传递现象-Transport-phenomenon-Lesson-23---Transport-in-Turbulent-Flow-(4).ppt

* * * * 注意和前面的区别。此处考虑了浓度的轴向分布。 * * * * * * * * * * * * * * * * * * * * * §21.5 Turbulent Mixing and TurbulentFlow with Second-order Reaction (3) One stream [in (a)] or one initial region [in (b)] contains solute A in solvent S, and the other contains solute B in solvent S. All solutions are sufficiently dilute that the solutes do not appreciably affect the viscosity, density, or species diffusivities. Then the behavior of the solute (A or B) in either system [(a) or (b)] is described by the non-time-smoothed diffusion equations §21.5 Turbulent Mixing and TurbulentFlow with Second-order Reaction (4) (21.5-1,2) at z=0 [in (a)] or t = 0 [in (b)] (21.5-3,4) over the A inlet port [in (a)] or the initial region [in (b)], and (21.5-5,6) over the B inlet port [in (a)] or the initial region [in (b)]. In addition, we consider all confining surfaces to be inert and impenetrable. §21.5 Turbulent Mixing and TurbulentFlow with Second-order Reaction (5) For this situation, the terms RA and RB are identically zero. We now define a single new independent variable (21.5-7) Then both Eqs.(21.5-1, 2) take the following form over the whole system: No Reaction Occurring (21.5-8) §21.5 Turbulent Mixing and TurbulentFlow with Second-order Reaction (6) (21.5-11) For equal diffusivities, the time-smoothed concentration profiles, ? (x, y, z, t) are identical for both solutes, where ?= 0 for (a) the entering A-rich stream, or (b) initially A-rich region; ? = 1 for (a) the entering B-rich stream, or (b) initially B-rich region. However, the fluctuating quantities ?’ are also of interest, as they are measures of “unmixedness.” §21.5 Turbulent Mixing and TurbulentFlow with Second-order Reaction (6) (21.5-12) Here d(x, y, z, t) is a dimensionless decay function, which decreases toward zero at large z for the static mixer, or at large t for the mixing tank. These can be equal only in a statistical sense. We subtract Eq.(21.5-11) from Eq.(21.5-7), and then square the resu