Advances in Biochemical Engineering & Biotechnology, Volume by Urs von Stockar (Editor), Luuk van der Wielen (Editor)

By Urs von Stockar (Editor), Luuk van der Wielen (Editor)

Strategy integration has been essentially the most energetic examine fields in Biochemical Engineering over the past decade and it'll stay so if bioprocessing is to develop into extra rational, effective and effective. This quantity outlines what has been accomplished in recent times. Written via specialists who've made very important contributions to the eu technological know-how, starting place application on approach Integration in Biochemical Engineering, the quantity makes a speciality of the growth made and the key possibilities, and also at the barriers and the demanding situations in bioprocess integration that lie forward. the idea that of bioprocess integration is handled at quite a few degrees, together with integration on the molecular, organic, bioreactor and plant degrees, but additionally accounting for the combination of separation and mass move operations and biology, fluid dynamics and body structure, in addition to simple technology and strategy know-how.

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To ameliorate the previously mentioned deficiencies in the standard k– e model, Chen and Kim [9] proposed a modification, which improves the dynamic response of the e equation by introducing an additional timescale k tP = (9) Pk 27 Integration of Physiology and Fluid Dynamics which is called the production-range timescale. The final expression of the transport equation for the dissipation rate is given as: 1st part 2nd part Ê 67 ˆ 4 4 8 6 4 74 8 Á ∂ (r e ) ∂ Pk Pk ∂ Ê u eff ∂ e ˆ e ˜ ˜ + + c3, CK – c 2, CK (r ui e ) = Ár ˜ + r Á c1, CK ∂t ∂ xi ∂ xi Ë s e , CK ∂ xi ¯ td tp td ˜ Á 42444 3 Á 144 ˜ Ë production term ¯ (10) The parameters of the Chen-Kim model are summarized in Table 2.

In addition to the velocity vector field, large arrows are used to illustrate the flow behavior. Each impeller creates a more or less independent symmetrical flow field. The multiple impeller system therefore shows very poor axial convection. The transport between the individual cells is performed mainly with the aid of axial turbulent dispersion. Integration of Physiology and Fluid Dynamics 37 Fig. 7. 67¥10–3 m3 s–1. Simulation with two-fluid model The results from similar simulations with two Rushton turbines and two pitched blade impellers as well as four pitched blade impellers are shown in Figs.

5. 12. 0. 0 For applications in two-phase flow the k– e models have been modified in different ways. One possibility is to insert additional sources into the transport equations for k and e [30–33]. An alternative is to consider an increase of the turbulent viscosity in the liquid phase caused by the bubbles. Ac- 33 Integration of Physiology and Fluid Dynamics cording to Sato [34] and Lopez de Bertodano et al. 6. Assuming that the optimized version of the Chen-Kim model is still valid, the transport equations for the turbulence quantities k and e for the two-phase system are given by: n ∂ (r L e L k) ∂ ∂ Ê ∂k ˆ + (r L e L uL, i k) = ∂ x ÁË r L e L s eff ∂ x ˜¯ ∂t ∂ xi i k, s i + and ∂ ∂ xi nt ∂ e L Ê ÁrL k Ë Sct ∂ xi ˆ ˜ + r L e L (Pk – e ) ¯ ∂ (r L e L e ) ∂ ∂ + (r L e L uL, i e ) = ∂ x ∂t ∂ xi i (27) n eff ∂ e ˆ Ê ÁrL eL s ˜ Ë e , CK ∂ xi ¯ ∂ Ê nt ∂ e L ˆ ÁrL e ˜ ∂ xi Ë Sct ∂ xi ¯ Ê e ˆ P P + r L e L Á cl , CK k + c 3, CK K – c 2, CK td tp t d ˜¯ Ë + (28) with Ê ∂ uL, i ∂ uL, j ˆ ∂ uL, i Pk = n t Á + ∂ xi ˜¯ ∂ x j Ë ∂ xj (29) As already discussed in context with the single-phase simulations, boundary conditions at the impeller are predicted from measured data of the averaged velocities.

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