Review of atomization mechanism and spray characteristics of a liquid jet in supersonic crossflow

Yozhi ZHOU, Zun CAI, Qinglin LI,*, Chenyng LI, Mingo SUN,Peio LI, Hongo WANG

a College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

b Beijing Institute of Tracking and Telecommunication Technology, Beijing 100094, China

KEYWORDS Atomization;Liquid fuels;Spray nozzles;Supersonic flow;Two phase flow

Abstract The injection and atomization process of a liquid fuel jet is critical for an ignition start of a scramjet engine.Airwall-mounted crossflow injection strategy is widely used in scramjet combustors,avoiding high total pressure loss and allowing the liquid fuel to rapidly undergo atomization,mixing,and evaporation.In this review,research progress on a liquid jet in supersonic crossflow was evaluated from aspects of atomization mechanism and spray characteristics.When a liquid jet is injected into a supersonic crossflow,primary and secondary breakups occur successively.The surface instability of liquid can significantly affect the breakup process.This review discusses the current understanding of the breakup process and spray characteristics of a liquid jet in supersonic crossflow including the mechanism of atomization and the characteristics of distribution and atomization.The development of windward Rayleigh-Taylor(R-T)unstable waves is the main factor in column breakup.The development of Kelvin-Helmholtz(K-H)unstable waves along the circumferential direction of the jet or droplets is the main factor of surface and droplet breakups.The liquid–gas momentum ratio is the most important factor affecting the penetration depth.The span width of the liquid jet is affected by the windward area.Breakup and coalescence lead to a transformation of the size distribution of droplets from S-or C-shaped to I-shaped,and the velocity distribution of the droplets on the central symmetry plane has a mirrored S-shape.The droplet distribution on the spanwise cross-section retains a structure similar to an‘‘Ω”shape.At last,some promising recommendations have been proposed,namely a theoretical predictive model which can describe the breakup mechanism of a liquid jet,the distribution characteristics and droplets size distribution of a liquid jet under a cavity combustion chamber,especially for enthalpy flows with complex wave structures.

1.Introduction

Scramjets are one of the most effective engines to achieve hypersonic flight1and simpler in structure than gas turbine aero-engines.2A scramjet does not need to carry a compressor and a turbine,but decelerates and pressurizes the incoming gas through a unique inlet.Unlike rocket engines,a scramjet does not need to carry additional oxidants.With higher specific impulses and lower launch costs,3,4there is significant research interest in the development and application of scramjets.5,6For next-generation atmospheric transportation applications,there is a significant need for increased focus on hypersonic vehicles.7The gas flow velocity in the combustion chamber is typically supersonic.8However, the limited length of the combustion chamber9and the short residence time of the fuel/air mixture10,11make it challenging to achieve ignition and flame stability.12,13Although hydrogen has good ignition characteristics and combustion performance,14use of this fuel requires a large space for low-temperature storage.Liquid hydrocarbon fuel(such as kerosene)is better for use in hypersonic vehicles with a relatively limited volume.Compared with hydrogen, kerosene has a higher volumetric energy density15and lower production cost,16with relatively easier and safer storage and transportation.17

Most practical applications use a scramjet in combination with other engines.For example, an aircraft equipped with a scramjet could use a rocket or ramjet engine for acceleration and to attain the relay Mach number.The temperature of the combustion chamber is low, and after passing through the regenerative cooling channel, fuel is injected into the combustion chamber in a liquid state.Complex physical and chemical processes occur in a scramjet, accompanied by complex flow, heat transfer, mass transfer, and chemical reaction.18Thus, it is very difficult to realize an ignition of liquid fuel in a scramjet engine.Due to the supersonic crossflow, there is a complex shock wave system structure in the combustion chamber.At the same time, there is strong coupling between the evaporation, mixing, and combustion of fuel droplets in high-speed and high-enthalpy gas flow.17For reliable ignition and flame stability of an engine, it is generally necessary to enhance the atomization effect of liquid fuel by reducing the average diameter of fuel droplets, increasing the surface area of fuel droplets, and shortening the evaporation distance of droplets.Generation of an initial core and flame propagation during ignition require good distribution and atomization characteristics of liquid fuel.

In recent years,nano-particle and gelled fuel has been used widely in scramjet and rocket engines.19–25Gelled fuel is a typical non-Newtonian fluid.From the physical properties of fluid, gelled fuel has the advantages of long storage time like solid propellant and easy adjustment of thrust like liquid propellant.For a Newtonian fluid, a large number of liquid fragments and droplets will be produced at the end of the primary breakup process.With an increasing viscosity of the liquid,the specific gravity of the produced liquid fragments will increase continuously.For a non-Newtonian fluid, it usually experiences tensile flow with large deformation in the process of primary breakup due to its elastic effect, and then produces physical phenomena such as wire drawing.Compared with Newtonian fluids, non-Newtonian fluids will also exhibit different droplet average sizes and size distributions with the same shear viscosity due to their different rheological properties.The breakup time of a non-Newtonian fluid jet also increases significantly at the same time.26Yang et al.27–29studied the instability process of a power-law cylindrical jet in sinusoidal and meander modes.They found that increasing the relative velocity and gas dynamic viscosity, or decreasing the liquid surface tension, liquid jet radius, air boundary layer,liquid consistency coefficient, or power-law index would improve the instability of the liquid jet and be advantageous for the breakup of the liquid jet.A large number of studies about the linear stability of viscoelastic liquids have been conducted by Yang et al.30–38A viscoelastic liquid film is more unstable than a Newtonian liquid film of a transverse electric field.

Compared with supersonic crossflow conditions, subsonic crossflow conditions are easier to create.Many researchers have examined the breakup mechanism, distribution characteristics, and atomization characteristics of a liquid jet in subsonic crossflow.39–46There are some similarities between a liquid jet in subsonic crossflow and one in supersonic crossflow.A detached bow shock wave appears before injection,which transforms supersonic crossflow into subsonic crossflow.Therefore,a liquid jet in supersonic crossflow only means that the velocity of the gas flow at the outlet of the supersonic nozzle is supersonic, and actual atomization still occurs in a subsonic environment.From the perspective of breakup mode,the breakup of a liquid jet in supersonic crossflow still includes column breakup47and surface breakup48as well as the breakup mode of the liquid jet in subsonic crossflow.The surface of the liquid jet column in subsonic crossflow is smoother due to a weaker aerodynamic force.The liquid jet leaves the nozzle as an unbroken column in subsonic crossflow.Even with the wall boundary layer and a detached bow shock, the air velocity before the jet column is still high.A large number of experiments49–51and simulation52,53results have shown that a liquid jet in supersonic crossflow has a stronger oscillation than that of a liquid jet in subsonic crossflow.Column Breakup Location (CBL)42is often mentioned in subsonic crossflow to judge whether the liquid column is broken.A liquid jet in supersonic flow is often more difficult to observe a clear CBL.The oscillation interval of the CBL in supersonic crossflow is significantly greater than that in subsonic crossflow.From the perspective of distribution characteristics, the penetration of a liquid jet in subsonic crossflow increases under the same liquid momentum.In fact, reducing the gas velocity increases the liquid–gas momentum ratio q.Due to a weaker surface breakup and a higher CBL,the dense atomization zone tends to be far away from the injection wall in subsonic crossflow.There are often no liquid droplets near the injection wall at a higher liquid–gas momentum ratio.On the contrary,there are a large number of liquid droplets near the injection wall even at a higher liquid-to-gas momentum ratio as a result of a stronger surface breakup and a lower CBL.From the perspective of atomization characteristics, the distribution trends of the droplet diameter and velocity in supersonic crossflow are similar to those in subsonic crossflow.However, the atomization effect of a liquid jet in subsonic crossflow is worse.The diameter of the droplets in subsonic crossflow is significantly larger than that in supersonic crossflow at the same position downstream.The droplets in supersonic crossflow will break up into relatively uniform small droplets more quickly.The droplets velocity decays faster along the normal direction,and the ability to follow the crossflow is stronger.

Fig.154represents the topological structure of a liquid jet flow field in supersonic crossflow.Based on the composition of a gas phase flow field, the separated shock, bow shock,and small shocks are successively located in front of the jet.The wall boundary layer separates under the action of an inverse pressure gradient, resulting in a separation zone.54From the perspective of liquid phase breakup mode and moving downstream from the nozzle outlet, the spray field can be summarized systematically from three aspects, i.e., the nearfield area (or the surface wave-dominated crushing area), the rapid atomization area,and the uniform mixing area.The liquid fuel jet is injected into the crossflow along the direction perpendicular to the incoming flow.The liquid jet column gradually bends downstream under the incoming flow pressure and then breaks rapidly to form a large number of irregular and discrete liquid blocks.The gas–liquid interface is unstable under the joint action of Kelvin-Helmholtz (K-H) and Rayleigh-Taylor (R-T) instability,55,56resulting in droplet formation.K-H instability is the instability of a material interface with different densities under a tangential velocity gradient.RT instability is the instability of this density interface under a normal acceleration.At the same time, strong shear causes a large number of small droplets to peel off from the jet column in a process called primary breakup.49The primary breakup process is closely related to the flow field structure(bow shock and separation zone).16The velocity of large droplets stripped from the jet column is significantly different from that of the mainstream gas, and this difference in velocity leads to a further breakup of large droplets into smaller droplets in a process called secondary breakup.57The secondary breakup process is closely related to the Weber number(We = ρu2d/σ) and the Ohnesorge numberThe Weber number can generally be the gas Weber number (Weg= ρgu2gdj/σ), liquid Weber number(Wej= ρju2j dj/σ), and gas–liquid relative Weber number(Weg-j= ρgu2g-jdj/σ).For certain types of liquid fuel, the relative flow velocity of gas–liquid two phases directly determines the gas–liquid relative Weber number.Compared with a liquid jet in subsonic crossflow, a liquid jet in supersonic crossflow has a higher gas–liquid relative Weber number, resulting in a more extensive secondary breakup process of droplets.Crossflow with a high total temperature can also strengthen the secondary breakup process of droplets, as seen in Fig.2.59

In an actual scramjet, when the airflow velocity is much greater than the flame propagation velocity,a cavity is usually introduced as a flame stabilization device.60,61The low-speed recirculation zone in the cavity will promote the mixing of fuel and air,increase the residence time of the mixture,avoid excessive total pressure loss,and effectively stabilize the flame.After the airflow passes through the front edge of the cavity, an expansion wave forms outside the cavity and a shear layer62,63is formed between the airflow inside and outside the cavity.Fuel droplets enter the cavity under the action of the shear layer and form a certain fuel distribution.Fuel can be injected from multiple positions such as upstream from the cavity, the bottom wall of the cavity,or the rear wall of the cavity.A mass exchange between the interior of the cavity and the main flow occurs through the cavity shear layer.The fuel distribution and the interaction between the liquid jet and the cavity are critical for ignition and flame stability.

Fig.1 Topological structure of a liquid jet flow field in supersonic crossflow.54

Fig.2 Atomization and mixing process of a liquid jet in supersonic crossflow with a high total temperature (Ma = 2.0).59

In this review, the study of a liquid jet in supersonic crossflow summarized systematically from three aspects, i.e., the breakup mechanism of the liquid jet, the distribution characteristics of the liquid jet, and the atomization characteristics of the liquid jet.Experimental conditions, gas parameters, liquid parameters, and nozzle internal geometric parameters can all determine the atomization characteristics of a liquid jet in supersonic crossflow,including droplet velocity and size distribution,droplet collision and evaporation,mixing rate,and fuel combustion efficiency.Based on the dimensionless number, it is reasonable to divide the breakup process of the liquid jet and identify the breakup state of the liquid jet to better understand the breakup mechanism of the liquid jet.An important concern is the spray characteristics of a liquid jet in an engine combustor,as these characteristics are subject to the size of the combustion chamber and the nozzle diameter.Liquid fuel can be atomized and evaporated more quickly in a finite-volume combustor and mixed with more gas due to higher lateral penetration and larger expansion.64The diameter and velocity distributions of fuel droplets are important determinants of the atomization characteristics of the liquid jet,and understanding these characteristics is necessary to optimally select a reliable ignition position in the engine.

2.Breakup mechanism of a liquid jet in supersonic crossflow

After a liquid jet is injected into supersonic crossflow,primary and secondary breakups will occur sequentially.The primary breakup includes liquid column breakup and surface breakup.The secondary breakup is also referred to as droplet breakup.The breakup modes of a liquid jet in crossflow differ in the Weber number of crossflow.40–42,65

2.1.Column breakup mechanism of a liquid jet in supersonic crossflow

Early studies39,66–68mainly focused on the deformation of the continuous liquid column in supersonic crossflow.In subsonic crossflow, the aerodynamic effect for a liquid jet is generally small, so the velocity of liquid droplets is low.The smallscale structure69and motion information66of the jet column can be obtained by high-speed photography or schlieren visualization.The gas–liquid interface is generally clear, and the liquid column can be considered as a continuous medium before breakup.70However, the liquid jet is often subjected to an extremely strong aerodynamic force in the supersonic crossflow, causing the gas–liquid interface to be fuzzy as visualized by pulsed laser background light imaging technology, a method with high temporal and spatial resolutions.After the liquid jet leaves the nozzle for a very short distance,the liquid column breaks rapidly and forms a thick liquid mist composed of a large number of small droplets.With the generation of a shock wave and a separation zone, the flow field structure becomes more complex,71,72and it is difficult to clearly capture the process of liquid column breakup, as seen in Fig.3.73Lin et al.73–77effectively overcame the influence of dense liquid mist and obtained the structure of the liquid column in the near-field using high-speed X-ray imaging technology, allowing a qualitative description of the formation, movement,and evolution process of the surface wave on the windward surface of the jet column, as seen in Fig.4.74According to the observed distribution of the liquid mass, the crosssectional profiles of the jet column can be reconstructed at different deformation stages.

Fig.3 Temporal evolution of liquid column breakup processes(Ma = 1.94, GLR = 4%).73

Fig.4 High-speed X-ray imaging results (Ma = 2.0).74

Fig.5 Pressure contours of central symmetry plane(Ma = 2.1).85

The surface wave is the main characteristic of jet breakup,dominating the liquid column breaking process.Schetz et al.68carried out more than 1000 experiments on the primary breakup process of a liquid jet in supersonic crossflow and found that the axial surface wave with a high frequency and a large amplitude was the dominant factor for liquid column breakup.Column breakup often occurs at the trough of two adjacent surface waves.This breaking mode is very similar to the classical breaking mode of a Rayleigh jet in still air,but with significantly different properties of surface waves and causes of fracture.The size of the large liquid block that breaks off from the liquid column is often the length of several surface waves.Under the combined action of aerodynamic force and surface tension, large liquid blocks are accelerated and decomposed into smaller liquid blocks downstream.Liquid physical parameters have little influences on the liquid column breakup process.At a low momentum ratio,the initial jet trajectory of the liquid jet will oscillate violently,but the initial jet trajectory is more stable at a high momentum ratio.Gravity, K-H instability, and vortices caused by turbulence may cause surface waves.Nejad and Schetz78studied the effects of liquid viscosity and surface tension on the breakup of the liquid column and found two main types of fluctuations on the jet surface: surface fluctuation caused by aerodynamics on the windward surface of the jet and capillary disturbance caused by turbulence.For these fluctuations, the wavelength of the viscous surface of the increased liquid decreases while the amplitude increases, and the surface wavelength of the reduced surface tension jet of the liquid increases concurrently with the amplitude.The flow field parameters at the gas–liquid interface (including pressure, density, and velocity) cannot be determined using existing experimental observation methods,and there has been little research on the interaction between the evolution of the gas–liquid interface and the flow field.Recently, researchers developed high-precision numerical methods based on interface tracking and conducted numerical simulations of jet breakup.79–83Xiao et al.84,85used the CLSVOF method to simulate the jet primary breakup process in supersonic crossflow, finding that the development of surface waves on the windward side of the liquid column is directly affected by flow after the shock wave.R-T instability likely dominates the development of surface waves and eventually leads to the breakup of continuous jets,as seen in Fig.5.85The interface tracking method can simulate the primary breakup of the jet in supersonic crossflow, but without ways to directly monitor this process,quantitative verification methods are lacking.Excessive calculation is also a problem, especially for capturing broken droplets.Current research efforts are focused on the development of a hybrid method that combines interface tracking and Lagrange drop tracing methods to simulate the complete spray.Using adaptive grid technology,Zhao et al.86carried out numerical simulation on the breaking process of a liquid jet in supersonic crossflow using CLSVOF and CLSVOF-LPT methods, as seen in Fig.6.86Compared with the CLSVOF method, the CLSVOF-LPT method transforms a liquid block into Lagrangian particles and coarsens the mesh at the transformation position for greatly improved calculation efficiency.

2.2.Surface breakup mechanism of a liquid jet in supersonic crossflow

Surface breakup is another primary breakup process of a liquid jet.87Nicholls and Ranger88identified that viscous shear action of high-speed air flow on droplets was the main breakup mechanism, and Theofanous89found that K-H unstable wave was the main mechanism of shear crushing.Hwang et al.90found that R-T unstable wave firstly caused droplets to break and form liquid blocks and then further breakdown of the liquid blocks occurred under the action of K-H unstable wave.

When a liquid jet enters supersonic crossflow, obstruction by the liquid jet causes the flow to turn around the jet column.Part of the flow moves upward along the upwind direction of the jet stream,and part continues to move downstream around the jet column.With the wall boundary layer and pre-jet separation zone,the liquid jet in the root region of the jet column is in a subsonic environment.There is only a small gas–liquid interaction force, so the jet surface remains smooth.With increase of the longitudinal height, the surface of the jet column becomes unstable and forms surface waves along the flow direction of the jet.This causes the jet column to deform,stretching upward and thinning at the edge as the liquid is stripped off under the action of circumferential flow gas.These small droplets with a longitudinal momentum are easy to dissipate and can accelerate quickly.Under the drive of supersonic airflow from the jet column body movement, the downstream process starts close to the wall.The position of the surface wave trough is subjected to the greatest impact of the supersonic crossflow and may produce a stagnation point in the flow.Continuous jet deformation at the position of the wave trough is the fastest, with a relatively large deformation degree.Circumferential flow will cause some large liquid blocks to fall from the position of the wave trough, as seen in Fig.7.53The first liquid filaments(or liquid blocks)that fall off are relatively few in number and small in volume.At this time, the trough position moves upward with the liquid jet,and new liquid filaments and liquid blocks fall off.These filaments are accelerated by the air flow to move downstream until the jet column breaks at the trough position.The later the fall of the liquid wire and liquid block is, the slower the speed is,allowing wire drawing to occur.Li et al.53numerically analyzed the mechanism of the wire drawing process and found downward sloping flow of gas and liquid when meeting liquid mist,resulting in downward sloping acceleration of droplets.The accelerations of broken droplets of different sizes differ,and droplet clusters form a series of liquid wire drawing structures along the local airflow direction, as shown in Fig.8.53Liu et al.91simulated the primary breakup process of a liquid jet in supersonic crossflow using adaptive grid technology, showing that small-scale instability along the transverse direction of the jet is an important contributor to the surface breakup of the liquid jet.The source of this smallscale instability is located in the transonic region of the gas flow field, as liquid is directly stripped off from the side of the liquid column.Due to the wall boundary layer and the separation zone before the jet flow, the liquid jet flow in the root region of the jet flow is in a subsonic environment,with a small gas–liquid interaction force and smooth jet surface.With an increase of the longitudinal height, the jet column is strengthened by the aerodynamic effect of supersonic flow, so the surface of the jet column is unstable and can form a surface wave along the jet flow direction.The jet column stretches in the spanwise direction, and droplets of different sizes are stripped from the circumferential direction under the action of the surrounding gas.Both the Reynolds and Weber numbers of the surrounding gas are large,so the diameter of the stripped droplets is generally small.After leaving the jet column, the droplets move rapidly downstream.The stripping process starts very close to the wall, with a large number of small droplets near the wall in the leeward area of the jet, as seen in Fig.9.91These stripped liquids are carried downstream by vortices that are generated around the liquid column in the form of rotation.The scale of surface breakup is much smaller than the spatial resolution of 3D simulation,so this method cannot fully capture the details of surface breakup.92Zhou et al.93numerically studied the primary breakup process of an elliptical liquid jet in supersonic crossflow using the CLSVOF method,and reported the change of the jet cross-section at different longitudinal heights of the liquid jet.Liquid on the upwind side of the liquid column was pushed by crossflow,moved to the sides of the liquid column,and was subsequently stripped.Surface breakup is affected by both gas flow and longitudinal liquid flow, with gas flow being the main factor affecting surface breakup.

Fig.6 Comparison between numerical results for LJISC by using CLSVOF and CLSVOF-LPT algorithms (Ma = 2.1).86

Fig.7 Wire drawing caused by surface breakup.53

Fig.8 Mechanism of liquid trailing phenomenon.53

2.3.Droplet breakup mechanism of a liquid jet in supersonic crossflow

Fig.9 Surface breakup due to transverse waves (Ma = 1.5).91

The secondary breakup process of a liquid jet in supersonic flow is the process of droplet breakup.In early studies,droplet breakup forms in airflow were mainly classified by We numbers, in an order from high to low, into five types,65,94,95i.e.,vibrational, bag, multimode, stripping, and catastrophic.Under different experimental conditions, the critical We numbers of these fracture forms can vary slightly, with different underlying physical mechanisms.These mechanisms can be contradictory, mostly due to differences in droplet breakup at high speed.In droplet breakup under a high-speed condition, a large number of small droplets are stripped from the droplet surface.This is different from what happens during droplet break under a low-speed condition, where small droplets are stripped and form liquid mist around the main droplets, seriously limiting observation of the droplet breakage process at high speed.The fuzzy images obtained from observation under these conditions are deceptive,suggesting inaccuracies about the droplet breakup mechanism in high-speed crossflow.Wilcox et al.96investigated the secondary atomization characteristics of Boger fluid droplets.The secondary atomization process of droplets produced by polymer solutions with different concentrations under supersonic crossflow was measured.Newtonian liquid drops are broken into very fine particles by a breakup mechanism which begins with stripping of the liquid from the surface of a drop.Drops of non-Newtonian liquids break up by formation of ligaments rather than by surface stripping and are broken into much larger particles.Even if the content of the polymer added is very low,the secondary atomization process of droplets will be delayed.Matta and Tytus97studied the size of the mass average diameter of Boger fluid droplets after secondary atomization in a high-speed wind tunnel.Boger fluid droplets are more difficult to break than Newtonian fluid droplets under the same flow conditions.The secondary atomization process of droplets with different diameters in a high-speed gas flow field was studied by Arcoumanis et al.98Dinh et al.99studied the secondary atomization process of hydrocarbon fuel droplets at a high Mach number and a low Weber number experimentally.They found that droplets formed a series of liquid filament structures with different sizes when the concentration of polymer in the droplet was high rather than breaking into small droplets.Snyder et al.100–102investigated the secondary breakup of elastic non-Newtonian liquid drops, and found that the dimensionless parameters (such as the Weber number, Ohnesorge number, etc.) used to characterize the deformation and breaking characteristics of droplets in traditional Newtonian fluids could not affect the deformation and breaking characteristics parameters of non-Newtonian fluids.Nicholls and Ranger88proposed that shear stripping could be caused by the unstable boundary layer at the droplet edge.This theory was supported by Chou et al.103and Igra et al.104However,Liu and Reitz105proposed an alternative framework, called sheet-stochastic, in which the inertial trailing of gas around a droplet created a very thin liquid envelope at the edge of the droplet, resulting in stripping of the liquid.Fishburn106and Joseph et al.107introduced the R-T instability mechanism to explain the process of early droplet breakup in a high-speed flow since the windward side of a droplet was subjected to a large acceleration.In recent years,experimental results of Theofanous et al.89,108,109provided significant insights into droplet breakup in supersonic crossflow, as seen in Fig.10.108Their results suggest that there are three modes of droplet breakage:Rayleigh-Taylor Piercing (RTP), Shear-Induced Entrainment(SIE), and RTP-SIE transition mode.The RTP mechanism includes characteristics of bag breakup and multi-mode breakup mechanisms,and is the breaking mechanism of liquid in low-Weber number flow.The SIE mechanism mainly includes the characteristics of the shear stripping mechanism,and is the breaking mechanism in high-Weber number flow.Laser Induced Fluorescence (LIF) images showed that droplets basically remained spherical under the action of highspeed crossflow, with many small-scale fluctuations being formed on the windward surface.These small-scale fluctuations may be caused by K-H instability rather than R-T instability.SIE is considered to be the ultimate mode of droplet breakage.At a larger We number, the SIE mechanism applies to both highly viscous and viscoelastic liquids.89After the initial disruption of a liquid jet, a large number of liquid blocks with different sizes are generated.For low-viscosity liquids with Oh < 0.1, the critical Weber number between RTP and SIE modes is about 100.Liu110roughly divided the process of droplet breaking in supersonic crossflow into three stages of surface instability, shear stripping, and breakup based on different morphological characteristics.In the stage of surface instability, the strong shear action of gas causes the start of small-scale instability on the droplet surface.This instability is due to liquid surface instability under the action of highspeed airflow, and the dominant mechanism is K-H instability.109,111Unstable fluctuation on the liquid surface causes an unstable structure in the circumferential direction, which is explained by R-T instability,as seen in Fig.11.110In the shear stripping stage, the airflow will form a high-pressure zone at the stagnation point on the windward side of the droplet and a low-pressure zone on the leeward side of the droplet.This pressure difference causes the droplet to continuously flatten and move downstream.Droplet surface instability occurs earlier than droplet flattening.In the breakup stage, after the droplet is flattened into a bowl-shaped liquid film, stripping break will begin to occur at the liquid edge.Once the droplet has been deformed into a liquid film,the thickness of the liquid is greatly reduced,and the central position of the liquid begins to undergo deformation that is different from those in the first two stages.Additionally, the liquid at the edge of the droplet continues to be stretched.The liquid film breaks into liquid filaments, and these filaments break into smaller liquid blocks or droplets,as seen in Fig.12.110With the continuous stripping of the liquid at the edge of the droplet,the liquid movement in the center of the liquid begins to lag behind the movement of the liquid at the edge,the central liquid forms a forward puncture structure, and then the liquid at the edge begins to gradually separate from this forward puncture structure.The liquid breaks into two parts, the central part of the liquid punctured forward and the liquid film formed by the liquid at the edge of the original droplet around the central liquid block.The edge of the independent puncture part then starts the process of liquid stripping, and the punctured structure shows characteristics of R-T instability.110

Fig.10 Droplet breakup modes.108

Fig.11 Q criterion contours of liquid droplet breakup in supersonic crossflow.110

Once the liquid jet injection enters the supersonic crossflow,primary and secondary breakups will occur successively.The primary breakup includes liquid column and surface breakups.During liquid column breakup, the jet column fractures, largely due to the development of R-T unstable wave on the windward side of the jet column.A typical feature of surface breakup is droplet stripping along the circumferential direction of the jet column due to the development of K-H unstable wave on both sides of the jet column.The secondary breakup of the liquid jet is droplet breakup, and this stage is mainly characterized by the continuous breakup of large droplets in the crossflow due to the development of K-H unstable wave on the windward side of the droplets.There are no optical experimental methods that can directly observe a liquid jet in supersonic crossflow with a high accuracy and a high resolution to investigate the surface breakup characteristics of the jet, surface wave length, wave velocity, and continuous liquid column shape, so the details of the liquid jet breaking mechanism remain unclear.Another limitation is that there are few theoretical models that can fully and reasonably describe the mechanism of liquid jet breakup and spray motion.Most existing theoretical models are based on breaking of a low-speed liquid jet in subsonic flow.Although the stress and breaking mechanism of a liquid jet are similar to breaking of a liquid jet in supersonic crossflow, the shock waves, wall boundary layer, and instability of the liquid jet all greatly increase the difficulty of theoretical modeling.In particular, additional work is required for in-depth analysis on the breakup position and breakup time of a liquid jet.

Fig.12 Three-dimensional simulation results of droplet breakup stage.110

3.Distribution characteristics of a liquid jet in supersonic crossflow

With strong turbulence, the breakup of a liquid jet in supersonic crossflow is a micro and dynamic process.Under specific airflow conditions, the spray will have a unique macroscopic distribution in three dimensions,and droplets of different sizes and velocities occupy different spatial locations.These macroscopic and static laws form the spray characteristics of the liquid jet.Given the practical application of scramjets,significant research efforts have been devoted to the spray characteristics of liquid jets, including spatial distribution and atomization characteristics.The spatial distribution of spray describes the spatial position occupied by the liquid fuel in the combustion chamber after entering the crossflow.This spatial dispersion of droplets after atomization affects the subsequent evaporation, mixing, and ignition processes.The spatial distribution of a liquid jet in supersonic crossflow includes the penetration depth and spanwise cross-sectional distribution in the spatial direction, and these parameters are typically calculated through an empirical relation.

3.1.Penetration depth of a liquid jet in supersonic crossflow

Penetration depth is a significant index that characterizes the longitudinal distribution of a liquid jet in supersonic crossflow.To investigate the penetration depth, researchers take photos of a liquid jet in supersonic crossflow for optical observation,and then obtain a large number of empirical formulas through image processing and jet boundary fitting.These empirical formulas are power, exponential, and logarithmic functions.Experimental results have shown that the liquid–gas momentum ratio q, the nozzle diameter d, and the injection angle θ are the main factors affecting the penetration depth of a liquid jet.Based on different experimental observation and image processing methods,different prediction effect and application conditions of penetration depth empirical formula have been reported by different researchers.Table 1.112–124lists experimental conditions, experimental methods, and empirical formulas used by previous researchers to study the penetration depth.

Yates112studied the penetration depth of water and alcohol in supersonic crossflow by using direct photography and analyzed the effects of the Mach number,viscosity of the jet medium,and surface tension on the penetration depth.They found that the penetration depth and spanwise width were only related to the liquid gas momentum flux ratio q, and fitted the dimensionless penetration depth and spanwise width by empirical formulas based on the effective diameter of the orifice.Less and Schetz125studied the breakup process and penetration depth of a liquid jet by adding solid particles into water, and found that solid particles of less than 40 μm in diameter had little effect on the breakup process of the liquid jet.Kush and Schetz113used high-speed photography to study the effects of the Mach number and physical properties of the injection medium on the breakup process and penetration depth, and found that the breakup process had strong unsteady characteristics, the breakup mode was mainly affected by q, and the liquid viscosity and surface tension almost had no effect on both the breakup process and penetration depth.Baranovsky and Schetz115studied the influence of the injection angle on the penetration depth and breakup process, integrated the injection angle information into Yates112empirical formula on penetration depth, and evaluated the injection effect of strut by comparison with flat plate injection.Lin et al.126studied the atomization structure and penetration depth of a bubble atomizer in supersonic crossflow(Ma = 1.85) using laser sheet illumination and shadow photography methods, and determined that the use of a bubble atomizer could increase the penetration depth.Lin and Kennedy127further studied the penetration depth of a bubble atomizer under different injection angles in supersonic crossflow (Ma = 1.94), and incorporated injection angle information into the empirical formula of penetration depth.Ghenai et al.121,128studied the penetration depth and atomization characteristics of a bubble atomizer in supersonic crossflow(Ma=1.5).Comparison of injection atomization under different void fraction conditions revealed that q and void fraction were the main factors affecting the penetration depth of the liquid jet in crossflow.For the same test conditions, the penetration depth of the liquid jet obtained by Phase Doppler Anemometry(PDA)was the largest,and the penetration depth of the liquid jet obtained by high-speed photography was the smallest,as seen in Fig.13.62Li et al.62introduced the concept of droplet volume fraction, which greatly reduced the uncertainty caused by insufficient statistical data and gave calculation results that were comparable to the experimental results of Lin,118Ghenai121and Wu123et al.

Zhu et al.92studied the effect of the pulse injection mode on the penetration depth of a liquid jet in supersonic crossflow(Ma=2.0)using experiments and numerical simulation.They found that the pulse injection mode had little effect on the penetration depth of the liquid jet.However, when the frequency of velocity pulsation reached the R-T instability frequency of the liquid jet itself, the velocity pulsation would replace the R-T instability and dominate the primary breakup of the liquid jet.At the same time, the velocity pulsation increased the vortex scale and spanwise width in the wake area to improve the penetration depth of the jet.Hu et al.50proposed a lateral liquid jet scheme with accompanying gas and studied the effect of an accompanying gas jet on the penetration depth of the liquid jet in supersonic crossflow (Ma = 2.85) by experimental and numerical simulation.They found that although the penetration of the liquid jet could be significantly improved with the addition of the gas jet,this addition could cause additional total pressure loss.Zhou et al.93studied the penetration depth of an elliptical liquid jet in supersonic crossflow (Ma = 2.0).They concluded that the windward area was an important factor affecting the penetration depth of the liquid jet.With an increased ratio of the long axis to the short axis of the elliptical orifice, the wavelength of the surface wave on the windward surface of the continuous liquid column gradually increased,the windward area of the jet gradually decreased,and the penetration depth gradually decreased.Sathiyamoorthy et al.124studied the effect of series combined injection on the penetration depth of a liquid jet in supersonic crossflow(Ma=1.9).A reasonable arrangement of hole spacing between series holes effectively improved the penetration depth of the liquid jet.Wu et al.123studied the gas turbulent boundary layer and defined the dimensionless parameter spray fraction as the ratio of the time that a certain point of the space is surrounded or occupied by liquid spray to the total test time, according to the following expression:

Fig.13 Comparison of simulated spray penetration with experiments.62

where tsprayis the time when the space points are surrounded or occupied by liquid spray, and t is the total test measurement time.The spray fraction that is always surrounded or occupied by spray is 1, and the spray fraction in the mainstream gas region is always 0.Based on spray fraction calculations, Wu et al.123established a boundary prediction model for liquid jet spray in supersonic crossflow.This describes the threedimensional boundary of spray, and the spray fraction and its gradient in space reflect the intensity of the nonoscillatory distribution of spray and the distribution of spray concentration in the boundary zone, as seen in Fig.14.123

Fig.14 Evaluation of spray boundary prediction model.123

There exist several studies specifically focused on liquid jet trajectory and penetration at High-Temperature and Standard-Pressure (HTSP) test conditions.HTSP studies129–131examined the impact of increasing the crossflow temperature on the liquid jet trajectory and its penetration.Stenzler et al.132reported that, at constant q and ug, increasing the temperature led to an increase in jet penetration.In fact,increasing the temperature reduced the gas density and thereby decreased Weg.Amighi and Ashgriz133related the jet trajectory to flow parameters, including jet and air velocities, pressure and temperature,as well as a set of non-dimensional variables in the experimental result.They added that the gas viscosity was added to the correlations to better predict the jet trajectory.

3.2.Span width of a liquid jet in supersonic crossflow

Span width is an important index to describe a liquid jet in supersonic crossflow, and is used as a significant reference parameter for determining the arrangement of engine nozzle holes.Lin et al.77,118studied the effect of the liquid void fraction on the spanwise expansion of a liquid jet through PDA.The spray presents a semicircular shape at the spanwise cross-section, and the outer edge of the cross-section begins to shrink to the center near the wall.With an increased downstream distance,the spray-spanning cross-section expands with an increased penetration depth, and the larger the liquid gas content is, the larger the spray cross-section area is.Limited by the intersection of two laser beams and the width of the test section, PDA generally cannot be used to obtain the droplet information near the wall.Thomas and Schetz87obtained the distributions of the spray-field cross-sectional pressure,gas mass flow rate, liquid mass flow rate, and liquid gas ratio using an intrusive measurement method.They found that onethird of the core area was subsonic and the remaining twothirds of this area was a supersonic zone.With an increase of the downstream distance, the cross-sectional area of spray increased.118Perurena et al.120obtained the spanwise distribution image of a jet by high-speed photography and detected the spanwise boundary.With an increase of the nozzle aspect ratio, the spanwise expansion of the jet increased.Lin et al.134obtained the distribution of a liquid jet in the downstream spanwise cross-section using laser wafer light technology,and found that the instantaneous distribution of the liquid jet in the spanwise cross-section was not uniform but presented an obvious fold structure, as seen in Fig.15.134Wu et al.123observed the distribution of the cross-section of a liquid jet in supersonic crossflow (Ma = 2.1) by three-dimensional PIV.The shape of the cross-sectional droplet distribution significantly varied at different times, with dramatic changes in the longitudinal height, the width of the spanning area, and the area occupied by the liquid change.The cross-sectional spray is a structure similar to the shape of ‘‘Ω”, with strong unsteady characteristics, as seen in Fig.16.123Wu54reconstructed by spray fraction on the cross-sectional spray distribution based on the oval curve equation and five coefficient models.Li et al.62obtained the liquid spray distribution by numerical calculation, and these simulation results were in good agreement with the experimental results of Wu.54As the jet develops downstream, the liquid spray expands, and the boundary area of the liquid spray becomes wider, as seen in Fig.17.62Zhou et al.93studied the effect of an elliptical orifice on the spanwise expansion angle of a liquid jet in supersonic crossflow (Ma = 2.0).Results showed that the upwind area of the nozzle affected the spanwise expansion angle of the liquid jet.Compared to the elliptical orifice with different upwind directions, the circular orifice has a larger spanwise expansion angle.Lin118and Dixon119et al.obtained the cross-sectional area of the spray using Phase Doppler Particle Analysis (PDPA) and analyzed the effects of the injection angle, the aerating Gas-to-Liquid mass Ratio (GLR), and the liquid gas momentum ratio q on the cross-sectional distribution of the jet.Table 2112,118–120shows the experimental conditions,experimental methods,and empirical formulas used by previous researchers to determine the span width.

The distribution characteristics of a liquid jet in supersonic crossflow are generally analyzed using empirical formulas that describe the penetration depth h and span width w.Liquid-air momentum ratio, nozzle diameter, and injection angle are the main factors affecting the penetration depth and spanwise width of a liquid jet.The overall spray spanwise crosssection is a structure similar in shape to ‘‘Ω”, with some variance in shape under different experimental conditions.With different experimental observation and image processing methods, the prediction effect and application conditions of the empirical formula of penetration depth differ for different researchers, suggesting that this approach cannot characterize the unsteady oscillation characteristics of spray in space.Thus,the prediction of a liquid jet’s penetration depth and jet trajectory remains imperfect.Empirical relationships are often derived from large-scale experimental results, which have a limited application scope or lack empirical or theoretical models to quickly predict jet trajectory and jet penetration depth.Overall, our understanding of the mechanisms of liquid jet spreading, mixing, gas–liquid motion, and droplet spreading remains limited.

4.Atomization characteristics of a liquid jet in supersonic crossflow

The atomization characteristics of a liquid jet in supersonic crossflow mainly include droplet size distribution and velocity distribution.After primary breakup, the liquid jet will form large irregular liquid blocks and large spherical droplets.With the movement of air flow, the large liquid blocks and droplets continue to break into smaller droplets,67forming a group of small droplets with a certain spatial distribution law.135The particle size distribution and velocity distribution of droplets after atomization affect the efficiency and stability of subsequent combustion, so it is important to study the atomization characteristics of the liquid jet in supersonic crossflow.

The general finding is that the global Sauter Mean Diameter(SMD)of the spray reduces with increasing the momentum flux ratio and increases with increasing the orifice diameter.136,137Based on experimental observations of surface wave growth and shear layer development between supersonic and subsonic crossflows, Reitz138proposed a droplet stripping model to predict droplet size variation by the theory of the K-H instability, taking into account the effects of liquid inertia,surface tension,and aerodynamic forces on the jet,as well as drop collision and coalescence and the effect of drops on turbulence in the gas.O’Rourke and Amsden139proposed a TAB model to predict droplet size variation with the assumption that the liquid jet behaves like a mass-spring system, and when the supersonic flow impacts the liquid jet, the jet deforms,vibrates,and then breaks up.By adopting both models,the stripping model used to simulate the primary break up zone and the TAB model used to simulate the secondary break up zone, Trinh and Chen140calculated the droplet size variation of a liquid spray with precision in supersonic crossflow.Im et al.141used a K-H/R-T hybrid model to calculate the droplet diameter of a liquid jet in supersonic crossflow.Most of the liquid jet break up models in supersonic flow focus on the local droplet stripping rate;however,the spray mixing with the air and the fuel vaporization in high-temperature crossflow is also important in supersonic combustion engine design,because the spray mixing efficiency influences the combustion performance, but there has been little literature discussing the liquid jet mixing efficiency in supersonic cross flow.The facts of spray droplets stripping by spray instability,vaporized droplets becoming gas phase in supersonic crossflow, twophase interaction, and gas-phase fuel mixing with air are very complicated,and the vortex induced from the spray interaction with the crossflow enhances the mixing between air and gasphase fuel.Mashayek et al.142modeled the deformation and trajectory of a liquid jet in crossflow and compared with some experimental and theoretical data available in the literature.They also developed a Multiple-Injector Model (MIM) to investigate the flow blockage and the effects of jet spreading on droplet dispersion in the wake of the jet, downstream droplet size,and velocity distributions.143Zhou et al.70proposed a theoretical prediction model which could simultaneously predict the jet trajectory and the three-dimensional shape of the jet column under supersonic conditions.Wu et al.144studied the primary breakup along surface turbulent liquids and provided the following correlation for the SMD(D32) of the droplets:

Fig.15 Cross-sectional distributions of spray (Ma = 1.94).134

Fig.16 Cross-sectional distributions of spray at four random moments (Ma = 2.1).123

Fig.17 Comparison of spray distributions between simulation and experiment in different cross-sectional planes.62

where the Weber number is defined as Weg= ρgDNV2g/σ,with ρgbeing the crossflow air density, ρjis the liquid density, μjis the dynamic viscosity of liquid,DNthe nozzle diameter(which is assumed to be the initial jet diameter), Vgthe crossflow velocity, and σ the liquid surface tension.

Becker and Hassa145performed experiments at higher pressures and found the following trend line for their results,where SMD is defined as a global diameter as follows:

Table 2 Empirical formula of spanwise width of a liquid jet in supersonic transverse flow.

Lee et al.146used pulsed shadowgraph and holograph observations to investigate the deformation and breakup properties of a round liquid jet and suggested the following correlation:

where Λ is the radial(cross-stream)integral length scale,WeLΛis the Weber number based on the jet exit radial(cross-stream)integral length scale: WeLΛ=ρjΛV2g/σ.

Bolszo et al.147investigated the resultant plume droplet size of natural unstable emulsions into a crossflow.They used Buckingham π theorem to identify the governing fluid processes through fluid parameters which are responsible for breaking up an emulsion liquid jet in the current geometry for the first time.They suggested the following correlation:

where Regis the gas Reynolds number and Wegis the gas Weber number, and S term is included to account for the effects of an emulsion on increasing jet in crossflow droplet size.

Liu et al.148used linear stability analysis to determine the disturbance growth rate on the surface of a liquid column and proposed a semi-theoretical relation to evaluate the droplet spatial distribution along the liquid column.They suggested the following correlation:

where D0is the diameter of the injector, and Regand Refare the gas and liquid Reynolds numbers,respectively.x is the horizontal distance between the breakup point and the injector exit, while y is the vertical distance between them.

In jet experiments of free jet or low-speed flow, there are two main optical diagnosis methods that can be used to obtain the droplet dynamic information.In the first approach,droplet size information is directly extracted from images with high temporal and spatial resolutions, and then the droplet motion information is obtained by calculating the droplet displacement difference between relevant images.Specific applications of this strategy include high-speed shadow method,149–151digital holographic microscopy,152,153PIV,151,154,155and microscopic imaging technology.70,156,157The other general approach uses the characteristic changes of laser after passing through droplets, applying specific methods of Doppler frequency shift, Doppler phase difference, scattered light angle,and light intensity.Phase Doppler Particle Analyzer(PDPA)158–160and Malvern161,162are widely used as diagnostic technologies.

The existing optical experimental methods(phase Doppler,schlieren,laser-induced fluorescence, high-speed photography,etc.) perform better in the downstream area.Unfortunately, it is tough to measure the near field of the spray exit of the liquid nozzle.We need some advanced optical experimental methods to analyze high-precision and high-resolution direct observation of spray(especially the jet surface breakup characteristics,surface wave length and wave velocity, and continuous liquid column shape) in a high-temperature and high-pressure flow field.The ballistic photon imaging technology is an advanced detection method that can reveal the internal structure of a spray.It uses a photon (ballistic photon) which is rarely scattered through the dense spray.163The technology can obtain a high-resolution164–166image of the dense droplet group near the nozzle.If ballistic imaging technology is applied to a liquid jet in supersonic crossflow, a clearer and more accurate nearfield jet image should be obtained,providing powerful support for in-depth analysis of the mechanism of jet breakup.Laser Sheet Drop Sizing(LSDS)is another advanced technique that can provide relative SMD mapping.Yeh et al.167firstly demonstrated the method of LSDS to measure the droplet diameters of spatially resolved sprays.The principle is based on a simultaneous application of two imaging techniques that generate two independent signals; the first technique LIF is proportional to the droplet volume whereas the second technique (Mie scattering) is proportional to the droplet surface area.The ratio of the LIF to Mie signal is proportional to the relative SMD and yields a 2D map of the droplet size distribution across the cross-section of a spray.Moreover, the LSDS technique is relatively less prone to the effect of multiple scattering contributions in spray fields.168To characterize a liquid jet in supersonic crossflow,researchers generally analyze the atomization characteristics of the liquid jet from two characteristic planes: the central symmetry plane and the spanwise cross-section, described in detail below.

4.1.Atomization characteristics of central symmetry plane

To ensure uniform and stable inlet air flow and continuous normal injection of a liquid nozzle, the spray field of a liquid jet in supersonic crossflow is considered symmetrical on the center symmetry plane.By measuring the information of droplets at different locations in the central symmetry plane,researchers can directly assess the particle size and velocity distributions of the spray in the direction of flow and in the longitudinal direction.Nejad and Schetz78,169studied the atomization characteristics of the central symmetrical plane of a liquid jet in supersonic crossflow (Ma = 3.0) by diffraction scattered light method.They found that the droplet diameter of an atomized liquid jet with a circular orifice with a diameter of 1.3 mm was about 10 μm, the droplet diameter decreased with an increase of q and increased with an increase of the orifice diameter d, and the liquid viscosity and surface tension had little effect on the atomization diameter.Lin et al.118used PDA to study the atomization characteristics of the central symmetry plane of a liquid jet in supersonic crossflow(Ma=1.94).Their results showed that the liquid jet was completely atomized at the downstream position of x/d=100,and the SMD of droplets basically did not change, with a size of about 10 μm.The droplet size distribution on the central symmetry plane was S-shaped along the longitudinal direction,the minimum droplet diameter occurred at y/h = 0.6, an increase of GLR made the droplet size distribution more uniform, and the velocity distribution of droplets on the central symmetry plane exhibited a mirror image S-shape.The velocity of large-diameter droplets was lower, and that of smalldiameter droplets was higher.Wu et al.57used PDA to study the atomization characteristics of a liquid central symmetry plane in supersonic crossflow (Ma = 1.86).They found that with the development of flow downstream,the droplet size distribution on the central symmetry plane gradually changed from a C-type distribution to an I-type distribution.The phenomenon of droplet breakup and coalescence caused a change of the droplet size distribution.Li et al.51used PDA to study the atomization characteristics of the central symmetrical plane of a liquid jet in supersonic crossflow(Ma=2.85).They observed significant differences in the movement of droplet groups at different heights for the same flow direction, with larger-size and lower-velocity droplets near the wall and the center of the spray.As the vertical height increased,the droplet size decreased, and the streamwise velocity u and longitudinal velocity v increased gradually, as seen in Fig.18.51Li et al.51also studied the particle size distribution and velocity distribution of droplets at different flow directions on the central symmetry plane, and used the local penetration depth of a liquid jet to deal with the dimensionless spatial position, as seen in Fig.19.51Their results showed that when y/h < 0.5, SMD decreased with an increase of x/d,and the average longitudinal velocity was close to 0.However, when y/h > 0.5, SMD increased with an increase of x/d,and the average longitudinal velocity increased significantly.The maximum value was detected at the maximum spray height.Li et al.51proposed that the upward movement trend of large droplets and the downward movement trend of small droplets were the key factors leading to an increase of SMD in the upper layer with an increase of x/d.

Amighi and Ashgriz170used the laser light sheet illumination technique to investigate water jet breakup and atomization in a high-temperature and high-pressure crossflow.They developed an unbiased method for analyzing images to measure droplet sizes.They also obtained a correlation between the global droplet size, jet velocity, air velocity, orifice diameter, air pressure, and air temperature.Becker and Hassa145investigated the injection of a plain jet of kerosene Jet A-1 fuel into a high-temperature and high-pressure crossflow experimentally.They found that a filmer plate led to an overall finer spray in a cold test condition.However,the plate did not generate a finer spray or accelerate evaporation in a hot test condition,which was about 70%complete at a location of 80 mm downstream from the point of injection.Hsiang et al.171used schlieren and Mie scattering observation technique to investigate the mixing of a liquid jet spray in supersonic highenthalpy airflow.Due to the vortex surrounding the spray, a strong stripping interaction between the droplets and the freestream turbulence enhanced the evaporation of droplets and reduced their sizes.They also found that the interactions between the oblique shock induced by boundary separation and the bow shock induced by the liquid jet crucially affected the mixing behavior between the spray and surrounding airflow too.The spray in high-enthalpy supersonic crossflow had a lot of surface gasification phenomena on the windward side.

4.2.Atomization characteristics of spanwise cross-section

The spanwise cross-section is another plane used to characterize the atomization characteristics of a liquid jet in supersonic crossflow.The cross-section of the spray exhibits a structure similar to the shape of ‘‘Ω”.Lin et al.77,118initially studied the atomization characteristics of the cross-section of a liquid jet in supersonic crossflow (Ma = 1.94) by PDPA, and obtained the SMD and velocity distributions of the sprayed cross-section, as seen in Fig.20.73Li et al.172used PDA to study the atomization characteristics of a liquid jet’s spanwise cross-section in supersonic crossflow (Ma = 2.85) and obtained the SMD and velocity distributions of three spanwise cross-sections downstream.The SMD distribution of the spray in the spanwise cross-section has a large center and small edges, as seen in Fig.21.172However, surface breakup near the nozzle can increase the SMD distribution of the downstream section close to the nozzle.Fig.22172shows the average streamwise velocity distribution of the three spanwise crosssections downstream.With an increased streamwise distance,the average velocity of droplets increases significantly at the edge of the sprayed cross-section.Compared with the SMD distribution of the spray, the average streamwise velocity shows an opposite trend,where the low-speed region has a larger SMD distribution,and the high-speed region has a smaller SMD distribution.Fig.23172shows the average longitudinal velocity distribution of the three downstream spanwise crosssections.The longitudinal motion of droplets can determine the penetration depth of the jet.Overall,the longitudinal average velocity gradually increases upward and downward from the middle of the cross-section, with maximum velocities in the positive and negative directions at the top and bottom of the cross-section, respectively.

Fig.18 Size-velocity correlations at various longitudinal heights (Ma = 2.85).51

Fig.19 SMD and average velocity distribution at different flow directions (Ma = 2.85).51

From the droplet information measured by PDA, we can intuitively understand the SMD and velocity distributions of the spray in the spanwise cross-section, but the underlying explanation of this distribution remains unclear.Li et al.52used numerical simulation to obtain rich flow field data to explain the formation of this special distribution.They found that the flow velocity of the gas phase is always higher than that of the liquid phase,both on the spray edge and in the central area of the spray.Therefore, a droplet will continue to be accelerated until the relative velocity between gas and liquid is zero.Since the average velocity of gas-phase flow in the center of the spray is much lower than that near the outer edge of the spray,the average velocity of droplet flow near the center area is always lower than that of droplet flow near the outer edge of the spray.Force analysis of the droplet reveals that the droplet is subjected to upward longitudinal and horizontal forces on both sides of the spray top, making the droplet gradually diffuse to the mainstream.However,a droplet inside the spray is mainly subjected to a downward longitudinal force,so acceleration points to the wall area.Fig.2452shows a cloud diagram of the moving streamlines and velocities of droplets for different spanwise cross-sections.In the periphery of y > 4 mm spray, droplets radiate out under inertial action and gas entrainment.Under the influence of the top reversal vortex pair, droplets in the central region are transported to the near-wall region.Under the influence of the wall reversal vortex, downward-moving droplets deviate from the vertical trajectory and move from the core region to either side.Some droplets with large inertia hit the wall at an inclined angle,but the rebounded droplets still move towards both sides of the mist.The presence of two reverse vortex pairs and the effect on the wall promote the transport of droplets to both sides in the near-wall region,which is conducive to the formation of the observed ‘‘Ω”structure.

Fig.20 Cross-sectional contour plots for plume and droplet properties from PDPA measurements(Ma = 1.94).73

Fig.21 SMD distributions on various cross-sectional planes from PDA experiments (Ma = 2.85).172

The atomization characteristics of a liquid jet in supersonic crossflow are generally studied based on the central symmetry plane and span-wise cross-sectional droplet information.The liquid–gas momentum ratio and nozzle diameter greatly affect the droplet diameter,while the viscosity and surface tension of liquid have little influence on the droplet diameter.The particle size distribution of the droplets on the central symmetry plane firstly decreases and then stabilizes along the flow direction,presenting an S or C shape along the longitudinal direction.With an increase of the downstream distance,droplet breakup and coalescence lead to a transformation of the particle size distribution from S-or C-shaped to I-shaped,and the velocity distribution of the droplets on the central symmetry plane is a mirrored S shape.The droplet distribution on the spanwise cross-section remains a structure similar to an ‘‘Ω”shape.The SMD distribution is characterized by the center and small edge.The mean flow velocity is opposite to the SMD distribution, i.e., the low-speed region corresponds to a larger SMD distribution, and the high-speed region corresponds to a smaller SMD distribution.The longitudinal average velocity of the droplets increases gradually from the middle of the cross-section upward and downward, with maximum positive and negative velocities at the top and bottom of the crosssection, respectively.PDPA remains the most commonly used droplet measurement technology,but due to the high time cost of measurement, the measurement efficiency of this method is still low.PLIF/Mie scattering technology111based on elastic/inelastic scattering technology is a new approach for rapid measurement of droplet size distribution in a spray field.By determining the relationships between fluorescence, scattering light intensity,and droplet size area and volume,the spray size distribution on a two-dimensional plane can be easily obtained by image processing.

Fig.22 Averaged streamwise velocity component distributions on various cross-sectional planes from PDA experiments(Ma = 2.85).172

Fig.23 Averaged longitudinal velocity distributions on various cross-sectional planes from PDA experiments (Ma = 2.85).172

Fig.24 Streamlines and velocity contours of droplets on different cross-sectional planes (Ma = 2.1).52

5.Remarks and conclusions

Liquid jet atomization in supersonic crossflow is a key technology required for a scramjet.This non-invasive injection method usually avoids a high total pressure loss and allows liquid fuel to atomize, mix, and evaporate in a short period of time.This review discussed recent work characterizing the primary breakup mechanism (including column breakup, surface breakup, and droplet breakup) and spray characteristics (including distribution and atomization characteristics) of a liquid jet in supersonic crossflow.Based on our evaluation of the literature, we reach the following conclusions:

(1) The growth and development of surface waves significantly dominates the breakup of a liquid jet.The development of windward R-T unstable waves is the main factor in column breakup, and the development of K-H unstable waves along the circumferential direction of the jet or droplets is the main factor of surface breakup and droplet breakup.Our current understanding of the liquid jet breakup mechanism comes from experiments and numerical simulations.However, for more comprehensive understanding of the breakup process of liquid jets, theoretical work is also required.

(2) Experimental conditions, gas and liquid parameters,and nozzle internal geometric parameters all influence the atomization characteristics of a liquid jet in supersonic crossflow.The liquid–gas ratio is the most important factor affecting the penetration depth.The span width of the liquid jet is affected by the windward area.There is significant interest in the distribution characteristics of a liquid jet in cavity, with growing attention to other special combustor configurations,such as tower cavity and round tube designs.

(3) Droplet breakup and coalescence transform the droplet size distribution from S- or C-shaped to I-shaped, and the velocity distribution of the droplets on the central symmetry plane exhibits a mirrored S shape.The droplet distribution on the spanwise cross-section retains a structure similar to an ‘‘Ω”shape.Compared with a fuel spray in low-enthalpy flow,a fuel spray in high-enthalpy flow can provide more guidance for engine ignition design.Some advanced measurement methods(such as ballistic imaging and laser sheet drop sizing)can be introduced to reveal the breakup mechanism or new phenomenon.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to express their sincere thanks for the supports from the National Natural Science Foundation of China (Nos.11902353, 12272408, 12102472, 11902351, and 12102462), the National Science Fund for Distinguished Young Scholars, China (No.11925207), and the Hunan Provincial Postgraduate Research Innovation Project, China(No.CX20210035).