Liquid Weber Number Research Articles

Wave characteristics of vertical upward adiabatic annular flow in pipes

Annular flow exists in many engineering applications, such as refrigerators, oil extraction, nuclear reactors and so on, due to its high heat and mass transfer efficiencies. Annular flow is characterized by liquid film on the wall and gas core at the center of the flow duct. The interface between the gas and liquid is composed of many different waves that play important role in mass, momentum and energy transfers between gas and liquid phases. Here three important parameters regarding wave characteristics, namely, wave velocity, base film thickness and wave height have been studied. For wave velocity, correlation has been proposed by two methods which are derived from liquid interfacial velocity and interfacial shear stress, respectively. For correlations of base film thickness and wave height, they are proposed in similar forms as that of average film thickness previously developed by the authors. These newly proposed correlations are functions of gas and liquid Weber numbers, and are simpler and more straightforward to use as compared to the existing ones. The newly proposed wave velocity, base film thickness and wave height correlations, respectively, have mean absolute percentage errors of 9.56%, 14.6% and 12.1% compared to current databases. They have shown an improved prediction accuracy compared to the other correlations in the literature.

Effect of heat and mass transfer on the instability of an annular liquid sheet

A temporal linear instability analysis has been conducted to investigate the effect of heat and mass transfer on the instability of an annular liquid sheet axially moving in the gas medium. The dispersion relation is obtained and solved numerically. Energy budget is calculated to provide physical insights of various instability driving mechanisms. The results show that heat and mass transfer promotes the wave growth rate mainly at small wave numbers. In contrast to the case without heat and mass transfer, the wave growth rate with strong heat and mass transfer peaks at zero wave number. Liquid viscosity is found to have a minimal stabilizing effect on the sheet instability. Regardless of the heat and mass transfer, increasing liquid Weber number suppresses the sheet instability below a crossover point of wave number at 1.15, and promotes the sheet instability above the crossover point. In the presence of strong heat and mass transfer, increasing gas-to-liquid density ratio reduces the wave growth rate at small wave numbers below 0.28, and beyond which increases the wave growth rate. Reducing sheet thickness promotes the sheet instability for all wave numbers. The energy budgets show that the inner gas disturbance is most responsible for promoting the wave growth rate at large liquid Weber numbers; and the inner interface dominates the outer one in destabilizing the annular liquid sheet.

Linear stability analysis of a non-Newtonian liquid jet in a coaxial swirling air

The instability behavior of a power law liquid jet moving in a swirling air is investigated theoretically. The power law model is selected to describe the viscosity of the non-Newtonian jet. The corresponding dispersion relation is obtained by a linear stability analysis. Besides, the effects of air swirl strength, non-axisymmetric mode, liquid Weber number, generalized Reynolds number, power law index and consistency coefficient on the instability of the power law liquid jet surrounded by a swirling gas are studied in the Rayleigh and Taylor modes. The results show that the shear-thickening liquid jet is more unstable than the Newtonian and shear-thinning liquids when the air swirl is introduced. The air swirl is a stabilizing factor on the instability of the power law liquid jet in Rayleigh and Taylor modes. It is also found, when the air swirl is introduced, the maximum growth rate of the power liquid jet decreases as the liquid Weber number increases in Rayleigh mode, while it increases in Taylor mode. Moreover, the viscous forces of the liquid always prevent the jet from breaking up.

Investigation of the primary breakup length and instability of non-Newtonian viscoelastic liquid jets

The temporal instability and primary breakup length of a non-Newtonian viscoelastic liquid jet moving in an inviscid gaseous environment were carried out by solving a set of linearized Navier-Stokes equations and employing the linear viscoelastic model, respectively. The dimensionless dispersion equation that governs the instability was derived and solved by a numerical method. The effects of fluid properties on the instability and primary breakup length of viscoelastic liquid jets were carried out. It could be seen that by increasing the growth rate, the instability range and the primary breakup length of the viscoelastic liquid jets could result in an increase in the liquid Weber number and the ratio of gas to liquid density. Moreover, the significant findings are that an increase in the time constant ratio, and also the Ohnesorge number reduced both of the growth rates of disturbances and primary breakup length. Though, increasing the elasticity number resulted in a higher growth rate of disturbances and enhanced the breakup mechanism.

Primary breakup dynamics and spray characteristics of a rotary atomizer with radial-axial discharge channels

An experimental investigation of primary breakup dynamics and spray characteristics of a rotary atomizer with high aspect ratio radial-axial discharge channel is described. A high-resolution shadow imaging technique with pulsed backlight illumination was used for spray visualization. For the rotary atomizer with high aspect ratio discharge channel and radial-axial orientation, visualization showed the occurrence of Centripetal–Coriolis-induced stream-mode injection for all operating conditions. In this mode of injection, a crescent liquid film forms in the channel exit and issues from the orifice as a liquid column or a thin liquid sheet depending on atomizer operating conditions. It was found that the liquid Weber number value determines the state of the injected liquid stream (column or sheet) during the breakup process. The breakup process was studied with the variation of rotational speed and liquid volume flow rate. A morphological classification of the different modes of breakup is obtained from the flow visualizations. Four breakup modes have been observed for the present range of test parameters. These include Rayleigh, bag, stretched ligament, and shear breakup modes. These modes are separated by transitional regimes. The results suggest qualitative similarities between the primary breakup of the present rotary atomizer with a non-turbulent liquid jet and a fan like liquid sheet under a gas cross flow. The maximum liquid stream penetration height was measured for some operating conditions. It is concluded that this parameter is depend on the momentum flux ratio and liquid Weber number. To further evaluate features of the spray, the droplet size measurements have been conducted using the PDIA technique. The results indicate that there is a relatively strong correlation between the SMD values and liquid Weber number, while a properly non-dimensionalized droplet size is well correlated with the momentum flux ratio and Rossby number.

Numerical investigation of the breakup behavior of an oscillating two-phase jet

Low emission combustion is critically influenced by fuel-air mixing quality. In the case of liquid fuels, atomization of the injected liquid is a vital component. Compared to standard injector nozzles, a spatially oscillating jet, as produced by a fluidic oscillator, has shown superior performance. To better understand and control breakup mechanisms of turbulent oscillating two-phase jets, numerical investigations are conducted for a jet with liquid Reynolds number Rel = 8701 and liquid Weber number Wel = 4759. Simulations are performed using a volume of fluid method. No explicit turbulence modeling is incorporated, but numerical viscosity of the discretization acts as an implicit subgrid scale model. Octree discretization in space in combination with adaptive mesh refinement allows for high-resolution interface capturing while allowing for moderate usage of computational resources. Two grid resolutions and refinement criteria are used to investigate the influence of spatial resolution and resolved turbulence on jet breakup. Inlet boundary conditions for the two-phase simulations are obtained from preceding single-phase, unsteady Reynolds-averaged Navier-Stokes simulations of a fluidic oscillator. The highest grid resolution shows an accurate representation of surface-tension- and inertia-induced breakup mechanisms, and turbulence effects along the interface appear sufficiently resolved. Besides Kelvin-Helmholtz instabilities, Rayleigh-Taylor instabilities, induced from jet oscillation, are observed. Superposition of these characterizes jet degradation and leads to early breakup. For validation, data from preceding flow experiments of a fluidic oscillator are used to compare droplet sizes and spatial development of the jet. Good agreement is found for all relevant properties.

Dynamic behavior of single droplet impacting on heptane pool with different depths

The paper presents dynamic behavior of single droplet impinging on the heptane pool with various impact Weber number and liquid depths. Liquid depth and Weber number have significant effects on the droplet impact behaviors. Three typical impact regimes, including penetration-secondary penetration/floating, crater-jet/crater-jet-secondary jet and bubble, can be observed in the impact process. The penetration occurs only for low Weber number. Especially, penetration-second penetration appears in a shallow pool for the dimensionless heptane depth of no more than 3.6, while penetration-floating does for the dimensionless heptane depth of no less than 5.4. With an increase in Weber number from 175 to 440, crater-jet appears in shallow pool while crater-jet-secondary jet appears in deep pool, and bubble begins to form as Weber number exceeds 564. Moreover, in order to quantitatively analyze the kinetic behavior, some key parameters were discussed in detail, such as maximum crater depth and width, jet height, bubble life time, loss rate of impact velocity, etc.

Dual-mode nonlinear instability analysis of a confined planar liquid sheet sandwiched between two gas streams of unequal velocities and prediction of droplet size and velocity distribution using maximum entropy formulation

Twin fluid atomizers utilize the kinetic energy of high speed gases to disintegrate a liquid sheet into fine uniform droplets. Quite often, the gas streams are injected at unequal velocities to enhance the aerodynamic interaction between the liquid sheet and surrounding atmosphere. In order to improve the mixing characteristics, practical atomizers confine the gas flows within ducts. Though the liquid sheet coming out of an injector is usually annular in shape, it can be considered to be planar as the mean radius of curvature is much larger than the sheet thickness. There are numerous studies on breakup of the planar liquid sheet, but none of them considered the simultaneous effects of confinement and unequal gas velocities on the spray characteristics. The present study performs a nonlinear temporal analysis of instabilities in the planar liquid sheet, produced by two co-flowing gas streams moving with unequal velocities within two solid walls. The results show that the para-sinuous mode dominates the breakup process at all flow conditions over the para-varicose mode of breakup. The sheet pattern is strongly influenced by gas velocities, particularly for the para-varicose mode. Spray characteristics are influenced by both gas velocity and proximity to the confining wall, but the former has a much more pronounced effect on droplet size. An increase in the difference between gas velocities at two interfaces drastically shifts the droplet size distribution toward finer droplets. Moreover, asymmetry in gas phase velocities affects the droplet velocity distribution more, only at low liquid Weber numbers for the input conditions chosen in the present study.

Spray characteristics of liquid-liquid Pintle injector

Liquid-liquid cross flow Pintle injector studies are of renewed interest due to their flow control characteristics. In Pintle Injectors, the interaction is between a thin annular sheet and radial jets of liquid. The cause of breakup of this liquid element and the formation of the spray are effectively brought out in this study. The spray pattern is investigated for different momentum ratio and its influence on the droplet formation and size distribution is demonstrated. Two configurations of Pintle injector were subjected to cold flow trails, ie., Type-I and Type-II. Laser shadowgraphy investigation was carried out on two momentum ratios of ξ = 1 and ξ = 0.7 for Type-I injector. The geometry of liquid before the formation of the spray is a hollow conical sheet. Radial impinging jets generate wave instabilities on the surface of the conical sheet. Instabilities grow in amplitude and the amplitude growth is a function of Weber number and λ/a (wavelength to sheet thickness ratio). Lower momentum ratio flows lead to better atomization as compared to higher momentum ratio flows. The D32 values obtained are 840 μm and 650 μm for ξ = 1 and ξ = 0.7 respectively. The influence of liquid sheet thickness and Weber number on the instability waves generated and the droplet size distribution is understood. The sheet thickness for the two cases of ξ = 1 and ξ = 0.7 were estimated by applying inviscid solution theory and the sheet thickness are 172 μm and 65 μm respectively. Type-II injector was designed based on the analysis of the Type-I injector test results. The annular gap in Type-II injector was reduced to 95 μm to achieve smaller sheet thickness and increased Weber number as compared to Type-I injector. Atomization of the liquid sheet is improved to a greater extend in Type-II injector, with droplet sizes of the order of 100 μm.

Annular liquid film thickness prediction in a vertical 180° return bend

Annular flow is predominant in gas wells. Liquid may be present in form of entrained droplets as well as in the liquid film on pipe wall. The knowledge of the average liquid film thickness is vital for detailed mechanistic modelling of churn–annular flow in engineering applications. So far, the models for liquid film thickness prediction are limited to vertical and horizontal pipes. These models were based on limited ranges of experimental data. In addition, exhaustive iterations are needed when these models are used to estimate liquid film thickness. In this work, a new correlation to predict liquid film thickness in a 180° bend under gas–liquid annular conditions was successfully proposed. The correlation was based on dimensionless numbers (modified gas and liquid Weber numbers and gas Froude number) which reflect the underlined physics governing gas–liquid interaction in the bend. The Weber numbers capture the two important forces (inertial and surface tension forces) which govern the formation of the liquid film thickness within the system while gas Froude number quantifies the interaction of two important forces (centrifugal and gravitational forces) which determines the distribution of the phases across a bend. The proposed liquid film thickness correlation was based on the experimental data obtained from a wide range of operating conditions. The liquid superficial velocities ranges from 0.02 to 0.2 m/s and gas superficial velocities from 3.5 to 16 m/s at different measurement locations of 45°, 90° and 135° of the bend with a diameter of 127 mm. The liquid film thickness in air–water and helium–water annular flow can be predicted by δ=28.4061(WeL)0.10318(WeG)-0.30954(FrG)-0.31423. The validation of the proposed correlation used to predict liquid film thickness in gas–liquid annular systems with different pipe diameters were examined against the available data in the literature. Good agreement was found between the predicted values of liquid film thickness with the experimental data at different measuring locations of the bend.

Thermocapillary instability of a liquid sheet with centrifugal force

The thermocapillary instability of liquid sheets subjected to a temperature gradient that is perpendicular to the gas–liquid interface and moving in a gas medium is investigated in this paper. A linear instability analysis accounting for the weak form of the centrifugal force along the flow direction is proposed. The instability of liquid sheets with a temperature gradient is compared to that of isothermal liquid sheets, and the effect of the temperature difference is analyzed. The effect of the centrifugal force is also investigated. Furthermore, the effect of the density ratio, viscosity of liquid sheet and Weber number are also discussed by solving the dispersion equation. The results show that, when the thermocapillary effects are taken into account, the temporal growth rate of the varicose mode can become greater than that of the sinuous mode, in contrast to the condition of an isothermal liquid sheet. When the Marangoni number is relatively small, the swirl decreases the maximum growth rate for the sinuous mode. In other conditions, the swirl has only minor effects on the stability of the liquid sheets. The increase of the density ratio and Weber number enhances the instability of the sheets, while the increased Prandtl number has the opposite effect. The effect of the Ohnesorge number is relatively complicated.

A new energy-based model to predict spray droplet diameter in comparison with momentum-based models

Purpose To estimate mean droplet diameter (MDD) of a spray, three different numerical models were used in this paper. One of them is investigation of the surface instability of the liquid sheet producing from an injector. Design/methodology/approach First, the linear instability (LI) analysis introduced by Ibrahim (2006) is implemented. Second, the improved (ILI) analysis already introduced by the present authors is used. ILI analysis is different from the prior analysis, so that the instability of hollow-cone liquid sheet with different cone angles is investigated rather than a cylindrical liquid sheet. It means that besides the tangential and axial movements, radial movements of the liquid sheet and gas streams have been considered in the governing equations. Beside LI theory as a momentum-based approach, a new model as a theoretical energy-based (TEB) model based on the energy conservation law is proposed in this paper. Findings Based on the energy-based approach, atomization occurs because of kinetic energy loss. The resulting formulation reveals that the MDD is inversely proportional to the atomization efficiency and liquid Weber number. Research limitations/implications The results of these three models are compared with the available experimental data. Prediction obtained by the proposed TEB model is in reasonable agreement with the result of experiment. Practical implications The results of these three models are compared with the available experimental data. Prediction of the proposed energy-based theoretical model is in very good agreement with experimental data. Originality/value Comparison between the results of new model, experimental data, other previous methods show that it can be used as a new simple and fast model to achieve good estimation of spray MDD.

Interfacial oscillation of liquid jets discharging from non-circular orifices

This work presents an experimental study on the oscillation behavior of liquid jets discharging from elliptical, triangular, and square shaped non-circular orifices. The measurements of wavelength and amplitude of jet oscillation are extracted from digital images of the liquid jets captured via still photography technique at different flow conditions using three different liquids (pure water, water-glycerol mixture, and Jet A-1 fuel). The measured wavelength of jet oscillation (λ), irrespective of the shape geometry of the tested non-circular orifices, increases linearly with increase in liquid jet velocity (Uo) and scales with the liquid jet Weber number (We) as λ/Deq ∝ We0.5. The experimental measurements of λ recorded at different flow conditions exhibit good agreement with the theoretical predictions obtained using the mathematical model proposed by Rayleigh (1879) for liquid jet undulating in its cross section. For a given Uo, the liquid jet of Jet A-1 displays higher value of λ and undergoes a larger increase in λ along the axis of the jet compared to the jets of other two liquids. Further the trends on the variation of maximum and minimum amplitudes of the first wave segment of liquid jets discharging from the elliptical and square orifices with Uo are discussed.

Penetration and breakup of liquid jet in transverse free air jet with application in suspension-solution thermal sprays

The penetration and breakup of water jets in transverse free air jets are experimentally studied at room conditions. After coming out of an orifice and forming a cylindrical jet, water interacts with a free air jet and disintegrates. In the current work, the effects of the instabilities of cylindrical liquid jets, the distance between the liquid orifice and gas nozzle, and the ratio of liquid orifice diameter to the gas nozzle diameter, on the breakup mechanisms and liquid structure are investigated. Moreover, general correlations for spray trajectory and location of the liquid column breakup point are developed. Experimental results indicate that the breakup mechanisms are mainly controlled by the gaseous and liquid Weber numbers. Like other studies, four breakup regimes, namely capillary, bag, multimode, and shear breakup are observed. It is found that, due to the presence of instabilities on the cylindrical liquid jet, large ligaments are formed close to the interaction point of liquid and gas flows. Furthermore, results indicate that the location of liquid column breakup point is mainly dependent on the momentum flux ratio, and perturbations on the liquid jet. This fundamental study is essential to investigate the spray structure of a suspension-solution jet in plasma spray.

Bubbling behaviors induced by gas-liquid mixture permeating through a porous medium

This paper investigates the bubbling behaviors induced by gas-liquid mixture permeating through porous medium (PM), which was observed in developing immersion lithography system and was found having great differences with traditional bubbling behaviors injected with only gas phase through the PM. An experimental setup was built up to investigate the bubbling characteristics affected by the mixed liquid phase. Both the flow regimes of gas-liquid mixture in micro-channel (upstream of the PM) and the bubbling flow regimes in water tank (downstream of the PM) were recorded synchronously by high-speed camera. The transitions between the flow regimes are governed by gas and liquid Weber numbers. Based on the image analysis, the characteristic parameters of bubbling region, including the diameter of bubbling area on PM surface, gas-phase volume flux, and dispersion angle of bubbles in suspending liquid, were studied under different proportions of gas and liquid flow rate. Corresponding empirical correlations were developed to describe and predict these parameters. Then, the pertinent bubble characteristics in different bubbling flow regimes were systematically investigated. Specifically, the bubble size distribution and the Sauter mean diameter affected by increasing liquid flow rate were studied, and the corresponding analysis was given based on the hydrodynamics of bubble-bubble and bubble-liquid interactions. According to dimensionless analysis, the general prediction equation of Sauter mean diameter under different operating conditions was proposed and confirmed by experimental data. The study of this paper is helpful to improve the collection performance of immersion lithography and aims to reveal the differences between the bubbling behaviors on PM caused by only gas flow and gas-liquid mixture flow, respectively, for the researches of fluid flow.

Empirical Correlation of the Primary Stability Variable of Liquid Jet and Liquid Sheet Under Acoustic Field

The investigation focuses on optimizing the length of wind-pipe that transmits acoustic energy from the compression driver to the cavity of twin-fluid atomizers. To accomplish this objective, the primary variable of stability, that is, the breakup length of liquid jet and sheet under acoustic perturbations has been experimentally characterized for a range of wind-pipe length and liquid velocity. The analysis considers liquid phase Weber number in the range of 0.7–8, and the results are compared with primary breakup data without acoustic perturbations. The range of Weber number tested belongs to Rayleigh breakup zone, so that inertia force is negligible compared to surface tension force. It shows the existence of unique stability functions based on dimensionless products up to an optimum wind-pipe length, which extends greater for liquid sheet configuration. The present results may find relevance in atomizer design that utilizes acoustic source to enhance liquid column breakup processes.

Early spray development at high gas density: hole, ligament and bridge formations

Three-dimensional temporal instabilities, leading to spray formation of a round liquid jet segment with an outer, coaxial high-density gas flow, are studied with Navier–Stokes and level-set computations. These computations predict the liquid surface shape showing the smaller structures on the conical wave crests, i.e. lobes, holes, bridges and ligaments, which are the precursors to droplet and spray formations. These structures and their time scales affect droplet size and velocity distributions as well as spray cone angles. The gas-to-liquid density ratio, liquid Reynolds number ($Re$) and liquid Weber number ($We$) range between 0.02–0.9, 320–16 000 and 2000–230 000, respectively, which cover three distinct physical domains. (1) At higher $Re$ and $We$, ligaments and then drops develop following hole and liquid bridge formations. (2) At higher gas densities throughout the $Re$ range, several holes merge forming two bridges per lobe before breaking to form ligaments; this hole merging is explained by slower development of hairpin vortices and lobe shape. (3) In cases where both gas density and $Re$ or $We$ are lower, the well-ordered lobes are replaced by more irregular, smaller-scale corrugations along the conical wave crest edge; ligaments form differently by stretching from the lobes before holes form. Thicker ligaments and larger droplets form in the low $Re$, low gas density range. The surface wave dynamics, vortex dynamics and their interactions are explained. Understandings of liquid stream break up and concurrent smaller structure formation are built upon an examination of both translation and rotation of the fluid. In all cases, hole formation is correlated with hairpin and helical vortices; fluid motion through a perforation in the thin sheet near the wave crest corresponds to these vortices. The hole formation process is dominated by inertial forces rather than capillary action, which differs from mechanisms suggested previously for other configurations. Circulation due to streamwise vorticity increases while the lobes thin and holes form. For larger surface tension, cavities in the jet core rather than perforations in a sheet occur. The more rapid radial extension of the two-phase mixture with increasing gas density is explained by greater circulation in the ring (i.e. wave crest) region. Experimental descriptions of the smaller structures are available only at lower $Re$ and lower density, agreeing with the computations. Computed scales of bridges, ligaments, early droplets and emerging spray radii agree qualitatively with experimental evidence through the high $Re$ and $We$ domains.

Breakup length and liquid splatter characteristics of air-assisted water jets

The breakup length and liquid splatter onset point of circular, air-assisted liquid water jets are experimentally and visually investigated over a range of parameters important to optimal impinging jet heat transfer. Liquid-only and air-assisted jets in the Rayleigh and first wind-induced breakup regimes are observed. The void fraction is used as a measure of bubble size and number density for air-assisted jets having a bubbly flow and it is found that increasing void fraction tends to decrease jet breakup length. It is hypothesized that bubbles may cause radial velocity components in the jet, leading to reduced breakup lengths. Linear jet stability analysis is used to show that dimensionless jet breakup length is related to the liquid Weber number, Ohnesorge number, and void fraction. The liquid splatter onset point is also measured experimentally. Liquid splatter is shown to occur in drop impingement and jet impingement splatter modes. The liquid splatter onset point and jet breakup length are shown to be related when splatter occurs in the drop impingement splatter mode.

Improved Linearized Breakup Model for the Liquid Sheets Produced by Swirl Atomizers

The performance of the swirl atomizers largely depends on the spray characteristics of the liquid sheets. In this context, a modified linear instability analysis accounting for the weak form of the centrifugal force along the flow direction is proposed and the breakup length of the conical liquid sheets is predicted. The investigation depends on the dispersion relation that covers both the viscous and the inviscid liquid sheets, with different wave modes (sinuous and varicose) and wave approximations (long and short). A newly identified transition zone across the long- and short-wave instability defines the liquid Weber number limit as . A breakup length relation accounting for the attenuating effect of the conical liquid sheets is formulated, and the results obtained from the theoretical breakup model were validated with the available experiment data in the literature. In brief, this paper elaborates the instability phenomenon in terms of relations and solutions. As found in the literature, this paper also notifies the destabilizing role of the density ratio and the stabilizing role of viscosity in the disturbance growth analysis.

Effect of liquid sheet and gas streams characteristics on the instability of a hollow cone spray using an improved linear instability analysis

AbstractThe breakup of a liquid sheet or jet is led to atomization phenomenon. The liquid sheet surface instability controls spray formation and determines the spray characteristics. Therefore, the instability study of the liquid jet has attracted a lot of attentions so that a lot of works have been carried out on this subject. The instability study of a swirling annular liquid sheet exposed to inner and outer gas streams is represented in the paper. A three‐dimensional flow for the liquid sheet and a two‐dimensional flow for inner and outer gas streams have been considered. In previous studies, a cylindrical liquid sheet has been considered, but in this study, the instability theory is implemented on a conical liquid sheet for different cone angles. The effects of swirl velocity of the liquid sheet and axial velocity of the gas streams on the sheet instability and breakup length have been investigated. Results show that liquid swirl Weber number has a destabilizing effect on a conical liquid jet. Study of the effect of ambient pressure shows that disturbance growth rate increases with increasing gas‐to‐liquid density ratio. The effect of spray angle on the instability of the liquid sheet is a very important issue in combustion chamber design especially when the available space and/or weight is limited. Higher spray angle enhances the instability of the liquid sheet, and it leads to a shorter breakup length and larger ligaments. Sheet thickness is another parameter that has been considered. Increasing sheet thickness enhances the sheet instability. These behaviors are consistent with the experimental observations. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.