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The continuum surface force (CSF) model in conjunction with the smoothed particle hydrodynamics (SPH) method is commonly used in the simulation of multi-phase flows with surface tension effect. However, it cannot be directly applied for modeling free-surface flows since the normalization requirement, which states that the integral of the surface delta function through the interface should be equal to one, is violated due to the particle deficiency issue. In this work, we propose an improved CSF model based on the SPH method with the aim of recovering the normalization requirement. The particle deficiency issue at the free surface is tackled by introducing the jump in color function into the calculation of the surface delta function. As a result, the accuracy of the surface tension measurement is significantly improved without using the virtual particles. Besides, this improved CSF model also allows an accurate and efficient implementation of the Robin boundary condition which is frequently encountered in heat transfer problems. Several benchmark problems are investigated to validate the performance of the proposed method. The numerical results verify that the improved CSF model in SPH method is well capable of simulating free-surface flows and heat transfer problems. [ABSTRACT FROM AUTHOR]

• A novel coupling approach of ES-FEM-SPH is developed for solving thermal-fluid-structure interaction (TFSI) problems. • The updated Lagrangian ES-FEM is developed for solving the coupled thermal elastic problems. • The SPH method, after integrating with particle shifting technique and kernel gradient correction, is robust and effective in modeling thermal fluid flows. • The ghost particle coupling algorithm is developed for treating fluid structure conjugate heat transfer. Thermal-fluid-structure interaction (TFSI) problems are significant in science and engineering, and usually pose great challenges for numerical simulations due to the coupled effects of thermal convection, fluid flow and structure deformation. In this paper, a novel coupling approach of smoothed finite element method (ES-FEM) with an improved smoothed particle hydrodynamic (SPH) method is developed for TFSI problems. In the coupling approach, the edge based ES-FEM is used to model solid domain and the Lagrangian SPH is used to model fluid flow. In ES-FEM, the temperature and velocity gradient smoothing technique are applied over the edge-based smoothing domain for thermal structure coupling problems. In SPH, some state-of-art algorithms including kernel gradient correction (KGC) and particle shift technique (PST) are integrated to ensure computational accuracy for simulating thermal fluid flows. A ghost particle coupling algorithm is developed to handle fluid-structure interaction and fluid-structure conjugate heat transfer, and the kinematic condition, dynamics conditions and conservation of energy are satisfied. Four numerical examples are tested to demonstrate the effectiveness of the present coupling approach of ES-FEM-SPH for TFSI problems. Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper presents a direct numerical simulation (DNS) technique, the Finite Element Fictitious Boundary Method (FEM-FBM) for the simulation of fluid-solid two-phase flows with heat transfer. The heat transfer equation is introduced to study thermal convection in fluid-solid two-phase flows. The Boussinesq approximation is considered for the coupling of momentum and temperature flow fields. Multi-grid finite element solver is used to compute flow equations of mass, momentum, and energy on a fixed Eulerian mesh which is independent of time and the solid particles are allowed to move freely in the whole computational domain. Fictitious boundary method (FBM) is used to treat the particles inside the fluid, FBM takes account of the thermal and momentum interaction between the fluid and the particles. The accuracy and stability of presented method are validated by comparing our test cases results with the results reported in the available literature. Numerical tests are performed to show that this method is potentially powerful and provides an efficient approach to simulate complex thermal convective particulate flows with a large number of particles. [ABSTRACT FROM AUTHOR]

• The semi-resolved CFD-DEM with a multi-smoothing distance scheme is further developed for the polydispersed particle system. • Grain-scale reconstruction by μCT images is employed to quantitatively characterize the heterogeneous porous media. • Particle-scale migration process and distribution characteristics of fine particles in porous media are examined. • The influences of powder properties and anisotropy effects on migration processes and heat transfer are studied. A comprehensive understanding of the migrating phenomena of microscale particles associated with fluid flows and heat exchange in porous media is essential for developing unconventional geo-resources. In this work, we further develop the kernel-based semi-resolved CFD-DEM and combine it with grain-scale reconstruction to numerically investigate particulate flows and associated heat transfer processes in porous media. To characterize wide grain size distributions and heterogeneity of rock skeleton, a 3D spherical-packed model is quantitatively assembled based on CT images of real rock. After a series of validations, it is found that the results from the improved semi-resolved CFD-DEM, including motion, heat transfer, and pressure drop behaviors of particulate systems, match better with experimental observations and analytical solutions than that obtained from the unresolved CFD-DEM. On this basis, the particle-scale migration and distribution characteristics of fine particles are further studied. It is found that the penetration distance, temperature, and energy distributions of particle systems rely on the variation of powder properties (i.e., concentration and size) and the effects of matrix anisotropy. In a higher powder concentration system, more deposited particles at the upper of the packed bed prevent the downward migration of powder particles and lower the quantity of heat exchange between the fine and matrix particles. In addition, this can also lead to a more pronounced jamming phenomenon and reduce the seepage capacity of the packed bed. As the powder diameter increases, the heat transfer capacity of fine particles increases and gradually dominates the temperature of particulate systems. The deposition patterns and temperature variation behaviors of fine particles along the migration direction caused by the anisotropy of the porous medium are also identified. Therefore, the developed computational framework can be a powerful tool to reproduce the dynamics of fine particles in heterogeneous porous materials and reveal the underlying mechanisms. [ABSTRACT FROM AUTHOR]

Heat transfer and flow structures for round jet impingement over rough surfaces have been investigated using the shear stress transport model (SST) with transition model. This model is first evaluated against the experimental data and other numerical results for the smooth surface with Reynolds number Re = 23,000 for the nozzle-plate spacing of 2. Based on the above evaluation, the effects of rough surfaces on the mean velocity, turbulence field, skin friction and heat transfer are investigated with equivalent sand grain roughness heights k s of 50, 100, 250 and 500 μm. Two trends of the effects of roughness on the velocity field are found. First, the mean velocity over rough surfaces becomes steeper than that over the smooth surface in very near the wall. However, for k s ≥ 250 μm, the velocity gradient in the axial direction does not increase with an increase of k s. Second, the decay of the mean velocity is found in the deceleration region, but minimal in the acceleration zone. In addition, it is observed that the increase of roughness height leads to the reduction of the wall shear stress in the stagnation region. On the contrary, downstream, large k s usually contributes to an augmentation of wall shear stress. For heat transfer, the enhancement of heat transfer due to roughness varies from 2.53% to 6.08% compared with the case of smooth surface. However, this enhancement is non-monotonic due to the change of the second peak of heat transfer which is believed to be the key factor. [ABSTRACT FROM AUTHOR]

• Four integrated SPH models are presented and compared for simulating natural convection. • The most suitable SPH model for natural convection is provided. • Natural convection for R a = 10 9 and Pr = 0.71 is successfully modeled for the first time by using the SPH method. • Mechanisms of the natural convection in a square cavity at different Rayleigh numbers are discussed. This paper conducts the simulation of natural convection in a differentially heated square cavity at high Rayleigh numbers by using the smoothed particle hydrodynamics (SPH) method. Due to the decrease of the accuracy and stability, it is challenging for the SPH method to simulate natural convection at high Rayleigh numbers, and there are few reported SPH literatures of natural convection at R a > 10 6 for air (Pr = 0.71). In this study, four integrated SPH models are presented to simulate the natural convection and their accuracy and stability are assessed. These four SPH models are associated with Kernel Gradient Correction (KGC) to improve approximation accuracy and Particle Shifting Technology (PST) to regularize particle distribution while they are different in treating density diffusion and calculating the pressure term. The numerical results show that SPH model_4 (KGC, PST, δ -SPH and asymmetric pressure approximation) is the most suitable for simulating the closed natural convection problems, especially at high Rayleigh numbers. Good agreements with reference solutions are obtained by SPH model_4 for the natural convection at 10 4 ≤ R a ≤ 10 8. Furthermore, the simulation of natural convection at R a = 10 9 is conducted by SPH model_4. The evolutions of thermal convection are described in detail. It is found that dynamics characteristic reveals that the dominant force is the pressure gradient, rather than the buoyancy force before the quasi-steady state. In addition, the chaotic motion at R a = 10 9 has significant influence to the heat transfer characteristic in the vertical boundary layers. [ABSTRACT FROM AUTHOR]