Wide Range Of Density Ratios Research Articles

Particle response to oscillatory flows at finite Reynolds numbers

The response of spherical particles to oscillatory fluid flow forcing at finite Reynolds numbers exhibits significant deviations from classical analytical predictions due to nonlinear convective contributions. This study employs finite element simulations to explore the long-term (stationary) behavior of such particles across a wide range of conditions, including various external and particle Reynolds numbers, Strouhal numbers, and fluid-to-particle density ratios. Key contributions of this work include determining the range of validity of Tchen's equation of motion for infinitesimal and finite Reynolds numbers and correlating particle response for a wide range of density ratios and flow conditions at high frequency oscillations. This work introduces a modified form of the history drag term in a newly proposed Lagrangian equation of motion. The new equation incorporates a parameter-dependent fractional-order derivative tailored to accommodate nonlinearities due to convective effects. These novel correlations not only extend the operational range of existing model equations but also provide accurate estimates of particle response under a range of external flow conditions, as validated by comparison with numerical solutions of the Navier–Stokes flow around the particles.

Effects of gas viscosity and liquid-to-gas density ratio on liquid jet atomization in crossflow

Atomization of liquid jets in gaseous crossflows has many natural and industrial applications, for example, in fuel atomization in gas turbine engines, rocket engines, film cooling, and, recently, suspension and solution precursor plasma spraying processes for the development of advanced coatings. Viscosity and density of the gaseous medium may significantly vary in applications such as plasma spraying, which can affect the instability waves on the liquid jet column, resulting in a major change in the mechanism of primary and secondary breakups. In this study, a numerical model is used to investigate the impact of gas viscosity on breakup mechanisms for a wide range of density ratios and Weber numbers. Due to many challenges, only a few comprehensive atomization measurements have been performed on this subject. However, novel computational models could provide the atomization process with a thorough picture in the last two decades. The incompressible variable-density Navier–Stokes equations are solved by using finite volume schemes, and a geometric volume-of-fluid technique is used to track the gas–liquid interface. In our parametric study, three sets of density ratios and Weber numbers are chosen. In each set, four cases with different orders of magnitude of gaseous Reynolds number are simulated. Different characteristics of jet atomization are analyzed, such as the jet trajectory, breakup location, and surface instabilities generated along the jet column. Ultimately, the effects of gaseous Reynolds number, density ratio, and Weber number on jet deformation and breakup mechanisms are discussed.

Growth mechanism of interfacial fluid-mixing width induced by successive nonlinear wave interactions.

Interfacial fluid mixing induced by successive waves, such as shock, rarefaction, and compression waves, plays a fundamental role in engineering applications, e.g., inertial confinement fusion, and in natural phenomena, e.g., supernova explosion. These waves bring nonuniform, unsteady external forces into the mixing zone, which leads to a complex mixing process. The growth rate of the mixing width is analyzed by decomposing the turbulent flow field into the averaged field and the fluctuating counterpart. The growth rate is thus divided into three parts: (i) the stretching or compression (S(C)) effect induced by the averaged-velocity difference between two ends of the mixing zone, (ii) the penetration effect induced by the fluctuations which represent the penetration of the two species into each other, and (iii) the diffusive effect, which is induced by the molecular diffusion and is negligible in high-Reynolds-number flows at Schmidt number of order unity. The penetration effect is further divided into the Richtmyer-Meshkov (RM) effect, which is induced by fluctuations that were deposited by earlier wave interactions, and the Rayleigh-Taylor (RT) effect, which is caused by the fluctuations that arise in an overall acceleration of the mixing zone. During the passage of the rarefaction waves, the mixing zone is stretched, while during the passage of the compression waves or shock waves, the mixing zone is compressed. To illustrate these effects, a physical model of RM mixing with reshock is used. By combining the S(C), RM, and RT effects, the entire evolution of mixing width is restructured, which agrees well with numerical simulations for problems with a wide range of density ratios.

Radially graded porous structure design for laser powder bed fusion additive manufacturing of Ti-6Al-4V alloy

Porous structures have been used in many areas particularly in medical, transportation, space and defense applications. The building of porous structure is formed by the lattices which have many unusual and interesting features that make them candidates for innovative designs. Such designs include creating porosity variation in structures and the aim is to achieve exceptional mechanical and biological efficiencies in terms of strength, stiffness, energy absorption capacity, and stimulating tissue ingrowth. In this paper, a design approach for uniform and graded porous structures is proposed to be produced by additive manufacturing. Pores were radially graded inside to outside by changing the lattice strut thickness, and vice versa. The additively manufactured structures were characterized by laboratory tests in the scope of producibility, morphological, chemical, and mechanical performance via caliper, precision scales, uniaxial compression test, optical light, and scanning electron microscope. The findings confirm that the wide range of porosities (60– up to 80 %) were achieved by using different strut thickness. Besides, porous structures with a wide range of density ratio from 0.88 to 1.22 g/cm3 were revealed by applying porosity variation strategies. The graded porous structures were evaluated based on their specific compressive strengths. The results have also shown that the density of struts, which increased radially inward to outward facilitated a 6% improvement. Deformation mechanism and failure behavior of the structures were strongly affected by the porosity variation strategy. The graded porous structures were found to exhibit distinct deformation behavior when compared to a uniform porous structure, where the energy absorption capacity is higher in graded porous structures compared to uniform structures.

Evolution of Rayleigh-Taylor instability under interface discontinuous acceleration induced by radiation.

Rayleigh-Taylor instability (RTI) under radiation background is commonly found in both engineering applications and natural phenomena. In the optically thin and incompressible limit, the corresponding problem can be simplified as an interface discontinuous acceleration (IDA) RTI problem, but to date has only been studied in the linear stage. In this paper, the entire IDA-RTI evolution was studied numerically and theoretically, particularly for the stages beyond the linear stage. The results show that the IDA-RTI problem is equivalent to the classical RTI with the effective acceleration g_{eff}^{*} that is introduced in this work. Moreover, our studies further show that IDA-RTI can occur if and only if g_{eff}^{*}>0 (from heavy fluid to light fluid). This criterion means that IDA-RTI can occur when (i) heavy fluid supports (or accelerates) the light fluid or (ii) the two fluids have the same density, in contrast to the classical RTI problem. Moreover, the quasisteady bubble and spike velocities are theoretically predicted with quantitative accuracy, showing good agreement with the results of numerical simulations in a wide range of density ratios and acceleration configurations.

Dynamics of formation and oscillation of non-spherical drops

Present study focuses on the shape of a drop during pinch-off and how the shape of a drop is affected by the flow parameters and different physical properties of the fluids. Both experimental and numerical investigations are performed to unveil the mechanism of non-spherical drop formation and the oscillatory motion of a drop after pinch-off. Numerical simulations are performed over a wide range of density ratios (0.001–0.9) and viscosity ratios (0.01–10) ranging from a gas-liquid system to a liquid-liquid system. The deformation of a drop at the incipience of pinch-off depends on the internal stress distribution within the drop. A larger velocity gradient inside the drop culminates in a stronger shear force within the drop leading to a non-spherical drop during pinch-off. We reveal that the shape of a drop remains either in prolate or in spherical form during pinch-off. A drop undergoes prolate-oblate-prolate oscillation while falling through the surrounding medium. The oscillatory motion is generated due to the local capillary pressure that develops across the drop surface because of the deformed shape of the drop after pinch-off. Present investigation reveals that the deformation of the drop because of the downward pull generated near the pinching region makes the drop shape non-spherical after pinch-off and initiates the oscillatory motion of the drop. The oscillation of a drop reduces substantially at higher relative strength of the viscous force.

Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows. The most striking feature of the model is that it enables to handle multiphase flows with large density ratio, which are unavailable in all previous axisymmetric LB models. The present model utilizes two LB evolution equations, one of which is used to solve fluid interface, and another is adopted to solve hydrodynamic properties. To simulate axisymmetric multiphase flows effectively, the appropriate source term and equilibrium distribution function are introduced into the LB equation for interface tracking, and simultaneously, a simple and efficient forcing distribution function is also delicately designed in the LB equation for hydrodynamic properties. Unlike many existing LB models, the source and forcing terms of the model arising from the axisymmetric effect include no additional gradients, and consequently, the present model contains only one non-local phase field variable, which in this regard is much simpler. In addition, to enhance the model’s numerical stability, an advanced multiple-relaxation-time (MRT) model is also applied for the collision operator. We further conducted the Chapman-Enskog analysis to demonstrate the consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn equation and hydrodynamic equations. A series of numerical examples, including static droplet, oscillation of a viscous droplet, breakup of a liquid thread, and bubble rising in a continuous phase, are used to test the performance of the proposed model. It is found that the present model can generate relatively small spurious velocities and can capture interfacial dynamics with higher accuracy than the previously improved axisymmetric LB model. Besides, it is also found that our present numerical results show excellent agreement with analytical solutions or available experimental data for a wide range of density ratios, which highlights the strengths of the proposed model.

On the trajectory of nonturbulent liquid jets in subsonic crossflows at different density ratios

ABSTRACT Numerical simulations using volume of fluid (VOF) method are performed to study the impact of liquid-to-gas density ratio on the trajectory of nonturbulent liquid jets in gaseous crossflows. In this paper, large eddy simulation (LES) turbulence model is coupled with the VOF method to describe the turbulence effects accurately. In addition, dynamic adaptive mesh refinement method with two refinement levels is applied to refine the size of the cells located at gas-liquid interface. Density ratio is changed from 10 to 5000 while other nondimensional numbers are kept constant. Large density ratios are considered in this paper since they are common in many practical applications such as solution precursor/suspension plasma sprays. Our simulations show that the penetration height, especially in the farfield, increases as the density ratio increases. A general correlation for the jet trajectory, which can be used for a wide range of density ratios, is developed based on our simulation results.

Investigation of 2D drop evaporation on a smooth and homogeneous surface using Lattice Boltzmann method

In this study, we present a numerical simulation on behavior of a liquid droplet on a heated horizontal substrate to investigate the contact line motion using multiphase Lattice Boltzmann method. For this purpose, the model of Lee is used which is applicable to a wide range of density ratios. A proper source term is incorporated at the liquid-gas interface to account for the phase change process and the passive scalar method is employed to simulate the temperature field. The cubic boundary condition is adopted to model the effects associated with the wall boundary. Effects of Stefan number and density ratio on the dynamic of the evaporation are illustrated. The adopted method allows us to carry out the simulations with density ratios up to 1000 which previous LB models were unable to analyse. Finally the contact line motion of an evaporating droplet on a smooth substrate is investigated. The results show that the properties of the surface play an important role on the dynamic of the evaporation which was observed in other researches.

Numerical investigation of film cooling on a 2D corrugated surface

ABSTRACTA detailed numerical study on the film cooling of a corrugated surface through a single slot has been presented in this paper. The effects of the blowing ratio, density ratio (DR), and injection angle on the film cooling of the corrugated surface are discussed. Numerical simulations are carried out over a wide range of DRs ranging from 0.2 to 5.0 at a fixed mainstream Reynolds number of 1.5 × 105, three blowing ratios of 1, 2, and 3, and five injection angles ranging from 30° to 90°. Results show that the velocity profile on a corrugated surface is strongly influenced by the injection of the secondary fluid. It is observed that the film cooling effectiveness of the corrugated surface increases monotonically with an increase in the blowing ratio. The density ratio and injection angle also have a strong influence on the film cooling.

Prediction of film cooling effectiveness over a flat plate from film heating studies

ABSTRACTFilm cooling is widely used to protect surfaces exposed to gases at a high temperature in gas turbine engines. Film heating is the reverse of film cooling, where hot secondary fluid is injected onto the walls to protect against a relatively cold mainstream. In the literature, the latter has often been used as an experimental analogue of the former, since mainstream flow rates are substantially higher, and it is relatively simpler to heat the smaller stream of secondary fluid for experiments. In this paper, the results obtained from a numerical study of film cooling and film heating over a flat plate through single-slot injection are presented. Since the objective of the work is to evaluate the suitability of film heating as a proxy for film cooling, it was decided to keep computational simple, using two-dimensional simulations. The effect of a density ratio of injectant-to-mainstream in the range of 0.2–5 is studied numerically to cover film heating and film cooling. Numerical simulations were carried out for three blowing ratios, M = 1, 2, and 3 at a fixed mainstream Reynolds number of 1.5 × 105 for three injection angles, 30°, 45°, and 60°. Numerical simulations were also carried out for a wide range of momentum flux ratio for film heating and film cooling at an injection angle of 30°. The results show that film heating and film cooling are not equivalent, especially when the density ratio deviates from unity substantially. Based on numerical study, it appears possible to predict film cooling effectiveness from film heating effectiveness for a wide range of density ratios, even though the effectiveness values obtained in regard to film cooling and film heating differ significantly.

A Numerical Study on the 2D Film Cooling of a Flat Surface

In this article, the results obtained from a detailed numerical investigation of 2D film cooling over a flat plate through single-slot injection are presented. The effects of mainstream Reynolds number, blowing ratio, density ratio, and injection angle on the effectiveness of film cooling were investigated in the present work. Numerical simulations were carried over a wide range of density ratio ranging from 1.1 to 5 at two mainstream Reynolds numbers (8 × 104 and 1.5 × 105), three blowing ratios (ranging from 1 to 3), and six injection angles (ranging from 15° to 90°). The results show that at lower injection angles of 15°–45°, maximum film-cooling effectiveness occurs at a particular value of velocity ratio which is found to be independent of mainstream Reynolds number, blowing ratio, and density ratio. Based on a combined effect analysis of blowing ratio, density ratio, and injection angle, a relation was obtained for velocity ratio that gives an optimum film-cooling effectiveness.

Simulation of the two-fluid model on incompressible flow with Fractional Step method for both resolved and unresolved scale interfaces

In the present paper, the Fractional Step method usually used in single fluid flow is here extended and applied for the two-fluid model resolution using the finite volume discretization. The use of a projection method resolution instead of the usual pressure-correction method for multi-fluid flow, successfully avoids iteration processes. On the other hand, the main weakness of the two fluid model used for simulations of free surface flows, which is the numerical diffusion of the interface, is also solved by means of the conservative Level Set method (interface sharpening) (Strubelj et al., 2009). Moreover, the use of the algorithm proposed has allowed presenting different free-surface cases with or without Level Set implementation even under coarse meshes under a wide range of density ratios. Thus, the numerical results presented, numerically verified, experimentally validated and converged under high density ratios, shows the capability and reliability of this resolution method for both mixed and unmixed flows.

A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows

In recent years, the immersed boundary method has been well received as an effective approach for the fully resolved simulations of particulate flows. Most immersed boundary approaches for numerical studies of particulate flows in the literature were based on various discrete delta functions for information transfer between the Lagrangian elements of an immersed object and the underlying Eulerian grid. These approaches have some inherent limitations that restrict their wider applications. In this paper, a sharp interface direct forcing immersed boundary approach based on the method proposed by Yang and Stern (Yang and Stern, 2012, “A Simple and Efficient Direct Forcing Immersed Boundary Framework for Fluid-Structure Interactions,” J. Comput. Phys., 231(15), pp. 5029–5061) is given for the fully resolved simulations of particulate flows. This method uses a discrete forcing approach and maintains a sharp profile of the fluid-solid interface. It is not limited to low Reynolds number flows and the immersed boundary discretization can be arbitrary or totally eliminated for particles with analytical shapes. In addition, it is not required to calculate the solid volume fraction in low density ratio problems. A strong coupling scheme is employed for the fluid-solid interaction without including the fluid solver in the predictor-corrector iterative loop. The overall algorithm is highly efficient and very attractive for simulating particulate flows with a wide range of density ratios on relatively coarse grids. Several cases are examined and the results are compared with reference data to demonstrate the simplicity and robustness of our method in particulate flow simulations. These cases include settling and buoyant particles and the interaction of two settling particles showing the kissing-drafting-tumbling phenomenon. Systematic verification studies show that our method is of second-order accuracy on very coarse grids and approaches fourth-order accuracy on finer grids.

Momentum Effects on the Spray Drop Size, Calculated from the Integral Form of the Conservation Equations

In this work, we consider an appropriate form of the viscous dissipation term in the integral form of the conservation equation, and examine the effects of momentum terms on the computed drop size in pressure-atomized sprays. The Sauter mean diameter (SMD) calculated in this manner agrees well with experimental data that included measurements of both the drop velocities and sizes. The revised treatment of liquid momentum also leads to quite stable calculations for a wide range of density ratios and injection velocities. Using this setup, injection parameters such as the spray cone angle and the atomization length can be directly input to the system of equations. Thus, this approach is capable of incorporating the effects of injection parameters, and can be used for further considerations of the drop and velocity distributions under a wide range of spray geometry and injection conditions.

Two-phase SPH modelling of advective diffusion processes

This paper deals with a two-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) technique for the evaluation of the concentration field of pollutants in water. A SPH model is formulated to solve the fickian diffusion equation applied to pollutants with the same density as the water. A lagrangian SPH formalism of the advective diffusion equation is also developed for pollutant-water, taking into account the effects of molecular diffusion and natural advection induced by differences between the fluid densities. These equations are coupled with the fluid mechanics equations. Attention is paid to the numerical aspects involved in the solution procedure and to the optimization of the model parameters. Environmental engineering problems concerning diffusion and natural advection phenomena occur in the presence of a pollutant in still water. Numerical tests referring to a strip and a bubble of contaminant in a water tank with different initial concentration laws have been carried out. The results obtained by the proposed SPH models are compared with other available SPH formulations, showing an overall better agreement with standard analytical solutions in terms of spatial evolution of the concentration values. Capabilities and limits of the proposed SPH models to simulate advective diffusion phenomena for a wide range of density ratios are discussed.

Experimental validation of a Richtmyer–Meshkov scaling law over large density ratio and shock strength ranges

A universal scaling law for the Richtmyer–Meshkov instability is validated with experimental results covering a wide range of density ratios and shock strengths. These results include the first membraneless, gas-phase, interface experiments for A>0.5 and M>1.5. The shock-accelerated, sinusoidal interface experiments are conducted in a vertical shock tube with a large square cross section and cover the experimental parameter space: 0.29<A<0.95, 1.1<M<3, and 3.1×104<Re<1.4×107. Results provide growth-rate data for comparison with computational fluid dynamics simulation codes and verify the nondimensional time and amplitude parameters chosen for scaling are the correct ones. Correct scaling is obtained by including a growth-reduction factor that accounts for diffusion at the interface. Planar imaging techniques are used to diagnose the instability development for a nearly single-mode interface, and results are reported for eight scenarios (including three distinct gas pairs) that span the linear and nonlinear growth regimes. Images from the strongly shocked, high A experiments are the first to provide evidence of bubble-growth suppression due to shock proximity.

Slumping of non-Boussinesq density currents of various initial fractional depths: A comparison between direct numerical simulations and a recent shallow-water model

Simulations of non-Boussinesq density currents of various initial fractional depths are performed, and a detailed comparison with a recent shallow-water model [18] is done for a wide range of density ratio 10 - 4 ⩽ ρ c / ρ a ⩽ 10 4 and initial depth ratio 1 ⩽ H ∗ ⩽ 50 in the regime of constant-speed initial phase. Good agreement is observed in a large region of the parameter space. The larger discrepancy is observed in the range of high H * and low- ρ c / ρ a for which the shallow-water model overpredicts the velocity of the current. Two possible reasons are suspected, namely the fluid motion in the ambient fluid which is not accounted for in the model, and the choice of the model for the front condition.

The full impulse response of two-dimensional jet/wake flows and implications for confinement

In this theoretical study, a linear spatio-temporal analysis is performed on unconfined and confined inviscid jet/wake flows in order to determine whether they are absolutely or convectively unstable. The impulse response is evaluated in the entire outer fluid, rather than just at the point of impulse, over a wide range of density ratios. This confirms that the dominant saddle point can validly migrate into the plane of diverging eigenfunctions. This reveals that, at certain density ratios and shear numbers, the response can grow upstream in some directions with a cross-stream component, even though it decays directly upstream of, and at, the point of impulse. This type of flow is convectively unstable when unconfined, but becomes absolutely unstable when confined. Other effects of confinement are described in a previous paper. Together, these articles have important implications for the design of fuel injectors, which often employ confined shear flows at high Reynolds number and large density ratios to generate strong mixing in combustion chambers.

Deflection, drift, and advective growth in variable-density, laminar mixing layers

Specific features of the variable-density mixing layers without gravity effects are studied using self-similar solutions to the laminar and time-evolving variant of this flow. Density variations come from either mass or temperature mixing, accounting for, in the latter case, the effect of the Mach number. The transverse profiles of the flow quantities, as well as the time evolutions of the global characteristic scales of the mixing layer, are given for a wide range of density ratio and Mach-number values. When compared to the constant-density case, it appears that most of the specificity of these flows comes from the emergence of a nonzero transverse component of the velocity. First, it produces a deflection of the flow that can be either confined in the core of the layer or global, the whole layer being tilted at an angle from the initial flow direction. In most cases, this deflection is such that some part of the higher-density fluid is “entrained” in the direction of the lower-density fluid, leaving no possibility to define a dividing streamline. Second, it leads to a shift between the density profile and the profiles of the other flow quantities. This shift scales on the (time-increasing) mixing-layer thickness and therefore appears as a time drift. When global deflection is present, the tilting of the layer can be shown to be equivalent to a global drift of the mixing/shear layer toward the light-fluid side of the flow. Third, transport by the transverse velocity component affects the spreading of the mixing layer, giving rise to an additional effect referred to as advective growth. Examination of the density-ratio and Mach-number effects leads to surprising results: While the momentum thickness is always observed to decrease when increasing these parameters, conventional thicknesses (based on the profiles of the different variables) can show opposite behaviors depending on the form of the diffusion model for the considered variable.