Application of Markov Chain Analysis and Tanks-in-Series Model in Mathematical Modeling of Impinging Stream Dryers

In spite of the fact that the principles of impinging stream reactors have been developed for more than half a century, the performance analysis of such devices, from a viewpoint of the mathematical modeling, has not been investigated extensively. In this study two models are proposed to describe the drying performance of particulate materials in two-impinging stream dryers. The models are developed based on the Markov chain analysis and the tanks-in-series model. The required parameters for each model are determined by using RTD data obtained in a two-impinging stream dryer and the governing equations are solved numerically. Comparison of the results of the models with available experimental data shows that the stirred tanks-in-series model successfully explains the drying behavior in impinging stream dryers. Nevertheless, the results of the model that is developed based on the Markov chain analysis are not in exact agreement with corresponding experimental data because of the extremely short residence time of the particles inside the dryer. Also, the effects of some operating parameters on the performance of such dryers are investigated. The results indicate that the drying efficiency of the dryer increases when solid-to-gas flow rate ratio, initial moisture content, and diameter of the particles decrease and when the temperature of the carrier gas increases.     

A physical description of solids transport in flighted rotary dryers

In this paper, a solids transport model for flighted rotary dryers is presented. Emphasis is placed on combining statistical and mechanistic modelling efforts to create a physically motivated compartment model involving pairs of perfectly mixed tank reactors linked in a series arrangement. Here, each tank pair, or cell, aims to physically describe a finite slice of a case study industrial rotary sugar dryer, and is hence governed primarily by flight geometry and dryer operational variables such as rotational speed and dryer inclination. Solids flow paths are structured to properly represent the different modes of transport in the rotary dryer, and values of transport coefficients are based on calculated rates of rotational and axial flows. A solids dispersion variable is used to correlate the model residence time distribution (RTD) prediction with available data from a tracer study conducted during industrial operation of a full-scale raw sugar dryer. RTD results from the model show intuitive responses to variations in solids feed rate, rotational speed and drum inclination.     

Prediction of Residence Time Distribution of Solid Wastes in a Rotary Dryer

The residence time distribution (RTD) of heterogeneous citrus waste particles was determined in a semi-pilot-scale rotary dryer with concurrent flow under several operational conditions. The experimental methodology was based on the stimulus-response technique, which consisted of injecting pulse-like tracers in the dryer feed stream. Measurements of RTD were performed to build up experimental curves that were numerically integrated to provide the mean residence time. A perfectly-stirred-tank in series model and a neural network model were derived. In addition, empirical and semi-empirical correlations from the literature were used to estimate residence time and the influence of operating conditions on this variable was investigated.     

Rotationszerstäuber für große Tropfen mit enger Größenverteilung zur Anwendung in kleinen Sprühtrocknern

A downscaled rotary atomizer, operated in the regime of laminar thread breakup, is presented. The atomizer allows for producing dropsizes of 70 – 200 µm and narrow size distribution. Due to the special design of the rotary atomizer the drops are detaching with low velocity and the spray can easily be deflected. The new technology can be applied in small scale spray dryers for the production of powder samples with quantities of several kg h^?1. Pilot scale spray dryers were equipped with this type of atomizer in order to carry out scale‐up experiments in small driers, but at particle sizes comparable to production‐scale conditions.     

Drying in a Pulsed-Fluid Bed with Relocated Gas Stream

ABSTRACT

Results of studies on cooling and drying of powdery and granulated material in a pulsed-fluid bed ( PFB) system with relocated gas stream presented here are related to hydrodynamics and kinetics of these processes. Generalized results in the form of dimensionless equations can be used to determine basic process parameters such as drying time, heat transfer coefficient, pulsed-fluidzation velocity. pressure drop, etc. Results of experimental investigations, supplemented with experiments carried out in a prototype industrial equipment, can be useful for dryer scale-up and are recommended for designing.

A comparison of technical and economic parameters of these dryers with the parameters of classical fluid-bed dryers shows many advantages of PFB systems, including, among othen. reduced gas consumption, uniform bed structure and stability of final parameters of the product.

Positive estimation of the operation and technological parameters suggests that PFB dryers with relocated gas stream can be applied successfully in industrial practice.     

Stochastic Modeling of the Particle Residence Time Distribution in an Opposed Multi‐Burner Gasifier

The gasification technology of impinging streams has been extensively applied to chemical production and power generation. Particle residence time distribution (RTD) is an important parameter required for modeling, designing and optimization of an impinging stream gasifier. A stochastic mathematical model based on the Markov chains model is developed for the opposed multi‐burner gasifier (OMBG), which closely describes the behavior of the flow pattern and particle RTD in the gasification system. The model simulates the motion of single particle moving in the gasifier using the Markov chains. The predicted results give a reasonable fit to the experimental data. This shows that the flow process of particles in the gasifier has recirculation eddies, which have a downward flow direction near the downflow core and an upward flow direction near the wall, but no short‐circuit. Finally, the effect of particle flux rate on the RTD is predicted, and the contrast between gas and particles RTDs at a laboratory scale and in an industrial gasifier are presented.     

Fortschritte in der Zerstäubungstrocknungs-Technologie

Progress in the technology of spray drying . Stringent quality demands on spray-dried goods have led to increasing use of nozzle spray dryers. In contrast to disk spray dryers, nozzle dryers yield microgranules and low-dust products directly. Although the process of nozzle spray drying is over 50 years old, the volume of available calculation material necessary for general application is sparse and limited mainly to special products or problems. This article presents new advances in the technology of nozzle spray dryers. An analytical formulation of the drying of a drop within the first drying phase decisive for granulation constitutes the basis of the general applicability of the fresh insights gained.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

A Three-Dimensional Simulation of a Spray Dryer Fitted with a Rotary Atomizer

Spray dryers fitted with rotary atomizers are commonly used in diverse industries to produce engineered powders on a large scale. Scale-up of such units is still largely empirical and based on prior experience and know-how. In the present study, a three-dimensional spray dryer with rotary atomizer is investigated numerically with a commercial CFD code. Continuous-phase, i.e., air, conservation equations are formulated in the Eulerian model while the droplet or particle equations are set up in the Lagrangian model. Two-way coupling between the continuous and dispersed phases is taken into account in the governing equations. The stochastic approach is used to predict the particle trajectories. The RNG k - ε turbulence model was used. Typical results, viz. air velocity, temperature, humidity profiles, and particle trajectories are presented and discussed. Compared with the pressure nozzle spray dryer, more volume of drying chamber is used effectively by the rotating disc type spray dryer. It is found that evaporation and drying take place mainly in the region and in the vicinity of first contact between air and spray. A parametric study is presented and, where appropriate, comparison is made with experimental data obtained with the simulated spray dryer.     

Thermodynamic characterization of single-stage spray dryers: Mass and energy balances for milk drying

Spray drying is an efficient unit operation applied in food drying that demands a high amount of energy compared to vacuum evaporation and membrane filtration. The objective of this work was to present a mathematical model-like basis for the construction of mass and energy balances. For this purpose, two lab-scale single spray dryers in milk drying with different evaporative capacities have been used as example. The values of the absolute humidity, mass and energy losses, energetic specific consumption (ESC), and the efficiency of the process were obtained by calculations developed in this work. The mathematical model was valid for the evaluation of mass and energy losses, and it allowed us to compare the efficiencies of spray dryers with different designs. From this model, it is possible to compare different drying processes and dryers.     

SCALE-UP OF SPRAY DRYERS WITH THE AID OF COMPUTATIONAL FLUID DYNAMICS

The scale-up of spray dryer chambers is difficult because of the complexity of gas and spray flow patterns. The principal concerns in designing a spray drying chamber are to ensure sufficient residence time for drying and to avoid particle-wall collisions. Dimensionless groups are of limited use because it is practically impossible to achieve dynamic similarity between small and large chambers. In the past, empirical, rather than theoretically based, rules generated by experience with existing plant have been used in the design and scale-up of spray dryer chambers but these models, because of their empirical nature, are limited in their range of applicability. Computational fluid dynamics (CFD) is potentially a powerful tool to aid spray dryer design allowing much more flexibility in design but because of the difficulties of modelling such complex phenomena, especially the gas turbulence, its predictions cannot, at present, be considered absolutely reliable and experimental validation of the results is required. However, by considering the principles of similarity, it is shown that validations carried out on pilot scale equipment under the correct conditions will prove the accuracy of CFD applied to spray dryers of any size.     

A Three-Dimensional Simulation of a Spray Dryer Fitted with a Rotary Atomizer

Abstract

Spray dryers fitted with rotary atomizers are commonly used in diverse industries to produce engineered powders on a large scale. Scale-up of such units is still largely empirical and based on prior experience and know-how. In the present study, a three-dimensional spray dryer with rotary atomizer is investigated numerically with a commercial CFD code. Continuous-phase, i.e., air, conservation equations are formulated in the Eulerian model while the droplet or particle equations are set up in the Lagrangian model. Two-way coupling between the continuous and dispersed phases is taken into account in the governing equations. The stochastic approach is used to predict the particle trajectories. The RNG k ? ? turbulence model was used. Typical results, viz. air velocity, temperature, humidity profiles, and particle trajectories are presented and discussed. Compared with the pressure nozzle spray dryer, more volume of drying chamber is used effectively by the rotating disc type spray dryer. It is found that evaporation and drying take place mainly in the region and in the vicinity of first contact between air and spray. A parametric study is presented and, where appropriate, comparison is made with experimental data obtained with the simulated spray dryer.     

Residence time distribution of solid particles in a continuous, high-aspect-ratio multiple-impeller stirred vessel

In this paper experimental information on the retention time distribution (RTD) of solid particles in a high-aspect-ratio vessel, stirred by three equally spaced Rushton turbines, is presented. The relevant data were obtained by a special technique named twin system approach (TSA) that greatly simplifies the handling of particle-laden streams and is therefore particularly suited for investigating particle RTD in flow systems. The technique fundamentals are first summarized, together with the data analysis procedure. This lastly requires a numerical deconvolution operation that is easily performed with the help of Z-transforms. Two different approaches for excluding the spurious contributions of the external piping required for the experimentation are tested and discussed.Particle tracing was performed by an effective particle-coating/optical-detection technique that allows particles recovery and reuse after each experimental run.The RTD data obtained indicate that a cascade of ideally mixed tanks with backflow results into very good agreement with experiment, with practically any number of tanks in series but one, provided that the backflow rate parameter is chosen accordingly. In all cases, the recirculation is large enough for the resulting flow model to be quite close to a single perfectly stirred vessel.     

SCALE-UP OF SPRAY DRYERS WITH THE AID OF COMPUTATIONAL FLUID DYNAMICS

Abstract

The scale-up of spray dryer chambers is difficult because of the complexity of gas and spray flow patterns. The principal concerns in designing a spray drying chamber are to ensure sufficient residence time for drying and to avoid particle-wall collisions. Dimensionless groups are of limited use because it is practically impossible to achieve dynamic similarity between small and large chambers. In the past, empirical, rather than theoretically based, rules generated by experience with existing plant have been used in the design and scale-up of spray dryer chambers but these models, because of their empirical nature, are limited in their range of applicability. Computational fluid dynamics (CFD) is potentially a powerful tool to aid spray dryer design allowing much more flexibility in design but because of the difficulties of modelling such complex phenomena, especially the gas turbulence, its predictions cannot, at present, be considered absolutely reliable and experimental validation of the results is required. However, by considering the principles of similarity, it is shown that validations carried out on pilot scale equipment under the correct conditions will prove the accuracy of CFD applied to spray dryers of any size.     

Estimation of the drying rate and moisture profiles in an industrial spray dryer by means of experimental investigations and a simulation study

A spray dryer simulation program is described. It is based on the known conservation laws and permits determination of temperature and moisture profiles and droplet trajectories inside spray dryers. An industrial spray dryer used in the manufacture of detergents serves as an example to demonstrate the applicability of the program; this approach required prior experimental determination of the flow field and an axial temperature profile. On the basis of a rough estimate of the drying rate in the spray dryer, good agreement was observed between experiment and simulation.     

A Novel Way to Measure the Concentration of a Spray in a Spray Dryer

A new experimental technique to capture milk concentrate droplets from inside a 150-kg powder/h pilot spray dryer is presented. The technique uses liquid nitrogen to capture the droplets in the dryer and to preserve their moisture content. The droplets are kept frozen until the moisture content can be measured. This technique can be applied to sample the sprays from any semi-commercial-scale spray dryer or similar apparatus.     

A Novel Way to Measure the Concentration of a Spray in a Spray Dryer

A new experimental technique to capture milk concentrate droplets from inside a 150-kg powder/h pilot spray dryer is presented. The technique uses liquid nitrogen to capture the droplets in the dryer and to preserve their moisture content. The droplets are kept frozen until the moisture content can be measured. This technique can be applied to sample the sprays from any semi-commercial-scale spray dryer or similar apparatus.     

Particle residence time distributions in circulating fluidised beds

This paper gives experimental measurements of the particle residence time distribution (RTD) made in the riser of a square cross section, cold model, circulating fluidised bed, using the fast response particle RTD technique developed by Harris et al. (Chem. Eng. J. 89 (2002a) 127). This technique depends upon all particles having phosphorescent properties. A small proportion of the particles become tracers when activated by a flash of light at the riser entry; the concentration of these phosphorescent particles can subsequently be detected by a photomultiplier. The influence of the solids circulation rate and superficial gas velocity on the RTD were investigated. The results presented are novel because (i) the experiments were performed in a system with closed boundaries and hence give the true residence time distribution in the riser and (ii) the measurement of the tracer concentration is exceedingly fast. The majority of previous studies have measured the RTD in risers with open boundaries, giving an erroneous measure of the RTD.Analysis of the results suggests that using pressure measurements in a riser to infer the solids inventory leads to erroneous estimates of the mean residence time. In particular, the results cast doubt on the assumption that friction and acceleration effects can be neglected when inferring the axial solids concentration profile from riser pressure measurements.An assessment of particle RTD models is also given. A stochastic particle RTD model was coupled to a riser hydrodynamic model incorporating the four main hydrodynamic regions observed in a fast-fluidised bed riser namely (i) the entrance region, (ii) a transition region, (iii) a core-annulus region and (iv) an exit region. This model successfully predicts the experimental residence time distributions.