New Two-Fluid Model Near-Wall Averaging and Consistent Matching for Turbulent Bubbly Flows

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Avinash Vaidheeswaran ◽  
Deoras Prabhudharwadkar ◽  
Paul Guilbert ◽  
John R. Buchanan ◽  
Martin Lopez de Bertodano

A new two-fluid model averaging in the near-wall region is proposed to ensure consistent matching of the two-phase k–ε turbulence model with the two-phase logarithmic law of the wall (Marie J. L., Moursali, E., and Tran-Cong, S., 1997, “Similarity Law and Turbulence Intensity Profiles in a Bubbly Boundary Layer,” Int. J. Multiphase Flow, 23(2), pp. 227–247). The void fraction distribution obtained with the averaging procedure is seen to conform to the two-phase wall function approach which is based on a double step function void fraction distribution. In particular, the proposed averaging technique is shown to achieve grid convergence in the near-wall region, which could not be obtained otherwise. Computational fluid dynamics (CFD) results with the proposed technique are in good agreement with experiments on upward bubbly flows over a flat plate, and upward and downward flows in pipes. An additional advantage of the proposed technique is that it replaces the wall force model, which has a significant degree of uncertainty in turbulent flow modeling, with a simpler geometric constraint.

Author(s):  
Hiroyuki Yoshida ◽  
Takeharu Misawa ◽  
Kazuyuki Takase

Two-fluid model can simulate two phase flow less computational cost than inter-face tracking method and particle interaction method. Therefore, two-fluid model is useful for thermal hydraulic analysis in large-scale domain such as a rod bundle. Japan Atomic Energy Agency (JAEA) develops three dimensional two-fluid model analysis code ACE-3D, which adopts boundary fitted coordinate system in order to simulate complex shape channel flow. In this paper, boiling two-phase flow analysis in a tight lattice rod bundle is performed by ACE-3D code. The parallel computation using 126CPUs is applied to this analysis. In the results, the void fraction, which distributes in outermost region of rod bundle, is lower than that in center region of rod bundle. At height z = 0.5 m, void fraction in the gap region is higher in comparison with that in center region of the subchannel. However, at height of z = 1.1m, higher void fraction distribution exists in center region of the subchannel in comparison with the gap region. The tendency of void fraction to concentrate in the gap region at vicinity of boiling starting point, and to move into subchannel as water goes through rod bundle, is qualitatively agreement with the measurement results by neutron radiography. To evaluate effects of two-phase flow model used in ACE-3D code, numerical simulation of boiling two-phase in tight lattice rod bundle with no lift force model (neglecting lift force acting on bubbles) is also performed. From the comparison of numerical results, it is concluded that the effects of lift force model are not so large on overall void fraction distribution in tight lattice rod bundle. However, higher void fraction distribution in center region of the subchannel was not observed in this simulation. It is concluded that the lift force model is important for local void fraction distribution in rod bundles.


2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Jamel Chahed ◽  
Lucien Masbernat

Abstract A two-fluid model with second-order turbulence closure is used for the simulation of a turbulent bubbly boundary layer. The turbulence model is based on the decomposition of the Reynolds stress tensor in the liquid phase into two parts: a turbulent part and a pseudo-turbulent part. The reduction in second-order turbulence closure in the near-wall region is interpreted according to a modified wall logarithmic law. Numerical simulations of bubbly boundary layer developing on a vertical flat plate were performed in order to analyze the bubbles effect on the liquid turbulence structure and to evaluate the respective roles of turbulence and of interfacial forces in the near-wall distribution of the void fraction. The two-fluid model with the second-order turbulence closure succeeds in reproducing the diminution of the turbulent intensity observed in the near-wall region of bubbly boundary layer and the increase in turbulence outside the boundary layer. The analysis of the interfacial force in the near-wall zone has led to the development of relatively simple formulation of the lift-wall force in the logarithmic zone that depends on dimensionless distances to the wall. After appropriate adjustment, this formulation makes it possible to reproduce the shape of the near-wall void fraction peaking observed in bubbly boundary layer experiments.


Author(s):  
M.-L. Bordas ◽  
A. Cartellier ◽  
P. Se´chet

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).


Author(s):  
Avinash Vaidheeswaran ◽  
John R. Buchanan ◽  
Paul Guilbert ◽  
Martin Lopez de Bertodano

A considerable amount of work has been done in the past to improve the solution methodology using the two-fluid model in the near-wall region. This includes the works of Larrateguy et al. [1], and Moraga et al. [2], based on a multi-scale bubble-center averaging technique. However one shortcoming is that the primitive variables must be recovered from the bubble-center averaged variables. This makes it difficult to implement it in a commercial CFD code. The current research focuses on an engineering approach to overcome this issue. A multi-scale near-wall averaging technique is proposed which separates the effects of bubble dynamics from its geometry in this region. In addition, the averaged volume fraction profile makes the CFD approach consistent with the modified logarithmic law of Marie et al. [3]. A step function volume fraction distribution was assumed in the near-wall region while developing the theory. However, the volume fraction prediction obtained from CFD calculations is not uniform in this region. The proposed near-wall averaging technique resolves this issue and makes the CFD implementation of the modified wall function approach consistent with the theory of Marie et al. [3].


Author(s):  
Wei Yao ◽  
Christophe Morel

In this paper, a multidimensional two-fluid model with additional turbulence k–ε equations is used to predict the two-phase parameters distribution in freon R12 boiling flow. The 3D module of the CATHARE code is used for numerical calculation. The DEBORA experiment has been chosen to evaluate our models. The radial profiles of the outlet parameters were measured by means of an optical probe. The comparison of the radial profiles of void fraction, liquid temperature, gas velocity and volumetric interfacial area at the end of the heated section shows that the multidimensional two-fluid model with proper constitutive relations can yield reasonably predicted results in boiling conditions. Sensitivity tests show that the turbulent dispersion force, which involves the void fraction gradient, plays an important role in determining the void fraction distribution; and the turbulence eddy viscosity is a significant factor to influence the liquid temperature distribution.


Author(s):  
Shimo Yu ◽  
Xiao Yan ◽  
Junyi Zhang

Two-phase flow is an important and common phenomenon in nuclear reactor systems, and the characteristics of two-phase flow such as heat transfer and pressure drop strongly depend on the radial distribution of void fraction. This paper is presenting the CFD simulation for void fraction radial distribution of mono- and poly-disperse air-water two phase flow using Euler-Euler two-fluid model. Interfacial forces including transverse forces such as lift, wall and turbulent dispersion forces are taken into account, Furthermore the bubble size distribution and bubble break-up and coalescence processes are taken into account in case of a poly-disperse flow by using the S-Gamma model. The sauter mean diameter and interfacial area concentration (IAC) distribution can also be obtained. The simulation results are compared to an experimental database of MT-LOOP test facility (FZD, Germany)[1].


2003 ◽  
Vol 2003 (0) ◽  
pp. 189
Author(s):  
Masaki Misawa ◽  
Akihiko Minato ◽  
Akio Suzuki ◽  
Naoki Ichikawa ◽  
Masaharu Kuroda

2002 ◽  
Vol 124 (4) ◽  
pp. 951-956 ◽  
Author(s):  
J. Chahed ◽  
C. Colin ◽  
L. Masbernat

The role of the turbulence in the void fraction distribution in bubbly pipe flow under microgravity condition is evaluated on the basis of numerical simulations using a Eulerian-Eulerian two-fluid model. In microgravity, the average relative velocity is weak and the void fraction distribution is mainly governed by the turbulence. The simulations show that the turbulent contributions of the added mass force play an important role in the phase distribution phenomenon. It is clearly proved that the turbulence acts on the bubbles distribution not only by the pressure term but also by the turbulent correlations obtained by averaging the added mass force.


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