Flow characteristic scale

Scale-Up Principles. Key factors affecting scale-up of reactor performance are nature of reaction zones, specific reaction rates, and mass- and heat-transport rates to and from reaction sites. Where considerable uncertainties exist or large quantities of products are needed for market evaluations, intermediate-sized demonstration units between pilot and industrial plants are usehil. Matching overall fluid flow characteristics within the reactor might determine the operative criteria. Ideally, the smaller reactor acts as a volume segment of the larger one. Elow distributions are not markedly influenced by... 

All scales reqmre continuous monitoring to assure that the desired set weight is maintained and does not drift off because of changes in product bulk-density or flow characteristics. Microprocessors can perform this task automatically. 

The PHI-TEC or VSP bench scale apparatus can be employed to determine information about the self-heat rate and vapor disengagement when this is not readily available. Additionally, the VSP equipment can be used for flashing flow characteristics using a special bottom vented test cell. Here, the flowrate, Gq (kg/sm ), is measured... 

Z. Ropiolek, S. Mierzwinski, M. Hurnik, j. Wojciechowski. Air flow characteristic in scale models of room ventilation. In Roomvent 9H Proceedings of the 6th International Conference on Air Distribution in Rooms, vol. 1, pp. 287-293.. Stockholm, Sweden, 1998. 

Thus, the available data related to transition in circular micro-tubes testify to the fact that the critical Reynolds number, which corresponds to the onset of such transition, is about 2,000. The evaluation of critical Reynolds number in irregular micro-channels will entail great difficulty since this problem contains a number of characteristic length scales. This fact leads to some vagueness in definition of critical Reynolds number that is not a single criterion, which determines flow characteristics. 

Assuming steady state in Eqs. (10.8-10.10) and (10.18-10.20), we obtain the system of equations, which determines steady regimes of the flow in the heated miero-channel. We introduce values of density p = pp.o, velocity , length = L, temperature r = Ti 0, pressure AP = Pl,o - Pg,oo and enthalpy /Jlg as characteristic scales. The dimensionless variables are defined as follows ... 

In Equation 5.2.2, it is assumed that acoustic wavelengths A are large when compared with any of the characteristic scales of the flow (A L) and that the measurement point r is far from the source region (r /l). The previous expression provides the sormd pressure in the far-field for a compact source, but it can be used indifferently for premixed or nonpremixed flames [30]. 

If the length scales associated with changes in velocity are normalized by Vv (characteristic length scale for Stokes flow), length scales associated with changes in curvature are normalized by Ss (typical striation thickness) and velocities normalized by V (a characteristic velocity), then the normal stress condition becomes,... 

In many applications, due to the large value of k, the first reaction is essentially instantaneous compared to the characteristic flow time scales. Thus, if the transport equation is used to solve for Y, the chemical-source term iS) will make the CFD code converge slowly. To avoid this problem, Y can be written in terms of by setting the corresponding reaction-rate expression (S ) equal to zero as follows ... 

Wall shear stress-flow characteristic curves and scale-up for laminar flow... 

Batch operation in a larger scale - in laboratory or even industrial applications - frequently is reahzed using a flowthrough cell with optimized flow characteristics, which is coupled by circulating pumps with reservoirs that contain the reaction solutions. 

The flame lift-off height, which is related to the ignition distance, was inversely affected by the excitation frequency. Since the flow time scale decreased with increasing frequency, the data were plotted as a function of the Damkohler number in Fig. 29.14, where the characteristic flow time scale was estimated by large-eddy turnover time as 1/17 and the characteristic chemical reaction time was computed using an ignition delay model [21] for ethylene jet. While the results did not show any evidence of critical Damkohler number, the range... 

Processes that involve the reaction of gases and solids are extremely difficult to handle mainly due to solid flow difficulties (Knowlton, 2000). The difficulty in the scale-up of these reactors constitutes then main disadvantage. The maximum scale-up factor for fluidized beds is usually between 50 and 100, whereas for fixed beds it could reach the value of 10,000. This is due to the fact that the flow characteristics are very different in the small and the large reactor the bubble diameter does not change upon scale-up, whereas reactor diameter does. 

A new set of flow characteristics gradually emerges as the concentration of polymer becomes large. The solution viscosity loses its direct dependence on solvent viscosity and comes to depend on the product of two parameters a friction factor C which is controlled solely by local features such as the free volume (or alternatively the segmental jump frequency), and a structure factor F which is controlled by the large scale structure and configuration of the chains (16) ... 

The distinguishing characteristics of the stagnation-flow subcases depend on the domain and on the rotation. The characteristic scales are different for the subcases, but the equations themselves are the same. The boundary conditions also differ among the subcases. Table 6.1 shows the applicable scales and nondimensional groups that apply to each of the four subcases. 

Most of this is because in a abort cylindrical tank, the entering fluid does not move through the tank with a uniform interface. The poor flow characteristics also are due partly to the deposition of solids, and scale, to corrosion of spreader pipes, etc. 

Previous workers have studied the influence of the ratio of the cross-section area of the downcomer to the riser [4,5], the reactor height [6,7], the gas-liquid separator configuration [8], and the distributor type and location [9]. All these affect the flow characteristics and mass transfer. Most previous works focus on global parameters, such as the liquid circulation velocity [10-13] and the average gas holdup in the riser [14-16]. Although much work has been carried out on EL-ALRs, the proper design and scale-up of an EL-ALR is still difficult because any variation in the physical properties of the gas or the liquid and the reactor structural feathers can have a considerable effect on the hydrodynamics... 

Time pulsing can be characterized by the Strouhal number (St), which is a dimensionless parameter describing the ratio of the flow characteristic time scale (L/V) to the pulse time period (1/j) [Eq. (1.8)] [26], where Lis the hydraulic diameter, V the average velocity in the outlet channel and/the pulsing frequency. For a pulsing frequency of 5 Hz, a Strouhal number of 0.375 derives. 

Other work has been mainly concerned with the scale-up to pilot plant or full-scale installations. For example, Beltran et al. [225] studied the scale-up of the ozonation of industrial wastewaters from alcohol distilleries and tomato-processing plants. They used kinetic data obtained in small laboratory bubble columns to predict the COD reduction that could be reached during ozonation in a geometrically similar pilot bubble column. In the kinetic model, assumptions were made about the flow characteristics of the gas phase through the column. From the solution of mass balance equations of the main species in the process (ozone in gas and water and pollution characterized by COD) calculated results of COD and ozone concentrations were determined and compared to the corresponding experimental values. 

Four characteristic times are involved those of reaction, tR, diffusion, tp, mixing (local motion), tjj, and macromixing (gross flow patterns), "t. The relative ratios of these characteristic times (Dai, Dan Pe) determine the reactor performance. tc is a characteristic scaling time that is chosen to be tp for "fast reactions" and tR for "slow reactions"(5). 

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