(84g) Simulation of Interfacial Rayleigh-Bénard Convection in the Gas-Liquid Mass Transfer Process Using a Lattice Boltzmann Method

Abstract

Interfacial convection caused by the interfacial density gradient produced by concentration gradient in interphase mass transfer process is cited as interfacial Rayleigh-B¨¦nard (IRB for short) convection. The Rayleigh-B¨¦nard convection at the interface displays an important role on mass transfer rate. Therefore, it is highly important to study the IRB convection for many engineering applications such as absorption, extraction, distillation, etc.. A large amount of experimental work and theoretical analysis have devoted to obtain observations of the structures of the IRB convection, measurements of enhanced mass transfer rate and the linear stability analysis of Rayleigh-B¨¦nard problem. In this paper, by introducing a mass transfer model of fixed disturbance(FDM for short), both flow and concentration fields of the two-dimensional IRB convection were simulated by the lattice Boltzmann method (LBM) at mesoscopic level with two-distribution model in the gas-liquid mass transfer process of CO₂ absorption into quiescent ethanol. The main purposes of simulation are to qualitatively compare the IRB convection patterns with the images taken by Schlieren technique and analyze the relationship between the IRB convection patterns and mass transfer rate and quantitatively analyze the relationship between liquid-phase mass transfer coefficient and number of fixed disturbance points on the interphase. The lattice Boltzmann method, of which the basic concept is to incorporate the physics of the problem into a simplified kinetic equation such that the correct macroscopic behavior of the fluid is recovered, have been widely used to study the Rayleigh-B¨¦nard convection phenomenon caused by heat transfer. However, to the author's knowledge, this is the first time the LBM approach is applied to investigate the Rayleigh-B¨¦nard convection caused by the mass transfer. In the present study, a series of disturbance points are set on the gas-liquid interphase with the assumption that once the convection structure is formed it continues at the fixed local position and never fade until the whole process is over. Considering the simplicity and accuracy, D2Q9 model of LBM is chosen for the simulation. In the D2Q9 model, also known as the two-dimensional nine-velocity model, the physical space is discretized into a square lattice. The corresponding particles at each node have 9 moving directions. In gas-liquid system of CO₂ absorption into quiescent ethanol, we only concern a two-dimensional unsteady and isothermal mass transfer of a vertical section of the liquid in the simulator.

At the beginning, pure ethanol was confined in a rectangle box and its free upper boundary contacted with CO₂. The mass transport of CO₂ absorption into quiescent ethanol took place through the upper boundary. The absorption system was Rayleigh-B¨¦nard unstable (Ra>0) and Marangoni stable (Ma<0). Therefore, the IRB convection appeared in liquid-phase if the density gradient induced by the diffusion of the solute into a vertical section of the liquid bulk was beyond a critical value. Considered of the lateral and lower wall effects, the inner space dimension of our simulator was 0.01m°Á0.02m, which the liquid thickness was selected 0.01m. The simulations were carried out on a uniform 30°Á60 grid. Physical properties of pure ethanol and its saturated CO₂ solution in absorption process for our LBM simulation are listed in Table 1.

Table 1 Physical properties of pure ethanol and saturated CO₂ solution at T=293.2 K, p=1 atm

Here ¦Ñ is the density of pure ethanol; ¦Ä¦Ñ is the differences between the properties of the pure ethanol and the saturated CO₂ solution; C_Sat is the concentration of saturated CO₂ solution and c_s is speed of sound in ethanol.

IRB convection phenomena is simulated for situations in which the number of fixed disturbance existing and uniformly distributed on the interface of CO₂ and ethanol are 1,2,3,4,5,9,11,14,19,29 and 59.

The case for n=5 and t=1s, 3s, 6s, 10s, the transient contours of CO₂ concentration are shown in Fig. 1.

Fig. 1 Transient contours of the CO₂ concentration for different t at n=5

From Fig. 1, at the beginning of mass transfer, the IRB convection appeared on the fixed disturbance points, and extended quickly to the whole interface; the interfacial convection intensity increased with the time. The critical contact time for the onset of the IRB convection was found to be less than 1s. Then the liquid with higher concentration began to stream downward in a plume density-driven convection pattern and reached the bottom of the bulk liquid accompanying by upward backflow with swing back and forth at t=10s. At last, two inverse-mushroom convective structures formed. It should be noted that there were mutual induction effects between two adjacent fixed disturbance points, and the mutual induction effect played an important role in forming the plume density-driven convection pattern in the mass transfer process.

When n≤5, heavy superficial liquid with nearly saturated with CO₂, descended in a downward plume density-driven convection pattern, when n≥9, the plumes drifted from the middle of the concentration contours to the sides and converged on the bottom, which was termed as the diverging flow pattern that the layers of nearly saturated liquid descended along rectangle lateral walls induced by wall effect; interfacial turbulence such as chaotic cells and short hook-like plumes seen in vicinity interface were not clear in concentration contours but charts of velocity vector.

The liquid-phase mass transfer coefficients with different number of fixed disturbance points were calculated by the concentration distributions for gas-liquid contact time 7s in mass transfer process of CO₂ absorption into quiescent ethanol as shown in Fig. 2.

Fig. 2 The liquid-phase mass transfer coefficient variation with number of fixed disturbance points

The liquid-phase mass transfer coefficient increases at first then decreases to a nearly stable value with the increase in number of disturbance points as shown in Fig. 2. And it can be seen that the curves for the liquid-phase mass transfer coefficient can be divided into two regions: (1) an increasing region with n≤5, where the mass transfer was controlled by the plume density-driven convection pattern; (2) an increasing at first then decreasing region with n≥9, where the mass transfer was controlled by two diverging flow patterns and number of interfacial turbulence patterns such as chaotic cells and short hook-like plumes. In the first region, k_L first increases markedly then slightly increases with the increase in n, and k_L is proportional to the plumes convection intensity increased nonlinearly with the increase in n. It is noteworthy that the compound plumes at n=4, n=5 are combined with single plume density-driven convection pattern by mutual induction effects between two adjacent fixed disturbance points, and the compound plume convection intensity is larger than single plume convection intensity. In the second region, k_L first increases considerably then decreases markedly to a nearly stable value with the increase in n that can be explained that: when n≥9 and n≤19, the diverging flow intensity and the number of interfacial turbulence patterns rapidly increases in spite of the decreasing interfacial turbulence intensity with the increase in n; when n≥19 and n≤29, the diverging flow intensity and number of short hook-like plumes convection intensity rapidly decreases in spite of the increasing number of interfacial turbulence patterns with the increase in n; when n≥29, although the diverging flow intensity decreases, the mass transfer intensity induced by molecular diffusion increases with the increase in n. Moreover, the transient stage of convection pattern where k_L slightly increases from n=5 to n=9 shown in Fig. 2 is that two compound plume density-driven convection patterns converted into two diverging flow patterns with nearly equal intensity. Consequently, the mass transfer rate depends on number of plumes and types of patterns in the IRB convection.

The present study is a heuristic investigation which attempt to relate the mass transfer rate with the types and intensity of the IRB convection structures by varying the number of disturbance points. We hope this result could be helpful to uncover the mechanism of interphase mass transfer and further work is needed in the future.