In the case of suspension flows, the rate of interphase momentum transfer M_k and thatof interphase energy transfer E_k, which were expressed as a sum of infinite discontinuitiesby Ishii, have been reduced to the sum ...In the case of suspension flows, the rate of interphase momentum transfer M_k and thatof interphase energy transfer E_k, which were expressed as a sum of infinite discontinuitiesby Ishii, have been reduced to the sum of several terms which have concise physical signifi-cance. M_k is composed of the following terms: (i) the momentum carried by the interphasemass transfer; (ii) the interphase drag force due to the relative motion between phases; (iii)the interphase force produced by the concentration gradient of the dispersed phase in apressure field. And E_k is composed of the following four terms, that is, the energy carriedby the interphase mass transfer, the work produced by the interphase forces of the second andthird parts above, and the heat transfer between phases. It is concluded from the results that (i) the term, (-α_k?p), which is related to thepressure gradient in the momentum equation, can be derived from the basic conservation lawswithout introducing the 'shared-pressure presumption'; (ii) the mean velocity of the actionpoint of the interphase drag is the mean velocity of the interface displacement, v_i. It isapproximately equal to the mean velocity of the dispersed phase, v_d. Hence the work termsproduced by the drag forces are f_(dc)·v_d. and f_(cd)·v_d, respectively. with v_i not being replacedby the mean velocity of the continuous phase, v_c; (iii) by analogy, the terms of the momentumtransfer due to phase change are v_dΓ_c. and v_dΓ_d. respectively; (iv) since the transformationbetween explicit heat and latent heat occurs in the process of phase change, the algebraic sumof the heat transfer between phases is not equal to zero. Q_(ic) and Q_(id) are composed of theexplicit heat and latent heat, so that the sum (Q_(ic)+Q_(id)) is equal to zero.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘In the case of suspension flows, the rate of interphase momentum transfer M_k and thatof interphase energy transfer E_k, which were expressed as a sum of infinite discontinuitiesby Ishii, have been reduced to the sum of several terms which have concise physical signifi-cance. M_k is composed of the following terms: (i) the momentum carried by the interphasemass transfer; (ii) the interphase drag force due to the relative motion between phases; (iii)the interphase force produced by the concentration gradient of the dispersed phase in apressure field. And E_k is composed of the following four terms, that is, the energy carriedby the interphase mass transfer, the work produced by the interphase forces of the second andthird parts above, and the heat transfer between phases. It is concluded from the results that (i) the term, (-α_k?p), which is related to thepressure gradient in the momentum equation, can be derived from the basic conservation lawswithout introducing the 'shared-pressure presumption'; (ii) the mean velocity of the actionpoint of the interphase drag is the mean velocity of the interface displacement, v_i. It isapproximately equal to the mean velocity of the dispersed phase, v_d. Hence the work termsproduced by the drag forces are f_(dc)·v_d. and f_(cd)·v_d, respectively. with v_i not being replacedby the mean velocity of the continuous phase, v_c; (iii) by analogy, the terms of the momentumtransfer due to phase change are v_dΓ_c. and v_dΓ_d. respectively; (iv) since the transformationbetween explicit heat and latent heat occurs in the process of phase change, the algebraic sumof the heat transfer between phases is not equal to zero. Q_(ic) and Q_(id) are composed of theexplicit heat and latent heat, so that the sum (Q_(ic)+Q_(id)) is equal to zero.
