Pseudo-turbulence

If the solid particles are very small (e.g., typically less than 100 /xm) and/or not tremendously denser than the fluid, and/or the flow is highly turbulent, the mixture may behave as a uniform suspension with essentially continuous properties. In this case, the mixture can be described as a pseudo singlephase uniform fluid and the effect of the presence of the particles can be... 

Venneker, B. C. H., Turbulent flow and gas dispersion in stirred vessels with pseudo plastic fluids , Ph.D. Thesis, Delft University of Technology, Delft, Netherlands (1999). 

For homogeneous turbulent flows (no walls, periodic boundary conditions, zero mean velocity), pseudo-spectral methods are usually employed due to their relatively high accuracy. In order to simulate the Navier-Stokes equation,... 

Fluidized-bed combustion (FBC) is a different technology from conventional pulverized-coal-fired boilers. A mixture of powdered rather than pulverized coal and a sorbent (usually limestone) are injected directly into the furnace and burned while suspended on a bed of high-velocity air. The turbulent mixing of coal and sorbent causes the solids to behave as a pseudo-fluid, enhancing heat generation and transfer at much lower temperatures (800-900 °C) compared to conventional pulverized-coal-fired furnaces (1500 °C) (US Department of Energy 1992). 

The last terms in each of Eqn. (5.2-9) and Eqn. (5.2-10) represent the divergence of the deviatoric stress including viscosity and pseudo-turbulence. The quantities /n L and uG are effective viscosities of each phase including bulk and shear viscosities. Fl and Fg represent the volume-averaged forces exerted on the liquid-and gas-phase (respectively) by the other phases across the common interfaces. 

Another variant devised by Martem Yanov et al. [16] ensures strong electrolyte stirring for generating turbulent fluctuations in solution. Assuming a pseudo hydrodynamical white noise, the responding current can be analyzed in the frequency domain to provide the same information as that obtained from any of the techniques mentioned above. 

Mercier P, Tochon P. Analysis of turbulent flow and heat transfer in compact heat exchangers by a pseudo-direct numerical simulation. In Shah RK, ed. Compact Heat Exchanger for the Process Industry. Begell House, 1997 223-230. 

Hence, the gas phase conversion for a pseudo-first order reaction in the churn turbulent regime can be calculated if the fractional gas holdups, rise velocities, and interfacial areas for the two bubble classes as well as the physicochemical data are known. 

The two bubble class model is applied here to the absorption of CO2 in NaOH, which conforms to a fast pseudo-first order reaction under certain operating conditions (15). In the data reported by Schumpe et al. ( 7 ), COo was absorbed during cocurrent flow in NaOH solution in a 0.102 m diameter bubble column. The gas phase consisted of approximately 10 vol % of CO2 in N2. The gas velocities ranged from 0.025 to 0.15 m/s. Since the churn turbulent regime prevailed for gas velocities greater than approximately 0.07 m/s, only the data in the range 0.07 m/s to 0.15 m/s were considered. 

The two-phase approach can be used to analyze the interaction between the fluid and individual particles, though it is not convenient for analyzing turbulent and time-dependent behavior of the system. Generally speaking, and in the author s opinion, the pseudo-fluid approach is more suitable for dilute two-phase flow, while the two-phase approach is more suitable for dense fluidization. 

Van Deemter (1980) compared the kinetic constant fcc calculated from A and E obtained in the laboratory with the pseudo-kinetic constants k c from several commercial and pilot plants, and found that the values for k c are always lower than those corresponding to kc, as shown in Fig. 13. It appears, therefore, that the process of coke burning is principally controlled by gas interchange and mass transfer in the bubbling or turbulent bed. Fast... 

Expanding the turbulent diffusion term, one obtains an additional pseudo-advective term ... 

In practical combustion systems, the predominant mode of heat transfer is usually not molecular conduction, but turbulent diffusion, except at the boundaries and the flame front. Conduction is the only mode of heat transfer through refractory walls, and it determines ignition and extinction behaviors of the flame. Turbulent diffusion, an apparent or pseudo conduction mechanism arising from turbulent eddy motions, will be discussed in Section 4.4. The relations from the theory of conduction heat transfer15-17 can be used to evaluate heat losses through furnace walls and load zones, and through the pipe walls inside boilers and heat exchangers, etc. 

Clearly, the reaction order and form of the empirical rate law could not have been predicted from the overall reaction. If we hold P , constant, for example assuming oxidation is in a turbulent, aerated stream, then the reaction is said to be pseudo first-order. Another example of a second-order rate is formation of the FeSOJ complex (see Section 2.7.1). 

To parameterize the new quantities occurring in these equations a few semi-empirical relations from the literature were adopted. The asymptotic value of bubble induced turbulent kinetic energy, fesia, is estimated based on the work of [3]. By use of the so-called cell model assumed valid for dilute dispersions, an average relation for the pseudo-turbulent stresses around a group of spheres in potential flow has been formulated. Prom this relation an expression for the turbulent normal stresses determining the asymptotic value for bubble Induced turbulent energy was derived ... 

Based on the model of Lee and Wiesler [90] and the measurements of Lee and Borner [88] Lee [87] formulated a set of governing equations for the mean motion of particles in a suspension turbulent flow. The model contained both pseudo Stokes drag and pseudo Saffman forces which were expressed in terms of a modified viscosity, and supposedly valid for larger particle Reynolds numbers. 

Van t Riet K, Bruijn W, Smith JM (1976) Real and Pseudo-Turbulence in the Discharge Stream Prom a Rushton Turbine. Chem Eng Sci 31 407-412 Van t Riet K, Smith JM (1975) The trailing vortex system produced by Rushton turbine agitators. Chem Eng Sci 30 1093-1105... 

Three manifold flow conditions were chosen with Reynold s numbers of 1800, 6000, and 10500. The first Is definitely laminar, the latter Is turbulent and the mid range corresponds to the mid-range of the PMS counter s flow rate capabilities. The pumping speed In the PMS Instrument was chosen so that the linear velocity In the tubing and In the sampling probe were equal, resulting In Isokinetic or pseudo-isokinetic sampling conditions. The raw data are presented In Table III and the calculated count ratios In Table IV,... 

The flow regimes discussed above are often used to describe systems with 0i 1. Other flow regimes occur for 0i 1 (e.g. bubbly flows) because additional force models (such as added mass) introduce new dimensionless parameters, and because the momentum of the continuous phase becomes dominant. For example, in bubbly flow when RCp > 1 the turbulent liquid wakes behind bubbles lead to pseudo-turbulence (Mudde et al, 2009 Riboux et al, 2010 Sato Sekoguchi, 1975) that changes the nature of bubble-bubble interactions through the continuous phase. 

Marchisio, D. L. Barresi, A. A. 2009 Investigation of soot formation in turbulent flames with a pseudo-bivariate population balance model. Chemical Engineering Science 64, 294-303. 

Figure 3. Possible conditions of the momentum boundary layer around a submerged solid sphere with increasing relative velocity. Key a, envelope of pseudo-stagnant fluid b, streamline flow c, flow separation and vortex formation d, vortex shedding e, localized turbulent eddy formation. Reproduced, with permission, from Ref. 38. Copyright 1981, Springer-Verlag.

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