西安建筑科技大学学报(自然科学版)

渗透现象是一种广泛应用于污水处理、海水淡化、渗透马达和微泵等领域的自然现象.而Kedem-Katchalsky(K-K)模型作为描述渗透现象的经典热力学模型,存在诸多不足之处,如对压强分布描述不够清晰、无法揭示壁面位移情况等.为更加深入的理解渗透现象,建立了边界滑移条件下基于CFD模拟单孔道数学模型.通过对K-K模型中溶质反射系数和纯水渗透系数的模拟,验证了模型的可靠性.在此基础上,模拟并研究了孔道内流场分布、压强分布及边界应力分布.同时合理地解释了溶质反向渗透及溶胀现象.

Osmosis phenomenon is a natural phenomenon, widely encountered in the fields of sewage treatment, seawater desalination, osmotic motor and micropump. The Kedem-Katchalsky(K-K)model, as the classical thermodynamic model for describing the osmotic phenomenon, has many shortcomings: the description of the pressure distribution is not clear and it can't reveal the wall displacement and so on. In order to understand the phenomenon of osmosis deeply, the mathematical model of a single channel, based on CFD simulation, was established under the condition of boundary slip. The reliability of the model was verified by the simulation of solute reflection coefficient and pure water permeability coefficient in the K-K model. On this basis, the flow field distribution, pressure distribution and boundary stress distribution were simulated and studied. At the same time, solute reverse osmosis and swelling were explained reasonably.

引言
1 物理模型
2 几何模型及边界条件
3 数值模拟结果与分析
4 结论与建议

图1 渗透现象中的壁面滑移示意图<br/>Fig.1 Schematic diagram of wall slip in osmosis

图1 渗透现象中的壁面滑移示意图
Fig.1 Schematic diagram of wall slip in osmosis

图2 几何模型
Fig.2 Geometric model

图3 滑移系数cslip随孔尺寸变化规律<br/>Fig.3 Variation of slip coefficient with pore size

图3 滑移系数cslip随孔尺寸变化规律
Fig.3 Variation of slip coefficient with pore size

图4 水通量QW模拟值与K-K模型计算值随ΔP/Δπ的变化规律:(a)ΔP恒定、Δc变化; (b)Δc恒定、ΔP变化<br/>Fig.4 Simulation of water flux value and calculation of K-K model value changes with ΔP / Δπ:ΔP is constant、Δc is changed; Δc is constant、ΔP is changed.

图4 水通量QW模拟值与K-K模型计算值随ΔP/Δπ的变化规律:(a)ΔP恒定、Δc变化; (b)Δc恒定、ΔP变化
Fig.4 Simulation of water flux value and calculation of K-K model value changes with ΔP / Δπ:ΔP is constant、Δc is changed; Δc is constant、ΔP is changed.

图5 孔道流体流动随ΔP/Δπ变化示意图,ΔP/Δπ为:(a)0(b)0.2(c)1(d)2(e)∞<br/>Fig.5 Schematic diagram of changes fluid flow in pore with ΔP/Δπ, ΔP /Δπ equal:(a)0(b)0.2(c)1(d)2(e)∞

图5 孔道流体流动随ΔP/Δπ变化示意图,ΔP/Δπ为:(a)0(b)0.2(c)1(d)2(e)∞
Fig.5 Schematic diagram of changes fluid flow in pore with ΔP/Δπ, ΔP /Δπ equal:(a)0(b)0.2(c)1(d)2(e)∞

图6 轴线处压强分布:(a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠0及Δc=9、ΔP= 0时浓度分布<br/>Fig.6 The distribution of pressure at the axes:(a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠0 The distribution of concentration:Δc=9、ΔP=0

图6 轴线处压强分布:(a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠0及Δc=9、ΔP= 0时浓度分布
Fig.6 The distribution of pressure at the axes:(a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠0 The distribution of concentration:Δc=9、ΔP=0

图7 孔道边界总应力示意图(a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠0 <br/>Fig.7 Schematic diagram of total stress at the hole boundary (a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠ 0

图7 孔道边界总应力示意图(a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠0
Fig.7 Schematic diagram of total stress at the hole boundary (a)Δc≠0、ΔP=0;(b)Δc=0、ΔP≠ 0

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备注

引言

1 物理模型

2 几何模型及边界条件

3 数值模拟结果与分析

4 结论与建议

期刊信息