Review on active thermal protection and its heat transfer for airbreathing hypersonic vehicles

Yinhi ZHU,Wei PENG,Ruin XU,Peixue JIANG,*

aKey Laboratory for Thermal Science and Power Engineering of Ministry of Education,Department of Energy and Power Engineering,Tsinghua University,Beijing 100084,China

bInstitute of Nuclear and New Energy Technology,Collaborative Innovation Center of Advanced Nuclear Energy Technology,Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education,Tsinghua University,Beijing 100084,China

KEYWORDS Film cooling;Hypersonic vehicle;Regenerative cooling;Thermal protection;Transpiration cooling

Abstract Hypersonic vehicles with turbojet,ramjet,and scramjet engines are expected to be widely applied to future transportation systems.Due to high-speed flight in the atmosphere,body outer surfaces suffer strong aerodynamic heating,and on the other hand,combustion chamber inter walls are under extremely high temperature and heat flux.Therefore,more efficient and stable active cooling technologies are required in hypersonic vehicles,such as regenerative cooling, film cooling,and transpiration cooling,as well as their combinations.This paper presents a comprehensive literature review on three active cooling methods,i.e.,regenerative cooling, film cooling,and transpiration cooling,and deeply analyzes the mechanism of each cooling method,including the fluids flow,heat transfer,and thermal cracking characteristics of different hydrocarbon fuels in regenerative cooling,the heat transfer and flow mechanism of film cooling under supersonic mainstream conditions,and the heat transfer and flow mechanism of transpiration cooling.

1.Introduction

A hypersonic vehicle with 5 times the speed of sound or higher flies in the atmosphere,which is a new and bright future aerospace technology.Unlike a rocket engine,the engine of a hypersonic vehicle itself does not carry an oxidant required for combustion;the combustion air is directly sucked from the atmosphere,as shown in Fig.1.The basic thermodynamic process of a hypersonic vehicle engine includes compression,combustion,and expansion.The main types include turbojet,ramjet,and scramjet categories.1A turbine or ramjet engine can not only be used alone,but also be combined with a rocket engine as shown in Fig.2,which is expected to be widely applied to hypersonic missiles,hypersonic aircraft,and space transportation systems.2

Fig.1 Schematic diagrams of turbojet,ramjet,and scramjet engines.1

Fig.2 Propulsion system cycles and efficiency as a function of Mach number.2

The United States and Russia launched the first research on hypersonic vehicles.3At present,the United States,Russia,France,Canada,Germany,and other countries are in the development of Mach numbers in 4–8 scramjets using hydrocarbon fuel.America from the mid-1960 s began to work on the development of scramjets,4and since the mid-1980s,they have started scramjet-powered aircraft programs.The maximum Mach number of the X-43A has reached 9.68 in a flight test in 2004.5In a test conducted by the U.S.Air Force in 2013,the Mach number of the X-51A has achieved 5 and lasted about 200 s.6Russia began early scramjet research work in 1966,and in 1991,performed the first successful supersonic flight tests.7From 1992 to 1992,under the support of the PREPHA plan,France carried out ground experiments of scramjets,and achieved breakthrough technologies on hydrogen dual mode scramjets.8In July 2002,Australia completed a flight test of supersonic combustion with Ma=7.6 under the HyShot plan.9China conducted the first flight test of an ultra-high speed vehicle in 2014,which reached up to 10 times the speed of sound.10

Due to high-speed flight in the atmosphere of hypersonic vehicles,the outer surface of a body receives intense friction with the atmosphere and suffers strong aerodynamic heating,especially at the leading edge of an aircraft,such as the nose cone, flange,and inlet.On the other hand,the combustion temperature can be up to 3000 K,and the combustion chamber wall and supports also need more efficient and stable cooling to meet working conditions.

Currently,active cooling technologies in hypersonic vehicles applications include regenerative cooling, film cooling,transpiration cooling,as well as their combinations.Regenerative cooling is to use coolant forced convection heat transfer in the cooling passage,which has a simple structure and high reliability.Film cooling is the primary technology for gas turbine thermal protection;it can also be used in active cooling for hypersonic vehicles.The coolant is injected into the mainstream at a certain inclination angle,forming a thin film on the wall to protect heat transfer from the mainstream to the protected wall.Transpiration cooling has a higher efficiency and with lower coolant consumption,which is a limited case of film cooling.The coolant flows through the porous wall into the mainstream,protecting the wall by forming a continuous film.

This paper focuses on a review on these three active cooling technologies and their recent progresses,including the fluids flow,heat transfer,and thermal cracking characteristics of different hydrocarbon fuels in active regenerative cooling;the heat transfer and flow mechanism of film cooling under supersonic mainstream conditions;and the heat transfer and flow mechanism of transpiration cooling.

2.Active regenerative cooling

Active regenerative cooling has been widely used in liquid rocket engines and gas turbines,and has been proven to be very effective.The engine fuel is chosen as the coolant,which avoids carrying extra coolant.11As shown in Fig.3,in active regenerative cooling for hypersonic vehicles,the hydrocarbon fuel firstly flows through the combustion chamber wall to remove heat and then is injected into the combustion chamber.12

The cooling passages in hypersonic vehicles have been widely studied.Scotti et al.13used an optimization technique to find the minimum coolant flow rate subject to temperature,pressure drop,mechanical stress,Mach number constraints,and thermal fatigue constraint.They considered two types of cooling panel construction:longitudinal fin and pin- fin cooling jackets.Youn and Mills14studied the optimization of rectangular cooling passages for a hypersonic aircraft cooling system.Their work considered hydrodynamic,thermal,and Mach number constraints,as well as smooth or rectangular ribroughened duct geometries.Powell et al.15performed a fuelcooled heat exchanger panel tested in the hypersonic technology(HyTech)program.The fabrication,performance,operability,and durability of a subscale fuel-cooled structure were investigated.Their work considered smooth rectangular channels and channels with fuel injection locations.Wenerberg et al.16conducted a combined experimental and computational project to quantitatively determine the enhancement physics of high-aspect ratio cooling channels.Supercritical nitrogen was used as the working fluid to simulate the coolant fuel.Results showed that the high-aspect ratio cooling channels could decrease the chamber wall temperature for a given pressure drop.Feng et al.17further studied the flow field and heat transfer characteristics of supercritical pressure hydrocarbon fuel around a local flow blockage structure.The optimum design of a cooling panel for the local flow blockage structure was investigated based on three-dimensional numerical simulation.

Fig.3 Active regenerative cooling and passages in a scramjet engine.12

An indirect method to increase fuel heat sink is a recooling cycle,which uses fuel heat sink repeatedly.18–20As shown in Fig.4,the cycle is mainly composed of the first and second cooling passages with a pump and a turbine.The purpose of the turbine is to decrease the fuel temperature after it absorbs the heat from the combustion wall.Analytical results showed that the cycle could well solve the problem of insufficiency of fuel heat sink.

Although using solid fuel to take full advantage of the phase change is a way to increase available heat sink from the fuel,21it is evidently lower than that from thermal cracking.When temperature is above approximately 150°C,hydrocarbon fuels will react with dissolved oxygen.Higher temperature generally above 480°C leads to significant thermal cracking.22Gas and liquid products will be generated during the thermal cracking reactions of hydrocarbon fuels,and bring additional chemical reaction heat sink.The composition and physical properties of the fuel mixture will be largely influenced by the temperature and the reaction conversion.The flow,convection heat transfer,and reaction of hydrocarbon fuel are highly coupled together in a regenerative cooling process.

This section will firstly briefly review the convection heat transfer mechanisms of fluids such as CO2at supercritical pressures,and then introduce the heat transfer and thermal cracking of different hydrocarbon fuels.

2.1.Convection heat transfer of CO2and hydrocarbon fuels at supercritical pressures

The regenerative cooling process with hydrocarbon fuels is very complex,since the coolant pressure usually exceeds the critical pressure,and the coolant temperature changes from sub-critical to super-critical.The physical properties of the coolant at supercritical pressures vary sharply with pressure and temperature.Convection heat transfer of hydrocarbon fuels at supercritical pressure conditions is strongly influenced by the variations of the thermo-physical properties.

Studies of heat transfer of fluids at supercritical pressures have been started since 1930s.Schmidt et al.found that the free convection heat transfer coefficient(HTC)of a fluid at a near-critical point was quite higher than that of the fluid at subcritical pressures.23In the 1950s and seventies,the emergence of supercritical pressure thermal power stations and proposal of supercritical pressure water-cooled nuclear reactors effectively promoted the research.24–27In recent years,supercritical pressure fluids have been widely used as working substances in various industries,such as advanced nuclear power,high-temperature solar energy,aerospace,CO2geological storage,enhanced geothermal systems,development of shale gas,gas hydrate exploitation,etc.28–30

Fig.4 Generic configuration of a scramjet engine with a recooling cycle.20

Fig.5 Thermal property variations of supercritical pressure fluids.

The notable feature of supercritical pressure fluid is the sharp variation of thermal properties,especially near the pseudo-critical temperature as shown in Fig.5,where p,ρ,λ,μ,cprepresent pressure,density,thermal conductivity,viscosity and heat capacity,respectively.Existing research has concluded that there are three heat transfer regimes for convection heat transfer of supercritical pressure fluid flowing inside vertical tubes24–27:(1)normal heat transfer regime,(2)heat transfer deterioration(HTD)regime,and(3)heat transfer enhancement(HTE)regime.Many researchers have confirmed that HTD may be caused by three reasons as follows.(1)The sharp variation of thermo-physical properties.(2)The effect of buoyancy force induced by a radial non-uniform density distribution.For a laminar flow,the buoyancy force increases heat transfer for an upward flow and decreases heat transfer for a downward flow in a vertical tube.For a turbulent flow,the buoyancy force decreases heat transfer firstly and then increases heat transfer for an upward flow,and always increases heat transfer for a downward flow in a vertical tube.(3)The effects of thermal expansion and flow acceleration induced by variations of temperature and pressure in the axial direction under a heating condition.Jiang et al.studied the convection heat transfer characteristics of supercritical pressure carbon dioxide in vertical heated circular tubes with inner diameters of 2.0 mm,1 mm,0.27 mm,and 99.2 μm.31–36They found that under experimental conditions,for a tube with an inner diameter of 2.0 mm,HTD is mainly because of buoyancy effects;as the inner diameter decreases,the flow acceleration becomes the dominant factor which results in an abnormal wall temperature distribution,while the buoyancy effect becomes small enough to be neglected,such as for a tube with an inner diameter of 99.2 μm.

Moreover,some non-dimensional parameters have been defined to predict the onset of HTD by drawing out the HTD mechanism:Jackson and Hall37introduced a nondimensional parameter,Bo*,in order to evaluate the buoyancy influence on the convection heat transfer behaviors of fluids at supercritical pressures in vertical channels:

where Re and Pr present Reynolds number and Prandtl number,and Gr*was calculated as

where g,β,d,qw,λf,ν represent gravity,volume expansivity,diameter,heat flux,thermal conductivity and kinematic viscosity,respectively.

The typical heat transfer performance of supercritical pressure CO2in a vertical heated tube for various buoyancy parameters is shown in Fig.6,where Nufis the Nusselt number calculated by the correlation without buoyancy and Nu is the experimental one.35Researchers,e.g.,Jackson and Hall,37Li et al.,35pointed out that for upward flows in vertical circular channels,buoyancy has no significant effect on convection heat transfer when Bo*≤5.6×10-737or Bo*≤2×10-7in region A35;buoyancy would deteriorate convection heat transfer due to a decrease of turbulence production caused by a decreased streamwise velocity gradient when 5.6×10-7＜Bo*＜1.2×10-637or 2×10-7＜Bo*＜6×10-7in region B35;with 1.2×10-6≤Bo*≤8×10-637or 6×10-7≤Bo*≤2×10-5,35heat transfer will be gradually reduced because of a reduction of turbulence caused by a reversed streamwise velocity gradient;with Bo*＞8×10-637or Bo*＞2×10-5,35heat transfer will be enhanced by a strongly reversed velocity due to buoyancy in region C.For downward flows,heat transfer will be enhanced dut to strong buoyancy as shown in region D.

McEligot and Jackson38proposed a non-dimensional parameter,KvT,to evaluate the influence of thermal acceleration on convection heat transfer of supercritical pressure fluids.When KvT≥3×10-6,turbulence may be significantly reduced or even re-laminarized,resulting in deteriorated convection heat transfer.Jiang et al.36introduced firstly a nondimensional parameter,KvP,to evaluate the flow acceleration effect induced by axial density variations due to an axial pressure decrease on convection heat transfer in a mini-or microtube.

Fig. 6 Nusselt number ratios for various buoyancy parameters.35

Although the basic convection heat transfer characteristics of hydrocarbon fuel at supercritical pressures are similar to those of water or carbon dioxide,the details could be different because of the difference of thermal property variations.39–50

Isaev and Abdullaeva41investigated experimentally the convection heat transfer of supercritical pressure n-heptane in a small-size channel for an efficient heat exchanging system for laminar flows with Reynolds numbers of 1087 to 2347,and developed a heat transfer correlation.Urbano and Nasuti42numerically investigated the forced convection HTD for channel flows of methane,ethane,and propane.Results showed that the heat flux to specific mass flow rate ratio should not be exceeded if HTD was to be avoided.Zhang et al.43investigated the flow and heat transfer of n-decane at supercritical pressures experimentally,and presented heat transfer correlations in laminar,transition,and turbulent flow regions.Feng et al.44established a 2D numerical model using time marching algorithms with preconditioning to investigate the heat and mass transfers of supercritical n-decane with pyrolysis in a mini-channel.

Liu et al.45experimentally investigated the convection heat transfer of supercritical pressure n-decane in vertical tubes with inner diameters of 0.95 and 2.00 mm.For high-inlet Reynolds number flows,there was no abnormal wall temperature to be observed.The wall temperature increased monotonically for both upward and downward flows(Fig.7).For lower inlet Reynolds numbers,buoyancy may significantly deteriorate heat transfer for an upward flow(Fig.8).A threshold for Bo*was obtained as 2.0×10-7,above which buoyancy would influence heat transfer of n-decane significantly.Two local Nusselt number correlations were developed for convection heat transfer of supercritical pressure n-decane with/without a significant buoyancy effect as follows:

(1)Local Nusselt number correlation without a buoyancy effect:

where

(2)Local Nusselt number correlation with a buoyancy effect:

Fig.7 Local temperatures and heat transfer coefficients for various wall heat fluxes at pin=3 MPa,Tin=150.0°C,Rein=2700,m=4 kg/h,and ρu=4925 kg/(m2·s).

Fig.8 Local temperatures and heat transfer coefficients for various wall heat fluxes at pin=3 MPa,Tin=150.0°C,Rein=4000,and ρu=506 kg/(m2·s).

where Nufis defined in Ref.45,and A=-8.45 × 105，a=-2.23，b=0.14 for an upward flow;A=3.62 × 105，a=-2.75，b=-1.84 for a downward flow.x/d represents the dimensionless axial coordinates normalized by the pipe diameter d,and n1is a temporary variable.The subscripts b,w and pc represent bulk fluid,wall and pseudo critical,respectively.FTD,Fv2and Fprare functions considering the effects of thermal development,thermal property variation and Pr number.

Experiments conditions:2.5 MPa＜p＜7 MPa,Tb(at exit)＜500 °C,and Re(at inlet)=2700–7000.m and u present mass flow rate and inlet velocity,respectively.

The convection heat transfer characteristics of China No.3 kerosene at supercritical pressures for a regenerative cooling system have been experimentally and analytically investigated.46–52Guo et al.49investigated convective heat transfer characteristics of supercritical pressure kerosene in small non-circular channels.The inlet temperature was found to be an important factor for heat transfer,while structural parameters mattered less.Liu et al.50studied heat transfer of China RP-3 in a vertical tube at supercritical pressure numerically,and obtained the threshold of the ratio of heat flux to mass flow rate for the onset of HTD.

The heat transfer characteristics of RP-3 kerosene at various mass fluxes,pressures,and heat fluxes were investigated by Huang et al.51and Zhang et al.52Results showed that increasing the mass flux reduced the wall temperature and separated the experimental section into three different parts.Two heat transfer correlations were proposed respectively for upward and downward flows as follows:

Upward:

Downward:

Experiments conditions:3.6＜p＜5.4 MPa,Tb(at exit)＜450 °C,and Re(at inlet)≈ 3500–10000.Here the subscript f indicates that the thermophysical properties are the weighted average properties in boundary layer.

The heat transfer and cracking behaviors of supercritical JP-7 in cylindrical tubes with a length of 4 mm and an internal diameter of 95 μm were investigated by Chen and Dang.53The results of JP-7 heat transfer tests were compared to those of water and ethanol.The average numbers calculated for the JP-7 tests revealed that it had far better cooling capabilities than those of water.Linne et al.investigated the potential of JP-7 as a coolant.The heat transfer at surface temperature up to 927°C was experimentally studied,and audible instabilities and carbon deposition were also investigated.54

The thermal stability and heat transfer were investigated using five common hydrocarbon fuels:JP-7,JP-8,JP-8+100,JP-10,and RP-1 by Stiegmeier et al.55Tests used resistively heated tube sections to simulate conditions in regenerative cooling.The influences of the carbon deposit on heat transfer and pressure drop were observed as shown in Fig.9.A simple power law correlation was developed for all of the fuels as

where constants a and b are listed in Table 1.

Fig.9 Effects of deposit shedding on tube pressure drop and local Nusselt number(JP-8,SS,1000°F/75 fps).55

Table 1 Constants a and b.

The operating pressures of hydrocarbon fuels in regenerative cooling are usually higher than their critical pressures.As a result, fluctuations in the temperature,pressure,and mass flow rate occur in many cases.56,57Instability is harmful to the safety of scramjet engines.When the relative pressure ratio is below 1.5,the fuel bulk temperature is lower than pseudo temperature,and the wall temperature is high than that,so instability is easy to occur.58,59Wang et al.60experimentally investigated the thermo-acoustic instability of hydrocarbon fuel at supercritical pressure in a vertical circular tube.Pressure drop fluctuations were found to be related to the characteristics of thermo-acoustic instability as shown in Fig.10.Some researchers have investigated methods to stabilize and enhance heat transfer for supercritical hydrocarbon fuels.Hitch and Karpuk61found turbulating insert could stabilize a flow as well as enhance heat transfer by up to 800%above that observed in an open tube.

2.2.Thermal cracking of supercritical pressure hydrocarbon fuels

In active regenerative cooling,the hydrocarbon fuel temperature gradually increases after heat absorption from endothermic cracking reactions.These endothermic cracking reactions could provide additional chemical heat sink.The total heat sink of a hydrocarbon fuel is composited from sensible enthalpy and endothermic chemical reactions.The chemical heat sink can be one third of the total heat sink at a fuel exit temperature of 723°C of JP-7(Fig.11).The chemical heat sink is a function of the fuel temperature,which affects the product distribution.

Fig.11 Overall and sensible heat sink available from endothermic cracking of JP-7.62

Fig.10 Variations of sound signal and pressure drop as a function of time.60

In the hydrocarbon fuel cracking process,H2,CH4,C2H4,C2H6,and other small gaseous hydrocarbon molecules are generated.63Composition of the product can be affected by a variety of factors,including the reaction temperature,the reaction pressure,the residence time,the reactant concentration,etc.64

Kossiakoff and Rice65described this decomposition process as occurring through a series of free radical reactions,which is initiated by a carbon-carbon bond fission along the parent n–alkane chain to form primary radicals with hydrogen abstraction.Secondary radicals can isomerize or decompose by a ‘‘β-scission” reaction to form an alkene and a smaller primary radical as follows:

The resulting small primary radicals can then undergo further reactions;therefore,cracking composes of thousands of chemical reactions.Most past modeling of cracking can be categorized into detailed kinetic modeling,lumped kinetic modeling,and global kinetic modeling.

Detailed kinetic models reveal the nature of a reaction process through detailed mechanistic models of each primitive reaction.66Dente et al.67established a detailed kinetic model containing 2200 kinetic equations,which includes 110 free radical molecules.Dahm et al.68developed a detailed kinetic model containing 1175 reactions for n-dodecane based on experimental data for thermal decomposition from 950 to 1050 K at atmospheric pressure.Xing et al.69investigated gas and liquid product distributions from 663 to 703 K and obtained the apparent activation energy and pre-exponential factor.Li et al.70and Jiao et al.71developed detailed mechanisms for large hydrocarbons using an in-house code‘Reax-Gen’.Detailed decomposition kinetic models for n-heptane and n-decane were constructed with 557 and 1072 reactions,respectively.However,these detailed kinetic models require a detailed knowledge of the feedstock structure,rate constants,and reaction pathways,which is difficult to obtain for heavy hydrocarbons.72

In lumped kinetic modeling,the components of a mixture are classified as kinetic lumps,which are then treated as pseudo-components.73–76Pseudo-components concentrations are then followed as reactions proceed.Parnas and Allen77extended compound class modeling by considering the average carbon number,and then developed a model containing 10 lumps.Weekman et al.studied conversion and gasoline yield using a kinetic mathematical model in isothermal fixed,moving,and fluid bed reactors.78A thermochemical mechanismoriented lumping strategy was described to summarize a large model in terms of a few parameters which could be over 5 orders of magnitude.79Jiang et al.80measured the concentrations of cracked products in a length-variable tube and developed a modified molecular reaction model containing 18 species and 24 reactions by introducing two middle-weight alkenes as lumped primary products of C5–C11 alkenes(C5+)and cycloalkanes(CC5+).Lumped modeling treats components of a fuel/product mixture as kinetic lumps,which are considered as pseudo-components.Thus,information about individual components is lost.

For low conversion cracking,defined as＜20%conversion as shown in Fig.12,products are formed with constant proportions with respect to other products.Thus,global modeling can be used in cracking with a low conversion rate,where only the rate equations for the primary fuel species or components are defined as

Fig.12 Measured 1-heptene formation.81

Fig.13 Averaged PPD over all of pressures,general PPD.81

Ward et al.64,81further studied mild thermal cracking for n-decane and n-dodecane.Results showed that products were generally consistent with the proportional product distributions assumption as shown in Fig.13.

Bao et al.82and Hou et al.83adopted the PPD assumption to model thermal cracking of pure hydrocarbons and kerosene fuels.A one-step global model for thermal cracking of kerosene without considering the liquid products was developed by Zhong et al.84Goel et al.85proposed a one-step global model to describe the pyrolysis of jet fuels by conducting experiments at different flow rates.Zhu et al.86investigated the flow and heat transfer behaviors of thermal cracking ndecane.A global reaction model including 18 main products species was developed for n-decane conversions less than 13%as follows:

Fig.14 Predicted fuel mixture and wall temperature contours.86

A CFD model was then established for thermal cracking of n-decane at supercritical pressures based on the above reaction model.The coupling effects of flow,heat transfer,and chemical reactions were analyzed as shown in Fig.14.

Endothermic hydrocarbon fuels are close to application in active regenerative cooling of hypersonic vehicles engines.The flow,heat transfer,and thermal cracking characteristics of supercritical pressure hydrocarbon fuels are the basic in active regenerative cooling design.Further research is needed to increase the heat sink of these fuels,and also to further understand the real fuel used in hypersonic vehicles,because the fuel usually contains thousands of components,causing very complex physical and chemical mechanisms.The mechanisms of HTD, flow instabilities,and interactions between cracking and heat transfer of hydrocarbon fuels at supercritical pressure need to be further investigated.

3.Supersonic film cooling

Film cooling is the employment of a secondary cooling fluid injected through holes or slots thus forming a cooling film to protect a surface exposed to a high-temperature environment(shown in Fig.15).Film cooling has become the main cooling method in modern gas turbines since firstly used in gas turbines in the 1970s.Because of its simple structure and good cooling performance, film cooling is also a promising way to protect the high-temperature components of rockets87and supersonic or hypersonic vehicles.88,89

According to the inlet velocities of the mainstream and the cooling stream, film cooling can be divided into subsonic and supersonic cases.

Fig.15 Model of tangential slot film cooling.90

For cases in which both the mainstream and cooling flow velocities are subsonic, film cooling is treated as subsonic film cooling.Since film cooling was firstly applied to solve the twodimensional slot hot-air discharge for de-icing of wings by Wieghardt91in the 1940s,research on subsonic film cooling has reached a considerable extent and depth,and there are various literature resources.The early stages of film cooling were summarized by Goldstein.92Han et al.93also showed a systematic summary of the heat transfer and cooling technology of gas turbine blades.The influencing factors of film cooling can be divided into geometric parameters and flow parameters.Geometric parameters include the shape of the film hole90,94,95and geometric features of the protected wall,96,97while flow parameters include the density ratio,98blowing ratio,99and momentum ratio as well as the mainstream of turbulence100and rotation,101the cooling stream entrance conditions,102–104and the influence of conjugate heat transfer.105

In general,when the mainstream and coolant inlet velocities are supersonic, film cooling is called supersonic film cooling.When a supersonic or hypersonic vehicle using a scramjet flies at supersonic or hypersonic conditions,there exist an intense aerodynamic heating on the outer surfaces of the vehicle and the high temperature or high heat fluxes role in its engine’s interior such as the isolator,combustion chamber,and nozzle walls.Therefore,it must rely on that active thermal protection should be used to protect these parts,of which supersonic film cooling is a promising concept.

3.1.Heat transfer and flow mechanism of supersonic film cooling

Cary and Hafner106pointed out that the performance of supersonic film cooling performance is better than that of the subsonic case because the mixture between the mainstream and the cooling stream is weaker in supersonic conditions than that in subsonic conditions.In addition,the cooling stream can reduce the wall friction.107,108Thus,supersonic film cooling is treated as an active thermal protection measure for a scramjet.However,as the development of scramjet engines came into a downturn time in the United States,1the number of studies of supersonic film cooling has been reduced accordingly since 1970s.With the development of aerospace technology in the 1990s,supersonic or hypersonic vehicles are becoming more and more important for their strategic position and application value.Many countries have returned to the study of supersonic film cooling due to its extensive application value in rocket engines,109scramjets,110and hypersonic aircraft.

For supersonic film cooling,there are many factors that influence the film cooling performance,such as the Mach number,inlet pressure,gas type,inlet height,and so on.Most of the above effects have been studied.Most of early studies on supersonic film cooling were focused on theoretical analysis and experimental investigations.Volchkov et al.111analyzed supersonic film cooling using the boundary-layer theory.Results showed that the gas compressibility of the coolant had little effect on the film cooling effectiveness,and equations obtained for quasi-isothermal conditions could be used for approximate calculations.However,Goldstein et al.112studied supersonic film cooling with both air and helium as the coolant gas by experiments on a Mach 3 wind tunnel,and analyzed the effects of the coolant inlet height and the mass flow rate.Results showed that compared to subsonic film cooling,supersonic film cooling had better film cooling performance.It was indicated that there existed a difference between supersonic film cooling and subsonic film cooling.Richard and Stollery113experimentally analyzed the effects of the coolant inlet height,mass flux rate,and gas type on supersonic film cooling,and proposed a discrete layer theory shown in Fig.16,where,u∞and ucrepresents the main flow and coolant flow velocity,ρ∞and ρcrepresents main flow and coolant flow density,and q0is the total heat flux onto the wall without the film protection,q represents the heat transfer flux after reduced by the film layer,x0is the distance from leading edge to the coolant inlet,x is the distance from the coolant inlet,S′is the slot height.Optimizations of film cooling effectiveness by which showed that hydrogen was the most efficient gas.However,some of the assumptions in the discrete layer theory such as the velocity across the profile of the layer remains constant and heat transfer through the boundary layer is diffused by one-dimensional heat conduction are not entirely consistent with the actual situations.

Fig.16 Discrete layer theory.113

George et al.114experimentally studied the impacts of the coolant gas inlet pressure and inlet height on supersonic film cooling.Results showed that when the coolant inlet pressure is the same as the mainstream inlet pressure, film cooling would show the best performance.Increasing the inlet height is beneficial for a higher effectiveness,and the plate thickness has little relationship with the film cooling performance.

Han et al.115experimentally studied a two-dimensional plate film cooling model for an interceptor fore-body configuration,in which the effects of the slot height,mass flow rate,cooling length,and injection angle between the mainstream and the cooling stream were involved.

Different kinds of coolant gas,such as hydrogen,helium,nitrogen,and carbon dioxide,have been studied for supersonic film cooling.Experiments by Sahoo et al.116studied the effects of cooling gases such as carbon dioxide,air,and helium on a bluff body,and results showed that besides the stagnation point,the lighter molecule weights were,the better the film cooling effectiveness was(shown in Fig.17);In Fig.17,s is the distance from the leading edge,Rnis the radius of the nosecone,St is Stanton number,H0is the specific enthalpy of the main flow.however,on the stagnation point,heavier molecule weights produced a better performance.In general,the performance of helium film cooling is the best.

Fig.18 Temperature and pressure ratios of heated helium and air injections.117

Juhany et al.117experimentally investigated supersonic film cooling using air and helium as the coolant,with results indicating that the film cooling effectiveness increases as the injection rate is increased,and the film cooling performance is better for gases with a higher thermal capacity(shown in Fig.18).In Fig.18,Trmis the recovery temperature on the wall,Ttiis the total temperature of injection,Tt∞is the total temperature of main flow,Mjis the Mach number of injection,r is the velocity ratio,λ is the mass flux ratio.P∞is the pressure of main flow,Pwis the wall static pressure.

Due to the complexity and difficulty of supersonic experiments,the numerical simulation method has been applied to investigations of supersonic film cooling.

Early research was mainly to demonstrate whether numerical simulations could be applied to the calculation of supersonic film cooling.O’Connor et al.118numerically studied the insulating effects of supersonic film cooling,with comparisons between experimental results and computational data showing that it is possible to use CFD methods for film cooling in a supersonic case(shown in Fig.19).In Fig.19,X is axial distance downstream from injection point,Tawis the local adiabatic wall temperature,Topis primary total temperature of primary flow.

In the application of CFD methods for supersonic film cooling,the choice of a turbulence model is very important for accuracy of calculation results.Therefore,some studies have applied different turbulence models to study supersonic film cooling.

Fig.17 Stanton number reduction over the surface.116

Fig.19 CFD and experimental data comparison.118

Aupoix et al.119carried out experimental and numerical research,with results indicating that a two-equation turbulence model is more suitable for supersonic film cooling when compared with experimental results.Yang et al.120studied the effects of coolant inlet conditions on supersonic film cooling numerically,and the effects of the coolant inlet geometry,coolant injection angle,and coolant flow turbulence on the heat transfer rate were also involved.Results showed that the k-ω turbulence model with dilatation-dissipation corrections gave more precise results.Peng and Jiang121used the SST k-ω turbulence model,RNG k-ε turbulence model,and SA turbulence model to calculate a supersonic film cooling case,and simulation results indicated that the SST k-ω turbulence model gave better results(shown in Fig.20).In Fig.20,H is the slot height,u is the velocity,y is the distance downstream from injection point,Macis the coolant Mach number,Ma∞is the mainstream Mach number,Ttcis the total temperature of coolant,Tt∞is the total temperature of mainstream.Martin et al.122used the large-eddy simulation(LES)method to study supersonic film cooling,with results showing that the LES method agreed well with experimental data.

Many studies have numerically investigated the effects of various factors on supersonic film cooling.Nair et al.123numerically investigated hypersonic film cooling on a bluff body,and their results demonstrated the importance of numerical studies in the design of hypersonic spacecraft.Wang et al.124numerically investigated the effects of the blowing ratio and hole shapes on supersonic film cooling,with results showing that the blowing ratio is an important factor,the film cooling effectiveness increases as the blowing ratio increases,and the configuration of cooling channels has effects on supersonic film cooling.Tang et al.125numerically analyzed the application of supersonic film cooling on an infrared window,and compared the film coverage lengths under different injection slot heights and pressure ratios under tangential jet and large-angle injection;the flow field was also investigated under different injection angles.Chen et al.126numerically investigated the film cooling effect in a supersonic turbine cascade channel.The effects of gas film hole angles and blow ratios on film cooling effectiveness were reported.

Generally,for supersonic film cooling,the inlet static pressure of the mainstream is equal to that of the cooling stream.The film cooling effectiveness under a supersonic case is usually defined as

where Tr∞is the mainstream recovery temperature,Tawis the protected wall temperature,and Trcis the cooling stream recovery temperature.

Without the impingement of the shock wave on the cooling stream boundary layer,the adiabatic film cooling effectiveness can be as a function of the non-dimensional distance downstream from the slot and the mass flux ratio of the cooling stream to the mainstream per unit area as follows:

where x is the distance downstream from the slot,s is the slot width,M is the mass flux ratio,A,B and C are the coefficients in the empirical correlation.The exponents are listed in Table 2,Where Mcis the coolant Mach number,M∞is the mainstream Mach number.

For film cooling,there are so many influencing factors,so it is difficult to get a general fitting equation to predict the film cooling effectiveness from these experimental results.

Juhany et al.117studied the effects of the coolant inlet Mach number and temperature on supersonic film cooling,with results indicating that increasing the coolant inlet Mach number is beneficial for improving film cooling effectiveness.The results showed that there is a better representation of the power law relationship between the film cooling effectiveness and the correlation parameter(shown in Fig.21,where Miis the Mach number of injection,M∞is the mainstreamMach number,Ttiis the total temperature of injection,Tt∞is the total temperature of mainstream,λ is the mass flux ratio,η is the cooling efficiency),i.e.,

Fig.20 Numerical results and experimental data comparison.121

Table 2 Exponents in published film cooling correlations with air as the coolant gas.127

Fig.21 Comparison between experimental results using the correlation parameter.117

Experiments by Bass et al.127investigated the effects of a group of parameters such as the coolant gas,the Mach number of the coolant,the slot height,the lip thickness,the total temperature of the mainstream,and the mass flux ratio of the coolant to the mainstream per unit area on supersonic film cooling.Results showed that the film cooling effectiveness for each gas can be collapsed to a single line on a log-log plot to a reasonable accuracy using the correlation parameteras follows:

Moreover,the results indicated that the mainstream turbulence level may be the most important reason that makes the correlations from different studies not be reconciled.

Peng and Jiang131investigated supersonic film cooling under different blowing ratios and different inlet heights of the coolant,and found the supersonic film cooling effectiveness can be sorted into the correlation as follows:

The correlation agrees well with experimental data obtained by Juhany et al.117(shown in Fig.22).Moreover,further analysis shows that the predicted value by this correlation will deviate with an increase of the mainstream turbulence intensity.

However,most of the previous studies focused on parameters such as the blowing ratio,Mach number,inlet pressure,gas type,inlet height,and so on.There are few studies focusing on the effects of the pressure gradient and turbulence intensity on supersonic film cooling.In a practical application,these factors inevitably exist.

Fig.22 Correction of supersonic film cooling.131

Peng and Jiang investigated the effects of free-stream acceleration132and turbulence level131on supersonic film cooling,with results indicating that increasing the free-stream acceleration improved the film cooling performance(shown in Fig.23),while increasing the free-stream turbulence reduced the adiabatic film cooling effectiveness;meanwhile,increasing the coolant inlet height and Mach number weakened the effect of the free-stream turbulence.

Martin et al.122studied supersonic film cooling with favorable or adverse pressure gradients conditions,with results showing that the film cooling effectiveness was significantly increased about 50%at a favorable pressure gradient,whereas an adverse pressure gradient would reduce the adiabatic film cooling effectiveness about 30%(shown in Fig.24).

Most of the above studies are fundamental research,which are mainly based on simplified models or structures.By now,there have been some application studies with actual structures.

Vijayakumar et al.133conducted research on a subscale model of a rocket engine nozzle to investigate supersonic film cooling by both experimental and computational methods(shown in Fig.25).Results showed that the heat transfer from the combustion gas to the wall was obviously reduced because of substantial cooling along the wall.

Fig.23 Effect of free-stream acceleration on supersonic film cooling.132

Fig.24 Supersonic film cooling under adverse and favorable pressure gradients.122

Fig.25 Schematic of a test facility.133

Experimental and numerical investigations based on a divergent section of a rocket nozzle were performed by Kumar et al.134to analyze the effect of the coolant injector configuration on film cooling.They studied two different injectors,one with shaped slots of a divergent angle and the other with fully divergent slots.Results showed that the film cooling effectiveness with the semi-divergent configuration was higher than that of the fully divergent slots configuration at all blowing ratios.

Gerdroodbary et al.135numerically investigated an active flow control conception which uses counter- flowing jets for the nose cone with an aerodisk.They found that a coolant jet would reduce the temperature and increase the heat transfer rate along the nose cone,and the cooling performance of helium was better than that of carbon dioxide at low pressure ratios.

Zhang et al.109numerically studied the hypersonic inlet in a scramjet engine with supersonic film cooling in the isolator based on a two-dimensional model.Results showed that coolant injection angles had little effect on the cooling performance,and a small injection angle could achieve both good cooling and aerodynamic performances.

Morris and Ruf136described a CFD analysis of supersonic film cooling based on SSFC experiments for liquid rocket nozzles.Comparing both 2D and 3D CFD simulation results with experimental data,it was shown that 3D simulation could predict the initial mixing of the coolant and mainstream in the adiabatic cooling region reasonably well,while the mixing in the developed region was generally predicted faster by CFD simulations.

3.2.Shock wave/cooling film interaction

Supersonic film cooling is different from subsonic film cooling.Firstly,gas under a supersonic condition is more compressible than that under a subsonic condition.Secondly,shock waves in supersonic flow fields will affect the film cooling boundary layer(shown in Fig.26),and may break film cooling and reduce the cooling effectiveness,which does not happen in subsonic cases.Therefore,the effect of shock waves on supersonic film cooling is an essential part of the research on supersonic film cooling.

Fig.26 Stream lines distributions in the shock wave interaction zone.121

There are two classes of shock wave/ film cooling interaction studies in the literature.One is focused on a shock wave’s effect on the heat transfer rate,and the other is focused on a shock wave’s effect on the adiabatic film cooling effectiveness.

There are some studies investigating the effects of a shock wave on heat transfer between a gas and a protected surface.Alzner and Zakkay137studied the effects of incipient shock waves injection on heat transfer and separation characteristics.Their results showed that reverse flow and separation of the boundary layer occurred due to a sharp unfavorable pressure gradient produced by the incident shock wave.It is also shown that coolant injection could reduce the peak heat transfer at the shock wave-impingement location.Kamath et al.138experimentally and numerically studied the impact of an incident oblique shock wave on supersonic film cooling.Numerical results agreed well with experimental data,and their results also indicated that the impinging shock wave enhanced heat transfer by increasing turbulence,and coolant mass flow rates five to ten times as high were needed to against shock wave induced heating.Ledford and Stollery139also analyzed the influence between shock wave and supersonic film cooling.However,they found that the cooling gas film had little effect on inhibiting shock wave heat-transfer.The difference in their results may be caused by the different shock wave intensities in their work.

There were some studies of interactions between shock wave and cooling flow on adiabatic walls.Basically,it is considered that the impingement of shock wave will reduce the supersonic film cooling effectiveness.George et al.114experimentally investigated the effects of shock wave on supersonic film cooling.Results indicated that film cooling deteriorated after a strong incident shock wave.Takita et al.140numerically investigated the impacts of combustion and shock wave on supersonic film cooling,with results indicating that combustion and shock wave had little effect on the flow fields between reactive and nonreactive coolants.Wang and Jiang141numerically analyzed a typical supersonic film cooling flow field and investigated the influences of the blowing ratio,slot height,and plate thickness on film cooling performance;their results showed that the cooling effectiveness decreased with the incidence of oblique shock waves.Juhany and Hunt142experimentally investigated a two-dimensional shock wave interaction with supersonic slot injection film cooling,which showed that the film cooling effectiveness decreased with the shock impingement.

As for the damage mechanism of shock wave on supersonic film cooling,Kanda et al.143,144considered the main reason as that a shock wave will increase the local pressure,thus reducing the Mach number in the coolant film boundary layer,and then deteriorating cooling performances.However,in the experimental studies by Kanda et al.,143,144only 6,7,and 8 degrees shock waves with the cooling gas of ammonia were investigated,and it did not investigate the effects of stronger shock waves and lighter-molecular weight coolants such as helium or hydrogen.

Peng and Jiang145numerically investigated shock waves effects on supersonic film cooling,in which the effects of different intensities of shock wave and coolant gas were involved.Results showed that the incidence of oblique shock waves would increase the local static pressure,so the local Mach number in the coolant boundary layer deduced,causing a reduction of the film cooling effectiveness.As for stronger shock waves or lighter gas coolants,shock wave also enhances the mixture between the mainstream and the cooling stream,as shown in Fig.27,resulting in decreasing the film cooling performance.In Fig.27,θ is the angle of shock wave generator.

Martin et al.146numerically studied supersonic film cooling with shock wave interaction using the large-eddy simulation method,and their results showed that the film cooling effectiveness decreased by 36%compared to that of the case with no shock wave within the potential-core region of the cooling stream,and the shock wave significantly increased the turbulence levels in the boundary layer,as shown in Fig.28,resulting in high temperature fluctuations occurring and more pronounced mixing happening because the hot main flow is transported toward the wall.In Fig.28,ρ∞is the mainstream density,u∞is the mainstream velocity,Tt∞is the mainstream total temperature,v′′is the Favre fluctuation of velocity,is the Favre fluctuation of total temperature.

Fig.27 Coolant helium mass-fraction distributions and stream lines near the wall.145

Fig.28 Nondimensionalized turbulent heat transfer.146

Most of the previous studies were focused on twodimensional supersonic film cooling models.However,supersonic film cooling with shock waves in three-dimensional flows occurs in practical applications.Peng et al.147studied the effects of various three-dimensional shock waves which were caused by three-dimensional shock wave generators,with results showing that a 30 mm shock wave generator for a 50 mm flow channel had the lowest film cooling effectiveness in the middle and downstream regions,mainly due to that the uneven pressure distribution by the uneven shock wave caused a z-direction secondary flow in the coolant boundary layer which would make the hot mainstream get involved in the cooling film and reduce the thickness of the cooling film layer(shown in Fig.29).

In practical applications,a shock wave will have damaging effects on supersonic film cooling.Therefore,it is important to find a way to restrain this destructive effect.

A slotted wall with a cavity,as shown in Fig.30,which aims to reduce the impact of a shock wave on the film cooling effectiveness,was proposed by Peng and Jiang,121and numerical results showed that the supersonic film cooling effectiveness was improved in the presence of the slotted wall.The reason is that the cooling stream flows into the cavity upstream from the slotted wall and flows out downstream,so more cooling gas will be bypassed to the surface downstream,resulting in weakening the effect of the shock wave on film cooling.

Fig.30 Physical model of a shock wave with a slotted wall.121

Fig.31 Impact of the coolant gas inlet height on supersonic film cooling.148

Moreover,Peng et al.148numerically analyzed the effect of the cooling flow inlet height while keeping the coolant mass flux rate constant for a given coolant gas on supersonic film cooling.Results indicated that for cases with a strong shock wave,reducing the coolant inlet height,which means increasing the Mach number,would improve supersonic film cooling effectiveness,shown in Fig.31,where s is the coolant stream inlet height.This is mainly due to that the coolant gas velocity increases when the coolant gas inlet height is reduced for a given coolant mass flow rate,which increases the coolant flow momentum,so the coolant gas more effectively resists the interference of the shock wave.

Above all,a considerable amount of work on supersonic film cooling has already been done.However,previous studies are mainly concerned with basic parameters such as flow,Mach number,temperature,etc.,but there are few studies investigating some important factors for practical applications,such as the pressure gradient and turbulence intensity.There is a lack of systematic evaluation of different coolants,especially for fuels as a coolant.There exist different points about the mechanism of shock wave influencing supersonic film cooling,which need more in-depth and systematic studies.Most of the previous studies use two-dimensional rearward-facing slot models, but there are few studies investigating three-dimensional supersonic gas film cooling,such as discrete holes or other three-dimensional gas film injection structures,and the three-dimensional effect of shock wave on film cooling.It has been proven that supersonic film cooling can be predicted rather well by large-eddy simulation(LES),for accurate computation of the interactions between the mainstream and coolant in supersonic film cooling,and more studies solving three-dimensional unsteady compressible Navier-Stokes equations by large-eddy simulation or direct numerical simulation(DNS)are needed.

Fig.29 Pressure,total temperature,and velocity distributions on the cross-section.147

4.Transpiration cooling

Transpiration cooling was firstly put forward for thermal protection of rocket engine throats in 1940s.The principle of transpiration cooling is schematically shown in Fig.32,149in which the cooling fluid flows through the porous wall into the mainstream,and forms a continuous thin film over the protected wall.In Fig,32,Tgis the mainstream temperature,Tcis the coolant temperature,ugis the mainstream velocity,ucis the coolant velocity.At the same time,the heat transfer from the mainstream to the porous wall is weakened by the film layer.Since the coolant consumption is small in transpiration cooling,it has a high cooling efficiency with a maximum cooling capacity of up to 6×107～1.4×109W/m2,150and thus is regarded as the most promising thermal protection technique for hypersonic propulsion systems.151,152

4.1.Heat transfer and flow mechanisms of transpiration cooling

Transpiration cooling research has mainly concentrated in the cooling rule and on the interaction mechanism between the mainstream and the coolant.The early days of research were spent mostly on transpiration cooling for porous plate structures.153,154

Fig.32 Schematic of transpiration cooling.149

Coolant flows through a porous material with intense heat convection in transpiration cooling.Therefore,the material in transpiration cooling is an important research aspect.The porous media in transpiration cooling is sintered metal particles or fibers,which generally has a high melting point.A matrix has many micro-pores with diameters of several micrometers.

Compared to a metal matrix,ceramic matrix composites(CMCs)are very suitable for transpiration cooling,which are lightweight and can suffer extreme high temperatures(exceeding 2500 K).155In an experiment by Otsu et al.,156a 750 kW arc-heater facility was used to simulate the reentry heating condition.A water-cooled porous ceramic leading edge was tested as illustrated in Fig.33.Experimental results showed that the heat transfer rate from the mainstream to the porous wall was significantly reduced with even a small amount of gas ejection.A model was developed by taking into consideration non-equilibrium thermochemical effects.Numerical results agreed well with experimental results.

Generally,gas coolants such as air,helium,and hydrogen have been used as injection fluid,but liquid coolants can improve the heat-absorbing capability because of evaporation.Transpiration cooling was experimentally investigated in a wind tunnel with coolants of air,nitrogen,argon,and helium.157The wind tunnel had a maximum velocity of 160 m/s at a gas temperature of 300°C.The friction and heat transfer were analyzed with detailed temperature and velocity information in the boundary layer.A dimensionless temperature correlation was also obtained to evaluate the transpiration cooling efficiency.Liu et al.158experimentally and numerically studied transpiration cooling in a nose cone of different fluids such as air,nitrogen,argon,carbon dioxide,and helium.The local transpiration cooling effectiveness was found to depend on the specific heat capacity.Helium performed better than other gases because of higher specific heat as shown in Fig.34.S is the distance from the leading edge along the nosecone surface,R is the radius of the nosecone,η is the cooling efficiency.

Fig.33 Test piece before and after 5100 s exposure.156

Fig.34 Cooling effectiveness for various coolants.158

Compared to gas coolants,liquid coolants usually have larger specific heat capacities.A lot of heat in the form of latent heat is absorbed during the phase change process.The evaporation of water provides additional cooling.Therefore,they can achieve higher cooling efficiency.The protective vapor layer covers a porous wall and blocks the heat flux from the mainstream.Luikov et al.159investigated steady two-phase cooling of a homogeneous porous plate.Laws of filtration movement with its phase conversions inside a porous wall were analyzed.Two-phase transpiration cooling static characteristics were obtained from a solution of the system of equations.Foreest et al.160experimentally investigated transpiration cooling with water coolant in a hypersonic wind tunnel.Results showed that water cooling was effective in a long-time test.The water mass flow could be reduced by using a lowporosity porous material.Potential materials such as C/C or C/C-SiC can withstand higher temperatures and have greater strengths.Wang et al.161experimentally investigated transpiration cooling with phase change applied to a porous wedgeshaped nose cone.Their results showed that the temperature significantly decreased with increasing the coolant injection ratio.The driving force for the coolant injection was minimum,and the cooling efficiency was high when the coolant passed through the porous media with a liquid state.Reimer et al.162tested the transpiration cooling performance of a leading edge made of a porous ceramic matrix composite(CMC)using liquid water as the coolant in an arc jet facility.Ice formed on the leading edge during the test.Coolant supply did not work as anticipated due to ice formation.Ma et al.163experimentally investigated transpiration cooling using liquid water as the coolant for a sintered steel porous plate.The mainstream temperature and coolant injection determined the phase change position.The cooling efficiency improved with increasing the coolant injection.More recently,Jiang et al.164developed a biomimetic self-pumping transpiration cooling system.Their experiments showed that the water coolant automatically flowed from the water tank to the hot surface with a height difference of 80 mm without any pump.

The local thermal equilibrium(LTE)model and the local thermal non-equilibrium(LTNE)model have been used to simulate the heat transfer in a porous media.The local thermal equilibrium model assumes that the solid matrix temperature is equal to the fluid temperature,which simplifies a simulation,but is not applicable for some problems.Recently,some studies have focused on the local thermal non-equilibrium model to more deeply describe the heat transfer in a porous media.165,166The internal particle-to- fluid heat transfer coefficient,hsf,describing the heat exchange between the fluid stream and the solid matrix of the porous medium,is a key parameter in the local thermal non-equilibrium model.Many researchers have obtained hsfcorrelations experimentally.The typical correlations proposed for packed beds(Wakao,167Dixon and Cresswell168)and sintered porous media(Kar and Dybbs169)are listed below:

where hsfis the heat exchange coefficient between the fluid stream and the solid matrix of the porous medium,αsfis the specific area.ε is the porosity,dpis the average diameter of porous media.

The particle diameters in porous walls for transpiration cooling are usually 1–30 μm.In the past twenty years,many studies have investigated gas flow in microscale tubes and channels where rarefaction effects are not negligible.170The Knudsen number,Kn,has been used as the criterion to classify the gas flow in micro-channels into four flow regimes:the continuum flow regime(Kn＜0.001),the slip flow regime(0.001＜Kn＜0.1),the transition flow regime(0.1＜Kn＜10),and the free molecular flow regime(Kn＞10).Xu et al.171experimentally investigated the internal convection heat transfer coefficients between particles and fluid in a micro porous media with particle diameters of 10–200 μm.They found that the measured internal convection heat transfer coefficients with particle diameters of 10 and 20 μm were much lower than previously published results.The internal heat transfer coefficients correlation for microporous media is listed below171:

where Redis the Reynolds number of the coolant.

In order to solve the equations,the boundary conditions of the fluid and solid particle matrix should be introduced.The heat transfer between the solid matrix and the coolant reservoir at the entrance and exit of the computational domain has been investigated in Refs.172,173.

The transpiration cooling efficiency is determined mainly on the properties of the coolant and the main flow,the blowing ratio,the geometry,and flow conditions.The convective heat transfer between the main flow and the hot wall is reduced due to transpiration cooling.The transpiration cooling efficiency can be evaluated by a dimensionless temperature relation174as

where F is the injection ratio of transpiration cooling,ReDis the Reynolds number of the mainstream.

4.2.Transpiration cooling under supersonic conditions

Existing supersonic transpiration cooling studies have mainly focused on verifying the thermal protection reliability of flow structures in specific main flow circumstances,such as scaled combustors and C/SiC composite porous nose cones.175,176

Soller et al.152experimentally investigated transpiration cooling for high-speed flight propulsion systems.A tested sample was subjected to a total temperature of Tt=600 K and a Mach number of 2.1.Four thermocouple positions are shown in Fig.35.The surface was effectively cooled due to the cold incoming boundary layer(Fig.36).

Friction characteristics will be changed on a transpiration cooled surface.Castiglone et al.177tested a skin friction drag measurement facility for potential scramjet fuel injection/wall cooling configurations in a Mach 2 air environment.The measured drag of this configuration was a full 46 percent lower than the flat plate drag.

Different from subsonic transpiration cooling,a shock always occurs in supersonic transpiration cooling.Nowak et al.178investigated transpiration cooling for a 12-inch diameter hemispherical model with helium as the coolant in a Mach 12.1 tunnel.Results showed that using 1/3 coolant mass flux was able to reduce the stagnation region heat flux to zero without shock/shock interference.

When water is used in supersonic transpiration cooling,the process will be much more complex,because of the phase change of water and the effects of shocks.Ding179experimentally studied phase change transpiration cooling of a sintered porous plate in a mainstream Mach number of Ma=2.19,T0=2400 K,and a heat flux of 1.4 MW/m2.Water was the transpiration coolant.Results showed that a superheated steam zone in the porous region would lead to a deterioration of the heat transfer.

Fig.35 DLR CMC sample installed in coolant plenum.152

Fig.36 Schlieren images of flow field on the transpiration cooling effectiveness.180

Huang et al.180investigated the flow and heat transfer of transpiration cooling through sintered porous flat plates in the supersonic mainstream.Experiments were conducted in a Mach 2.8 wind tunnel with porous materials of bronze and stainless steel.Surface temperature distributions were measured by an infrared camera.Shock wave structures were measured by a Schlieren imaging system.Results showed that the shock wave decreased the transpiration cooling performance,and with increasing the thermal conductivity,the temperatures of the protected surface was reduced(shown in Fig.37),where F is the injection ratio of transpiration cooling,η is the cooling efficiency.

Transpiration cooling has been widely applied in combustion chamber walls,cones,and injection struts.Hald et al.181proposed the design and functional aspects of a transpiration-cooled C/C cryogenic combustion chamber for a rocket propulsion system as shown in Fig.38.The characteristic and potential benefits of C/C were weight and cost reductions,which increased reliability and lifetime.

Sözen and Davis182developed a mathematical model to simulate transpiration cooling for the porous wall of a combustion chamber of liquid rocket engines with supercritical hydrogen as the coolant.The model used both compressible and incompressible flow assumptions with a local thermal equilibrium model.Zhu et al.183investigated transpiration cooling coupled with combustion in a H2∕O2liquid rocket thrust chamber with a transpiration-cooled injector plate.Results showed that the relatively small thermal conductivity of the porous media was also shown to decrease the plate surface temperature,but increase the thermal stress in the plate.

Fig.37 Influence of the porous matrix thermal conductivity.180

Fig.38 Microstructure of a C/C material.181

In a scramjet combustion chamber,the strut is used to inject fuel into the core region.The strut is in the supersonic flow at very high temperatures.In the references of Xiong et al.184and Huang et al.185,they reported numerical studies on the strut using transpiration cooling.The optimal strut wedge angle was analyzed.The transpiration cooling effectiveness of the strut firstly increases and then decreases as the wedge angle increases.In addition,the optimum wedge angle is near 30°.Recently,Huang et al.186tested a porous strut injector using transpiration cooling in a wind tunnel with Ma=2.5 and total temperature=1774 K.Methane gas was used as the coolant of transpiration cooling.Results showed that transpiration cooling was effective with only limited ablation on the top of the strut as shown in Figs.39 and 40.T1-T5are the thermal couples welded on the strut surface from the leading edge to the tail.Transpiration cooling is shown to be a solution for handling extreme aerodynamic heating of strut injectors.Both numerical and experimental results showed that an inclined porous strut could withstand a severe thermal environment with adequate transpiration cooling.185,187The highest temperature was about 475 K at the base of the leading edge(Fig.40).An inclined strut was beneficial for reducing aerodynamic heating compared to a vertical strut.

Fig.39 Results of a vertical strut.186

Fig.40 Results of an inclined strut.187

Fig.42 Textured injectors190

Jiang et al.188designed a porous strut with micro holes on the leading edge as shown in Fig.41.Most part of the porous strut was protected by transpiration cooling,while the leading edge was protected by film cooling to further decrease the temperature on the strut leading edge based on investigations by Xiong et al.184and Huang et al.185.Schlieren images showed that the combined cooling had little influence on the flow stability.Experimental results showed that the combined cooling more effectively utilized the limited coolant.The maximum temperature of the strut using the combined transpiration and film cooling method decreased,and the temperature distribution on the strut surface became more uniform compared to that using pure transpiration cooling.Huang et al.189numerically investigated combined transpiration and opposing jet cooling for porous struts with micro-slits in the leading edge.The combined transpiration and opposing jet cooling was more effective than pure transpiration cooling for cooling the strut.The maximum temperature of the strut significantly decreased.Different transpiration cooling injectors based on permeable C/C-SiC materials were tested in a ramjet/scramjet engine(Fig.42).190R1 is a certain shape of injector.Their results showed that the lowest surface temperature was measured for transpiration cooling injectors compared to conventional passive cooling injectors.

The program SHEFEX(sharp edge flight experiment)comprises of a series of platforms for reentry experiments.190,191A transpiration-cooled experiment using a porous and permeable C/C ceramic was conducted during flight(Fig.43).The temperature was significantly reduced by the coolant as shown in Fig.44.C3:transpiration-cooled;C7:uncooled.K29-K46 are the serial numbers of thermocouples.The temperature of the porous sample decreased about 87 K by transpiration cooling,while the temperature of the downstream wall decreased 75 K.Results showed that transpiration cooling has been successfully demonstrated during atmospheric re-entry.

Transpiration cooling has very high efficiency because of the intense heat transfer between the coolant and the porous matrix due to twisty micro channels and a large heat transfer area within the porous media.In the literature,the flow and heat transfer mechanisms of transpiration cooling have been theoretically and experimentally investigated,especially in subsonic main flow conditions.The conditions for scramjet engines and hypersonic aircraft are in supersonic flow,so the flow and heat transfer mechanisms of transpiration cooling need to be further investigated in supersonic flow conditions.

Fig.43 Side view of the transpiration-cooled sample.190

Fig. 44 Comparisons between transpiration-cooled and uncooled surface temperatures.190

Some studies have verified that transpiration cooling has thermal protection reliability in supersonic flow conditions.However,there have been few experimental studies on the influences of structural parameters and coolant properties,including the coolant blowing ratio,porous matrix thermal conductivity,and porous media structure.Furthermore,the interaction between the coolant and the supersonic main flow boundary layer has also not been well explored.

5.Conclusions and outlooks

Active cooling is the essential key for advanced hypersonic vehicle design.Regenerative cooling, film cooling,and transpiration cooling have different features and are suitable at different locations in hypersonic vehicles.This paper presents not only a basic background and principles for these three active cooling technologies,but also recent improvements in active cooling.The following conclusions can be drawn from the reviewed works:

(1)Endothermic hydrocarbon fuels are nearing applications in active regenerative cooling of hypersonic vehicles engines.The flow,heat transfer,and thermal cracking characteristics of hydrocarbon fuels under supercritical pressures have been investigated in active regenerative cooling conditions.Several correlations are available for heat transfer and thermal cracking of supercritical pressure flow calculations.However,the real fuel used in hypersonic vehicles contains thousands of components,which has very complex physical and chemical mechanisms.Continuing research is needed to further understand the heat-sink capability and endothermic properties of the real fuel.In addition,the mechanisms of heat transfer deterioration, flow instabilities,and interactions of cracking and heat transfer of hydrocarbon fuels at supercritical pressure should be paid more attentions to because they are practical problems in active regenerative cooling of hypersonic vehicles engines.

(2)Many studies have been done on supersonic film cooling mainly about basic parameters such as flow,Maher number,temperature,gas type,the influence of shock wave,etc.A systematic evaluation of different coolants is needed,especially when fuels are used as a coolant.Modeling of supersonic film cooling should be extended to three-dimensional,and then discrete holes or other three-dimensional gas film injection structures as well as the three-dimensional effect of shock waves on film cooling can be considered.Some numerical studies using the large-eddy simulation(LES)approach or DNS method have been reported.Results showed that supersonic film cooling could be predicted rather well by LES and DNS simulations.Further efforts to solve threedimensional unsteady compressible Navier-Stokes equations and compute the mixing process between the mainstream and the cooling stream in supersonic film cooling are needed.

(3)The flow and heat transfer mechanism of transpiration cooling has been theoretically and experimentally investigated,especially in subsonic main flow conditions.At supersonic flow conditions,a shock wave has significant effects on the blockage of the coolant and the heat transfer between the main flow and the surface.More experimental studies on the influences of structural parameters and coolant properties,including the coolant blowing ratio,porous matrix thermal conductivity,and porous media structure,are needed to further understand the flow and heat transfer mechanisms of supersonic transpiration cooling.

Acknowledgements

This project was co-supported by the National Natural Science Foundation of China(No.51536004)and the Science Fund for Creative Research Groups of NSFC(No.51621062).