended to simulate flow of supercritical carbon dioxide. The second part of this paper, therefore, presents a comparative study of the turbulence models i. e. standardk-ε, RNGk-ε, realizablek-εand SSTk-ωmodels. This study emphasises on the predictions and evaluations of the velocity profiles at different flow regimes namely recirculation, recovery and near-wake. Simulations were carried out to determine the velocity profiles at subcritical and supercritical conditions by varying Reynolds numbers (2000 and 20,000), pressures (65 and 80 bar) and temperatures (283.15 and 308.15K). Simulation results indicate that the predicted results are consistent with the literature data. Interesting flow features were identified for all the simulations. The results of this study also reveal that the SSTk-ωturbulence model was able to better capture the flow characteristics near-wake of the sphere.