Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power-exponential law controlled by an exponent γ and a shift parameter u_{0} and examine how these parameters depend on the porosity. We find that γ has a universal value 1/2 at the percolation threshold and grows with the porosity, but never exceeds 2.

Tortuosity is one of the most elusive parameters of porous media. The fundamental question is whether it may be computed from the geometry only or the transport equations must be solved first. Elimination of the transport equations would significantly decrease the computation time and memory consumption and thus allow investigating larger samples. We compare the geometric to hydraulic tortuosity of a sphere-packed porous media. We applied the Discrete Element Method to generate a set of virtual beds based on experimental data taking into account the real porosity and particle distribution, the Lattice Boltzmann Method to compute the hydraulic tortuosity and geometrical approach, i.e. so-called Path Tracking Method, to calculate the geometrical tortuosity. Our study shows that the calculation time can be reduced from hours (if the LBM is used) to seconds (if the PTM is applied) without losing the accuracy of the final results. The relative error between average values of the tortuosity obtained for both used methods is less than 3%. We show that the applied geometrical method may serve as an attractive alternative to hydraulic tortuosity, particularly in large granular systems.

Models of porous media are often applied to relatively small systems, which leads not only to system-size-dependent results, but also to phenomena that would be absent in larger systems. Here we investigate one such finite-size effect: anisotropy of the permeability tensor. We show that a nonzero angle between the external body force and macroscopic flux vector exists in three-dimensional periodic models of sizes commonly used in computer simulations and propose a criterion, based on the ratio of the system size to the grain size, for this phenomenon to be relevant or negligible. The finite-size anisotropy of the porous matrix induces a pressure gradient perpendicular to the axis of a porous duct and we analyze how this effect scales with the system and grain sizes. We also analyze how the size of the representative elementary volume (REV) for anisotropy compares with the REV for permeability.

The main goal of this study is to investigate the evaporation process of a coolant (water droplets) which is injected through spray nozzles mounted on a steam turbine bypass pipeline in a co-generator system. The study includes several important factors: (1) the effects of four elbows on the flow pattern and evaporation process of the water particles, (2) heat transfer that affects the steam temperature and also the evaporation rates, and (3) the effects of inserting a perforated plate on the flow pattern and evaporation process. The first goal of this study is to investigate whether or not the existence of elbows in the pipeline will enhance the evaporation process of water droplets. Two effects have been observed so far. One is that the generation of turbulence increases in the core of the elbow which results in a higher heat transfer rate between particles and steam and the other is that particles are forced to impinge onto the outer side of the pipe wall in the elbow due to the centrifugal inertia force of the flow in the curvature path. The second goal is to carefully study the heat transfer effects of three different modes; i.e., the heat exchange between the steam and the water particles, the heat transfer of flow to the wall due to turbulence convection, and the conjugate heat transfer by means of heat conduction through the pipe wall and insulation materials. The last goal of the research is to investigate the effect of the insertion of a perforated plate downstream from the cooling water spray nozzles. A detailed analysis was conducted by microscopically modeling the flow through each hole of the perforated plate. Modeling of the high-pressure turbulent steam flow was based on a non-staggered finite volume method in three-dimensional, turbulent, compressible, two-phase dispersed flow formulations. The investigation of the structure of liquid spray jets during the transition into the gaseous phase was accomplished by developing a physical model of a particle tracking technique to investigate evaporation processes of the liquid droplets in a highly turbulent flow. Computations were performed by separating the entire pipeline system into four sections, each of which was generated in a three-dimensional grid system for more efficient computations by maintaining a sufficiently large number of meshes for each section. Flow calculations were made in each region separately by patching the end conditions from one pipe to the inlet conditions of the next one. Through this research, numerous data have been acquired and analyzed for heat transfer mechanisms of the cooling water droplets in the pipeline system. The results of the computations were verified by comparing them with theoretical models, and were shown to be quite reliable.

This paper presents a study of the numerical simulations of a steam flow and heat transfer behavior when subjected to a cooling water spray in the pipe downstream from a high-pressure turbine bypass valve. The structure of a cooling water spray injected into a steam flow was studied for the purpose of developing a physical model to investigate the dissipation and evaporation processes of the cooling water droplets in a high temperature, high turbulent steam flow passage. Heat transfer rates were calculated for a better understanding of the temperature variations in the entire system. A dispersed two-phase model was incorporated for the particle tracking of the droplets injected into the steam flow and the water evaporation process was observed. Further, this study was continued by installing a perforated plate in the pipe section downstream from the water cooling injections. The results of the calculations are quite reasonable, and show a physically sound state.