Stability conditions for displacement processes in porous media

1969 ◽  
Vol 47 (2) ◽  
pp. 209-214 ◽  
Author(s):  
A. E. Scheidegger
Keyword(s):  
Porous Media ◽  
Steady State ◽  
Stability Conditions ◽  
Displacement Processes ◽  
Frontal Displacement

A general discussion is presented of the possibility of the development of a steady state in frontal displacement processes with and without "fingers" in porous media. It is shown that, based on the theories available to date, such displacement processes always appear to be unstable; i.e., the "length" of the "front" over which the transition from the displaced fluid to the displacing one occurs, grows indefinitely.

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

scholarly journals Determination of Permeability and Inertial Coefficients of Sintered Metal Porous Media Using an Isothermal Chamber

2018 ◽  
Vol 8 (9) ◽  
pp. 1670 ◽  
Author(s):  
Wei Zhong ◽  
Xiang Ji ◽  
Chong Li ◽  
Jiwen Fang ◽  
Fanghua Liu
Keyword(s):  
Porous Media ◽  
Steady State ◽  
Flow Rate ◽  
Pressure Difference ◽  
Testing Time ◽  
Sintered Metal ◽  
Steady State Method ◽  
Volume Limit ◽  
Inertial Coefficient

Sintered metal porous media are widely used in a broad range of industrial equipment. Generally, the flow properties in porous media are represented by an incompressible Darcy‒Forchheimer regime. This study uses a modified Forchheimer equation to represent the flow rate characteristics, which are then experimentally and theoretically investigated using a few samples of sintered metal porous media. The traditional steady-state method has a long testing time and considerable air consumption. With this in mind, a discharge method based on an isothermal chamber filled with copper wires is proposed to simultaneously determine the permeability and inertial coefficient. The flow rate discharged from the isothermal chamber is calculated by differentiating the measured pressure, and a paired dataset of pressure difference and flow rate is available. The theoretical representations of pressure difference versus flow rate show good agreement with the steady-state results. Finally, the volume limit of the isothermal chamber is addressed to ensure sufficient accuracy.

The Modelling and Coupling Methodology of ANSYS CFX Using Porous Media for PB-AHTR

2013 ◽  
Author(s):  
Linsen Li ◽  
Haomin Yuan ◽  
Kan Wang
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Steady State ◽  
High Temperature ◽  
Monte Carlo Code ◽  
First Principle ◽  
Pebble Bed ◽  
Coupled Calculation ◽  
Ansys Cfx ◽  
High Temperature Reactor

This paper introduces a first-principle steady-state coupling methodology using the Monte Carlo Code RMC and the CFD code CFX which can be used for the analysis of small and medium reactors. The RMC code is used for neutronics calculation while CFX is used for Thermal-Hydraulics (T-H) calculation. A Pebble Bed-Advanced High Temperature Reactor (PB-AHTR) core is modeled using this method. The porous media is used in the CFX model to simulate the pebble bed structure in PB-AHTR. This research concludes that the steady-state coupled calculation using RMC and CFX is feasible and can obtain stable results within a few iterations.

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