E. Daniel, R. Saurel, M. Larini and J.C. Loraud
This paper investigates the multi‐phase behaviour of dropletsinjected into a nozzle at two separate wall locations. The physical featuresof the droplets (rate of mass, density and…
Abstract
This paper investigates the multi‐phase behaviour of droplets injected into a nozzle at two separate wall locations. The physical features of the droplets (rate of mass, density and radius) at each injector location are identical. This system can be described by a two‐phase Eulerian—Eulerian approach that yields classical systems of equations: three for the gaseous phase and three for the dispersed droplet phase. An underlying assumption in the two phase model is that no interaction occurs between droplets. The numerical solution of the model (using the MacCormack scheme) indicates however that the opposite jets do interact to form one jet. This inconsistency is overcome in the current paper by associating the droplets from a given injection location with a separate phase and subsequently solving equations describing a multiphase system (here, three‐phase system). Comparison of numerical predications between the two‐phase and the multiphase model shows significantly different results. In particular the multiphase model shows no jet interaction.
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L. Allançon, B. Porterie, R. Saurel and J.C. Loraud
A numerical analysis is given for the prediction of unsteady,two‐dimensional fluid flow induced by a heat and mass source in aninitially closed cavity which is vented when the…
Abstract
A numerical analysis is given for the prediction of unsteady, two‐dimensional fluid flow induced by a heat and mass source in an initially closed cavity which is vented when the internal overpressure reaches a certain level. A modified ICE technique is used for solving the Navier–Stokes equations governing a compressible flow at a low Mach number and high temperature. Particular attention is focused on the treatment of the boundary conditions on the vent surface. This has been treated by an original procedure using the resolution of a Riemann problem. The configuration investigated may be viewed as a test problem which allows simulation of the ventilation and cooling of such cavities. The injection of hot gases is found to play a key role on the temperature field in the enclosure, whereas the vent seems to produce a distortion of the dynamic flow‐field only. When the injection of hot gases is stopped, the enclosure heat transfer is strongly influenced by the vent. A comparison with the results obtained when the radiative heat transfer between the walls of the enclosure is considered, indicate that radiation dominates the heat transfer in the enclosure and alters the flow patterns significantly.
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T. Basset, E. Daniel and J.C. Loraud
Presents validation of the Eulerian approach for unsteady two‐phase flows, whose behaviour depends on the coupling between the two phases, on the basis of the study of…
Abstract
Presents validation of the Eulerian approach for unsteady two‐phase flows, whose behaviour depends on the coupling between the two phases, on the basis of the study of attentuation and dispersion of an acoustic wave propagating into a one dimensional two‐phase flow. This approach and the corresponding numerical aspects are accurate enough for later applications in more complex geometries, where “vortex shedding” phenomena take place. Attenuation and dispersion of a pressure wave in a two‐phase medium of rest was previously studied by Temkin and Dobbins. Present work is an extension of this theory to the case of a two‐phase flow. This theoretical approach leads to a numerical solution of the problem. Compares the derived results with those obtained from a direct numerical simulation based on MacCormack scheme in a finite volume formulation. Verifies that analytical and numerical approaches are in good agreement.
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D. Morvan, B. Porterie, J.C. Loraud and M. Larini
Reports numerical simulations of an unconfined methane‐air turbulent diffusion flame expanding from a porous burner. Turbulent combustion is simulated using the eddy dissipation…
Abstract
Reports numerical simulations of an unconfined methane‐air turbulent diffusion flame expanding from a porous burner. Turbulent combustion is simulated using the eddy dissipation concept (EDC) which supposes that the reaction rate is controlled by the turbulent structures which enhance the mixing of fuel and oxidant. Two statistical k‐ε turbulence models have been tested: a standard high Reynolds number (HRN) and a more recent model based on the renormalization group theory (RNG). Radiation heat transfer and soot formation have been taken into account using P1‐approximation and transport submodels which reproduce the main phenomena encountered during soot production (nucleation, coagulation, surface growth). The set of coupled transport equations is solved numerically using a high order finite‐volume method, the velocity‐pressure coupling is treated by a projection technique. The numerical results confirm that 20‐25 percent of the combustion heat released is radiated away from the flame. Unsteady and unsymmetrical flame behaviour is observed for small Froude numbers which results from the development of Rayleigh‐Taylor like instabilities outside the flame surface. For higher Froude numbers the steady‐state and symmetrical nature of the solution is recovered.
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Numerical results are reported for a dilute turbulent liquid‐solid flow in an axisymmetric sudden‐expansion pipe with an expansion ratio 2:1. The two‐phase flow has a mass‐loading…
Abstract
Numerical results are reported for a dilute turbulent liquid‐solid flow in an axisymmetric sudden‐expansion pipe with an expansion ratio 2:1. The two‐phase flow has a mass‐loading ratio low enough for particle collision to be negligible. The numerical predictions for the dilute two‐phase flow are based on a hybrid Eulerian‐Lagrangian model. A nonlinear k‐ε model is used for the fluid flow to account for the turbulence anisotropy and an improved eddy‐interaction model is used for the particulate flow to account for the effects of turbulence anisotropy, turbulence inhomogeneity, particle drift, and particle inertia on particle dispersion. The effects of the coupling sources, the added mass, the lift force and the shear stress on two‐phase flow predictions are separately studied. The numerical predictions obtained with the improved and conventional particle dispersion models are compared with experimental measurements for the mean and fluctuating velocities at the different measured planes.
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Eric Daniel and Jean‐Claude Loraud
A numerical simulation of a two‐phase dilute flow (droplet‐gas mixture) is carried out by using a finite volume method based on Riemann solvers. The computational domain…
Abstract
A numerical simulation of a two‐phase dilute flow (droplet‐gas mixture) is carried out by using a finite volume method based on Riemann solvers. The computational domain represents a one‐ended pipe with holes at its upper wall which lead into an enclosure. The aim of this study is to determine the parameters of such a flow. More specially, an analytical solution is compared with numerical results to assess the mass flow rates through the vents in the pipe. Inertia effects dominate the dynamic behaviour of droplets, which causes a non‐homogeneous flow in the cavity. The unsteady effects are also important, which makes isentropical calculation irrelevant and shows the necessity of the use of CFD tools to predict such flows. No relation can be extracted from the numerical results between the gas and the dispersed mass flow rates across the holes. But a linear variation law for the droplet mass flow versus the position of the holes is pointed out, which is independent of the incoming flow when the evaporating effects are quite low.
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Manmatha K. Roul and Sukanta K. Dash
The purpose of this paper is to compute the pressure drop through sudden expansions and contractions for two‐phase flow of oil/water emulsions.
Abstract
Purpose
The purpose of this paper is to compute the pressure drop through sudden expansions and contractions for two‐phase flow of oil/water emulsions.
Design/methodology/approach
Two‐phase computational fluid dynamics (CFD) calculations, using Eulerian–Eulerian model, are employed to calculate the velocity profiles and pressure drops across sudden expansions and contractions. The pressure losses are determined by extrapolating the computed pressure profiles upstream and downstream of the expansion/contraction. The oil concentration is varied over a wide range of 0‐97.3 percent by volume. The flow field is assumed to be axisymmetric and solved in two dimensions. The two‐dimensional equations of mass, momentum, volume fraction and turbulent quantities along with the boundary conditions have been integrated over a control volume and the subsequent equations have been discretized over the control volume using a finite volume technique to yield algebraic equations which are solved in an iterative manner for each time step. The realizable per phase k‐ ε turbulent model is considered to update the fluid viscosity with iterations and capture the individual turbulence in both the phases.
Findings
The contraction and expansion loss coefficients are obtained from the pressure loss and velocity data for different concentrations of oil–water emulsions. The loss coefficients for the emulsions are found to be independent of the concentration and type of emulsions. The numerical results are validated against experimental data from the literature and are found to be in good agreement.
Research limitations/implications
The present computation could not use the surface tension forces and the energy equation due to huge computing time requirement.
Practical implications
The present computation could compute realistically the two‐phase pressure drop through sudden expansions and contractions by using a two‐phase Eulerian model and hence this model can be effectively used for industrial applications where two‐phase flow comes into picture.
Originality/value
The original contribution of the paper is in the use of the state‐of‐the‐art Eulerian two‐phase flow model to predict the velocity profile and pressure drop through industrial piping systems.
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Mehdi Mohamadi and AmirMahdi Tahsini
The purpose of this study is to investigate the combustion of the n-Heptane droplets in the supersonic combustor with a cavity-based fuel injection configuration. The focus is on…
Abstract
Purpose
The purpose of this study is to investigate the combustion of the n-Heptane droplets in the supersonic combustor with a cavity-based fuel injection configuration. The focus is on the impacts of the droplet size on combustion efficiency.
Design/methodology/approach
The finite volume solver is developed to simulate the two-phase reacting turbulent compressible flow using a single step reaction mechanism as finite rate chemistry. Three different fuel injection settings are studied for the considered physical geometry and flow conditions: the gas fuel injection, small droplet liquid fuel injection and big droplet fuel. The fuel is injected as a slot wall jet from the bottom of the cavity.
Findings
The results show that using the small droplet size, the complete fuel consumption and combustion efficiency can be achieved but using the big droplet sizes, most fuel exit the combustor in the liquid phase and gasified unburned fuel. It is also demonstrated that the cavity's temperature distribution of the liquid fuel case is different from the gas fuel, and two flame branches are observed there due to the droplet evaporation and combustion in the cavity.
Originality/value
To the best of the authors’ knowledge, this study is performed for the first time on the combustion of the n-Heptane fuel droplets in scramjet configuration, which is promising propulsion system for the future economic flights.
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Van Luc Nguyen, Tomohiro Degawa and Tomomi Uchiyama
This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume.
Abstract
Purpose
This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume.
Design/methodology/approach
Small bubbles are released into quiescent water from a cylinder tip. They rise under the buoyant force, forming a plume. A vortex ring is launched vertically upward into the bubble plume. The interactions between the vortex ring and the bubble plume are numerically simulated using a semi-Lagrangian–Lagrangian approach composed of a vortex-in-cell method for the fluid phase and a Lagrangian description of the gas phase.
Findings
A vortex ring can transport the bubbles surrounding it over a distance significantly depending on the correlative initial position between the bubbles and the core center. The motion of some bubbles is nearly periodic and gradually extinguishes with time. These bubble trajectories are similar to two-dimensional-helix shapes. The vortex is fragmented into multiple regions with high values of Q, the second invariant of velocity gradient tensor, settling at these regional centers. The entrained bubbles excite a growth rate of the vortex ring's azimuthal instability with a formation of the second- and third-harmonic oscillations of modes of 16 and 24, respectively.
Originality/value
A semi-Lagrangian–Lagrangian approach is applied to simulate the interactions between a vortex ring and a bubble plume. The simulations provide the detail features of the interactions.
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Van Luc Nguyen, Tomohiro Degawa and Tomomi Uchiyama
This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume.
Abstract
Purpose
This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume.
Design/methodology/approach
The bubbles, released from the annulus located at the bottom of the domain, rise owing to buoyant force. These released bubbles have diameters of 0.15–0.25 mm and satisfy the bubble flow rate of 4.1 mm3/s. The evolution of the three-dimensional annular bubble plume is numerically simulated using the semi-Lagrangian–Lagrangian (semi-L–L) approach. The approach is composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase.
Findings
First, a new phenomenon of fluid dynamics was discovered. The bubbly flow enters a transition state with the meandering motion of the bubble plume after the early stable stage. A vortex structure in the form of vortex rings is formed because of the inhomogeneous bubble distribution and the fluid-surface effects. The vortex structure of the flow deforms as three-dimensionality appears in the flow before the flow fully develops. Second, the superior abilities of the semi-L–L approach to analyze the vortex structure of the flow and supply physical details of bubble dynamics were demonstrated in this investigation.
Originality/value
The semi-L–L approach is applied to the simulation of the gas–liquid two-phase flows.