Generalized description of fluid flow, void fraction, and pressure drop in fixed beds with embedded tubes

1990 ◽  
Vol 29 (6) ◽  
pp. 968-977 ◽  
Author(s):  
Felix A. Schneider ◽  
David W. T. Rippin ◽  
Esmond Newson
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Void Fraction ◽  
Flow Void ◽  
Fixed Beds

A One Dimensional Two-Fluid Model for Bubbly Flows in Fixed Beds

2002 ◽  
Author(s):  
M.-L. Bordas ◽  
A. Cartellier ◽  
P. Se´chet
Keyword(s):  
Pressure Drop ◽  
Void Fraction ◽  
Bubble Size ◽  
Fluid Model ◽  
Bubbly Flows ◽  
Two Phase ◽  
The Mean ◽  
Two Fluid Model ◽  
Fixed Beds ◽  
Two Fluid

Pressure drop and gas void fraction are important parameters for the design of multiphase packed bed reactors which are widely used in petrochemical industry. Several experimental studies have been devoted to the hydrodynamics of two-phase cocurrent upflow or downflow through fixed beds, and various correlations of limited range of validity are available in the literature. However, there is not yet a clear agreement on the form of the momentum equations to be used in such systems. Early attempts devoted to the pressure drop estimate were based on an extension of the Lockhart-Martinelli approach (Sweeney 1967), Rao et al. 1983). More recently, Attou at al. (1999) proposed the first serious attempt to adapt the Eulerian two-fluid model to cocurrent bubbly flows through packed beds. From an analysis of their proposal, it happens that the basic mechanical equilibrium for the gas phase needs to be reconsidered. In this scope, we derived a new model on the basis of the so-called hybrid approach initially developed for bubbly flows in ducts in absence of shear-induced turbulence (Achard and Cartellier 2000). As a first application, we considered a mean unidirectional flow of a bubbly mixture through a porous medium composed of beads uniform in size. For steady and fully established flows, and assuming a flat void fraction (α) profile, the resulting momentum equations for each phase write: Liquidphase:−dpdz=ρLg+fLS−fLG1−α(1)Gasphase:−dpdz=ρGg+fLS+fLGα(2) where fLS is the resultant of the liquid shear stress exerted on beads surface and on exterior walls, and where the quantity fLG = α F* / Vp represents the interaction force density between the gas and the liquid (F* is the mean force on bubbles and Vp = 4πa3/3 denotes the bubble volume, a being the bubble radius). The main difference with the model derived by Attou et al. is the presence of the fLS term in the gas phase equation. Without this term, the relative velocity of bubbles would be controlled by the axial pressure gradient dP/dz even in non accelerating flows which is unphysical. On the opposite, in the present model (1–2) the relative movement of bubbles is simply due to buoyancy. The set of equations (1–2) provides a mean to exploit the experimental data to derive the required closures, namely the evolution of the friction fLS with the gas content and that of the momentum exchange between phases fLG. Notably, from (1) and (2), one gets fLG=α(1−α)(ρL−ρG)g(3) In order to establish reliable closures, available experimental data of the literature are currently revisited under this framework. For the friction term, which is the principal contribution to the pressure drop, the usual closure law for fLS as given by an Ergun equation adapted to two-phase flows is under analysis. For the interfacial momentum transfer, the objective is to evaluate an “apparent” drag coefficient defined as Cd = F*/[ρL Ur2 π a2 / 2] where the mean relative velocity Ur is defined as the difference between the mean gas and liquid velocities averaged over a volume. Indeed, paralleling an approach already exploited for bubbly flows in ducts (Riviere and Cartellier 1999), it happens that the mean void fraction can be derived from equations (1) and (2) assuming a flat void fraction profile: β(1−β)−α(1−α)=(4π/3)α(1−α)[gδ2VSLνc](aδ)2fd(4) where δ is the typical size of the pores and where fd = (π/2) Rep Cd is expected to be a function of the bubble size, the porosity ε and the void fraction. To extract fd or Cd from (4), a characteristic bubble size must be specified. As shown Fig.1, the bubble size is controlled by the bed geometry and evolves between 0.2 δ and 3 δ in the dilute limit (Bordas et al. (2001)). Analysis of the existing data will be presented based on these size estimates, and comparison will be performed of this “apparent” drag with values measured for isolated bubbles in fixed beds (Fig.2).

Study of fluid flow through a channel deformed by piezoelement

2018 ◽  
Vol 13 (3) ◽  
pp. 1-10 ◽  
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh Nasibullaeva ◽  
O.V. Darintsev
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Flow Rate ◽  
Contact Surface ◽  
Piezoelectric Element ◽  
Neumann Boundary ◽  
Differential Pressure ◽  
Physical Parameters ◽  
Flow Through

The flow of a liquid through a tube deformed by a piezoelectric cell under a harmonic law is studied in this paper. Linear deformations are compared for the Dirichlet and Neumann boundary conditions on the contact surface of the tube and piezoelectric element. The flow of fluid through a deformed channel for two flow regimes is investigated: in a tube with one closed end due to deformation of the tube; for a tube with two open ends due to deformation of the tube and the differential pressure applied to the channel. The flow rate of the liquid is calculated as a function of the frequency of the deformations, the pressure drop and the physical parameters of the liquid.

scholarly journals The Influence of Different Types of Nanofluid on Thermal and Fluid Flow Performance of Liquid Cold Plate

2018 ◽  
Vol 7 (4.35) ◽  
pp. 148 ◽  
Author(s):  
Nur Irmawati Om ◽  
Rozli Zulkifli ◽  
P. Gunnasegaran
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Pressure Drop ◽  
Volume Fraction ◽  
Cold Plate ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Different Types ◽  
Volume Method

The influence of utilizing different nanofluids types on the liquid cold plate (LCP) is numerically investigated. The thermal and fluid flow performance of LCP is examined by using pure ethylene glycol (EG), Al2O3-EG and CuO-EG. The volume fraction of the nanoparticle for both nanofluid is 2%. The finite volume method (FVM) has been used to solved 3-D steady state, laminar flow and heat transfer governing equations. The presented results indicate that Al2O3-EG able to provide the lowest surface temperature of the heater block followed by CuO-EG and EG, respectively. It is also found that the pressure drop and friction factor are higher for Al2O3-EG and CuO-EG compared to the pure EG.

Two-Phase Friction Factor Obtained From Various Void Fraction Models During Condensation of R134A in Vertical Downward Flow at High Mass Flux

2008 ◽  
Author(s):  
Ahmet Selim Dalkilic ◽  
Suriyan Laohalertdecha ◽  
Somchai Wongwises
Keyword(s):  
Void Fraction ◽  
Annular Flow ◽  
Smooth Tube ◽  
High Mass ◽  
Two Phase ◽  
Void Fractions ◽  
Mass Fluxes ◽  
Friction Factors ◽  
Flow Void ◽  
Fraction Models

Void fractions are determined in vertical downward annular two-phase flow of R134a inside 8.1 mm i.d. smooth tube. The experiments are done at average saturated condensing temperatures of 40 and 50°C. The average qualities are between 0.84–0.94. The mass fluxes are around 515 kg m−2s−1. The experimental setup is explained elaborately. Comparisons between the void fraction determined from 35 void fraction correlations are done. According to the use of various horizontal and vertical annular flow void fraction models together with the present experimental condensation heat transfer data, similar void fraction results were obtained mostly for the smooth tube. The experimental friction factors obtained from void fraction correlations are compared with the friction factors determined from graphical information provided by Bergelin et. al. Effect of void fraction alteration on the momentum pressure drop is also presented.

scholarly journals Pressure drop and average void fraction measurements for two-phase flow through highly permeable porous media

2016 ◽  
Vol 94 ◽  
pp. 422-432 ◽  
Author(s):  
N. Chikhi ◽  
R. Clavier ◽  
J.-P. Laurent ◽  
F. Fichot ◽  
M. Quintard
Keyword(s):  
Porous Media ◽  
Pressure Drop ◽  
Void Fraction ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Through

Compact Modeling of Fluid Flow and Heat Transfer in Straight Fin Heat Sinks

2004 ◽  
Vol 126 (2) ◽  
pp. 247-255 ◽  
Author(s):  
Duckjong Kim ◽  
Sung Jin Kim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Heat Sink ◽  
Volume Averaging ◽  
Thermal Design ◽  
Heat Sinks ◽  
Compact Modeling ◽  
Flow And Heat Transfer

In the present work, a compact modeling method based on a volume-averaging technique is presented. Its application to an analysis of fluid flow and heat transfer in straight fin heat sinks is then analyzed. In this study, the straight fin heat sink is modeled as a porous medium through which fluid flows. The volume-averaged momentum and energy equations for developing flow in these heat sinks are obtained using the local volume-averaging method. The permeability and the interstitial heat transfer coefficient required to solve these equations are determined analytically from forced convective flow between infinite parallel plates. To validate the compact model proposed in this paper, three aluminum straight fin heat sinks having a base size of 101.43mm×101.43mm are tested with an inlet velocity ranging from 0.5 m/s to 2 m/s. In the experimental investigation, the heat sink is heated uniformly at the bottom. The resulting pressure drop across the heat sink and the temperature distribution at its bottom are then measured and are compared with those obtained through the porous medium approach. Upon comparison, the porous medium approach is shown to accurately predict the pressure drop and heat transfer characteristics of straight fin heat sinks. In addition, evidence indicates that the entrance effect should be considered in the thermal design of heat sinks when Re Dh/L>∼O10.

A Study on Flow Boiling in Microchannel With Piranha Pin Fin

2015 ◽  
Author(s):  
X. Yu ◽  
C. Woodcock ◽  
Y. Wang ◽  
J. Plawsky ◽  
Y. Peles
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Heat Transfer Performance ◽  
Flow Boiling ◽  
Transfer Performance ◽  
Flow Conditions ◽  
Pin Fin ◽  
Flow And Heat Transfer

In this paper we reported an advanced structure, the Piranha Pin Fin (PPF), for microchannel flow boiling. Fluid flow and heat transfer performance were evaluated in detail with HFE7000 as working fluid. Surface temperature, pressure drop, heat transfer coefficient and critical heat flux (CHF) were experimentally obtained and discussed. Furthermore, microchannels with different PPF geometrical configurations were investigated. At the same time, tests for different flow conditions were conducted and analyzed. It turned out that microchannel with PPF can realize high-heat flux dissipation with reasonable pressure drop. Both flow conditions and PPF configuration played important roles for both fluid flow and heat transfer performance. This study provided useful reference for further PPF design in microchannel for flow boiling.

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