Perturbation Solutions of Transient Heat Transfer to a Porous Medium from a Fluid Stream

1981 ◽  
Vol 103 (1) ◽  
pp. 159-164 ◽  
Author(s):  
P.-C. Lu
Keyword(s):  
Porous Medium ◽  
Single Phase ◽  
Sudden Change ◽  
Thermal Response ◽  
Fluid Stream ◽  
Two Phase ◽  
Diffusive Model ◽  
Oncoming Stream ◽  
Thermal Link ◽  
Perturbation Solutions

Asymptotic behavior of the two-phase, thermal response of a porous medium, with a fluid throughflow, to a sudden change of the oncoming stream temperature is examined via four cases of perturbation solutions: (1) massive blowing, fast interphase (thermal) link, small conductivity, and small (thermal) interaction at the entrance, (2) moderate blowing, and fast interphase link, (3) massive blowing, moderate interphase link, and small interaction at the entrance, and (4) small conductivity, as well as weak interphase link. Schumann’s classical, two-phase, and non-diffusive model is shown to be just the outer limit of Case (1). The “single-phase model” is derived. Associated boundary layers are displayed. Certain numerical trend reported in the literature is also explained.

scholarly journals FEATURES OF THE FRACTIONAL-DIFFERENTIAL APPROACH IMPLEMENTATION TO DESCRIBE THE PROCESS OF FEEDING A TWO-PHASE ZONE DURING SOLIDIFICATION OF METALS AND ALLOYS

2021 ◽  
pp. 88-91
Author(s):  
Tatjana Selivyorstova ◽  
Vadim Selivyorstov ◽  
Yuliia Mala
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Nonlinear Equation ◽  
Mathematical Models ◽  
Single Phase ◽  
Phase Zone ◽  
Two Phase ◽  
Diffusion Type ◽  
Differential Approach ◽  
Fractional Differential

To describe filtration processes in complex dendritic-porous media, a number of fractional-differential mathematical models of diffusion type have been proposed.A nonlinear equation containing fractional Riemann-Liouville derivatives with respect to time is described, which can be used to correctly describe the single-phase filtration of a non-Newtonian fluid in a porous medium.

Fluidelastic Instability in Tube Arrays Subject to Two-Phase Cross Flow: A Porous Medium Approach

2015 ◽  
Author(s):  
Eliott Tixier ◽  
Cédric Béguin ◽  
Stéphane Étienne ◽  
Dominique Pelletier ◽  
Alexander Hay ◽  
...  
Keyword(s):  
Porous Medium ◽  
Numerical Simulations ◽  
Power Plants ◽  
Single Phase ◽  
Stokes Equations ◽  
Direct Numerical Simulations ◽  
Two Phase ◽  
Coupled Equations ◽  
Integration Schemes ◽  
Fluidelastic Instability

In nuclear power plants, heat exchangers undergo important flow induced vibrations, fluidelastic instability (FEI) being the most damaging one. Direct numerical simulations of such a phenomenon is currently an impossible task because of the considerable number of tubes and the two-phase nature of the flow. The novelty of the present approach is to use a porous medium to model the tube bundle and the surrounding flow. The Navier-Stokes equations are averaged on a control volume and the tubes materialized by a porosity field and source terms that model the interactions between the fluid and the solid. New sets of fully coupled equations were developed and solved with a finite element solver using high order time integration schemes. The unsteady porous medium approach already developed for single-phase flow is extended to the Euler-Euler formulation to describe the two-phase mixture. Validation and calibration of the parameters are achieved by comparing the critical flow rate and the forces acting on the tubes with results from direct numerical simulations and experimental data for single-phase flows.

A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow

2011 ◽  
Vol 47 (10) ◽  
Author(s):  
K. Mosthaf ◽  
K. Baber ◽  
B. Flemisch ◽  
R. Helmig ◽  
A. Leijnse ◽  
...  
Keyword(s):  
Porous Medium ◽  
Single Phase ◽  
Free Flow ◽  
Two Phase

A TEM study of the influence of microstructure on the superplastic behavior of a U-5.8 wt.% Nb alloy

1986 ◽  
Vol 44 ◽  
pp. 568-569
Author(s):  
G. Mackiewicz Ludtka
Keyword(s):  
Grain Size ◽  
Heating Rate ◽  
Phase Field ◽  
Single Phase ◽  
Superplastic Behavior ◽  
Two Phase ◽  
Single Phase Field

Historically, metals exhibit superplasticity only while forming in a two-phase field because a two-phase microstructure helps ensure a fine, stable grain size. In the U-5.8 Nb alloy, superplastici ty exists for up to 2 h in the single phase field (γ1) at 670°C. This is above the equilibrium monotectoid temperature of 647°C. Utilizing dilatometry, the superplastic (SP) U-5.8 Nb alloy requires superheating to 658°C to initiate the α+γ2 → γ1 transformation at a heating rate of 1.5°C/s. Hence, the U-5.8 Nb alloy exhibits an anomolous superplastic behavior.

Measurements of single-phase and two-phase flows in a vertical pipe using ultrasonic pulse Doppler method and ultrasonic time-domain cross-correlation method

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Tat Thang Nguyen ◽  
Hiroshige Kikura ◽  
Ngoc Hai Duong ◽  
Hideki Murakawa ◽  
Nobuyoshi Tsuzuki
Keyword(s):  
Time Domain ◽  
Cross Correlation ◽  
Single Phase ◽  
Ultrasonic Pulse ◽  
Phase Flow ◽  
Beam Diameter ◽  
Vertical Pipe ◽  
Two Phase ◽  
Ultrasonic Time ◽  
Pulse Doppler

Ultrasonic Velocity Profile (UVP) method for measurement of single-phase and two-phase flow in a vertical pipe has recently been developed in the Laboratory for industrial and Environmental Fluid Dynamics, Institute of Mechanics, VAST. The signal processings of the UVP method include the ultrasonic pulse Doppler method (UDM)and the ultrasonic time-domain cross-correlation (UTDC) method. For two-phase flow, simultaneous measurements of both liquid and gas are enabled by using a multi-wave ultrasonic transducer (multi-wave TDX). The multi-wave TDX is able to emit and receive ultrasound of two different center frequencies of 2 MHz and 8 MHz at the same time and position. 2 MHz frequency with beam diameter 10 mm is exploited for measurement of gas. 8 MHz one with beam diameter 3 mm is used for liquid. Measurements have been carried out for laminar and turbulent single-phase flows and bubbly counter-current two-phase flows in two flow loops using two vertical pipes of 26 mm inner diameter (I.D.) and 50 mm I.D. respectively. Based on the measured results, assessment of each method is clarified. Applicability of each method for different conditions of pipe flow has been tested. Suggestions for application of the two methods have been recommended.

On the Problem of “Two-Phase” Activated Sludge

1991 ◽  
Vol 24 (7) ◽  
pp. 59-64 ◽  
Author(s):  
R. W. Szetela
Keyword(s):  
Activated Sludge ◽  
Single Phase ◽  
Phase System ◽  
Two Phase ◽  
Wastewater Treatment Process ◽  
Sludge Stabilization ◽  
Technological Advantage ◽  
In Series ◽  
State Models ◽  
Activated Sludge Systems

Steady-state models are presented to describe the wastewater treatment process in two activated sludge systems. One of these makes use of a single complete-mix reactor; the other one involves two complete-mix reactors arranged in series. The in-series system is equivalent to what is known as the “two-phase” activated sludge, a concept which is now being launched throughout Poland in conjunction with the PROMLECZ technology under implementation. Analysis of the mathematical models has revealed the following: (1) treatment efficiency, excess sludge production, energy consumption, and the degree of sludge stabilization are identical in the two systems; (2) there exists a technological equivalence of “two-phase” sludge with “single-phase” sludge; (3) the “two-phase” system has no technological advantage over the “single-phase” system.

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