A revisit of pressure drop-flow rate correlations for packed beds of spheres

Erdim, Esra; Akgiray, Ömer; Demir, İbrahim

doi:10.1016/j.powtec.2015.06.017

Cited by 114 publications

(68 citation statements)

References 40 publications

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“…where g [m/s 2 ] is the acceleration due to gravity, d [m] is the characteristic pore length by means of the particle diameter, v [m 2 /s] is the kinematic viscosity of the fluid, n [−] is the porosity, A is the Ergun constant that equals 150 and B is the Ergun constant that equals 1.75 (Ergun 1952). Many variations on the Ergun relation for different kinds of porous media and flow regimes are given in the literature (e.g., Engelund 1953;Irmay 1964;Mac-Donald et al 1979;Du Plessis 1994;Sedghi-Asl and Rahimi 2011;Erdim et al 2015;Guo et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

et al. 2019

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Under certain flow conditions, fluid flow through porous media starts to deviate from the linear relationship between flow rate and hydraulic gradient. At such flow conditions, Darcy's law for laminar flow can no longer be assumed and nonlinear relationships are required to predict flow in the Forchheimer regime. To date, most of the nonlinear flow behavior data is obtained from flow experiments on packed beds of uniformly graded granular materials (C u = d 60 /d 10 < 2) with various average grain sizes, ranging from sands to cobbles. However, natural deposits of sand and gravel in the subsurface could have a wide variety of grain size distributions. Therefore, in the present study we investigated the impact of variable grain size distributions on the extent of nonlinear flow behavior through 18 different packed beds of natural sand and gravel deposits, as well as composite filter sand and gravel mixtures within the investigated range of uniformity (2.0 < C u < 17.35) and porosity values (0.23 < n < 0.36). Increased flow resistance is observed for the sand and gravel with high C u values and low porosity values. The present study shows that for granular material with wider grain size distributions (C u > 2), the d 10 instead of the average grain size (d 50) as characteristic pore length should be used. Ergun constants A and B with values of 63.1 and 1.72, respectively, resulted in a reasonable prediction of the Forchheimer coefficients for the investigated granular materials.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

et al. 2019

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“…Based on an extensive comparison of the computational equations for determining the pressure drop through the packed bed performed in Reference [17], the computational equations listed in Table 3 were selected.…”

Section: Pressure Dropsmentioning

confidence: 99%

“…This is not an exhaustive list of all available computational equations to determine the friction coefficient as the medium flows through the packed bed. Other equations can be obtained in References [15,17].…”

Section: Pressure Dropsmentioning

confidence: 99%

Review of Design and Modeling of Regenerative Heat Exchangers

Kilkovský¹

2020

Energies

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Heat regenerators are simple devices for heat transfer, but their proper design is rather difficult. Their design is based on differential equations that need to be solved. This is one of the reasons why these devices are not widely used. There are several methods for solving them that were developed. However, due to the time demands of calculation, these models did not spread too much. With the development of computer technology, the situation changed, and these methods are now relatively easy to apply, as the calculation does not take a lot of time. Another problem arises when selecting a suitable method for calculating the heat transfer coefficient and pressure drop. Their choice depends on the type of packed bed material, and not all available computational equations also provide adequate accuracy. This paper describes the so-called open Willmott methods and provides a basic overview of equations for calculating the regenerative heat exchanger with a fixed bed. Based on the mentioned computational equations, it is possible to create a tailor-made calculation procedure of regenerative heat exchangers. Since no software was found on the market to design regenerative heat exchangers, it had to be created. An example of software implementation is described at the end of the article. The impulse to create this article was also to broaden the awareness of regenerative heat exchangers, to provide designers with an overview of suitable calculation methods and, thus, to extend the interest and use of this type of heat exchanger.Energies 2020, 13, 759 2 of 27 Another difficulty when calculating these devices is finding suitable computational equations to describe the heat transfer between the gas and the packed bed material. Although these equations can be found in the literature, they are usually given only for spherical shapes. In addition, different equations give different results. It is, therefore, necessary to choose a suitable calculation equation in order to get the best results. A better situation is in the calculation of pressure drops, for which many computational equations can be found in the literature. However, some of them give different results from those measured. This paper, therefore, provides an overview of suitable computational equations so that a complete computational algorithm of regenerative heat exchangers can be compiled.

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“…Accordingly, in our permeability model, this common denominator takes on the dual role of (a) being the radius of the obstacle responsible for the fluid friction due to viscous considerations, and, (b) at the same time, represents the hydraulic radius of the flow channel responsible for the fluid friction due to kinetic considerations. We exploit this feature in our theory by providing a mechanism for normalizing fluid resistance by either (1) surface area contact (k1 =4rh 2 /3 = 67), or, (2) reciprocal channel circumference (k2 = 1/ (2rh) = 1/25).…”

Section: B Rh-the Fluid Drag Normalization Coefficientmentioning

confidence: 99%

Quinn’s Law of Fluid Dynamics Pressure-Driven Fluid Flow through Closed Conduits

Quinn¹

2019

Preprint

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In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the normalized dimensionless pressure gradient, PQ, and the normalized dimensionless fluid current, CQ. The relationship is expressed mathematically as: PQ = k1 +k2CQ. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k1, and as the fluid acceleration increases, it varies with a slope of k2 as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.

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A revisit of pressure drop-flow rate correlations for packed beds of spheres

Cited by 114 publications

References 40 publications

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Review of Design and Modeling of Regenerative Heat Exchangers

Quinn’s Law of Fluid Dynamics Pressure-Driven Fluid Flow through Closed Conduits

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A revisit of pressure drop-flow rate correlations for packed beds of spheres

Cited by 114 publications

References 40 publications

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Review of Design and Modeling of Regenerative Heat Exchangers

Quinn&rsquo;s Law of Fluid Dynamics Pressure-Driven Fluid Flow through Closed Conduits

Contact Info

Product

Resources

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Quinn’s Law of Fluid Dynamics Pressure-Driven Fluid Flow through Closed Conduits