Begell House Inc.
Journal of Porous Media
JPM
1091-028X
12
11
2009
Dynamic Compaction of Soft Compressible Porous Materials: Experiments on Air-Solid Phase Interaction
1019-1035
10.1615/JPorMedia.v12.i11.10
Michel
Al-Chidiac
Department of Mechanical Engineering, The City College of New York, CUNY
Parisa
Mirbod
City college
Yiannis
Andreopoulos
Department of Mechanical Engineering, The City College of New York, CUNY
Sheldon
Weinbaum
Department of Biomedical Engineering, The City College of New York, CUNY
An experiment has been designed to examine the generation of dynamic lift forces during compaction of soft highly compressible fibrous materials in a piston/cylinder apparatus. Novel experimental techniques have been developed to simultaneously measure and separate out the dynamic forces acting on the compressing piston by the air and solid phases, respectively. The measurements clearly demonstrate that the excess pore pressure builds up inside the porous material and reaches its maximum before there is any significant rise in the solid-phase force. The air pressure subsequently decays due to air venting into the ambient environment at the edges of the testing apparatus as the solid phase force rapidly rises. We also examine the internal stresses and strains within the solid phase that develop as a result of friction forces along the sidewalls of the cylinder and show that these lead to important hysteresis effects when the loads on the piston are gradually removed. The experiments are performed on a polyester material with a trace of silk, which has recently been proposed for a soft porous track wherein a high-speed train is supported by a large planing surface or ski that rides within a confined channel in which this venting is substantially reduced or eliminated (Mirbod et al, 2009).
Application of Soft Porous Materials to a High-Speed Train Track
1037-1052
10.1615/JPorMedia.v12.i11.20
Parisa
Mirbod
City college
Yiannis
Andreopoulos
Department of Mechanical Engineering, The City College of New York, CUNY
Sheldon
Weinbaum
Department of Biomedical Engineering, The City College of New York, CUNY
This paper explores the performance of an airborne jet-ski train that flies on a soft porous track within centimeters of the earth’s surface at speeds approaching current commercial jet aircraft. The jet train employs a lift mechanism first described for red cells gliding on the endothelial glycocalyx and subsequently used to predict the lift forces generated in skiing and snowboarding by the transiently trapped air beneath their planing surfaces. Using an asymptotic analysis for large values of the permeability parameter H/√Kp, where H is the porous layer thickness and Kp the Darcy permeability we first show that it is possible to support a 70 metric ton jet train carrying 200 passengers on a confined porous material if its Kp is approximately 5 × 10−9 m2. For this Kp one finds that the tilt of the planform is < 0.1 deg and the liftoff velocity is < 5 m/s. This value of Kp can be satisfied by a random fiber matrix with a fiber radius of 5 μ;m and a void fraction of 0.995. Compression tests on a fiber-fill material with these properties show that the fibers contribute < 0.2% of the total lift at maximum compression, and hence, the friction force of the fiber phase is negligible. Using jet engines of 10,000 lbf thrust, about 1/5 that of a 200 passenger jet aircraft, one is able to obtain a cruising velocity approaching 700 km/hr. This would allow for huge fuel savings and greatly reduce greenhouse emission.
Flow and Diffusion of Chemically Reactive Species over a Nonlinearly Stretching Sheet Immersed in a Porous Medium
1053-1063
10.1615/JPorMedia.v12.i11.30
Seripah Awang
Kechil
Center of Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor
The flow and mass transfer of a chemically reactive species over a nonlinearly stretching sheet in a porous medium is considered. The boundary layer theory and the similarity procedure are used to obtain a system of nonlinear ordinary differential equations. A feasible approximate analytical solution for the system is obtained and the influences of the physical parameters on the flow and mass transfer characteristics are analyzed. The permeability parameter reduces the velocity profiles and increases the momentum and concentration boundary layers thickness. The destructive chemical reaction reduces the concentration boundary layers.
Effect of Porous Fraction and Interfacial Stress Jump on Skin Friction and Heat Transfer in Flow Through a Channel Partially Filled with Porous Material
1065-1082
10.1615/JPorMedia.v12.i11.40
G. P. Raja
Sekhar
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302
V. V.
Satyamurty
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302 , India
D.
Bhargavi
Department of Mathematics, National Institute of Technology, Warangal, India-506004
Changes in skin friction coefficient and Nusselt number were examined when a porous layer was attached to one of the walls of a parallel plate channel subjected to constant heat flux. The flow and thermal fields were assumed to be fully developed. It was found that the net change in skin friction coefficient and Nusselt number with porous fraction is more significant than the changes due to stress jump coefficient, except for the extreme value of unity for the stress jump coefficient. Further, it was shown that the increase in the Nusselt number on the fluid side is higher than the decrease on the porous side for a porous fraction above a certain value, which depends on the Darcy number. The existence of optimum thickness for the porous layer is established. Further studies on optimizing the porous layer thickness subject to the constraints of fixed flow rate, pressure gradient, or pressure drop need to be undertaken.
Numerical Analysis of Natural Convection in Porous Cavities with Partial Convective Cooling Conditions
1083-1100
10.1615/JPorMedia.v12.i11.50
W.
Pakdee
Department of Mechanical Engineering, Faculty of Engineering, Thammasat University, Rangsit Campus, Klong Luang, Pathumtani 12120
P.
Rattanadecho
Faculty of Engineering, Thammasat University (Rangsit Campus), Pathumthani 12121
Transient natural convection flow through a fluid-saturated porous medium in a square enclosure with a partially cooling surface condition was investigated using a Brinkmann-extended Darcy model. The physical problem consists of a rectangular cavity filled with porous medium. The cavity is insulated, except the top wall that is partially exposed to an outside ambient. The exposed surface allows convective transport through the porous medium, generating a thermal stratification and flow circulations. The formulation of differential equations is nondimensionalized and then solved numerically under appropriate initial and boundary conditions using the finite difference method. The finite difference equations handling the convection boundary condition of the open top surface are derived for cooling conditions. In addition to the negative density gradient in the direction of gravitation, a lateral temperature gradient in the region close to the top wall induces the buoyancy force under an unstable condition. The two-dimensional flow is characterized mainly by the clockwise and anti-clockwise symmetrical vortices driven by the effect of buoyancy. The directions of vortex rotation generated under the cooling condition are in the opposite direction as compared to the heating condition. Unsteady effects of associated parameters were examined. The modified Nusselt number (Nu) was systematically derived. This newly developed form of Nu captures the heat-transfer behaviors reasonably accurately. It was found that the heat-transfer coefficient, Rayleigh number, Darcy number, as well as flow direction strongly influenced characteristics of flow and heat-transfer mechanisms.
Criterion for Local Thermal Equilibrium in Forced Convection Flow Through Porous Media
1103-1111
10.1615/JPorMedia.v12.i11.60
Xuewei
Zhang
Huazhong University of Science and Technology, School of Energy and Power Engineering, Wuhan 430074
Wei
Liu
School of Energy and Power Engineering, Huazhong University of Science & Tecnology, 1037 Luo Yu Rd. Hongshan District, Wuhan 430074, China
Zhichun
Liu
School of Energy and Power Engineering, Huazhong University of Science & Tecnology, 1037 Luo Yu Rd. Hongshan District, Wuhan 430074, China
In this paper, a general criterion for local thermal equilibrium is presented in terms of parameters including the effective fluid Prandtl number, the particle Reynolds number, the effective solid-to-fluid thermal conductivity ratio, the Darcy number, the Nusselt number, and porosity. In order to check the validity of the proposed criterion for local thermal equilibrium, the forced convection phenomena in the porous medium between two parallel plates subjected to constant temperature are studied by a numerical method based on the Brinkman-Forchheimer extended Darcy model. The proportion of temperature difference between solid and fluid phases in a representative elementary volume to the temperature rise of fluid is studied by comparing the effects of relevant parameters in this new criterion. In addition, the proposed criterion is consistent with the existing experimental and numerical results for convection heat transfer in porous medium.
Analytic Solution for Free Convection in an Open Vertical Rectangular Duct Filled with a Porous Medium
1113-1120
10.1615/JPorMedia.v12.i11.70
C. Y.
Wang
Department of Mathematics and Mechanical Engineering, Michigan State University, East
Lansing, Michigan 48824, USA
An analytic solution for the fully developed free convection in a vertical rectangular duct filled with a Brinkman-Darcy porous material is found. The solution depends on the aspect ratio and a nondimensional parameter (s) that signifies the relative importance of the viscosity ratio to permeability. For large s, velocity boundary layers exist on the heated wall. Asymptotic expansions show that the mean velocity is proportional to s 2 for small s and approaches a constant of 1/s for larges.
Homotopy Perturbation Method for General Form of Porous Medium Equation
1121-1127
10.1615/JPorMedia.v12.i11.80
Jafar
Biazar
University of Guilan, Department of Mathematics, Faculty of Sciences, P.O. Box 1914 P.C. 41938, Rasht
Zainab
Ayati
University of Guilan, Department of Mathematics, Faculty of Sciences, P.O. Box 1914 P.C. 41938, Rasht
Hamideh
Ebrahimi
University of Guilan, Department of Mathematics, Faculty of Sciences, P.O. Box 1914 P.C. 41938, Rasht
In this work we consider the homotopy perturbation method to solve the general form of porous medium equations. This equation has been widely used as a simple model for nonlinear heat propagation in a reactive medium. The results will be compared with the Adomian decomposition method. To illustrate the reliability of the method, some special cases of the equation are solved as examples.