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Forced Convection in Porous Media
Published in Yasser Mahmoudi, Kamel Hooman, Kambiz Vafai, Convective Heat Transfer in Porous Media, 2019
Pourya Forooghi, Benjamin Dietrich
as the governing equation for momentum transport in a porous medium (Joseph et al., 1982), where u denotes the superficial velocity. The permeability K and form-drag coefficient cF are both geometric properties depending on the microscopic structure of the porous medium. According to Equation (3.1), the pressure gradient in the porous medium balances with contributions from viscous and form-drag terms, the first and second terms on the right-hand side also referred to as Darcy and Forchheimer terms, respectively. At low velocities, the quadratic Forchheimer term becomes insignificant and Equation (3.1) reduces to the Darcy’s law. As will be discussed in Section 3.4 of this chapter, other extensions to the Darcy’s law are also suggested in the literature, but we continue with Equation (3.1), as it serves our purpose for the time being.
Catalytic Two-Phase Reactors
Published in Salmi Tapio, Mikkola Jyri-Pekka, Wärnå Johan, Chemical Reaction Engineering and Reactor Technology, 2019
Salmi Tapio, Mikkola Jyri-Pekka, Wärnå Johan
The flow velocity (w) is based on the entire cross-section of the reactor (superficial velocity). The real average flow velocity (w′), interstitial velocity, is higher, since the fluid de facto passes through the empty spaces between the particles. The velocities, w and w′, are related by the bed porosity: w=εw′.
Hydrodynamics of Two-Phase Flow
Published in L. S. Tong, Y. S. Tang, Boiling Heat Transfer and Two-Phase Flow, 2018
where J is the mixture average superficial velocity, or the total volumetric flux, which is constant in one-dimensional, steady flow: () J=uGαG+uLαL
Thermal effect on cavitation characteristics of a hydraulic torque converter
Published in Numerical Heat Transfer, Part A: Applications, 2022
Meng Guo, Cheng Liu, Jiahua Zhang, Shiqi Liu, Qingdong Yan, Boo Cheong Khoo
The superficial velocity is a common method to describe the velocity of each phase in multiphase flow, it is defined as the ratio of the liquid or vapor volumetric flowrate to the total cross-sectional area. The superficial velocity of oil and vapor on both sides of the blades surface shows that the velocity on the head and tail of both the turbine and the stator blades was far greater than that in the middle section, and it increased with the rising temperature, which would promote the occurrence of cavitation. It is worth noting that the velocity value, as well as the high-velocity area, on blades surface of stator were larger than that on the turbine blades, which is one of the reasons why the coverage of cavitation bubbles on the surface of the stator blades is higher than the turbine, as shown in Figure 18.
Effect of airflow rate on drying air and moisture content profiles inside a cross-flow drying column
Published in Drying Technology, 2018
Sangeeta Mukhopadhyay, Terry J. Siebenmorgen
While a few deep-bed studies included the effect of Q in cfm/bu (commonly used in the USA, especially in bin-drying; cfm/bu refers to the volume of air flowing through a unit volume of grain), it is difficult to apply this knowledge in terms of the actual superficial velocity of the air flowing through a bed of grain since dryer dimensions were not provided in these studies. Superficial velocity, also known as “apparent velocity,” refers to the product of the true interstitial velocity of air and the porosity/void fraction of the packed bed of particles.[32] In addition, rice cross-flow dryers are often operated at elevated temperatures (40–70°C) to achieve high throughput rates. The drying conditions from deep-bed studies or other dryer configurations are different from those used in a cross-flow dryer, for example, natural air in bin-drying uses ambient air (3–8°C) to dry rice over a period of weeks, even months[33] or slightly warm air (25–38°C),[34] mixed flow dryers use heated air at 43–78°C,[35] and fluidized-bed dryers use drying air temperatures as high as 140–150°C.[36] As a result, the insights gained from such studies cannot be directly applied to cross-flow dryers.
A Discussion About Two-Phase Flow Pressure Drop in Proton Exchange Membrane Fuel Cells
Published in Heat Transfer Engineering, 2020
Mehdi Mortazavi, Mahbod Heidari, Seyed A. Niknam
Transporting an excess amount of liquid water to a GDL can eventually obstruct the flow of reactants to the catalyst layer. This causes GDL flooding, which adversely impacts PEM fuel cell performance [6–8]. Liquid water can also enter flow channels by emerging as droplets at some preferential locations [9–12]. Water transport mechanisms in PEM fuel cell flow channels were classified by Zhang et al. [13]. It was observed that when both the water production rate and the superficial gas velocity are low, water drains from inside the channel by spreading over hydrophilic channel walls and transports through the corners, forming corner flow. The fluid's superficial velocity is its bulk velocity within the cross-sectional area of the flow channel. For a moderate water production rate, corner flow may not be adequate to remove liquid water, and therefore, it changes to annular film flow. Finally, for high water production rate, the annular film flow may change to slug flow within the flow channels. The latter may cause channel flooding which can ultimately lower the performance of the cell [14–16]. Another two-phase flow pattern may occur in PEM fuel cell flow channels, which requires high superficial gas velocities. In this case, the shear force from the gas stream can detach the water droplets from the surface of the GDL, which forms mist flow. Mortazavi and Tajiri [17] studied liquid water droplet detachment from the surface of the GDL caused by shear force from the gas stream. In addition, enhanced water removal techniques from the flow channels of PEM fuel cells have been proposed by externally exciting water droplets around their natural frequencies [18, 19].