Basic Models of Computational Mass Transfer
The computational mass transfer (CMT) aims to find the concentration profile in a process equipment, which is the most important basis for evaluating the process efficiency, as well as, the effectiveness of an existing mass transfer equipment. This chapte
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Basic Models of Computational Mass Transfer
Abstract The computational mass transfer (CMT) aims to find the concentration profile in a process equipment, which is the most important basis for evaluating the process efficiency, as well as, the effectiveness of an existing mass transfer equipment. This chapter is dedicated to the description of the fundamentals and the recently published models of CMT for obtaining simultaneously the concentration, velocity and temperature distributions. The challenge is the closure of the differential species conservation equation for the mass transfer in turbulent flow. Two models are presented. The first is a two-equation model termed as c02 ec0 model, which is based on the Boussinesq postulate by introducing an isotropic turbulent mass transfer diffusivity. The other is the Reynolds mass flux model, in which the variable covariant term in the equation is modeled and computed directly, and so it is anisotropic and rigorous. Both methods are proved to be validated by comparing with experimental data.
Keywords Computational mass transfer (CMT) Reynolds averaging Closure of time-averaged mass transfer equation Two-equation model Turbulent mass transfer diffusivity Reynolds mass flux model
Nomenclature c ct C C+ c′ c02 D De Dt Dt g [I]
Instantaneous mass concentration of species i, kg m−3 Molar concentration of species i in Sect. 1.4.2, mol s−3 Total molar concentration of component i per m3, mol m−3 Time average concentration, kg m−3 Dimensionless concentration Fluctuating concentration, kg m−3 Variance of fluctuating concentration, kg2 m−6 Molecular diffusivity, m2 s−1 Effective mass diffusivity, m2 s−1 Isotropic turbulent mass diffusivity, m2 s−1 Anisotropic turbulent mass diffusivity, m2 s−1 Gravity acceleration, m s−2 Identity matrix, dimensionless
© Springer Nature Singapore Pte Ltd. 2017 K.-T. Yu and X. Yuan, Introduction to Computational Mass Transfer, Heat and Mass Transfer, DOI 10.1007/978-981-10-2498-6_1
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1 Basic Models of Computational Mass Transfer
Table 1.1 Influence of u0i c0 on mass transfer for different processes Process Process Sn @u0i c0 @u0 c0 Scomb ¼ @xi i þ Sn @xi concentration profile and u0i c0 profile
Influence on mass transfer
Consistent Favorable Absorption + − Scomb > Sn Not consistent Unfavorable Desorption − − Scomb < Sn (regeneration) Adsorption + + Scomb < Sn Not consistent Unfavorable Consistent Favorable Desorption − + Scomb > Sn (regeneration) a Absorption process characterized by decreasing concentration profile Desorption (regeneration) process characterized by increasing concentration profile
Jw k [k] l p′ P Pe rc S Sc Sct t T0 T 02 T u u′ uτ u+ U, V, W y+ αt δ ε εc′ εt μ μt
Mass flux at wall surface, kg m−2 s−1 Fluctuating kinetic energy, m2 s−2 Mass transfer coefficient, m s−1 Matrix of mass transfer coefficients, m s−1 Characteristic length, m Fluctuating pressure, kg m−1 s−2 Time average pressure, kg m−1 s−2 Peclet number Ratio of fluctuating velocity dissipation time and fluctuating concentration dissipation
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