Towards numerical simulations of supersonic liquid jets using ghost fluid method

A computational tool based on the ghost fluid method (GFM) is developed to study supersonic liquid jets involving strong shocks and contact discontinuities with high density ratios. The solver utilizes constrained reinitialization method and is capable of switching between the exact and approximate Riemann solvers to increase the robustness. The numerical methodology is validated through several benchmark test problems; these include one-dimensional multiphase shock tube problem, shock–bubble interaction, air cavity collapse in water, and underwater-explosion. A comparison between our results and numerical and experimental observations indicate that the developed solver performs well investigating these problems. The code is then used to simulate the emergence of a supersonic liquid jet into a quiescent gaseous medium, which is the very first time to be studied by a ghost fluid method. The results of simulations are in good agreement with the experimental investigations. Also some of the famous flow characteristics, like the propagation of pressure-waves from the liquid jet interface and dependence of the Mach cone structure on the inlet Mach number, are reproduced numerically. The numerical simulations conducted here suggest that the ghost fluid method is an affordable and reliable scheme to study complicated interfacial evolutions in complex multiphase systems such as supersonic liquid jets.     

A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

The interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of viscous flow: Buckling of planar jets

The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Taylor (1968). This paper is concerned with demonstrating that a numerical method, GENSMAC, is capable of simulating this physical instability. A table of the parameter values (e.g. the Reynolds number, the Froude number, inlet width, inlet velocity and aspect ratio) is provided giving details of when buckling occurs and when it does not. This allows the deduction of a possible buckling condition in terms of the Reynolds number and the ratio of height of the jet to the inlet width, modifying a previous hypothesis. Visualization of jet buckling is provided. This work has been motivated by the need of industry to understand jet filling of containers; jet buckling can lead to air entrapment and this is undesirable. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental and numerical analysis of steam jet pump

Steam jet pump is the best choice for pumping radioactive and hazardous liquids because it has no moving parts and so no maintenance. However, the physics involved is highly complicated because of the mass, momentum and energy transfer between the phases involved. In this study the characteristics of SJP are studied both experimentally and numerically to pump water using saturated steam. In the experimental study the static pressure, temperature along the length of the steam jet pump and the steam and water flow rates are recorded. The three dimensional numerical study is carried out using the Eulerian two-phase flow model of Fluent 6.3 software and the direct-contact condensation model developed previously. The experimental and CFD results, of axial static pressure and temperature, match closely with each other. The mass ratio and suction lift are calculated from experimental data and it is observed that the mass ratio varies from 10 to 62 and the maximum value of suction lift is 2.12 m under the conditions of the experiment.     

Thermal modulation and breakup of liquid jets

In this paper, we study the breakup behavior of Newtonian liquid and non‐Newtonian liquid jets with an arbitrary variation surface tension imposed along its length. The effect of duty cycle, fluid properties, and the various profiles of the surface tension is investigated. It is shown that the breakup behavior of a jet can be constructed by using the Fourier expansion of the surface tension profile. When the dimensionless wavenumber k is larger than 0.5, the jet breakup behavior is determined by the lowest frequency of the Fourier series expansion of the surface tension profile. As k decreases, higher frequency Fourier modes come to play. In general, for k between, 1∕(n+ 1) and 1∕n,n Fourier modes are needed to determine the jet breakup behavior. The current nonlinear model differs from the existing linear slender jet model in the literature in several ways. While the principle of superposition is valid for the linear model, it is not generally valid for the current nonlinear model. For the linear model, the jet will never break up when the wavenumber is larger than 1. The current model, however, shows clearly that the jet can indeed break up when the wavenumber is larger than 1. Furthermore, the current nonlinear model predicts a breakup time substantially higher than that from the linear model.Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical investigation of the flow and heat behaviours of an impinging jet

The flow and temperature fields of a turbulent impinging jet are rather complex. In order to accurately describe the flow and heat-transfer process, two important factors that must be taken into account are the turbulence model and the wall function. Several turbulence models, including κ–? turbulence models, κ–ω turbulence models, low-Re turbulence models, the κ–κ_l–ω turbulence model, the Transition SST turbulence model, the V2F turbulence model and the RSM turbulence model, are examined and compared to experimental data. Furthermore, for the near wall region, various wall functions are presented for comparison and they include the standard wall function, the scale wall function, the non-equilibrium wall function and the enhanced wall function. The distribution features of velocity, turbulent kinetic energy and Nusselt number are determined in order to provide a reliable reference for the multiphase impinging jet in the future.     

Modelling and experimental investigation of horizontal buoyant gas jets injected into stagnant uniform ambient liquid

In this article, an experimental and theoretical study on the buoyant non-condensable gas jet that is injected horizontally into a high-density liquid ambient at different initial conditions is performed. Direct and instantaneous global measurements of the interface were performed using a high-speed photography. The position and motion of the entire gas jet were captured by a high-velocity camera and the images were processed, averaged and analyzed to extract the jet parameters and interface position. In the mathematical model, the rate of entrainment is assumed to be a function of the jet centerline velocity, the ratio of the mean jet and the ambient densities, while the entrainment coefficient depends on the local Froude number at the jet region. An interfacial shear stress acting at the interface between the jet flow and the water ambient in the opposed direction to the main jet momentum flux is considered. The results showed that the model is able to accurately predict the jet parameters: trajectory, spread, jet angles and penetration lengths as well as the jet regimes. An overall good agreement was obtained between the simulation and experimental results over a large range of Froude numbers and jet diameters. The developed model has proven to be an adequate tool to predict the different jet parameters.     

A numerical investigation of aerofoil boundary-layer manipulator profile for cruise-flight conditions

A computational study has been conducted to determine the variation of device drag with profile shape and angle of attack for aerofoil boundary-layer manipulators (LEBUs) operating at high subsonic Mach numbers. Calculations have been made at a free-stream Mach number of 0.80 for both symmetrical and asymmetrical NACA-00xx and 44xx series devices including an inverted cambered NACA-4409 profile. The LEBUs considered were located in a turbulent boundary-layer at a mid-chord heighth equivalent to 0.67 from the wall. The present investigations sought to confirm suggestions based upon experimental observations that there may be some advantage in replacing a symmetrical device by an inverted asymmetrical profile form.The computations were performed using an unstructured adaptive-mesh 3D Navier-Stokes code incorporating a Lam and Bremhorst low-Reynolds number two-equationk — turbulence model. The calculated flow field around a NACA-0009 aerofoil at zero angle of attack was initially verified against experimental interferometric data.The calculated device drag coefficient at zero incidence was 0.026 for the NACA-0009, similar to that measured in experiments. However predicted drag for an inverted NACA-4409 was 0.085, this being considerably higher than anticipated. The results suggested that a slightly positive angle of attack may help minimise device drag but neither profile is appropriate for use in transonic conditions. Improved results may be obtained from inverted flat-topped profiles designed to minimise losses associated with localised shocks.     

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT （Ⅰ）—— VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant vertical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.     

A detailed experimental investigation of well-defined,turbulent evaporating spray jets of acetone

This paper aims at investigating the detailed structure of turbulent non-reacting dilute spray flows using advanced laser diagnostics. A simple spray jet nozzle is designed to produce a two-phase slender shear flow in a co-flowing air stream with well-defined boundary conditions. The carrier flow is made intentionally simple and easy to model so that the focus can be placed on the important aspects of droplet dispersion and evaporation, as well as turbulence–droplet interactions. Phase Doppler interferometry is employed to record droplet quantities, while planar laser-induced fluorescence imaging is applied separately to obtain acetone vapour data. Measurements are conducted for four acetone spray jets in air at several axial stations starting from the nozzle exit. The combined liquid and vapour mass fluxes of acetone integrated across the jet at downstream locations agree satisfactorily with the total mass flow rate of acetone injected.     

Experimental and numerical investigation of combined isotropic-kinematic hardening behavior of sheet metals

To prevent a sheet specimen from buckling subjected to a tension-compression cyclic loading, a new fixture has been developed to use with a regular tensile-compression machine. The novelty of this device lies in 4-block wedge design with pre-loaded springs. This design allows blocks to freely move in the vertical direction while providing the normal support to the entire length of the specimen during the tension-compression cycle. The entire test is easy to setup, which is another advantage of this design. In order to measure the strain accurately, the transmission type laser extensometer was utilized together with the implementation of double-side fins in the specimen. Experimental results of tension-compression tests are presented followed by a review of existing testing methods. In order to describe the accurate cyclic tension-compression behavior, the combined isotropic-kinematic hardening law based on the modified Chaboche model and the practical two-surface model based on Dafalias-Popov and Krieg models have been modified in this work, considering the permanent softening behavior during reverse loading and the non-symmetric behavior during reloading. Through tension-compression tests, the material characterization has been performed for three base materials, BH180, DP600 steels and AA6111-T4 sheets.     

Experimental and numerical study of Marangoni convection in shallow liquid layers

An experimental and numerical study of thermal Marangoni convection in shallow liquid layers was carried out for a range of temperature differences and layer depths. This was done to permit earth based experiments to be undertaken in situations where Marangoni convection dominated the flow. Particle image velocimetry (PIV) was used to obtain the flow patterns and velocity vectors. The experimental results were compared to numerical models created using FLUENT V6. Both results are in good agreement. The liquid free surface profile due to the presence of the menisci is shown to be critical for good quantitative validation. The layer depths are also proven to be shallow enough for Marangoni convection to dominate over buoyancy under normal gravity conditions.     

A time-dependent numerical analysis of flow in a mechanical heart valve: Comparison with experimental results

There is a great need to fabricate heart valves that have similar haemodynamic properties with the natural ones. Towards this goal, we examine the dynamics of fluid flow in a mechanical heart valve with one leaflet. The fluid is incompressible and Newtonian and the leaflet is a neo-Hookean material. The Arbitrary Lagrangian Eulerian method is used to model the fluid-leaflet interaction, and the system of equations is solved using the Finite Element method. The pseudo solid approach along with a set of algebraic equations are used to deform the mesh, while care is taken to avoid remeshing of the domain, at the moment of valve closure. The computational results are compared against the experimental results, and we find an excellent agreement for the time period of valve closure, the time the valve is fully opened, and the value of the maximum valve opening angle. This study indicates that the present model is capable of describing the valve dynamics in physiological geometries.     

A numerical and experimental investigation into residual stress in thermally sprayed coatings

This paper is concerned with an investigation into the thermal spray process and is particularly concerned with the residual stresses that arise when a steel-alloy coating is sprayed onto a copper-alloy substrate. This material combination was used recently to enhance the thermal and mechanical efficiency of the pressure die casting process. A difficulty with the spraying of steel on copper is the attainment of appreciable thickness of the coating due to debonding during the thermal spraying process. Prominent among possible causes of debonding is residual stress, which is the focus of the research presented in the paper. An investigation into the thermal spray process is performed using experimentation, simplified numerical modelling and finite element modelling. The development of residual stress for a range of process parameters, i.e. deposited layer thickness, interval of layer deposition and the number of layers in a coating (i.e. block deposition versus multilayer deposition for a desired coating thickness) is recorded. The results from the three investigation methods agreeably indicate a progressive change in average interfacial residual stress from compressive towards tensile with increase in thickness of deposited layer; and a tensile interfacial stress in a two-layer coating, which increases with increase in interval of deposition between the two layers. On the whole, the observations from the results suggest an increase in potential for coating debonding with increase in both deposited layer thickness and layer deposition interval. The results further suggest higher potential for coating debonding with block deposition compared to multilayer deposition for a desired coating thickness.     

An experimental investigation on flow structures of confined and unconfined impinging air jets

The flow characteristics of both confined and unconfined air jets, impinging normally onto a flat plate have been experimentally investigated. The mean and turbulence velocities, and surface pressures were measured for Reynolds numbers ranging from 30,000 to 50,000 and the nozzle-to-plate spacings in range of 0.2–6. Smoke-wire technique is used to visualize the flow behavior. The effects of Reynolds number, nozzle-to-plate spacing and flow confinement on the flow structure are reported. In the case of confined jet, subatmospheric regions occur on both impingement and confinement surfaces at nozzle-to-plate spacings up to 2 for all Reynolds numbers in consideration and they lie up to nearly the same radial location at both surfaces. However, there is no evidence of the subatmospheric region in unconfined jet. It is concluded that there exists a linkage among the subatmospheric region, turbulence intensity and the peaks in heat transfer coefficients for low spacings in impinging jets.     

Experimental investigation and theoretical modeling of liquid entrainment in a horizontal tee with a vertical-up branch

This article describes a comprehensive literature review of liquid entrainment in horizontal pipes with vertical-up branches. Deficiencies in the available data and correlations were identified. The Air–water Test Loop for Advanced Thermal–hydraulic Studies (ATLATS) was constructed and entrainment onset and steady-state data were collected for a wide range of flow conditions. Using new insights gained from experimental testing, the authors developed a model for predicting the onset of entrainment and steady-state entrainment rate. Previously published correlations, along with the new model, are compared against all available data. The new model shows very good agreement with the onset data, but is not very good at predicting branch quality at high liquid flow rates.     

Experimental and analytical investigation of liquid sheet breakup characteristics

The main objective of this research is to study analytically and experimentally the liquid sheet breakup of a flat fan jet nozzle resulting from pressure-swirling. In this study the effects of nozzle shape and spray pressure on the liquid sheet characteristics were investigated for four nozzles with different exit widths (1.0, 1.5, 2.0 and 2.5 mm). The length of liquid sheet breakup, liquid sheet velocity and the size of formed droplets were measured by a digital high speed camera. The breakup characteristics of plane liquid sheets in atmosphere are analytically investigated by means of linear and nonlinear hydrodynamic instability analyses. The liquid sheet breakup process was studied for initial sinuous and also varicose modes of disturbance. The results presented the effect of the nozzle width and the spray pressure on the breakup length and also on the size of the formed droplets. Comparing the experimental results with the theoretical ones for all the four types of nozzles, gives a good agreement with difference ranges from 4% to 12%. Also, the comparison between the obtained results and the results due to others shows a good agreement with difference ranged from 5% to 16%. Empirical correlations have been deduced describing the relation between the liquid sheet breakup characteristics and affecting parameters; liquid sheet Reynolds number, Weber number and the nozzle width.     

Structural behaviour of aluminium self-piercing riveted joints: An experimental and numerical investigation

The present paper deals with the structural behaviour of self-piercing riveted joints based on aluminium and steel rivets. Two T-components made of two open aluminium profiles in alloy AA6063 temper T4 joined by 6 and 12 rivets, respectively, were designed and tested under quasi-static loading conditions. A new test device was designed to perform the tests of the T-components under two different load cases. Experimental results of the T-components joined by using aluminium self-piercing rivets were then compared with the corresponding components joined by using steel rivets in terms of force-displacement curves, deformation modes of the components as well as rivet failure modes. Further, the experimental results of the T-components based on aluminium rivets were used to validate a resultant-based point-connector model for self-piercing rivets proposed by Hanssen et al. (2010) using shell elements.