Multi-fluid Flows Research Articles

Sensor and Numerical Simulator Evaluation for Porous Medium Desiccation and Rewetting at the Intermediate Laboratory Scale

Soil desiccation, in conjunction with surface infiltration control, is considered at the Hanford Site as a potential technology to limit the flux of technetium and other contaminants in the vadose zone to the groundwater. An intermediate‐scale experiment was conducted to test the response of a series of instruments to desiccation and subsequent rewetting of porous media. The instruments include thermistors, thermocouple psychrometers, dual‐probe heat pulse sensors, heat dissipation units, and humidity probes. The experiment was simulated with the multifluid flow simulator STOMP, using independently obtained hydraulic and thermal porous medium properties. All instrument types used for this experiment were able to indicate when the desiccation front passed a certain location. In most cases the changes were sharp, indicating rapid changes in moisture content, water potential, or humidity. However, a response to the changing conditions was recorded only when the drying front was very close to a sensor. Of the tested instruments, only the heat dissipation unit and humidity probes were able to detect rewetting. The numerical simulation results reasonably match the experimental data, indicating that the simulator captures the pertinent gas flow and transport processes related to desiccation and rewetting and may be useful in the design and analysis of field tests.

A numerical study of shock-induced cavity collapse

The flow field resulting from the interaction between a planar incident shock in a solid and an embedded ellipsoidal gas cavity is examined computationally. The study is motivated by the need for improved understanding of the role of embedded cavities in the initiation of reaction in a heterogeneous explosive following the application of a shock. The system is modeled as a compressible multi-fluid flow with a sufficiently strong shock in the solid. A high-resolution, Godunov-type capturing scheme is employed to solve the governing equations numerically. The calculations are performed in parallel and use adaptive mesh refinement to obtain well-resolved solutions. The goal is to identify regions in which the shock-cavity interaction results in pressures that are substantially higher than the post-shock pressure that existed prior to the beginning of the interaction. Also of interest are the ways in which the magnitude of the elevated pressure, the extent and location of the regions where it develops, and the mechanisms that underlie such a development are influenced by the strength of the shock and the geometry of the cavity.

A turbulent Eulerian multi-fluid reactive flow model and its application in modelling sorption enhanced steam methane reforming

A turbulent multi-fluid reactive fluid model is presented in the paper, which is a combination of a kinetic theory granular flow multi-fluid model(Chao et al., 2011) and the reaction kinetics description(Lindborg, 2008). A two dimensional in-house code was developed to simulate the gas-catalyst-sorbent three-phase reactive flow in the sorption enhanced steam methane reforming fluidized bed reactor. In the simulation, Ca-based sorbents and Ni/MgAl2O3 catalysts are used. The simulation results show that a high production of hydrogen in SE-SMR is obtained compared with the conventional SMR process. The increase of the gas fluidization velocity does not affect the purity of the product hydrogen apparently,while it can shorten the time to get to the breakthrough apparently. The increase of the steam/carbon ratio can increase the purity of the product hydrogen. A homogeneous gas temperature distribution is found which is due to the gas, particle turbulent flows and the heat balance of the SMR-CO2 adsorption reactions. These simulation results are in good agreement with the experimental results from Johnsen et al. (2006a).

CFD study of droplet atomisation using a binary nozzle in fluidised bed coating

An Eulerian–Lagrangian computational fluid dynamics (CFD) model was built to describe two-fluid atomisation in a tapered fluidised bed coater using the air-blast/air-assisted atomiser model. Atomisation was modelled both with and without the inclusion of the solid phase (i.e. gas–liquid and gas–solid–liquid multiphase modelling). In addition, a multi-fluid flow model (Eulerian–Eulerian framework) combined with a population balance model was used as an alternative approach for modelling the spray produced by a two-fluid nozzle. In this approach, the CFD solver couples the population balance equation along with the Navier–Stokes equations for predicting the droplet diameter and mass fraction distribution. Comparison between simulated spray pattern (gas–liquid model) and that experimentally visualised by means of UV illumination was made and a good agreement was obtained. Parametric studies were done in order to investigate the effects of operating conditions on spray cone and liquid mass fraction inside the reactor. Furthermore, comparison of time-averaged fluidised bed behaviour with the inclusion of sprays obtained by both gas–solid–liquid multiphase modelling methods is presented.

Two phase flow models in DxUNSp code platform

The aim of this work is to find an efficient implementation for a two phase flow model in an existing URANS CFD code platform (DxUNSp), initially based on unsteady URANS equations with a k- turbulence model and various other extensions, ranging from a broad selection of wall laws up to a very efficient LES model. This code has the capability for development for nonreacting/reacting multifluid flows for research applications and is under continuous progress. It is intend to present mainly three aspects of this implementation for unstructured mesh based solvers, for high Reynolds compressible flows: the importance of the 5/7 equation model, performance with respect to a basic test cases and implementation details of the proposed schemes. From a numerical point of view, we propose a new approximation schemes of this system based on the VFRoe-ncv.

Incompressible smoothed particle hydrodynamics simulation of multifluid flows

SUMMARYThis paper presents an incompressible SPH (ISPH) technique to simulate multifluid flows. The SPH method is a mesh‐free particle modeling approach that can treat free surfaces and multi‐interfaces in a simple and efficient manner. The ISPH method employs an incompressible hydrodynamic formulation to solve the fluid pressure that ensures a stable pressure field. Two multifluid ISPH models are proposed following different interface treatments: the coupled ISPH model does not distinguish the different fluid phases and applies the standard ISPH technique across the interface, whereas the decoupled ISPH model first treats each fluid phase separately and then couples the different phases by applying pressure and shear stress continuities across the interface. The two proposed models were used to investigate a gravity underflow with a low density ratio in a Generalized Reservoir Hydrodynamics (GRH) flume and a horizontal lock exchange flow with a high density ratio. Comparisons with data and relevant numerical error analysis indicated that the decoupled model performed well in cases of both low and high density ratios because of the accurate treatment of interface boundaries. Copyright © 2011 John Wiley & Sons, Ltd.

A simple incompressible flux splitting for sharp free surface capturing

SUMMARY This paper first applies a flux vector-type splitting method based on the numerical speed of sound for computing incompressible single and multifluid flows. Here, a preconditioning matrix based on Chorin's artificial compressibility concept is used to modify the incompressible multifluid Navier–Stokes equations to be hyperbolic and density or volume fraction-independent. The current approach can reduce eigenvalues disparity induced from density or volume fraction ratios and enhance numerical stability. Also, a simple convection-pressure flux-splitting method with high-order essentially nonoscillatory-type primitive variable extrapolations coupled with monotone upstream-centered schemes for conservation laws-type volume fraction recompressed reconstruction is used to maintain the preservation of sharp interface evolutions in multifluid flow simulations. Benchmark tests including a solid rotation test of a notched two-dimensional cylinder, the evolution of spiral and rotational shapes of deformable circles, a dam breaking problem, and the Rayleigh–Taylor instability were chosen to validate the current incompressible multifluid methodology. An incompressible driven cavity was also chosen to check the robustness of the proposed method on the computation of single fluid incompressible flow problems. Copyright © 2011 John Wiley & Sons, Ltd.

Steady state solutions for a lubrication multi-fluid flow

We describe possible solutions for a stationary flow of two superposed fluids between two close surfaces in relative motion. Physically, this study is within the lubrication framework, in which it is of interest to predict the relative positions of the lubricant and the air in the device. Mathematically, we observe that this problem corresponds to finding the interface between the two fluids, and we prove that this interface can be viewed as a square root of a polynomial of degree at most 6. We solve this equation using an original method. First, we check that our results are consistent with previous work. Next, we use this solution to answer some physically relevant questions related to the lubrication setting. For instance, we obtain theoretical and numerical results, which can predict the occurrence of a full film with respect to physical parameters (fluxes, shear velocity, viscosities). In particular, we present a figure giving the number of stationary solutions depending on the physical parameters. Moreover, we give some indications for a better understanding of the multi-fluid case.

Violent flows in aqueous foams I: Physical and numerical models

Mitigation of blast waves by aqueous foams is an important technological issue. Despite many theoretical and experimental works on the subject, it has not been possible until now to have simple analytical expressions or abaci giving the pressure as a function of the distance to the charge, of its strength and of the characteristics of the foam. This naturally leads to attempts at using numerical simulations to obtain the desired results. The flow in an aqueous foam is complex as three fluids (air, steam and water) and phase transitions are involved, and moreover, the geometry of the free surfaces between these fluids is quite complicated. In this work, our aim is to build a code to handle this question. We rely on the classical averaged model for multifluid flow, which allows bypassing the local geometrical complexity of the flow at the cost of new variables, the volumetric rate of presence of each fluid. Since our goal is to simulate blast waves from a point, we shall safely assume that the flow has spherical symmetry. Hence, the models derived will be one dimensional. In this paper, we shall introduce closed systems of equations and describe their discretization via a finite volume method, the efficiency of which has already been demonstrated in the context of thermohydraulics. We restrict ourselves to the one-dimensional Cartesian case. Numerical benchmarks are provided in order to check the correct behavior of the code in terms of numerics and physics ( e.g. phase transition). In the companion paper, D’Alesio et al. [29], we extend the code to the spherical case and give simulation results in the case of strong shock waves propagating in foams.

Turbulence structure and interaction with steep breaking waves

Large-eddy and interface simulation using an interface tracking-based multi-fluid flow solver is conducted to investigate the breaking of steep water waves on a beach of constant bed slope. The present investigation focuses mainly on the ‘weak plunger’ breaking wave type and provides a detailed analysis of the two-way interaction between the mean fluid flow and the sub-modal motions, encompassing wave dynamics and turbulence. The flow is analysed from two points of views: mean to sub-modal exchange, and wave to turbulence interaction within the sub-modal range. Wave growth and propagation are due to energy transfer from the mean flow to the waves, and transport of mean momentum by these waves. The vigorous downwelling–upwelling patterns developing at the head and tail of each breaker are shown to generate both negative- and positive-signed energy exchange contributions in the thin sublayer underneath the water surface. The details of these exchange mechanisms are thoroughly discussed in this paper, together with the interplay between three-dimensional small-scale breaking associated with turbulence and the dominant two-dimensional wave motion. A conditional zonal analysis is proposed for the first time to understand the transient mechanisms of turbulent kinetic energy production, decay, diffusion and transport and their dependence and/or impact on surface wrinkling over the entire breaking process. The simulations provide a thorough picture of air–liquid coherent structures that develop over the breaking process, and link them to the transient mechanisms responsible for their local incidence.

Modified Baer-Nunziato Model for the Simulation of Interfaces Between Compressible Fluids

AbstractIn this paper we proposed a modified Baer-Nunziato model for compressible multi-fluid flows, with main attention on the energy exchange between the two fluids. The proposed model consists of eleven PDEs; however, the use of the particular phase evolving variables may reduce the model to have only six PDEs. The main advantage of the model is that the Abgrall's UPV criterion on mixture velocity and pressure is satisfied without affecting either its hyperbolicity or its conservations of the two individual masses, momentum or total energy. An Lax-Friedrichs scheme is built for a particular case of the proposedmodel. When the two fluids in the fluid mixture are both of the linear Mie-Gruneisen type, the scheme satisfies the Abgrall's UPV criterion on mixture velocity and pressure. Numerical experiments with polytropic, barotropic, stiffened and van der Waals fluids show that the scheme is efficient and able to treat fluids characterized with quite different thermodynamics.

Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids

Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-layer flows that are linearly stable for Re = ∞. The basic methodology consists of two steps. First we eliminate interfacial instabilities by using a yield stress fluid in one fluid layer and ensuring that for the base flow configurations studied we maintain an unyielded plug region at the interface. Secondly we eliminate linear shear instabilities by ensuring a strong enough Couette component in the second fluid layer, imposed via the moving interface. We show that this technique can be applied to both shear-thinning and visco-elastic fluids.

A front-tracking method with projected interface conditions for compressible multi-fluid flows

A front-tracking method for compressible multi-fluid flows is presented, where marker points are used both for tracking fluid interfaces and also for constructing the Riemann problem on the interfaces. The Riemann problem between the two fluid phases (defined in the interface normal direction) is solved using the exact Riemann solver on the marker points. The solutions are projected onto fixed grid points and then extrapolated into the corresponding ghost-fluid regions, to be used as boundary conditions. Each fluid phase is solved separately as in the ghost-fluid method. The proposed procedures, especially the projection of the exact Riemann solutions onto the fluid grids, are designed to be simple and consistent in any spatial dimensions. Several multi-fluid problems, including the breakup of a water cylinder induced by the passage of a shock wave were computed in order to demonstrate the capability of the proposed method.

LEIS for the prediction of turbulent multifluid flows applied to thermal-hydraulics applications

The paper centres on the use of the so-defined LEIS approach (Large-Eddy & Interface Simulation) for turbulent multifluid flows present in thermal-hydraulics applications. Interfacial flows involving deformable, sheared fronts separating immiscible fluids are shown to be within reach of this new approach, featuring direct resolution of turbulence and sheared interface deformations within the interface tracking (ITM) framework, such as level sets and VOF. In this technique supergrid turbulence and interfacial scales are directly solved whereas the sub-grid (SGS) parts are modelled, at least the turbulence part of it. First results are shown (feasibility), and difficulties and open issues are discussed. The connection between these two particular scales will also be discussed, and potential modelling routes evoked, including combining two-fluid and ITM, local grid refinement, or combing particle tracking and ITM for sub-grid inclusions smaller than the grid size.

Unified formulation for URANS and LES in DxUNSp code

The aim of this work is to find a unified and efficient implementation of a LES turbulence model in an existing URANS CFD code, initially based on unsteady RANS equations with a k-e turbulence model. This code has the capability to be developed for nonreacting/reacting multifluid flows in research applications. The paper intends to present mainly three aspects of this implementation for unstructured mesh based solvers, for high Reynolds compressible flows: the influence of the numerical reconstruction scheme on the results for compressible LES, the influence of the compressible SGS modeling and the efficient implementation of a wall-law based approach for complex geometry. The results will be presented for a test case (3D flow over a square cylinder at Reynolds = 22.000 [0]) and compared with experimental data and other simulations. Some details for the computational efficiency and implementation on parallel computer cluster at INCAS will also be presented [0].

An Hamiltonian interface SPH formulation for multi-fluid and free surface flows

In the present work a new SPH model for simulating interface and free surface flows is presented. This formulation is an extension of the one discussed in Colagrossi and Landrini (2003) and is related to the one proposed by Hu and Adams (2006) to study multi-fluid flows. The new SPH scheme allows an accurate treatment of the discontinuity of quantities at the interface (such as the density), and permits to model flows where both interfaces and a free surface are present. The governing equations are derived following a Lagrangian variational principle leading to an Hamiltonian system of particles. The proposed formulation is validated on test cases for which reference solutions are available in the literature.

Desiccation of Unsaturated Porous Media: Intermediate‐Scale Experiments and Numerical Simulation

Soil desiccation (drying), involving water evaporation induced by air injection and extraction, is a potentially robust vadose zone remediation process to limit migration of inorganic or radionuclide contaminants through the vadose zone. Desiccation also has the potential to improve gas‐phase‐based treatments by reducing water saturation and therefore increasing sediment gas‐phase permeability. Before this technology can be deployed in the field, concerns related to energy limitations, osmotic effects, and potential contaminant remobilization after rewetting must be addressed. A series of detailed, intermediate‐scale laboratory experiments, using unsaturated homogeneous and heterogeneous systems, was conducted to improve our understanding of energy balance issues related to soil desiccation. The experiments were subsequently simulated with the multifluid flow simulator STOMP, using independently obtained hydraulic and thermal porous medium properties. In all experiments, the injection of dry air proved to be an effective means for removing essentially all moisture from the test media. Observed evaporative cooling generally decreased with increasing distance from the gas inlet chamber. The fine‐grained sand embedded in the medium‐grained sand of the heterogeneous system showed two local temperature minima associated with the cooling. The first one occurred because of evaporation in the adjacent medium‐grained sand, whereas the second minimum was attributed to evaporative cooling in the fine‐grained sand itself. Results of the laboratory tests were simulated accurately only if the thermal properties of the flow cell walls and insulation material were taken into account, indicating that the appropriate physics were incorporated into the simulator.

On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow

In this work, the HLLC Riemann solver, which is much more robust, simpler and faster than iterative Riemann solvers, is extended to obtain interface conditions in sharp-interface methods for compressible multi-fluid flows. For interactions with general equations of state and material interfaces, a new generalized Roe average is proposed. For single-phase interactions, this new Roe average does not introduce artificial states and satisfies the U-property exactly. For interactions at material interfaces, the U-property is satisfied by introducing ghost states for the internal energy. A number of numerical tests suggest that the proposed Riemann solver is suitable for general equations of state and has an accuracy comparable to iterative Riemann solvers, while being significantly more robust and efficient.

Multi-fluid flows with the Particle Finite Element Method

Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied on it. In this paper the Particle Finite Element Method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density. To evaluate the external applied forces to each particle, the incompressible Navier–Stokes equations are solved at each time step using a Lagrangian formulation. All the information in the fluid is transmitted via the particles. All kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free-surfaces, breaking waves and fluid separations may be easily solved with this methodology.

Numerical entropy production and error indicator for compressible flows

In the case of multifluid flows, it is classical to refine the mesh in order to improve the precision. As mesh refinement criterion, we propose to use the numerical entropy production. In a refinement procedure by bitree, we check the relevance of this criterion. Our objective is to validate the mesh refinement before integrating it into a three-dimensional parallel code. To cite this article: F. Golay, C. R. Mecanique 337 (2009).