Turbulent liquid flows

Duties other than turbulent liquid flow 26/442... 

Series Scaleup of Turbulent Liquid Flows. For series scaleup of an incompressible fluid, the tube length is increased in proportion to the desired increase in throughput. Equation (3.31) is satisfied with Sr = Stubes = 1 and Sl = S. 

Liquid core temperature and velocity distribution analysis. BankofT (1961) analyzed the convective heat transfer capability of a subcooled liquid core in local boiling by using the turbulent liquid flow equations. He found that boiling crisis occurs when the core is unable to remove the heat as fast as it can be transmitted by the wall. The temperature and velocity distributions were analyzed in the singlephase turbulent core of a boiling annular flow in a circular pipe of radius r. For fully developed steady flow, the momentum equation is given as... 

An important class of stirred tank applications involves suspending discrete solid particles in a continuous liquid phase where the turbulent-liquid-flow... 

The dominant role of asperity contact is also apparent from analysis of the texture of polished surfaces. Figure 9 illustrates a typical post CMP surface as examined via atomic force microscopy (AFM). Surface texture is composed of innumerable randomly oriented nanogrooves of a width and depth consistent with traveling Hertzian loaded contact [12] particle bombardment during turbulent liquid flow produces profoundly different texture. All classes of semiconductor materials examined show similar textures, indicating the general nature of the process. From the data to date, it appears that asperity contact is the dominant wear mechanism in CMP. 

The transition from laminar to turbulent liquid flow was reported to... 

When a gas stream is introduced into a turbulent liquid flow in a motionless mixer, the gas is broken up into bubbles. The breakup is due mainly to the turbulent shear force of the liquid but also partly to the collision between gas and the leading edge of an element. 

A control valve can also be viewed as variable-area flow meter. Therefore, smart valves can measure their own flow by solving the appropriate valvesizing equation. For example, in the case of turbulent liquid flow applications, where the valve capacity coefficient... 

Jenne, M. and Reuss, M. (1999), A critical assessment on the use of k-e turbulence model for simulation of the turbulent liquid flow induced by a Rushton turbine in baffled stirred tank reactor, Chem. Eng. ScL, 54, 3921-3941. 

Baresi A.A., Experimental investigation of interaction between turbulent liquid flow and solid particles and its effects on... 

Osenbroch LKH (2004) Experimental and Computational Study of Mixing and Fast Chemical Reactions in Turbulent Liquid Flows. PhD Thesis, Aalborg University, Esbjerg... 

Nevertheless, the turbulent dispersion force acting on bubbles in turbulent liquid flow is commonly modeled using the gradient hypothesis (e.g., [20]) ... 

Kuboi R, Komasawa I, Otake T (1972) Behavior of dispersed particles in turbulent liquid flow. J Chem Eng Japan 5 349-355... 

Overall heat transfer coefficient is either a function of (1) local position only (laminar gas flow) U, (2) temperature only (turbulent liquid flow) U, or (3) both local position and teirj perature (a general case) U. U(T) in Urepresents a position average overall heat transfer coefficient evaluated at a local temperature. Integration should be performed numerically and/ or can be approximated with an evaluation at three points. The values of the correction factor K are presented in Fig. 17.29. 

For confirmation of adequacy of chosen technique for experimental determination of distributions of reagents residence times in tubular turbulent apparatus numerical calculation of three-dimensional turbulent liquid flow with the use of CFD soft PHOENICS was carried out. 

The transport equations describing the instantaneous behavior of turbulent liquid flow are three Navier-Stokes equations (transport of momentum corresponding to the three spatial coordinates r, z, in a cylindrical polar coordinate system) and a continuity equation. The instantaneous velocity components and the pressure can be replaced by the sum of a time-averaged mean component and a root-mean-square fluctuation component according to Reynolds. The resulting Reynolds equations and the continuity equation are summarized below ... 

The numerical solution of equations for turbulent liquid flows using the C-e turbulence model (Equations 2.1-2.12) confirms this assumption [39, 40]. Formation of an... 

As for gas-liquid and gas-solid sterns, the liquid depth must be sufficiently great to minimize the suspending effects of turbulent liquid flow. As discussed in S on 3.2, the particles will not be resuspended provided the flow velocity is less than about 20 times the terminal velocity. To be conservative the flow velocity should be 10 times the particle terminal velocity. Thus, the flow area (Ap) is given by... 

Hjertager LK, Hjertager BH, Solberg T (2002) CFD modelling of fast chemical reactions in turbulent liquid flows. Com and Chem Eng 26(4-5) 507-515... 

Cp constant for determining the total liquid hold-up of packings (for turbulent liquid flow)... 

Equation (4-32) was used to determine the liquid hold hL for turbulent liquid flow Rcl > 2. This equation is obtained by substituting the Froude number of the liquid, according to Eq. (4-31), into Eq. (4-26). 

Discussion of Experimental Results - Turbulent liquid Flow... 

The evaluation of the large amount of experimental hquid hold-up data leads to the conclusion that turbulent liquid flow can be expected in packed columns at Rep > 2, whilst laminar liquid flow is expected at Rcl < 2. This corresponds approximately to the model presented by Gelbe [22]. 

Comparing Calculated and Experimental Values for Turbulent Liquid Flow... 

Daughter bubbles can be generated by introducing a mother bubble into a highly turbulent liquid flow. Martinez-Bazan et al. [9] found that the bubble size probability density function of the daughter bubbles depends not only on the size of the mother bubble, but also on the value of the dissipation rate of turbulent kinetic energy. 

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