Numerical and experimental investigation of transverse injection flows

The flow field resulting from a transverse injection through a slot into supersonic flow is numerically simulated by solving Favre-averaged Navier–Stokes equations with κ − ω SST turbulence model with corrections for compressibility and transition. Numerical results are compared to experimental data in terms of surface pressure profiles, boundary layer separation location, transition location, and flow structures at the upstream and downstream of the jet. Results show good agreement with experimental data for a wide range of pressure ratios and transition locations are captured with acceptable accuracy. κ − ω SST model provides quite accurate results for such a complex flow field. Moreover, few experiments involving a sonic round jet injected on a flat plate into high-speed crossflow at Mach 5 are carried out. These experiments are three-dimensional in nature. The effect of pressure ratio on three-dimensional jet interaction dynamics is sought. Jet penetration is found to be a non-linear function of jet to free stream momentum flux ratio.     

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.     

Measurements of concentration per size class in a dense polydispersed jet using planar laser-induced fluorescence and phase Doppler techniques

In dense two-phase flows, it is well known that phase Doppler anemometry is not well suited for the measurement of concentration and mass flux. Laser diagnostics based on fluorescence can provide the dispersed phase concentration but without discrimination between size classes. We present a new method of coupling the two techniques, in order to extract the local value of concentration and flux per size class. The method is applied to an axisymmetric turbulent jet, laden with polydispersed droplets 1–90 μm. Droplet concentration profiles are obtained in the development zone (x/d ₀ < 20) of the dense jet and are used to study droplet dispersion. The results are then introduced into the momentum transport equations to analyze the influence of droplets on the carrier phase. We show that the local decrease of the rate of variation of mean momentum with mass loading is due both to an increase in interfacial transfer rate and to a decrease in turbulent diffusion effects. Received: 20 November 2000 / Accepted: 3 April 2001     

A two-fluid model for critical vapour-liquid flow

One-dimensional two-fluid equations are used to calculate the mass flux of initially saturated or subcooled water discharging from a pipe in critical flow. The model allows in a general way for thermal non-equilibrium between the liquid and vapour bubbles, and for interphase relative motion. The theory is shown to be in good agreement with the measured critical flow-rates of pressurised water over a wide pressure range for a single choice of parameters characterising (i) the density of nucleation sites in the liquid, (ii) the liquid superheat required to cause bubble nucleation. Predictions are made of the critical mass flux of initially saturated water in pipes of the range of sizes of interest in water-reactor blowdown safety analysis. Results indicate that for pipes up to ten diameters in length flows will be significantly higher than values obtained from conventional homogeneous thermal equilibrium flow theory.     

Calculation of two-phase swirling flows

The results of calculating the diffusion of a dispersed admixture in turbulent swirling jet flows using the model of momentum transfer in a turbulent gas—dispersion flow proposed by the authors are presented. These results are compared with experimental data and with calculations based on various mathematical models. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 71–78, January–February, 1994.     

Numerical simulations of compressible flows using multi-fluid models

Numerical simulations of two-fluid flow models based on the full Navier–Stokes equations are presented. The models include six and seven partial differential equations, namely, six- and seven-equation models. The seven-equation model consists of a non-conservative equation for volume fraction evolution of one of the fluids and two sets of balance equations. Each set describes the motion of the corresponding fluid, which has its own pressure, velocity, and temperature. The closure is achieved by two stiffened gas equations of state. Instantaneous relaxation towards equilibrium is achieved by velocity and pressure relaxation terms. The six-equation model is deduced from the seven-equation model by assuming an infinite rate of velocity relaxation. In this model, a single velocity is used for both fluids. The numerical solutions are obtained by applying the Strang splitting technique. The numerical solutions are examined in a set of one, two, and three dimensions for both the six- and seven-equation models. The results indicate very good agreement with the experimental results. There is an insignificant difference between the results of the two models, but the six-equation model is much more economical compared to the seven-equation model.     

A Phenomenological Approach to Modeling Transport in Porous Media

The objective of this article is to make use of the phenomenological approach to construct models for the transport of extensive quantities, such as mass of a fluid phase, mass of a component of a fluid phase, momentum of a phase and energy, in porous medium domains. Special attention is devoted to express the fluxes of these extensive quantities, especially the non-advective ones, as functions of their relevant driving forces, obeying the principle of minimum entropy production. It is shown that for each extensive quantity, we have a linear diffusive flux term, a non-linear diffusive term, and a dispersive flux term. The latter is shown to be proportional to the velocity squared. In each case, the number of moduli that describe fluid and porous matrix properties is determined. The momentum balance equation for a porous medium domain, which is the “motion equation,” is analyzed and simplified for special cases, leading to Darcy’s law and to Brinkman’s equation.     

Uniqueness of free-boundary flows under gravity

A class of steady potential flows of an ideal fluid is considered in which the fluid flows between fixed boundaries and then emerges as a jet with one free boundary. Gravity acts on the fluid perpendicularly to the direction of the jet at infinity downstream. An inverse Froude number α is defined in terms of the flux Q and the depth d of the fluid at the separation point. It is proved that for each α>0 there is at most one flow which reaches to a supercritical uniform stream depth at infinity downstream. Monotonicity properties are proved for various flow parameters, and the behaviour of the flow as α → 0 is described.     

Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.     

A numerical scheme for Euler–Lagrange simulation of bubbly flows in complex systems

An Eulerian–Lagrangian approach is developed for the simulation of turbulent bubbly flows in complex systems. The liquid phase is treated as a continuum and the Navier–Stokes equations are solved in an unstructured grid, finite volume framework for turbulent flows. The dynamics of the disperse phase is modeled in a Lagrangian frame and includes models for the motion of each individual bubble, bubble size variations due to the local pressure changes, and interactions among the bubbles and with boundaries. The bubble growth/collapse is modeled by the Rayleigh–Plesset (RP) equation. Three modeling approaches are considered: (a) one‐way coupling, where the influence of the bubble on the fluid flow is neglected, (b) two‐way coupling, where the momentum‐exchange between the fluid and the bubbles is modeled, and (c) volumetric coupling, where the volumetric displacement of the fluid by the bubble motion and the momentum‐exchange are modeled. A novel adaptive time‐stepping scheme based on stability‐analysis of the non‐linear bubble dynamics equations is developed. The numerical approach is verified for various single bubble test cases to show second‐order accuracy. Interactions of multiple bubbles with vortical flows are simulated to study the effectiveness of the volumetric coupling approach in predicting the flow features observed experimentally. Finally, the numerical approach is used to perform a large‐eddy simulation in two configurations: (i) flow over a cavity to predict small‐scale cavitation and inception and (ii) a rising dense bubble plume in a stationary water column. The results show good predictive capability of the numerical algorithm in capturing complex flow features. Copyright © 2010 John Wiley & Sons, Ltd.     

Mixed convection in gravity-driven nano-liquid film containing both nanoparticles and gyrotactic microorganisms

Analysis of a gravity-induced film flow of a fluid containing both nanoparticles and gyrotactic microorganisms along a convectively heated vertical surface is presented. The Buongiorno model is applied. Two kinds of boundary conditions, the passive and the active boundary conditions, are considered to investigate this film flow phenomenon. Through a set of similarity variables, the ordinary differential equations that describe the conservation of the momentum, the thermal energy, the nanoparticles, and the microorganisms are derived and then solved numerically by an efficient finite difference technique. The effects of various physical parameters on the profiles of momentum, thermal energy, nanoparticles, microorganisms, local skin friction, local Nusselt number, local wall mass flux, and local wall motile microorganisms flux are investigated. It is expected that the passively controlled nanofluid model can be much more easily achieved and applied in real circumstances than the actively controlled model.     

Comparison of results from DNS of bubbly flows with a two-fluid model for two-dimensional laminar flows

Results from direct numerical simulations of laminar bubbly flow in a vertical channel are compared with predictions of a two-fluid model for steady-state flow. The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as downflow. In all cases the results agree reasonably well, even though the simulated void fraction is considerably higher than what is assumed in the derivation of the model. The results do, however, suggest a need to understand the lift and the wall repulsion force on bubbles better, particularly in dense flows.     

Wall pressure fluctuations and topology in separated flows over a forward-facing step

Laboratory measurements of wall pressure fluctuations and aerodynamic fields were made in separated flows over a forward facing step (h = 30, 40 and 50 mm with U _e = 15–40 m/s). An array of 16 off-set pressure probes extending in the streamwise and the spanwise directions was especially developed for sensing the wall pressure fluctuations. The flow field was also investigated by wall flow visualizations and PIV to analyze the flow topology in an open section wind tunnel. The results show a different behavior of the flow depending on the aspect ratio l/h and δ/h for high Reynolds numbers. The space time correlations between the wall pressure and the velocity fields were highlighted. The results show that high levels of these correlations are located at the top of the recirculation bubble, mainly in the shear layer and are extended downstream of the re-attachment point. Indeed, the results indicate that the flapping motion at the separation is important in the flow organization at the re-attachment point.     

Simulation of bluff body stabilized flows with hybrid RANS and PDF method

The motivation of this study is to investigate the turbulence–chemistry interactions by using probability density function (PDF) method. A consistent hybrid Reynolds Averaged Navier–Stokes (RANS)/PDF method is used to simulate the turbulent non-reacting and reacting flows. The joint fluctuating velocity–frequency–composition PDF equation coupled with the Reynolds averaged density, momentum and energy equations are solved on unstructured meshes by the Lagrangian Monte Carlo (MC) method combined with the finite volume (FV) method. The simulation of the axisymmetric bluff body stabilized non-reacting flow fields is presented in this paper. The calculated length of the recirculation zone is in good agreement with the experimental data. Moreover, the significant change of the flow pattern with the increase of the jet-to-coflow momentum flux ratio is well predicted. In addition, comparisons are made between the joint PDF model and two different Reynolds stress models. The project supported by the National Natural Science Foundation of China (50506028), and Action Scheme for Invigorating Education Towards the twenty-first century.     

Modeling of three-phase heavy oil–water–gas bubbly flow in upward vertical pipes

A bubbly gas–bubbly oil flow pattern may occur when water, heavy oil and gas flow simultaneously in vertical pipes in such a way that water is the continuous phase. In this work, a one-dimensional, thermal, transient two-fluid mathematical model, for such flow, is presented. The model consists of mass, momentum and energy conservation equations for every phase whose numerical solution is based on the finite difference technique in the implicit scheme. The model is able to predict pressure, temperature, volumetric fraction and velocity profiles. For accurate modeling of multiphase flows, the key issue is to specify the adequate closure relationships, thus drag and virtual mass forces for the gas and oil phases were taken into account and special attention was paid on the gas–oil drag force. When this force was included into the model it was found that: (1) such force had the same order of magnitude than the oil drag force and both forces were smaller than the gas drag force, (2) the pressure, gas and oil velocities and gas and oil volume fraction profiles were affected, (3) the numerical stability was increased. The model predictions are in agreement with experimental data reported in literature.     

The setting up of the equations for two-phase flows by the kinetic theory method

The fundamental equations for two-phase flows are deduced from the Boltzmann's equation. The collision terms are treated with a method similar to what is used in the classical kinetic theory for handling the transport properties of dense gases. It is shown that collision pressure and collision thermal flux exist in gas-particle flows in addition to the general partial pressure and partial thermal flux. Their physical natures are quite different from those of the general partial pressure and partial thermal flux. The applicability of the binary collision assumption and the molecular chaos assumption to gas-particle flows is also discussed. Finally, the equations for two-phase flows obtained by the method of the kinetic theory are compared with those obtained by average continuum models and by the model of particle clouds. The results from the kinetic theory show clearly the physical significance of various parameters and clarify some confusing concepts. Institute of Mechanics, Academia Sinica     

Numerical investigation of static flow instability in a low-pressure subcooled boiling channel

A three-dimensional two-fluid model to predict subcooled boiling flow at low pressure is presented. The model is adopted to investigate the two-phase flow and heat transfer characteristics in a heated channel. The presence of bubbles as a consequence of heating flow through a vertical rectangular channel has a significant effect on the overall pressure drop along the channel. Numerical results were compared against a series experimental data performed at various conditions – mass flux, heat flux, inlet temperature and exit pressure. Good agreement on the overall pressure drop was achieved. The onset of flow instability velocity was also accurately determined when compared against measurements. Predicted results of void fraction provided useful information towards a more fundamental understanding of the occurrence of onset of nucleate boiling, onset of significant voiding and onset of flow instability. The phenomenon of boiling onset oscillations was also predicted through the use of the two-fluid model.     

Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state,and the flow is frequently unsteady and turbulent.To assess the state-of-the-art of computational capabilities for unsteady cavitating flows,different cavitation and turbulence model combinations are conducted.The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics.The kε turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively.We have also blended these alternative cavitation and turbulence treatments,to illustrate that the eddy viscosity near the closure region can significantly influence the capture of detached cavity.From the experimental validations regarding the force analysis,frequency,and the cavity visualization,no single model combination performs best in all aspects.Furthermore,the implications of parameters contained in different cavitation models are investigated.The phase change process is more pronounced around the detached cavity,which is better illus-trated by the interfacial dynamics model.Our study provides insight to aid further modeling development.