Flow gases

A standard approach to modeling transport phenomena in the field of chemical engineering is based on convection-diffusion equations. Equations of that type describe the transport of a certain field quantity, for example momentum or enthalpy, as the sum of a convective and a diffusive term. A well-known example is the Navier-Stokes equation, which in the case of compressible media is given as 

The Navier-Stokes equation defines a set of three relations for four unknown quantities, iq, Uj, M3 and p. Another equation is needed to close the set, which is the equation of mass conservation  

Similar convection-diffusion equations to the Navier-Stokes equation can be formulated for enthalpy or species concentration. In all of these formulations there is always a superposition of diffusive and convective transport of a field quantity, supplemented by source terms describing creation or destruction of the transported quantity. There are two fundamental assumptions on which the Navier-Stokes and other convection-diffusion equations are based. The first and most fundamental is the continuum hypothesis it is assumed that the fluid can be described by a scalar or vector field, such as density or velocity. In fact, the field quantities have to be regarded as local averages over a large number of particles contained in a volume element embracing the point of interest. The second hypothesis relates to the local statistical distribution of the particles in phase space the standard convection-diffusion equations rely on the assumption of local thermal equilibrium. For gas flow, this means that a Maxwell-Boltzmann distribution is assumed for the velocity of the particles in the frame-of-reference co-moving with the fluid. Especially the second assumption may break dovm when gas flow at high temperature or low pressure in micro channels is considered, as will be discussed below. 

The principle quantity determining the flow regime of gases and deviations from the standard continuum description is the Knudsen number, defined as 

Kn is the ratio of two length scales, the mean free path of the gas molecules A and a characteristic length scale of the flow domain L, for example the channel diameter. For molecules interacting as hard spheres of diameter d, the mean free path is given as (see, e.g., [4]) 

---

It was noted earlier that dryers are quite difierent in character from both distillation and evaporation. However, heat is still taken in at a high temperature to be rejected in the dryer exhaust. The appropriate placement principle as applied to distillation columns and evaporators also applies to dryers. The plus/minus principle from Chap. 12 provides a general tool that can be used to understand the integration of dryers in the overall process context. If the designer has the freedom to manipulate drying temperature and gas flow rates, then these can be changed in accordance with the plus/minus principle in order to reduce overall utility costs. 

In such a plant the gas stream passes through a series of fractionating columns in which liquids are heated at the bottom and partly vaporised, and gases are cooled and condensed at the top of the column. Gas flows up the column and liquid flows down through the column, coming into close contact at trays in the column. Lighter components are stripped to the top and heavier products stripped to the bottom of the tower. 

The gaseous tracer method yields the equivalent piston flow linear velocity of the gas flow in the pipe without any constraints regarding flow regime under the conditions prevailing for flare gas flow. 

The method is based on the international standard ISO 4053/IV. A small amount of the radioactive tracer is injected instantaneously into the flare gas flow through e.g. a valve, representing the only physical interference with the process. Radiation detectors are mounted outside the pipe and the variation of tracer concentration with time is recorded as the tracer moves with the gas stream and passes by the detectors. A control, supply and data registration unit including PC is used for on site data treatment... 

The detailed consideration of these equations is due largely to Kozeny [50] the reader is also referred to Collins [51]. However, it is apparent that, subject to assumptions concerning the topology of the porous system, the determination of K provides an estimate of Ao- It should be remembered that Ao will be the external area of the particles and will not include internal area due to pores (note Ref. 52). Somewhat similar equations apply in the case of gas flow the reader is referred to Barrer [53] and Kraus and co-workers [54]. 

A sehematie diagram of a SIFT apparatus is shown in figure Bl.7.12. The instrument eonsists of five basie regions, the ion soiiree, initial quadnipole mass filter, flow tube, seeond mass filter and finally the deteetor. The heart of the instrument is the flow tube, whieh is a steel tube approximately 1 m long and 10 em in diameter. The pressure in the flow tube is kept of the order of 0.5 Torr, resulting in earrier gas flow rates of... 

The heat capacity of a gas at constant pressure is nonually detenuined in a flow calorimeter. The temperature rise is detenuined for a known power supplied to a gas flowing at a known rate. For gases at pressures greater than about 5 MPa Magee et al [13] have recently described a twin-bomb adiabatic calorimeter to measure Cy. 

The concept of macroscopic kinetics avoids the difficulties of microscopic kinetics [46, 47] This method allows a very compact description of different non-thennal plasma chemical reactors working with continuous gas flows or closed reactor systems. The state of the plasma chemical reaction is investigated, not in the active plasma zone, but... 

When a pure gas flows through a channel the accompanying fall in pressure is accounted for partly by acceleration of the flowing stream and partly by momentum transfer to the stationary walls. Since a porous medium may be regarded as an assembly of channels, similar considerations apply to flow through porous media, but in the diffusional situations of principal interest here accelerational pressure loss can usually be neglected. If more than one molecular species is present, we are also interested in the relative motions of the different species, so momentum transfers by collisions between different types of molecules are also important. 

To appreciate the questions raised by Knudsen s results, consider first the relation between molar flow and pressure gradient for a pure gas flowing through a porous plug, rather than a capillary. The form predicted by the dusty gas model can be obtained by setting = 1, grad = 0 in equation... 

The technique just described requires the porous medium to be sealed in a cell, so It cannot be used with pellets of irregular shape or granular material. For such materials an alternative technique Introduced by Eberly [64] is attractive. In Eberly s method the porous pellets or granules are packed into a tube through which the carrier gas flows steadily. A sharp pulse of tracer gas is then injected at the entry to the tube, and Its transit time through the tube and spreading at the exit are observed. A "chromatographic" system of this sort is very attractive to the experimenter,... 

A variable-size simplex optimization of a gas chromatographic separation using oven temperature and carrier gas flow rate as factors is described in this experiment. 

A common liquid chromatography column is somewhat larger in diameter than a nanocolumn. Consequently, the flow of solution along such a column is measured in terms of one or two milliliters per minute, and spraying requires the aid of a gas flowing concentrically around the end of the inlet tube (Figure 10.2c). An electrical potential is still applied to the end of this tube to ensure adequate electrical chaiging of the droplets. 

A plasma of electrons, ions, and neutrals produced in gas flowing through concentric tubes is maintained and heated to 5000 to 8000 K by inductive coupling to a high (radio) frequency... 

If a gas flows over the surface of a liquid, certain effects ensue. Only the relative velocity of the liquid surface and gas is important in giving rise to nebulization. Thus, some pneumatic nebulizers... 

---