Experimental and numerical characterization of the transverse dispersion at the exit of a short ceramic foam inside a pipe

Pereira, J. C. F.; Malico, Isabel; Hayashi, Thamy; Raposo, J.

doi:10.1016/j.ijheatmasstransfer.2004.08.001

Cited by 13 publications

(5 citation statements)

References 39 publications

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“…Finally, the good agreement between the data and the model for the contribution from the spatially heterogeneous velocity field based on Koch & Brady (1986)'s analytical solution at φ > 0.20 suggests that lateral dispersion predictions based on Stokes flow analysis may be applicable at higher Reynolds numbers at sufficiently high φ. Indeed, Hackert et al (1996) and Pereira et al (2005)'s transverse dispersion measurements, which also agree with a Stokes flow solution (discussed above), were collected at pore Reynolds numbers of 10-300, where inertia is clearly non-negligible.…”

Section: Discussionmentioning

confidence: 54%

Lateral dispersion in random cylinder arrays at high Reynolds number

Tanino¹,

2008

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Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction φ=0.010–0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where φ≥0.5. This paper focuses on pore Reynolds numbers greater than Res=250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and Kyy/(Upd), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, Up, and the cylinder diameter, d, are independent of Res. First, Kyy/(Upd) increases rapidly with φ from φ =0 to φ=0.031. Then, Kyy/(Upd) decreases from φ=0.031 to φ=0.20. Finally, Kyy/(Upd) increases again, more gradually, from φ=0.20 to φ=0.35. These observations are accurately described by the linear superposition of the proposed model of turbulent diffusion and existing models of dispersion due to the spatially heterogeneous velocity field that arises from the presence of the cylinders. The contribution from turbulent diffusion scales with the mean turbulence intensity, the characteristic length scale of turbulent mixing and the effective porosity. From a balance between the production of turbulent kinetic energy by the cylinder wakes and its viscous dissipation, the mean turbulence intensity for a given cylinder diameter and cylinder density is predicted to be a function of the form drag coefficient and the integral length scale lt. We propose and experimentally verify that lt=min{d, 〈sn〉A}, where 〈sn〉A is the average surface-to-surface distance between a cylinder in the array and its nearest neighbour. We farther propose that only turbulent eddies with mixing length scale greater than d contribute significantly to net lateral dispersion, and that neighbouring cylinder centres must be farther than r* from each other for the pore space between them to contain such eddies. If the integral length scale and the length scale for mixing are equal, then r*=2d. Our laboratory data agree well with predictions based on this definition of r*.

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Section: Discussionmentioning

confidence: 54%

Lateral dispersion in random cylinder arrays at high Reynolds number

Tanino¹,

2008

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“…Reactor: 4 cm in diameter, 12 m in length; catalyst: 10% Ag/α-Al 2 O 3 , 5-mm rings. Inlet conditions: 46% C 2 H 4 , 4% CO 2 , 11% O 2 , and 39% CH 4 ; gas hourly space velocity, GHSV = 2890; 242 °C; 20 atm (from ref ). …”

Section: Examples Of Exothermic and Endothermic Processesmentioning

confidence: 99%

“…A better understanding of the heat management impact of the foam replacement comes from a 2-D model simulation (Figure 8) of the commercial process for ethylene epoxidation under typical industrial conditions. 58 Strong axial and radial temperature gradients develop at the front of the bed, reaching a center peak at 269 °C, with a radial gradient of 20 °C and temperature runaway predicted at 274 °C, so there is very little flexibility. To prevent the occurrence of runaway, conversion is limited to 9.3%, which requires expensive recycle of the unconverted ethylene.…”

Section: Examples Of Exothermic and Endothermic Processesmentioning

confidence: 99%

Fundamentals and Applications of Structured Ceramic Foam Catalysts

Twigg

Richardson

2007

Ind. Eng. Chem. Res.

321

222

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This paper reviews the use of ceramic foams as structured catalyst supports. They are open-cell ceramic structures that may be fabricated in a variety of shapes from a wide range of materials, and they exhibit very high porosities with good interconnectivity. These characteristics result in a lower pressure drop than that observed with packed beds and high convection in the tortuous megapores, which, in turn, enhances mass and heat transfer. They are easily coated with high-surface-area catalytic components, using well-established techniques. Research in the past decade has produced a large amount of fundamental information that elucidates the desirable properties of ceramic foams. In addition, many applications involving important reactions have appeared in the open and patent literature, especially for catalytic processes that suffer certain limitations, such as those encountered in relieving high pressure drop with low-contact-time reactions at high space velocities or with narrow reactors in heat-transfer-limited systems and in controlling axial and radial temperature profiles in highly exothermic and endothermic reactions. These important contributions are discussed, and the advantages and shortcomings of using ceramic foams as structured catalyst supports to benefit commercial operations are considered.

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“…In particular, fluid flow through granular beds has attracted attention due to its importance in many important industrial processes, such as chromatographic separation technology [3,4], packed bed reactor and contacting device design [5,6], catalytic exhausters [7], modeling of contaminant transport in hydrogeological and environmental systems [8] and studies of perfusion in biological media [9,10].…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigations of Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds in a Cylindrical Coordinates System

et al. 2007

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Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through a random packing of non-overlapping spheres at moderate Reynolds numbers, spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study. This observation suggests that no transition to turbulence could occur in the range of the Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. In addition to numerical calculations, to describe the concentration profile of solute, an approximate solution for the mass transport equation in a bounded granular bed in a cylindrical coordinates system is proposed. Lateral fluid dispersion coefficients are then calculated by fitting the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number. IntroductionTransport phenomena in disordered systems are a subject of considerable scientific and engineering importance [1,2]. In particular, fluid flow through granular beds has attracted attention due to its importance in many important industrial processes, such as chromatographic separation technology [3,4], packed bed reactor and contacting device design [5,6], catalytic exhausters [7], modeling of contaminant transport in hydrogeological and environmental systems [8] and studies of perfusion in biological media [9,10].Henry Darcy was first to report that at low velocities, where the inertial forces are negligible compared to those due to viscous effects, the volume rate of flow through a packed pipe is proportional to the pressure gradient, namely (dp/dx) ∝ V. 1)Later, researchers [11,12] derived Darcy's Law by averaging, in one form or another, the one-dimensional form of the NavierStokes equation by neglecting the fluid inertial forces. As fluid inertia forces increase, the ratio of pressure drop to velocity gradually deviates from Darcy's Law. In fact, Forchheimer [13] suggested a quadratic expression between the pressure gradient and the fluid velocity when the effect of fluid inertia cannot be neglected, namely (dp/dx) = aV + bV 2 . A number of quadratic expressions have been proposed for the deviation from Darcy's Law for which the nonlinear term was obtained by averaging the Navier-Stokes equation, which includes the inertial terms [14][15][16][17]. It would be expected that by increasing the fluid inertial forces, the transition from laminar to turbulent flow should be observed. However, ...

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Experimental and numerical characterization of the transverse dispersion at the exit of a short ceramic foam inside a pipe

Abstract: The paper theoretically and numerically describes and experimentally studies transverse dispersion of a passive tracer in highly porous ceramic foams of different pore sizes. The pore

Cited by 13 publications

References 39 publications

Lateral dispersion in random cylinder arrays at high Reynolds number

Lateral dispersion in random cylinder arrays at high Reynolds number

Fundamentals and Applications of Structured Ceramic Foam Catalysts

Numerical Investigations of Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds in a Cylindrical Coordinates System

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