Search

Heat conduction in multi-layer and composite materials is one of the fundamental heat transfer problems in many industrial applications. Due to different materials types, interface conditions, and various geometries of these laminates, the heat conduction mechanism is more complicated than that of one-layer isotropic media. Analytical solutions are the best ways to study and understand such problems in depth. In this study, different existing analytical solutions for heat conduction in multi-layer and composite materials are reviewed and classified in rectangular, cylindrical, spherical, and conical coordinates. Applied boundary conditions, internal heat source, and thermal contact resistance as the most critical parameters in the solution complexity investigated in the literature, are discussed and summarized in different tables. Various types of multi-layer structures such as isotropic, anisotropic, orthotropic, and reinforced laminates are included in this study. It is found that although more than half a century has passed since the beginning of the research on heat transfer in multi-layer composites, new researches that can help with a better understanding in this area are still being offered. The challenges and shortcomings in this area are also discussed to guide future researches.

In this paper, based on simplified Boltzmann equation, we explore the inverse-design of mesoscopic models for compressible flow using the Chapman-Enskog analysis. Starting from the single-relaxation-time Boltzmann equation with an additional source term, two model Boltzmann equations for two reduced distribution functions are obtained, each then also having an additional undetermined source term. Under this general framework and using Navier-Stokes-Fourier (NSF) equations as constraints, the structures of the distribution functions are obtained by the leading-order Chapman-Enskog analysis. Next, five basic constraints for the design of the two source terms are obtained in order to recover the NSF system in the continuum limit. These constraints allow for adjustable bulk-to-shear viscosity ratio, Prandtl number as well as a thermal energy source. The specific forms of the two source terms can be determined through proper physical considerations and numerical implementation requirements. By employing the truncated Hermite expansion, one design for the two source terms is proposed. Moreover, three well-known mesoscopic models in the literature are shown to be compatible with these five constraints. In addition, the consistent implementation of boundary conditions is also explored by using the Chapman-Enskog expansion at the NSF order. Finally, based on the higher-order Chapman-Enskog expansion of the distribution functions, we derive the complete analytical expressions for the viscous stress tensor and the heat flux. Some underlying physics can be further explored using the DNS simulation data based on the proposed model.

In this paper, turbulent pipe flows laden with finite-size particles are investigated, using the direct numerical simulations based on the lattice Boltzmann method. Our focus is on the modulation of turbulence statistics in the pipe due to the presence of finite-size neutrally buoyant particles, and the question if the characteristics of modulation differ from those in a turbulent channel flow under comparable system parameters in order to reveal the effect of curved walls in the pipe. The mechanisms responsible for modulations of the turbulent intensity in the pipe flow are clarified through a quantitative budget analysis of the turbulent kinetic energy.

A parallel direct-forcing fictitious domain method is applied in fully-resolved numerical simulations of particle-laden turbulent flows in a square duct. The effects of finite-size heavy particles on the mean secondary flow, the mean streamwise velocity, the root-mean-square velocity fluctuation, and the particle concentration distribution are investigated at the friction Reynolds number of 150, the particle volume fraction of 2.36%, the particle diameter of 0.1 duct width, and the Shields number ranging from 1.0 to 0.2. Our results show that the particle sedimentation breaks the up-down symmetry of the mean secondary vortices, and results in a stronger secondary-flow circulation which transports the fluids downward in the bulk center region and upward along the side walls at a low Shields number. This circulation has a significant impact on the distribution of the mean streamwise velocity, whose maximum value occurs in the lower half duct, unlike in the plane channel case. The flow resistance is increased and the turbulence intensity is reduced, as the Shields number is decreased. The particles accumulate preferentially at the face center of the bottom wall, due to the effect of the mean secondary flow. It is observed that the collision model has an important effect on the results, but does not change the results qualitatively.

A b s t r a c t This paper describes implementation of the warm-rain bin microphysics in a LES model based on the EULAG fluid flow solver. The binmicrophysics EULAG is applied to the case of shallow nonprecipitating tropical convection to investigate the impact of the secondary activation of cloud droplets above the cloud base. In a previous study applying the EULAG model with the double-moment bulk warm-rain microphysics scheme, the in-cloud activation was shown to have significant implications for the mean microphysical and optical characteristics of the cloud field. By contrasting the simulations with and without in-cloud activation as in the previous study, we show that the in-cloud activation has qualitatively similar but quantitatively smaller eect. In particular, the concentration of cloud droplets in the bin simulation without in-cloud activation decreases with height not as strongly as in corresponding simulations applying the double-moment bulk scheme.