Hydrodynamics axial

Authors Axial dispersion Axial hydrodynamic gradients... 

Zheng Y, Zhu J-X, Wen J, Martin SA, Bassi AS, Margaritis A. The axial hydrodynamic behavior in a liquid olid circulating fluidized bed. Can J Chem Eng 77 284-290, 1999. 

Vibration peaks at specific speeds/high axial vibration is often present. Siib-harmomc Usually occurs as a result of loose components or as a result of aerodynamic or hydrodynamic excitations areas to be investigated for coiTection are seals, thrust clearance, couplings, and rotor/stator clearance... 

Heat transfer in micro-channels occurs under superposition of hydrodynamic and thermal effects, determining the main characteristics of this process. Experimental study of the heat transfer in micro-channels is problematic because of their small size, which makes a direct diagnostics of temperature field in the fluid and the wall difficult. Certain information on mechanisms of this phenomenon can be obtained by analysis of the experimental data, in particular, by comparison of measurements with predictions that are based on several models of heat transfer in circular, rectangular and trapezoidal micro-channels. This approach makes it possible to estimate the applicability of the conventional theory, and the correctness of several hypotheses related to the mechanism of heat transfer. It is possible to reveal the effects of the Reynolds number, axial conduction, energy dissipation, heat losses to the environment, etc., on the heat transfer. 

Micromixing Models. Hydrodynamic models have intrinsic levels of micromixing. Examples include laminar flow with or without diffusion and the axial dispersion model. Predictions from such models are used directly without explicit concern for micromixing. The residence time distribution corresponding to the models could be associated with a range of micromixing, but this would be inconsistent with the physical model. 

Scheraga-Mandelkern equations (1953), for effective hydrodynamic ellipsoid factor p (Sun 2004), suggested that [rj] is the function of two independent variables p, the axial ratio, which is a measure of shape, and Ve, the effective volume. To relate [r ] to p and Ve, introduced f, the frictional coefficient, which is known to be a direct function of p and Ve. Thus, for a sphere we have... 

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

Open-channel monoliths are better defined. The Sherwood (and Nusselt) number varies mainly in the axial direction due to the formation ofa hydrodynamic boundary layer and a concentration (temperature) boundary layer. Owing to the chemical reactions and heat formation on the surface, the local Sherwood (and Nusselt) numbers depend on the local reaction rate and the reaction rate upstream. A complicating factor is that the traditional Sherwood numbers are usually defined for constant concentration or constant flux on the surface, while, in reahty, the catalytic reaction on the surface exhibits different behavior. 

The UASB tractor was modeled by the dispensed plug flow model, considering decomposition reactions for VFA componaits, axial dispersion of liquid and hydrodynamics. The difierential mass balance equations based on the dispersed plug flow model are described for multiple VFA substrate components considaed... 

The effect could be elucidated by ad tional axial dispersion characterization of GPC 1. An alternate approach is to utilize only THF in botii GPC 1 and 2 and to observe whether slices exit at the expected hydrodynamic volume. 

The flow domain of TCP can be described by two dimensionless hydrodynamic parameters, corresponding to the rotational speed of the inner cylinder and the imposed axial flow rate the Taylor number, To, and the axial Reynolds number, Re, respectively ... 

This section focuses on steady and unsteady hydrodynamic modes that emerge as the rotational speed of the inner cylinder (expressed by Ta) and pressure-driven axial flow rate (scaled by Re) are varied, while the outer cylinder is kept fixed. These modes constitute primary, secondary and higher order bifurcations, which break the symmetry of the base helical Couette-Poiseuille (CP) flow and represent drastic changes in flow structure. Figure 4.4.2 presents a map of observed hydrodynamic modes in the (Ta, Re) space, and marks the domain where all of the hydrodynamic modes that interest us appear. We will return to this figure shortly. 

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... 

Flow boiling of other alkali metals CHF data for other alkali metals were reported by Fisher et al. (1964, 1965), who tested rubidium and cesium in axial and swirl flow and potassium in swirl flow. The data were correlated by postulating a mist or fog flow model for the hydrodynamic situation in the heated section in which CHF occurs. These investigations were motivated by the potential use of alkali metals as Rankine cycle working media in space applications and have not been pursued further, because there is no longer interest in such concepts. 

If the vapor-phase temperature is to be evaluated from the Clausius-Clapeyron equation, the pressure in the two-phase tubular contactor must be known at each axial position. This need once again illustrates the necessity of obtaining an understanding of the hydrodynamics of two-phase systems in order to carry out the design of heat-transfer contactors. 

The interaction of parametric effects of solid mass flux and axial location is illustrated by the data of Dou et al. (1991), shown in Fig. 19. These authors measured the heat transfer coefficient on the surface of a vertical tube suspended within the fast fluidized bed at different elevations. The data of Fig. 19 show that for a given size particle, at a given superficial gas velocity, the heat transfer coefficient consistently decreases with elevation along the bed for any given solid mass flux Gs. At a given elevation position, the heat transfer coefficient consistently increases with increasing solid mass flux at the highest elevation of 6.5 m, where hydrodynamic conditions are most likely to be fully developed, it is seen that the heat transfer coefficient increases by approximately 50% as Gv increased from 30 to 50 kg/rrfs. 

Concerning the hydrodynamics and the dimensioning of the test reactor, some rules of thumb are a valuable aid for the experimentalist. It is important that the reactor is operated under plug-flow conditions in order to avoid axial dispersion and diffusion limitation phenomena. Again, it has to be made clear that in many cases testing of monolithic bodies such as metal gauzes, foam ceramics, or monoliths used for environmental catalysis, often needs to be performed in the laminar flow regime. 

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