Impact of Stefan flow on the interphase scalar transfer in flow past random particle arrays

Highlights

• The variation of Nu caused by Stefan flow is more evident than drag coefficient.

• The increase in Re and c can only partially offset the reduction of Nu.

• Stefan flow induces the variation of Re and Nu along the streamwise direction.

• A heat transfer correction factor is developed based on the simulation data.

Abstract

By using a particle-resolved direct numerical simulation, the impact of Stefan flow on interphase heat transfer in flow past static random particle arrays is investigated. The findings demonstrate that the temperature boundary layer of particles is thickened/thinned by the outward/inward Stefan flow and therefore hinders/improves the contact between main gas flow and particles. With the impact of positive Stefan Reynolds number (Re_sf), the maximum percentage reduction of Nusselt number could be over 3 times of the maximum percentage reduction of drag coefficient at the same condition. The rise in particle Reynolds number (Re) or solid volume fraction (c) can partially offset the impact of Stefan flow. Finally, the simulation data are used to develop a correction factor for interphase heat transfer considering the impact of Stefan flow for −3 < Re_sf < 6, 0 < Re < 100, and 0 < c < 0.5. Note that the scalar in current work is chosen to be the dimensionless temperature, but the results are general and applicable to any passive scalar.

Introduction

The thermo-chemical conversion of combustible particles, such as biomass gasification and coal pyrolysis, becomes a promising technology in recent decades for reducing the generation of greenhouse gases and improving the energy utilization efficiency [1], [2]. Because of the superb heat and mass exchange capacities, fluidized bed reactor (FBR) is widely applied in the thermo-chemical conversion process, in which the intense interphase interaction occurs between the gaseous species and solid particles [3]. During the thermo-chemical conversion process, the radial gaseous mass flux generates from the surface of reactive particles owing to evaporation, devolatilization reaction, etc. This radial mass flux, namely Stefan flow, hinders the contact between combustible particles and the main gas flow, thus the gas–solid interphase momentum, heat and mass transfer is also affected [4], [5]. It is reported that Stefan flow could cause an interphase drag force reduction of up to 30%, while the reduction percentage of interphase heat transfer rate induced by Stefan flow even reaches 78.2% [6], [7].

Due to the rapid increase in computing power, computational fluid dynamics (CFD) has emerged as a crucial tool for the study of the thermo-chemical conversion processes in FBR. Compared to the experimental method, the CFD method could provide rational prediction about the detailed information inside the FBR, and the expense of CFD method is minimal. To date, numerous numerical studies about the gas–solid reacting flow in FBRs have been reported [8], [9], [10], [11], [12], [13]. In fact, the simulation accuracy of gas–solid reacting flow strongly depends on the rationality of interphase interaction models (drag model and heat/mass transfer model) [14], [15], [16]. Since the formation of Stefan flow strongly affects the interphase interactions, thus this effect should be taken into consideration in these interphase interaction models [17], [18].

Since the particle-resolved direct numerical simulation (PR-DNS) is a first-principle approach for creating accurate models, interphase interaction models are typically obtained using this method. Many PR-DNSs have been performed for the flow past particle arrays without Stefan flow, and the corresponding interphase interaction models (interphase drag model, heat transfer model, etc.) were proposed based on the simulation results [19], [20], [21], [22], [23]. Because the effect of Stefan flow is not considered in these PR-DNSs, these interphase interaction models cannot reflect the practical relationship between gas and solid particles during the thermo-chemical conversion. For the purpose of revealing the impact of Stefan flow on the interphase interaction, several PR-DNSs have been performed in the past decades to probe the impact of Stefan flow on the gas–solid drag force, heat transfer, and mass transfer processes in flow past single particle or particle pair. For instance, Kurose et al. performed PR-DNS about flow past single sphere with outward Stefan flow to probe its impact on drag and shear lift [24]. They found that outward Stefan flow reduces the drag force. Kestel carried out PR-DNS about the impact of Stefan flow on interphase drag force and heat transfer [17]. It is observed that raising the Stefan Reynolds number reduces both the Nusselt number and drag coefficient. Jayawickrama et al. investigated the impact of Stefan flow on the gas–solid interphase drag force [25]. The simulation findings demonstrate that the outward Stefan flow is what reduces the drag coefficient, and this relationship is almost linear. Additionally, when the Reynolds number rises, the magnitude of the reduced drag coefficient increases. Afterwards, they performed PR-DNS to probe the impact of Stefan flow on the interphase drag force and heat transfer in non-isothermal flow past single sphere [7]. The results shown that the changes in gas thermophysical properties under non-isothermal condition strongly affect the variations of drag coefficient and Nusselt number caused by Stefan flow. Recently, Jin et al. and Wang et al. performed several PR-DNSs to probe the impact of Stefan flow on drag force and heat transfer characteristics of single particle, particle pair, and regular monolayer particle array in the supercritical water cross flow [26], [27], [28], [29]. All of these studies illustrate that the impact of Stefan flow is vital and should be considered in the macro-scale CFD simulation. Nevertheless, it should be noted that these PR-DNSs mainly focused on the single particle or dual particle systems. The results of previous studies may not be applicable to particles in practical gas–solid systems where multiple particles are involved and the flow passing through the considered particles is always affected by surrounding particles.

Lately, our research team performed the PR-DNS based on a second-order accurate immersed boundary-lattice Boltzmann method (IB-LBM) to probe the impact of Stefan flow on interphase drag force in multiple particle system [6]. After analyzing the combined effects of the solid volume fraction, Stefan Reynolds number, and particle Reynolds number on drag force, a corrected drag model taking these factors into account is created. Later on, we investigated how Stefan flow affects the drag force of a single reactive particle that is surrounded by several inert particles because such condition is widely encountered during the coal/biomass gasification process in FBR [30]. The results demonstrate that the drag force is reduced and the thickened boundary layer induced by Stefan flow is suppressed by the surrounding inert particles, however, the impact of Stefan flow is still notable even at high solid volume fraction. These studies reveal the relationship between Stefan flow and the drag force in multi-particle system, but it still needs to be quantitatively investigated how Stefan flow affects interphase heat and mass transfer in multi-particle systems.

In current work, the IB-LBM model with second-order accuracy proposed by Zhou and Fan [31] is modified to accommodate passive scalar transport and the impact of Stefan flow. Here, the Stefan flow denotes the radial fluid flux generated from the particles’ surfaces, while the fluid physical properties and components are assumed to be constant and uniform in the entire system. Based on the modified IB-LBM model, we systematically probe the impact of Stefan flow on the interphase heat transfer in flow past static random particle arrays. Finally, based on the simulation data, an interphase scalar transport model is created. Note that the scalar is chosen to be the fluid temperature, but the results are general and applicative to any passive scalar.