Hybrid Reynolds Mass Flux Model

In order to reduce the computer load of standard Reynolds mass flux model, the complicated Eq. (1.23a) for expressing m-m can be replaced by the simpler Eq. (1.8). Then, the model becomes the combination of Reynolds mass flux and the Boussinesq postulate (two-equation model). It is called hereafter as hybrid Reynolds mass flux model. The model equations are given below. 

Momentum conservation equation Eq. (1.4) u lUj equation (Boussinesq postulate)  

The unknown quantities in this model are (/, Uj, Uu, P, K , Pi, C, u[c, Ujc, u d, totally eleven versus eleven model equations available. Since this model employ Boussinesq postulate, it is isotropic. 

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The hybrid Reynolds mass flux model and algebraic Reynolds mass flux model, which only need to solve simpler Eq. (1.8) instead of complicated Eq. (1.23), may be a proper choice for multiple tray computation if their simulated results are very close to the standard Reynolds mass flux model. For comparison, the simulated column trays in Sect. 4.1.1.1 for separating n-heptane and methylcyclohexane are used. Li [17] simulated concentration profiles of all trays at different levels above the tray floor, among which the tray number 8 and tray number 6 are shown in Fig. 4.17a and b. 

The simulated result by using hybrid Reynolds mass flux model can also compared with that obtained by using two-equation model as shown in Fig. 4.17, in which the agreement between them can be seen except in the region near inlet weir and column wall where the hybrid Reynolds mass flux model gives more detailed concentration distribution than the two-equation model. 

The verification of hybrid Reynolds mass flux model can also be made by comparing with the experimental outlet concentration of each tray as shown in Figs. 4.18 and 4.19, in which the result by using two-equation model is also presented. It can be seen that the hybrid Reynolds mass flux model gives closer outlet concentration to the experimental measurement than the two-equation model, although both of them are considered to be verified by experiment. 

Fig. 4.17 Concentration contour of x-y plan on trays by hybrid Reynolds mass flux model, a 20 mm above tray floor of tray number 8, b 70 mm above tray floor of tray number 8, c 20 mm above tray floor of tray number 6, and d 70 mm above tray floor of tray number 6 [16]...

Fig. 4.18 Comparison between hybrid Reynolds mass flux model and two-equation model by simulated concentration contours of 20 mm above tray floor on tray number 8. a Hybrid Reynolds mass flux model (reprinted from Ref. [7], Copyright 2011, with permission from Elsevier) and b c - Be two-equation model (reprinted from Ref [4], Copyright 2005, with permission from American Chemical Society)...

Fig. 4.19 a Comparisons of simulated results by different models with experimental data [16] tray efficiency and outlet Cg concentration, b Comparisons of the outlet Ce concentration between standard and hybrid Reynolds mass flux model simulations and experimental data [16]... 

Reyuolds mass flux model at 70 mm above the tray floor, b standard Reynolds mass flux model at 20 mm above the tray floor, c hybrid Reynolds mass flux model at 70 mm above the tray floor, d hybrid Reynolds mass flux model at 20 mm above the tray floor, e algebraic Reynolds mass flux model at 70 mm above the tray floor, and f algebraic Reynolds mass flux model at 20 mm above the tray Hoot... 

The hybrid Reynolds mass flux model can be further reducing the complexity of model equations by setting the convection term on the left side of Eq. (3.26a) equal to the turbulent and molecular diffusions term on the right side under steady condition to obtain Eq. (3.27) as shown below. 

The comparison of simulated result on radial averaged axial concentration between hybrid Reynolds mass flux model and two-equation model is given in... 

The simulated Cg concentration profiles of the whole column are shown in Fig. 4.44, which is substantially identical with Fig. 4.40 by hybrid Reynolds mass flux model simulation. 

The weakness of this model is requiring heavy computer work. For simplifying the computation, the complicated equations Eq. (3.25a) can be replaced by Eq. (1.8), which is called hybrid mass flux model. Another simplification is made by letting Eq. (3.31) to replace Eq. (3.25a) for calculating mJc, called algebraic Reynolds mass flux model. These simplified models are able to give similar simulated results in comparision with the standard model. 

Li [7] simulated the packed column as described in Sect. 4.2.1 by using Reynolds mass flux model instead of two-equation model and compared their difference. The simulated results for three forms of Reynolds mass flux model (standard, hybrid, and algebraic) are given in subsequent sections. 

The simulated radial averaged axial concentration distribution is compared with experimental data and the simulated result by using standard Reynolds mass flux model as shown in Fig. 4.41. These figures display no substantial difference between hybrid and standard Reynolds mass flux models. 

The verification of algebraic Reynolds mass flux model as well as the comparison with hybrid model is shown in Fig. 4.45. At low F factor, these two models are in agreement with experiment, but at high F factor the algebraic Reynolds mass flux model shows greater deviation from the experimental data. 

Abstract In this chapter, the two CMT models, i.e., c — Eci model and Reynolds mass flux model (in standard, hybrid, and algebraic forms) are used for simulating the chemical absorption of CO2 in packed column by using MEA, AMP, and NaOH separately and their simulated results are closely checked with the experimental data. It is noted that the radial distribution of Di is similar to a, but quite different from fit. It means that the conventional assumption on the analogy between the momentum transfer and the mass transfer in turbulent fluids is unjustifled, and thus, the use of CMT method for simulation is necessary. In the analysis of the simulation results, some transport phenomena are interpreted in terms of the co-action or counteraction of the turbulent mass flux diffusion. 

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