Analysis of Brinkman-Extended Darcy Flow in Porous Media and Experimental Verification Using Metal Foam

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Porous Media ◽  
Metal Foam ◽  
Waste Heat ◽  
Darcy Number ◽  
Momentum Transport ◽  
Flow In Porous Media ◽  
Mean Velocity ◽  
Ground Water Pollution ◽  
The Mean ◽  
Media Flows

Momentum transport in porous media exists in numerous engineering and process applications, e.g., ground water pollution, storage of nuclear waste, heat exchangers, and chemical reactors. In many of such applications, the porous medium is confined by solid boundaries. These impermeable boundaries give rise to shear stress and boundary layers. The Brinkman-extended Darcy equation describes the momentum transport due to Newtonian fluid flow in confined porous media. This equation is solved analytically in a cylindrical system, employing an existing fully-developed boundary-layer concept particular to porous media flows. The volume-averaged velocity increases as the distance from the boundary increases reaching a maximum at the center. The mean and maximum velocities are obtained and their behavior is investigated in terms of pertinent flow parameters. The friction factor is defined based on the mean velocity and is found to be inversely proportional to the Reynolds number, the Darcy number, and the mean velocity. The analytical results are verified by experiments using two types of metal foam. In the Darcy regime, reasonably good agreement is found between the analytical and the experimental friction factors for the 20-pore-per-inch foam, while a poor agreement is found for the 10-pore-per-inch foam.

Analysis of Darcy Flow in Confined Porous Media Including Wall Effect

2011 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Heat Exchange ◽  
Velocity Field ◽  
Darcy Number ◽  
Momentum Transport ◽  
Mean Velocity ◽  
Viscous Shear ◽  
The Mean

Effective cooling lies at the heart of reactor design and safe operation. Materials for cooling systems include solid porous media (e.g. metal foam). This is due to the large surface area per unit volume and the random internal structure of such porous medium. The former promotes heat exchange rates by providing large surface area, while the latter enhances it by providing vigorous mixing of the working fluid, which gives rise to what is called dispersion (an added mechanism of heat transfer). Hence, momentum transport in porous media is critical for heat transfer analysis, computation and design. Porous media are also used as storage of nuclear waste. In such applications, the porous medium is confined by solid boundaries. These impermeable boundaries give rise to shear stress and boundary layers, which strongly influence the velocity field and the pressure drop inside the porous medium. The velocity field directly influence the heat transfer rate, while the pressure drop determines the required pumping power. The Brinkman-extended Darcy equation describes the momentum transport due to fully developed Newtonian fluid flow in confined porous media. This equation is an extension of the famous Darcy equation, and it contains the viscous shear at the boundaries as well as the viscous shear on the internal surface of the porous medium. The equation is solved analytically inside and outside the boundary layer in a cylindrical porous-media system. As, expected, the volume-averaged velocity decays as the distance from the boundary increases. The mean and maximum velocities are obtained and their behavior is investigated in terms of the Darcy number and the ratio of the effective to the actual fluid viscosity. The friction factor is defined based on the mean velocity and is found to be inversely proportional to the Reynolds number, the Darcy number and the mean velocity. The analytical velocity can be directly substituted in the governing convection heat transfer equation to assess the heat transfer performance of confined cylindrical heat exchange systems.

Heat transfer analysis of a ventilated room with a porous partition: LB-MRT simulations

2020 ◽  
Vol 91 (2) ◽  
pp. 20904
Author(s):  
Zouhira Hireche ◽  
Lyes Nasseri ◽  
Djamel Eddine Ameziani
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Natural Convection ◽  
Reynolds Numbers ◽  
Darcy Number ◽  
The Other ◽  
Flow In Porous Media ◽  
Heat Transfer Analysis ◽  
Maximum Deviation ◽  
Important Conclusion

This article presents the hydrodynamic and thermal characteristics of transfers by forced, mixed and natural convection in a room ventilated by air displacement. The main objective is to study the effect of a porous partition on the heat transfer and therefore the thermal comfort in the room. The fluid flow future in the cavity and the heat transfer rate on the active wall have been analyzed for different permeabilities: 10−6 ≤ Da ≤ 10. The other control parameters are obviously, the Rayleigh number and the Reynolds number varied in the rows: 10 ≤ Ra ≤ 106 and 50 ≤ Re ≤ 500 respectively. The transfer equations write were solved by the Lattice Boltzmann Multiple Relaxation Time method. For flow in porous media an additional term is added in the standard LB equations, to consider the effect of the porous media, based on the generalized model, the Brinkman-Forchheimer-extended Darcy model. The most important conclusion is that the Darcian regime start for small Darcy number Da < 10−4. Spatial competition between natural convection cell and forced convection movement is observed as Ra and Re rise. The effect of Darcy number values and the height of the porous layer is barely visible with a maximum deviation less than 7% over the ranges considered. Note that the natural convection regime is never reached for low Reynolds numbers. For this Re values the cooperating natural convection only improves transfers by around 10% while, for the other Reynolds numbers the improvement in transfers due to natural and forced convections cooperation is more significant.

Porous Medium Interconnector Effects on the Thermohydraulics of Near-Compact Heat Exchangers Treated as Porous Media

2006 ◽  
Vol 129 (3) ◽  
pp. 273-281 ◽  
Author(s):  
K. Sumithra Raju ◽  
Arunn Narasimhan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Heat Exchangers ◽  
Fluid Transport ◽  
Energy Transport ◽  
Metal Foam ◽  
Volume Ratio ◽  
Numerical Data ◽  
Darcy Number ◽  
Compact Heat Exchangers

A novel approach of treating near-compact heat exchangers (NCHX) (surface to volume ratio, α=100-300m2∕m3 with hydraulic diameter DM∼6mm) as a “global” porous media, whose thermohydraulic performance is being influenced by the presence of “local” tube-to-tube porous medium interconnectors, connecting the in-line arrangement of tubes (D=2mm) having square pitch of XT=XL=2.25, is investigated in this study using numerical methods. The thermohydraulics of the global porous media (NCHX) are characterized by studying the effect of transverse thickness (δ) and permeability (represented by Dai) of the local metal foam type porous medium interconnectors on the global heat transfer coefficient (Nu) and nondimensional pressure drop (ξ). The fluid transport in the porous medium interconnectors is governed by the Brinkman–Darcy flow model while the volume averaged energy equation is used to model energy transport, with the tube walls kept at constant temperature and exchanging heat with the cooling fluid having Pr=0.7 under laminar flow (10<Re<100). For the chosen NCHX configuration, ξ and Nu increases for an increase in Re and also with an increase in the thickness (δ) of the interconnecting porous medium. However, as the local Darcy number (Dai) of the interconnecting porous medium increases, the ξ decreases but the Nu increases. Treating the heat exchanger as a global porous media this result translates to an increase in the ξ and Nu as the global permeability (represented by Dag) decreases, where the decrease in Dag is because of either an increase in δ or a decrease in Dai. Separate correlations predicting ξ and Nu as a function of Re and Dag (which in turn is correlated to δ and Dai) have been developed for the chosen NCHX configuration, both of which predict the numerical data with ±20% accuracy.

Imaging of Single Phase Flow in Porous Media by High Resolution MRI

2010 ◽  
Vol 113-116 ◽  
pp. 126-131 ◽  
Author(s):  
Lan Lan Jiang ◽  
Yong Chen Song ◽  
Yu Liu ◽  
Yue Chao Zhao ◽  
Ning Jun Zhu ◽  
...  
Keyword(s):  
Porous Media ◽  
High Resolution ◽  
Velocity Distribution ◽  
Flow Direction ◽  
Spin Echo ◽  
Flow Distribution ◽  
Flow In Porous Media ◽  
Mean Velocity ◽  
High Resolution Mri ◽  
Spin Echo Sequence

This paper presents the single flow in porous media to investigate CO2 flow velocity in porous media.We used high resolution MRI to visualize the fluid flow distribution and measure axial mean velocity in porous media.In the experiment, the porous media sample was packed with glass beads, with a porosity of around 0.4. Based the traditional spin echo sequence, we modified the sequence with flow encoding gradients in the flow direction .The sample was saturated. The water flow rates were 1ml/min、2ml/min、3ml/min and 5ml/min,respectively. First, the sequence was calibrated by pipe flow without porous media. As expected, the experimental images show parabolic velocity distribution. The velocity in the centre is high. Then the sample was measured with the same sequence. The images show that the velocity distribution is homogeneous in the porous media. In the boundary of the sample, the velocities are low because of wall-effect. Moreover, the mean velocities calculated from MRI images agree with the real velocities.These errors between calculated velocities and real velocities are small. It may be reduced by changing the experiment conditions.MRI is a useful technology for measuring flow in porous media.

Kinematical measurement of hydraulic tortuosity of fluid flow in porous media

2015 ◽  
Vol 26 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Y. Jin ◽  
J. B. Dong ◽  
X. Li ◽  
Y. Wu
Keyword(s):  
Porous Media ◽  
Flow Direction ◽  
Estimation Method ◽  
Mean Value ◽  
Calculation Model ◽  
Flow In Porous Media ◽  
Porous Media Flow ◽  
Average Value ◽  
The Mean ◽  
The Impact

It is hard to experimentally or analytically derive the hydraulic tortuosity (τ) of porous media flow because of their complex microstructures. In this work, we propose a kinematical measurement method for τ by introducing the concept of local tortuosity, which is defined as the ratio of fluid particle velocity to its component along the macro flow. And then, the calculation model of τ is analytically deduced in terms of that τ is the mean value of the local tortuosity. To avoid the impact from the singularity of local tortuosity, the velocity is normalized, and τ is then approximated by the ratio of the mean normalized velocity to the average value of its component along the macro-flow direction. The new estimation method is verified by flow through different types of porous media via the lattice Boltzmann method, and the relationships between permeabilities and tortuosities obtained by different methods are examined. The numerical results show that tortuosity by the novel approach is in good agreement with the existing theory, and the kinematic definition of hydraulic tortuosity is also proven.

Outline of a theory of turbulent shear flow

1956 ◽  
Vol 1 (5) ◽  
pp. 521-539 ◽  
Author(s):  
W. V. R. Malkus
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Boundary Conditions ◽  
Momentum Transport ◽  
Turbulent Shear ◽  
Spectral Structure ◽  
Turbulent Shear Flow ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

In this paper the spatial variations and spectral structure of steady-state turbulent shear flow in channels are investigated without the introduction of empirical parameters. This is made possible by the assumption that the non-linear momentum transport has only stabilizing effects on the mean field of flow. Two constraints on the possible momentum transport are drawn from this assumption: first, that the mean flow will be statistically stable if an Orr-Sommerfeld type equation is satisfied by fluctuations of the mean; second, that the smallest scale of motion that can be present in the spectrum of the momentum transport is the scale of the marginally stable fluctuations of the mean. Within these two constraints, and for a given mass transport, an upper limit is sought for the rate of dissipation of potential energy into heat. Solutions of the stability equation depend upon the shape of the mean velocity profile. In turn, the mean velocity profile depends upon the spatial spectrum of the momentum transport. A variational technique is used to determine that momentum transport spectrum which is both marginally stable and produces a maximum dissipation rate. The resulting spectrum determines the velocity profile and its dependence on the boundary conditions. Past experimental work has disclosed laminar, ‘transitional’, logarithmic and parabolic regions of the velocity profile. Several experimental laws and their accompanying constants relate the extent of these regions to the boundary conditions. The theoretical profile contains each feature and law that is observed. First approximations to the constants are found, and give, in particular, a value for the logarithmic slope (von Kármán's constant) which is within the experimental error. However, the theoretical boundary constant is smaller than the observed value. Turbulent channel flow seems to achieve the extreme state found here, but a more decisive quantitative comparison of theory and experiment requires improvement in the solutions of the classical laminar stability problem.

scholarly journals Application of the modified vorticity transport theory to the turbulent spreading of a jet of air.

1938 ◽  
Vol 165 (920) ◽  
pp. 65-72 ◽  
Author(s):  
S. Tomotika ◽  
Geoffrey Ingram Taylor
Keyword(s):  
Axial Velocity ◽  
Transport Theory ◽  
Momentum Transport ◽  
Circular Aperture ◽  
Mean Velocity ◽  
Unpublished Paper ◽  
The Mean ◽  
Calculated Distribution ◽  
Vorticity Transport ◽  
Good Agreement

1. The turbulent spreading of a jet of air emerging from a small circular aperture has been discussed by Tollmien (1926) on the basis of Prandtl’s momentum transport theory of turbulence, by making some appropriate assumptions. He has calculated the distribution of mean velocity in the jet at distances which are sufficiently great compared with the diameter of the aperture and it has been found that the calculated distribution of mean axial velocity is in satisfactorily good agreement with observations made at Göttingen. The same problem seems to have been discussed also by L. Howarth in an unpublished paper on the basis of Taylor’s vorticity transport theory of turbulence, by assuming that not only the mean motion, but also the turbulent motion, is symmetrical about the axis of a jet. It appears, how­ever, that the agreement between Howarth’s results of calculations and the Göttingen measurements is not so good as in the case of Tollmien’s results of calculations on the momentum transport theory.

Finite Difference Investigation of a Polluted Non-Isothermal Variable-Viscosity Porous Media Flow

2020 ◽  
Vol 26 ◽  
pp. 145-156 ◽  
Author(s):  
Chinedu Nwaigwe ◽  
Oluwole Daniel Makinde
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Variable Viscosity ◽  
Darcy Number ◽  
Porous Media Flow ◽  
Flow Parameters ◽  
Manufactured Solutions ◽  
Temperature Parameter ◽  
Media Flows ◽  
The Impact

We extend previous studies of channel flows to porous media flows with combined effects ofboth heat and mass transfer. We consider a temperaturedependent viscosity fluid and a concentrationdependent diffusivity in an unsteady and pressuredriven nonisothermal Brinkman flow. This leads to the governing equations for velocity, concentration and temperature. By lagging nonlinear coefficients, in time, a convergent finite difference scheme is formulated. We adopt the method of manufactured solutions to verify the convergence and second order spatial accuracy of the scheme. The impact of the flow parameters on the flow fields are numerically investigated. The results show that increase in the Darcy number and temperature parameter both increase the velocity while the increase in the pollutant diffusion parameter decreases the pollutant concentration.

scholarly journals A combined experimental/numerical approach to study the thermal dispersion in porous media flows

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 463-474 ◽  
Author(s):  
Ehsan Languri ◽  
Krishna Pillai
Keyword(s):  
Porous Media ◽  
Individual Case ◽  
Numerical Approach ◽  
Flow In Porous Media ◽  
Dispersion Matrix ◽  
Thermal Dispersion ◽  
Dispersion Tensor ◽  
Single Scale ◽  
Media Flows ◽  
The Mathematical Model

The non-isothermal transport during flow in porous media is studied for single- and dualscale porous media. A new combined experimental/numerical approach to estimating the thermal dispersion tensor is introduced and applied for both isotropic (single-scale) and anisotropic (dualscale) porous media. The equivalence between the heat and mass transfer is exploited and a 1-D flow experimental setup is employed to study the spreading of a dye. Later, the mathematical model for such a spreading of concentration (equivalent to the temperature) around a point input in a constant velocity field is solved using the finite element based code COMSOL. Thus obtained numerical spreading pattern is fitted onto the experimentally observed one using the dispersion matrix (tensor) as a fitting parameter. A few cases of single- and dual-scale porous media are studied and the dispersion tensors are reported for each individual case. In one case, the results are validated with the available experimental data in the literature which shows a good match.

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