Introduction

The main purpose of this chapter is to briefly recapitulate what is learned in a first course in classical thermodynamics. As defined in Chapter 1, thermodynamics is the science of relationships among heat, work and the properties of the system. Our first task, therefore, will be to define the keywords in this definition: system, heat, work, and properties. The relationships among these quantities are embodied in the first and the second laws of thermodynamics. The laws enable one to evaluate change in the states of the system, as identified by the changes in its properties. In thermodynamics, this change is called a process, although, in common everyday language, the processes may be identified with terms such as cooling, heating, expansion, compression, phase-change (melting, solidification, evaporation, condensation), or chemical reaction (such as combustion or catalysis). As such, it is important to define two additional terms: state and process.

The last point is of particular importance, because the statements of thermodynamic problems are often couched in everyday language. However, with the help of the definitions given in the next section, it will become possible not only to to deal with all processes in a generalized way but also to recognize whether a given process can be dealt with by thermodynamics. Thus, adherence to definitions is very important in thermodynamics. Establishing a connection between the problem statement in everyday language and its mathematical representation is best helped by drawing a sketch by hand.

Introduction

Our interest now is to study chemical reactions in the presence of fluid motion so that fluid mixing effects can be incorporated in the determination of the product composition. In the study of transport phenomena in moving fluids, the fundamental laws of motion (conservation of mass and Newton's second law) and energy (first law of thermodynamics) are applied to an elemental fluid known as the control volume (CV).

The CV may be defined as an imaginary region in space, across the boundaries of which matter, energy, and momentum may flow. It is a region within which a source or a sink of the same quantities may prevail. Further, it is a region on which external forces may act.

In general, a CV may be large or infinitesimally small. However, consistent with the idea of a differential in a continuum, an infinitesimally small CV is considered. Thus, when the laws are to be expressed through differential equations, the CV is located within a moving fluid. In the Eulerian approach, the CV is assumed fixed in space and the fluid is assumed to flow through and around the CV. The advantage of this approach is that any measurements made using stationary instruments (velocity, temperature, mass fraction, etc.) can be compared directly with the solutions of differential equations.

Introduction

Diffusion flames were introduced in the previous chapter (see Figure 8.2) as flames in which fuel and air are physically separated. Diffusion flames occur in the presence of flowing or stagnant air such that the fuel moves outward and air moves inward to create a reaction zone at the flame periphery. Figure 9.1 shows a typical laminar diffusion flame configuration in stagnant surroundings.

Fuel issues from a round nozzle (diameter D) with axial velocity U0 into stagnant surroundings. As there are no effects present to impart three-dimensionality to the flow, the flow is two-dimensional and axisymmetric. The fuel burns by drawing air from the surroundings forming a flame that is visible to the eye. The flame develops to length Lf and assumes a shape characterized by flame radius rf(x), which is a function of axial distance x.

The energy release is thus principally governed by the mixing process between air and fuel. As such, the chemical kinetics are somewhat less important, being very fast. For this reason, diffusion flames are often termed physically controlled flames. Flames formed around burning volatile liquid droplets or solid particles (whose volatiles burn in the gaseous phase) are thus physically controlled diffusion flames.

The two main objectives of developing a theory of diffusion flames are to predict

1. The flame length Lf and

2. The shape of the flame, that is, the flame radius rf(x).

Introduction

As mentioned in Chapter 1, the main purpose of combustion science is to aid in performance prediction or design of practical equipment, as well as to aid in prevention of fires and pollution. This is done by analyzing chemical reactions with increasing refinements, namely, stoichiometry, chemical equilibrium, chemical kinetics, and, finally, fluid mechanics. Such, analyses of practical equipment are accomplished by modeling. The mathematical models can be designed to varying degrees of complexity, starting from simple zero-dimensional thermodynamic stirred-reactor models to one-dimensional plug-flow models and, finally, to complete three-dimensional models. At different levels of complexity, the models result in a system of a few algebraic equations, a system of ordinary differential equations, or a system of partial differential equations.

Practical combustion equipment typically has very complex geometry and flow paths. The governing equations of mass, momentum, and energy must be solved with considerable empirical inputs. The size of the mathematical problem is dictated by the reaction mechanism chosen and by the chosen dimensionality of the model. The choice of the model thus depends on the complexity of the combustion phenomenon to be analyzed, the objectives of the analysis, and the resources available to track the mathematical problem posed by the model.

In this chapter, a few relevant problems are formulated and solved as case studies to help in understanding of the art of modeling as applied to design and performance prediction of practical combustion equipment.

Introduction

In a system consisting of a liquid and solids dispersed within it, such as slurries and pasty materials, the structure and characteristic properties are defined by the solids concentration, shape, and size distribution. A variety of solid–liquid mixtures, such as suspensions, dispersions, sludges, and pulps, is included in these categories. Solutions with a solute that crystallizes out on evaporation are also included. The drying of solutions in beds of inert particles of spoutable size was developed in the late 1960s at the Lenigrad Institute of Technology for applications in which the dried solids are ultimately required in the form of a fine powder. Spouting with inert particles was applied successfully by the Leningrad group to dry organic dyes and dye intermediates, lacquers, salt and sugar solutions, and various chemical reagents. Since then, a large number of materials have been successfully dried, demonstrating the applicability and versatility of this method. A partial list of dried materials is given in Table 12.1.

Drying process

Description

The drying of pastes (or slurries or solutions, all referred to henceforth in this chapter generically as pastes) is performed in the presence of inert particles, which are both a support for the paste and a source of heat for drying. The paste may be atomized or dropped into the bed by a nozzle or dropping device. An example of an experimental facility for research in paste drying is shown in Figure 12.1.

Principle of mechanical spouting

One of the main advantages of the conventional spouted bed is the characteristic recirculation particle mixing provided by a high-velocity gas jet through a nozzle at the conical bottom of the equipment. This ensures very effective “quasi-countercurrent” gas–solid contact. Because of the circulation of the particles, local overheating within the bed can be avoided and thus uniform product quality can be effected.

Disadvantages include fluid motive-power consumption that occurs especially at the start of operation, but also persists under stable conditions owing to the vertical particle transport in the spout and the high pressure drop of the nozzle. In addition, conditions for heat and mass transfer can be obtained only within a limited range of gas flowrate because the velocity of the gas, usually air, is determined mainly by the size and density of the particles.

These disadvantages of the spouted bed can be eliminated, while keeping its advantages, by the mechanically spouted bed (MSB), in which the most important characteristics of conventional spouted beds can be found. According to the developed prototype, the typical spouted circulating motion is ensured by an open conveyor screw, installed along the vertical axis of the device, independent of the airflow rate. The diameter of the screw is nearly equal to the diameter of the gas channel (spout), around which a similar dense sliding layer (annulus) is formed.

This chapter focuses on analyzing the design of spouted bed dryers for particulate solids whose drying curve is characterized by the falling rate period only (Figure 11.1a), as well as those displaying both constant and falling-rate drying periods (Figure 11.1.b).

Because compromise among costs, efficiency, product quality, and a clean environment is required in the design and operation of any process equipment, simulation and optimization of the drying process are the best ways to obtain the appropriate dimensions and operating conditions for a dryer and its ancillary equipment. This chapter starts with a brief review of recent developments in the drying of particulate solids in spouted beds (SBs). A concise analysis of various possible dryer design models follows. Three different model levels, which have been used for modeling SB drying of particulate solids, are considered.

Various spouted bed dryers for particulate solids

The SB technique, originally developed by Mathur and Gishler for drying wheat, has found numerous applications, not only for drying of particulate solids, but also in combined operations, such as drying–powdering, drying–granulation, drying–coating, and drying–extraction. Therefore this chapter also provides information for the design of such combined operations, which are considered elsewhere in this book.

This chapter is a systematic summary of the characteristics and applications of spouted beds, called powder–particle spouted beds (PPSBs), consisting of fine powders contacted with coarse particles. The main aspect of conventional spouting that is relevant to PPSBs is the final elutriation of the dried or partially dried fines, often produced by attrition, from a coarse particle bed.

Figure 10.1 shows the operating conditions of several kinds of fluidization for particles of density 2500 kg/m, according to Geldart's classification, indicating also the fine particle size and gas velocity ranges in four reported studies of PPSBs. The two solid lines show the superficial gas velocity at minimum fluidization (Umf) and the terminal velocity of a single particle (Ut). In a PPSB, as one of the operating conditions, the gas velocity is determined by the diameter and density of the coarse particles and is usually greater than Ut of the fine powders, so the fines are elutriated from the coarse particle bed.

Description of powder–particle spouted beds

Conceptual illustrations of a PPSB are shown in Figure 10.2. Group D particles in Geldart's classification usually act as the coarse particles and Group A, B, or C particles as the fine powders. As shown in Figure 10.2a, for a Group C–D particle system, the coarse particles in the bed are first spouted and raw powders (fine particles) in a dry or partially dried state are then continuously fed to the bottom of the spouted bed with spouting gas.

Introduction

In a bed packed with particles, the introduction of an upward-flowing fluid stream into the column through a nozzle or opening in a flat or conical base creates a drag force and a buoyancy force on the particles. A cavity forms when the fluid velocity is high enough to push particles aside from the opening, as illustrated in Figure 2.1(a). A permanent and stable vertical jet is established if the nozzle-to-particle-diameter ratio is less than 25 to 30. Further increase in fluid flow rate expands the jet, and an “internal spout” is established, as in Figure 2.1(b). Eventually, the internal spout breaks through the upper bed surface, leading to the formation of an external spout or fountain, as in Figure 2.1(c). Such an evolution process to a spouted bed, involving cavity formation, internal spout/jet expansion, and formation of an external spout, was well documented in the 1960s.

Figure 2.2 shows the evolution of measured total pressure drop in a half-circular conical bed for 1.16-mm-diameter glass beads and ambient air, starting with a loosely packed bed, Run 1. It is seen that the total pressure drop increases with increasing gas velocity in the gas flow ascending process (shown by closed squares), and reaches a peak value before decreasing to approximately a constant value with a further increase in the gas velocity.

The spout-fluid bed is a very successful modification to the conventional spouted bed. It reduces some limitations of spouting and fluidization by combining features of spouted and fluidized beds. In spout-fluid beds, in addition to supplying spouting fluid through the central nozzle, auxiliary fluid is introduced through a porous or perforated distributor surrounding the central orifice. Compared with spouted beds, spout-fluid beds obtain better gas–solid contact and mixing in the annular dense region and reduce the likelihood of particle agglomeration, dead zones, and sticking to the wall or base of the column. However, the hydrodynamics of spout-fluid beds are more complex than those of conventional spouted beds. This chapter briefly presents up-to-date information on the fundamentals and applications of spout-fluid beds without draft tubes, based on the limited reported work.

Hydrodynamic characteristics

Flow regimes and flow regime map

Different flow regimes occur in a spout-fluid bed when the central spouting gas flowrate and the auxiliary gas flowrate are adjusted. A schematic representation of familiar flow regimes is presented in Figure 6.1. These are the fixed bed (FB), internal jet (IJ), spouting with aeration (SA), jet in fluidized bed with bubbling (JFB), jet in fluidized bed with slugging (JFS), and spout-fluidizing (SF) regimes.