A survey on numerical simulations of drag and heat reduction mechanism in supersonic/hypersonic flows

Xiwn SUN , Wei HUANG ,*, Min OU , Ruirui ZHANG , Shiin LI

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

b National Innovation Institute of Defense Technology, Chinese Academy of Military Sciences, Beijing 100071, China

KEYWORDS Aerospike;Drag and heat reduction;Energy deposition;Forward-facing cavity;Opposing jet

Abstract Along with the survey on experimental investigations drawing attention to the drag and heat reduction mechanism, the authors simultaneously focus on the recent advances of numerical simulations on the schemes applied to supersonic/hypersonic vehicles. The CFD study has evolved as an irreplaceable method in scheme evaluation and aircraft optimization.Similar to our previous experimental survey,the advances in drag and heat reduction schemes are reviewed by similar kinds of mechanism in this article, namely the forward-facing cavity, the opposing jet, the aerospike, the energy deposition and their combinational conf igurations.This review article puts an emphatic eye on the flow conditions, numerical methods, novel schemes and analytical conclusions given in the simulations. Further, the multi-objective design optimization concept has also been illustrated due to the observable advantages of using CFD over experimental method, especially those performances conducted in drag reduction and thermal protection practice,and this would possess reference value in the design of aircraft system.

1. Introduction

Drag and heat flux reduction mechanism applied to supersonic/hypersonic vehicles has been an ever-increasing focus worldwide for the purpose of flow control and aerodynamic conf iguration protection.1,2In our previous survey,3the differences of active and passive protection schemes are distinguished firstly, and the research progress of dominant techniques by experimental method has been introduced detailedly in sequence, including the forward-facing cavity,an opposing jet issued at the stagnation point, an aerospike ahead of the blunt nose,concentrated energy deposition along the stagnation streamline and their combinational concepts.Readers are recommended to inquire Ref.3since research information by respective mechanism in partial literature is categorized by list format for the convenience in assessing the numerical results.

Due to the rapid progress of numerical algorithm and computing power, the practical cost of CFD method has been affordable for small-scale research teams, especially with the appearance of commercial software such as ANSYS FLUENT, FASTRAN, XFLOW, etc. Firstly, it is worth noting that most experimental results would be simulated numerically for mutual verif ication by scholars, and usually results would show high consistency.Apart from such primary reliability of CFD method, scholars have simulated the flowfields of a number of novel schemes (especially for combinational concepts) with any data in flowfield recorded clearly,and revealed the complicated flow mechanism and heat transfer characteristic without wind tunnel test because of the difficulty in realizing the operating conditions and physical conf igurations in experiment. Further, the drag and heat reduction mechanism might be regarded as a process during the design of the aircraft, so that conducting optimization should be the core likewise. This process calls for the accumulation of massive test data in order to evaluate scheme and establish surrogate relationship, where automation might be possible for CFD method4but wind tunnel ceases to be feasible except from some extremely simple studies on performance parameters like jet operating conditions5and spike geometric dimensions.6Therefore, numerical simulation has been and will continue to be an irreplaceable method in the investigation of drag and heat reduction mechanism.

In the current study, the research advances of numerical simulation will be reviewed in terms of the same grouping method mentioned in the first paragraph as Ref.3. We put an emphatic eye on the flow conditions, numerical method,proposed novel schemes and analytical conclusions given in the literature. Whereafter, as the observable advantages using CFD over experimental method, the multi-objective design optimization concept has also been introduced, especially those instances conducted in drag reduction and thermal protection practice, and this would show great reference value in the design of the aircraft. In the following discussion, we recommend Ref.3to the readers for basic principle of each mechanism and detailed information of relative experiments.Likewise,table or chart is provided to summarize information at the end of each section for readers’ convenience.

2. Forward-facing cavity

Forward-facing cavity is utilized as a thermal protection method while extra drag force will also been induced. The blunt missile model with forward-facing cavity in hypersonic flow tested by Saravanan et al.7has been a classical case for numerical validation.The authors themselves conducted a simulation on the steady-state nose-tip flows with the cavity diameters being 6 mm and 12 mm using unstructured grids and eff icient Finite Difference Method (FDM) in Ref.7. Interestingly, the non-dimensional heat flux by CFD method showed high consistency with the measurement data, while the force and moment coefficients deviated from the test results distinctively. Further, Lu et al.8-11conducted deep numerical researches on this model as one of the basics for combinational concepts. The authors employed k-ε turbulent model to solve the steady flowfield,and pointed out that the heat flux distribution of the outside surface decreased at a longer cavity. Lu et al. indicated that the aerodynamic heating inside the cavity could be neglected,and also caught the‘cool’ring region near the cavity edge8,11previously observed by Yuceil and Dolling.12Such cool region has also been revealed by Engblom et al.13both numerically and experimentally on a blunt body with lip rounded as reported in Ref.3.

It should be noticed that the flowfield around a blunt nose with forward-facing cavity is always unsteady in the strict sense due to‘Hartmann whistle’effect14,while such numerical simulation is seldom reported in the open literature. Engblom et al.13,15observed the modest sensitivity of the amplif ication parameter to small changes in lip radius in an artif icially disturbed freestream with peak-to-peak amplitude of ±0.02P∞(P∞denotes the freestream static pressure).Steady assumption is acceptable for only scheme evaluation,but revealing complicated flow mechanism induced by cavity calls for detailed records of time-dependent variables to calculate the heat flux fluctuation and other unsteady aerodynamic parameters. The unsteady simulation is essential when conf iguration changes.After the experimental investigations of the delaying ablation effect induced by cavity with rounding lip, Silton and Goldstein16conducted a numerical simulation of the unsteady flowfield using FLUENT. The authors used the laminar assumption rather than employing k-ε turbulent model as the result of better ability in assuming onset ablation and saving computation time, and also the flowfield could not be judged as transition. An enlightening conclusion17was proposed that rounding the cavity lip and optimizing the geometric dimensions might contribute to uniform ablation of the outside surface.

The changeable physical parameters of traditional cylindrical cavity are limited, hence optimization is often focused on the diameter and depth of the cavity and the lip radius. However,Huang et al.18substituted the cavity by the one with trailing edge (see Fig. 1, in which the variables D, L and R denote the respective spike length while α and θ represent the angle values), and revealed the most benef icial conf iguration for the heat flux reduction by parametric study. Another conf iguration was proposed by Yadav and Guven19in which the traditional cavity was replaced by a ellipsoid one.The mechanism of stagnation point heat reduction for such a cavity is the formation of a pair of vortices inside the cavity,and the presence of recirculating fluid ensures very little flow entering the cavity(see Fig. 2) in the hypersonic freestream. Spalart-Allmaras (SA) turbulent model was employed in their numerical simulation, and the thermal protection improved when the ratio of long to short axis increased just like the traditional conf iguration. Yadav and Guven20deepened the cavity and simulated the reacting flow in Mach number 10.1 freestream. Even though the overall ability of cooling was presented, the detrimental peak value of heat flux near the edge inside the cavity was 3.5 times that of the original blunt surface, which would prevent this novel scheme from practical application.

Fig. 1 Forward-facing cavity with trailing edge.18

Fig. 2 Sketch of streamlines for ellipsoid cavities.17

Apart from the numerical work above, Seiler et al.21and Bazyma et al.22attested their respective experimental investigation by a simple CFD process, as mentioned in Ref.3.

Finally, it is worth mentioning that the two-equation k-ε and Shear Stress Transport (SST)k-ω turbulent models are commonly-used in flowsimulation in aerodynamic conf iguration design. We further compared their usability in forwardfacing cavity flows, and undoubtedly the k-ε model is more reliable (Ref.23). Since the flow is attached on the surface,the advantage of SST k-ω model in solving rotating vortex fails to show. Information of forward-facing cavity in partial literature is summarized in Table 1.

3. Counterflowing jet

As a promising method in both drag and heat reduction,Huang24reported the recent advances of counterflowing jet in detail along with its combinations. This technique belongs to interaction between transverse injection and mainstream,25,26and the obvious drawback in the experiment is the complex injection device. However, only an inflow boundary condition needs to be simply provided in the simulation,so that a large amount of research results by CFD method as well as novel ideas are generated every year.

The surface heat flux distributions in the classical experiment employing nitrogen as the counterflowing coolant gas conducted by Hayashi et al.5,27has been frequently employed as the verif ication case for numerical simulation by scholars28,29, in whom the authors themselves are included. During their research, only Pressure Ratio (PR) larger than 0.2 were studied for the purpose of steady flow since unstable gas injection provided opposite effects in thermal protection experiment. The jet PR is defined as

Herein, P0jand P0∞are total pressures of the jet and freestream respectively. The axisymmetric assumption and SST k-ω turbulent model were used, and nitrogen jet was replaced by compression air because of their similar molecular weight.The density contours, as well as the positions of Mach disk and reattached shock wave, were consistent with the experimental results.However,even though the St distributions were somewhat subnormal, they presented similar peak value positions with the test data. Rong et al.30,31lucubrated this model in supersonic flow and kept nitrogen as the jet component.Stanton number, denoted as St, is defined as

Herein, qwis the surface heat flux, Tawis the adiabatic wall temperature, Twis the wall temperature, ρ∞, u∞, T∞and Ma∞are the freestream density, velocity, temperature and Mach number, respectively, Pr is the Prandtl number, cp∞is the specific heat, and γ is the ratio of specific heats. The grids near the potential position of shock wave were refined artif i-cially for accurate capturing. An effective parameter RPA=(P0j/P0∞)(Aj/Abase)32,33was proposed to represent the intensity of opposing jet and analyze its impact on flowfield,and herein the subscripts j and base denote jet and forward-facing base.To be specific,similar RPAinduced the same shock wave position,drag force coefficient and heat transfer according to simulation results. Lu and Liu34also simulated the threedimensional flowfield under different angles of attack (AoA),and indicated that the existing misalignment between the injection and freestream would considerably impair its effect on thermal protection. Apart from the researches above, Wang et al.35and Tian et al.36studied this sphere with coolant gas in supersonic flow.The flowfield of Wang’s research35included the injection nozzle region and excluded the impact generated from the difference between air and nitrogen injection by idealgas theory correction.

Table 1 Information of forward-facing cavity in partial literature.

With regard to numerical method, it is worth noting that unlike other scholars, Lu and Rong employed k-ε turbulent model to solve the flow, and they also acquired satisfactory results. We also studied the impact of turbulent model in axisymmetric flows(see Fig.6(c)and(d)in Ref.23),and turned to SST k-ω turbulent model in ANSYS FLUENT. However,Huang et al.37commented the similar ability in surface pressure prediction but considered the SST k-ω model to be more suitable with axisymmetric assumption.Further,we also questioned the rationality of axisymmetric assumption,and readers are advised to compare the results in the ‘Numerical Approach’section in Refs.23,38.Since FLUENT is widely used in this field, another key issue that deserves mentioning is the inconformity of defining St between the software and Eq. (2).To be specific, the temperature difference in FLUENT is Twall-Tref, and the St distribution from simulation calls for correction.

Apart from the varying jet PRs of the sphere in Mach number 4 freestream mentioned above, performance parametric studies are widely reported in the open literature. Benjamin et al.39investigated the drag and heat-transfer reduction effect caused by supersonic opposing jet at the freestream of Mach number 6.5 and altitude of 30 km. The diameters of jet orifice and the Mach numbers of injection varied in wide ranges,which bring about the highest drag reduction ratio of 55%and heat transferring inversely from 550 K isothermal surface to the hypersonic freestream. The authors also attempted to reveal the drag reduction mechanism by analyzing the skinfriction drag decrease as a result of upstream injection.Josyula et al.40conducted a comprehensive research on the drag reduction performance parameters of counter flowing injection. The forehead conf igurations were set as hemispherical cylinder and ogive, and the freestream Mach numbers were 5.84, 4 and 3 with jet issuing from orifice at PR=1.4 and 2.6. Threedimensional flowfields were simulated and S-A turbulent model was introduced. Results showed that the opposing jet would perform better in drag reduction for blunt forehead especially under high Mach number (Ma∞＞4), since relatively higher viscous resistance might retain for sharp-nosed bodies.

Normally a higher PR induces a more steady flowfield and increasing attention has been focused on the inner mechanism of transitional threshold. As remarked in Ref.3, Finley41theoretically pointed out that the transition occurs at the total pressure ratio at which the location of the jet terminal shock coincides with that of the first intersection of barrel shocks in a jet cell. This theory was validated by Fujita et al.42using the axisymmetric Navier-Stokes equations to compute a hemispherical nose with a sonic opposing jet in a freestream of Mach number 2.5. For a higher PR at 1.633, the flow turned to show steadiness with long-penetration mode. The transitional phenomenon was also investigated by He et al.43, and the authors commented that an increasing jet flow rate leads to higher reactive resistance and lower wave drag, so that an optimal match of jet area and PR might be essential. As we consider, the unsteady-to-steady transition is a key question in revealing the internal mechanism of opposing jet, and the unclear long/short penetration mode makes a difference in its efficiency as concluded by Daso et al.44,45. The advantage of the counter flowing jet in the drag reduction in supersonic flows was proved by Deng et al.46by means of comparing with the flowfield properties induced by the aerospike, and its jet oscillation mechanisms in the long and short penetration modes were explored numerically.47Recently,the pulsed counterflowing jet was employed by Zhang et al.48,49to reduce the drag and heat flux around the blunt body in the supersonic flow, and a typical periodical and hysteresis phenomenon was observed. This scheme is proved to be benef icial in the heat flux reduction, but not in drag reduction.

In order to uncover the mechanism of opposing jet by parametric method, Tamada et al.50,51analyzed the numerical results of the spherical and blunt ogive bodies in both supersonic and hypersonic freestreams in detail.The authors considered the Static Pressure Ratio (SPR) of jet and freestream(SPR=pj/pstag,∞) rather than the total one as an appropriate parameter to predict the flowfield. The parameter lgSPR was plotted against the shock stand-off distance, and logarithmic correlation showed the approximately linear relationship.Further, the dimensionless shock stand-off distance was drawn with the momentum ratio, and their power-function relation was easily discovered.These parameters were also successfully applied to the explanation why blunt ogive could reach steady thermal protection status under a relatively smaller PR in Mach number 8 freestream. We regard the data processing and analyzing method as an instructive example,while the reliability of simulating the flow with opposing jet should be included in the numerical verif ication process instead of a simple blunt case.

Fig. 3 Shapes of jet orifice.52

Even though traditional circular orifice is easy to be drilled in practice and discretized by grid system,novel shapes of orifice were put forward by Li et al.52(see Fig. 3). Undoubtedly,three-dimensional simulation is inevitable since asymmetric effect was introduced by such geometric conf igurations. After comprehensive comparison,the square shape showed best efficiency in peak heat flux and drag force decrease among all the projects. The authors kept the injection areas unchanged for different orifices because the same issuing area represents identical mass flow rate consumed under given jet condition for comparability.

Despite the fact that the mechanism induced by single jet has not been thoroughly recognized, Gerdroodbary et al.53embarked on the novel micro-jets scheme (see Fig. 4) numerically in hypersonic freestream. Given the same effective area,injections ejecting from several orifices showed better drag reduction and cooling efficiency than those from the typical single one. The authors illustrated that each orifice could provide much weaker jet in the new concept,which would lead to less penetration but more coolant attachment to the vehicle surface. Further, Li et al.54combined the porous opposing jet with the variable blunt hypersonic vehicle, and the porous jet design is proved to be useful in improving the overall performance of the blunt hypersonic vehicle.The number,spacing and radius of injection orifices have the most optimal combination for the porous opposing jet injection for drag and heat flux reduction.

Lastly, information of counterflowing jet in partial literature is summarized in Table 2.

4. Aerospike

Among the concepts of reducing drag force by pushing away the attached shock wave, the aerospike is the simplest and may be the primary form of counterflowing jet and energy deposition. However, due to the ablation of spike tip along with the reattachment flow hitting the surface, this scheme can only be considered as a drag reduction concept. As mentioned in Ref.3, Ahmed and Qin55has conducted a detailed survey of aerospike and provided readers with experimental or numerical freestream conditions, the spike conf iguration and relative aerodynamic characteristics in table format. The same as Ref.3, we focus on the numerical studies which were not reviewed by them in this section.

Fig. 4 Schematic representation of flowfield features around blunt cone with array of micro jets.53

Ahmed and Qin56simulated the three-dimensional steady and unsteady flowfields in hypersonic freestream induced by long and short spikes respectively to discuss the rationality of axisymmetric assumption.He suggested that except the separation zone, the assumption is reasonable if there exists no AoA and the flowfield is steady-state. For unsteady flowfield by long spike,the contours showed extreme asymmetry in each axial cross section.Peng et al.57simulated the projectile in freestreams with AoA, and pointed out that the drag-reduction spike has no influence on the lift and pitch moment while the drag decrease rate keeps almost unchanged at hypersonic flows.

Except for the above investigation, the typical pointed or cylindrical spiked bodies are rarely studied in present research,which are usually replaced by diversif ied forehead conf igurations for flow control.58Massive numerical achievements have also been reported by Huang.24Detailed information of grid layout, governing equations and boundary condition set were illustrated by Mehta,59and mounting a flat disk at the spike forehead would not only improve the anti-drag effect but also relieve the aerodynamic heating of the spike head.60Rajarajan et al.61also concluded that the spike with disk would contribute to higher drag reduction. Tu and Jin62simulated the flowfield disturbed by a spike with disk cap, and attested the efficiency of drag reduction at only small AoA.

Despite the advantage of implementing simpleness over other drag reduction scheme, the severe aerodynamic heating on the surface generated by reattached flow has been realized by a few scholars. Obviously, both the length of the spike and the diameter of the aerodisk ahead have a slight impact on the static temperature distribution.63Yadav et al.64processed the aerospike research in reacting hypersonic flows,and suggested a spike with two hemispherical knobs located at the head and middle respectively (see Fig. 5, in which the variables l1, l2, r1and r2denote the respective spike length or sphere radius). This would not only induce higher drag reduction rate but also mitigate the heating on the blunt body surface. Elsamanoudy et al.65created a complex spike conf iguration, mounting a reattachment ring to eliminate the direct impingement of the shear layer upon the shoulder of the nose and enlarging the recirculation zone at the cost of ring tip ablation(see Fig.6).As a result,the pressure and heat flux distributions on body surface dropped considerably, and a proper ring length seemed deserved to be optimized.However,the uncompleted solution to the ablation on spike tip must be reserved to combinational concept with opposing jet.

Another obvious drawback,just like the counterflowing jet,is the rapid descending of drag reduction efficiency in freestream with AoA. Geng and Yan66proposed the selfaligning concept applied to spiked blunt cone (see Fig. 7),and several steady-state flowfields were simulated with different AoAs. The aerospike was still effective in drag reduction even under high AoA. Another similar concept is the selfaligning aerodisk mounted before the blunt nose (see Fig. 8),and Schnepf et al. conducted complex numerical investigations67,68on this model together with experiments69in supersonic freestream. A hybrid unstructured grids were chosen to discretize the surface and the boundary layer region, and the flow solver DLR TAU-code was coupled with the flight equations to study the dynamic characteristics of the blunt nose.Even under the 20° AoA, a 6.5% drag reduction rate was still attained.It is not surprising that the phenomenon of misalignment, namely hysteresis, which was observed in experiment,also occurred in this numerical result. We suggest that it isnecessary to simulate the whole flowfield including the rolling bearing and stabilizer in the cases above since they are exposed to severe aerodynamic heating in freestream. Apart from the self-aligning concept, Han and Jiang70proposed a bayonet shaped plate mounted at the side of spike (see Fig. 9) to improve the aerodynamic characteristics,and this plate helped to form a circulation zone and shear layer at windward side,and weaken the penetration at leeward counterpart.

Table 2 Information of counterflowing jet in partial literature.

Fig. 5 A generic blunt body with double spike.64

Fig. 6 3D view of reattachment ring.65

Likewise, information of aerospike in partial literature is summarized in Table 3.

Fig. 7 Sketch of self-aligning spike concept.66

Fig. 8 Model nose with self-aligning spike.67

Fig. 9 A spike with bayonet plate.70

5. Energy deposition

Additional energy source put in front of the vehicle would induce inevitable ablation, so that energy deposition should also be only considered as a drag reduction concept assessed by the efficiency η defined as

Herein, U∞, ΔD, f and E are the freestream velocity, drag reduction value, energy frequency and single pulse energy respectively. As mentioned in Ref.3, Knight has reviewed the research progress of numerical investigations in Ref.71, and only unreported advances are included in the following discussion.

Due to the difficulty in simulating the unsteady high-energy flow,simulation attempts are obviously less than WT tests.To simplify, Euler rather than Navier-Stokes equations are usually solved to predict the flowfield with energy source in the open literature. As predicted by Sakai et al.72, neglecting the impact of viscosity in numerical investigation is reasonable when only force coefficients are taken into consideration with the energy calculation excluded.The author converted the real non-simulable deposited energy to an additional heat source by Eqs. (1)-(3) in Ref.73, and focused on the impact of different shapes of truncated bodies on the drag reduction efficiency(see Fig.10,in which the variables s,φt,φ and φt/φ denote the respective length or ratio). Different conf igurations of blunt body are rarely reported in present numerical work.As a result of the small vortex pair at head nose to sharpen the geometry,the increasingly blunt conf iguration might realize higher drag decrease rate. Also, the authors came to the fact that higher frequency of heat source would induce better drag reduction effect and the flowfield tended to show steadiness.

Table 3 Information of aerospike in partial literature.

Fig. 10 Truncated blunt bodies used in Ref.73.

In addition to the research above,the parameters of energy deposition are more commonly investigated to draw qualitative conclusions, among which the advantages of repetitive energy resource over single pulse is the most eye-catching topic. Hong et al.74and Fang et al.75investigated the effect of single pulse on the shock stand-off distance. The value increased four times on the symmetric axis compared with the basic case,and this effect quite resembled a spike mounted on the nose. Continuous repetitive laser energy deposition undoubtedly resulted in better drag reduction potential, and there existed an optimized deploying position L/D=1.5.76Yu and Yan77studied a two-dimensional cylinder in hypersonic flow with additive laser energy, and simplif ied to a blast wave interaction to substitute the multi-disciplinary process including electron release, gas ionization, plasma formation and blast wave propagation. A single laser pulse hardly contributed to pressure decrease on the blunt nose surface while a 33% reduction of stagnation pressure was realized at a frequency of 100 k Hz, indicating that higher frequency was the key parameter to the wave drag reduction,since the vortex pair generated near the forehead is the cause of pressure minimum values (see Fig. 11). Also, the time-averaged surface pressure reduced relatively large with the deposition place longer than 4/3 radius.

Fig. 11 Vortex pair in numerical schematic images with energy deposition.77

The geometry of blunt body and intensity of additive energy are also drawn attention to. Azarova et al. conducted massive numerical and experimental investigations78in energy deposition in supersonic freestream. Microwave and laser gas heating located at L/D=1 was under consideration in Ref.79, and potential controllable drag technique could be attained by varying the dimension scale of heated raref ied channel (see Fig. 12, in which the variables Ma symbolizes the freestream Mach number while Δl, d and D denote the respective length value, and αρis a density ratio of the inflow and energetic values added). In their following study,80,81an improved concept of combined filament was raised for uneven heat spot. They fulfilled the laser impulses of the energy equal to 13 mJ, 127 mJ and 258 mJ, and the results showed that the drag reduction efficiency improved at a thinner plasma flow.Even at 13 mJ, a remarkable anti-drag effect was observed with combined heated raref ied channels. Further, details of the interaction of laser and microwave discharges with supersonic flow past a hemisphere-cylinder and hemisphere-conecylinder were analyzed.82

As an interdisciplinary subject of laser and aerodynamics,another promising scheme of femtosecond-duration laser pulse has been proposed by Fu et al. to replace the traditional nanosecond one.83According to the simulation result, when the femtosecond laser energy is 0.06 mJ,the femtosecond laser plasma can reduce the drag by 98%. The authors explained that the pulse width of femtosecond laser was much lower,and the generated plasma would ref lect less incident laser and keep the anti-drag energy. Hence, multidisciplinary knowledge should be introduced to drag reduction and thermal protection practice. Information of energy deposition in partial literature is summarized in Table 4.

6. Combinational conf iguration

As suggested in Ref.3,the single schemes mentioned above are still worth studying,while the combinational schemes can usually receive better drag and heat efficiency.Most novel combinations are challenging to be implemented in wind tunnel, so that numerical simulation plays a signif ication role in promoting relative researches.In this section,we focus on the various kinds of proposed schemes and neglect detailed numerical method and results.

6.1. Combinational opposing jet and forward-facing cavity concept

Recent concepts for opposing jet and forward-facing cavity combinations with traditional cylindrical cavity from Lu et al.84-87and‘open’and acoustic cavity from Huang et al.28,29have been reviewed in Ref.23, and actually the cavity contributes to the acceleration and expansion of gas flow. Since there is no referable quantitative experimental result,the single opposing jet test could be employed as the verif ication case since they share many similar flow characteristics,such as flow reattachment and Mach disk.

Fig. 12 Sketch of heated raref ied channel.79

Table 4 Information of energy deposition in partial literature.

The authors Sun et al.23,38substituted the conventional cavity conf iguration by the thrust nozzle for the original idea of higher efficiency. However, after detailed parametric study of the effects of jet operating conditions, freestream angles of attack and physical dimensions, it is aff irmed that the shock stand-off distance would be lengthened and the surface pressure distribution might decrease, but no better drag reduction and thermal protection efficiency was attained compared with conventional cylindrical cavity. We commented that the opposing injection possessed higher energy without experiencing intensive shock inside the cavity,and regarded the necessity in multi-objective optimization approach to minimize both the drag force coefficient and heat transfer rate, and this attempt will be introduced later in this survey.

6.2. Combinational counterflowing jet and aerospike concept

The efficiency of counterflowing jet and aerospike will be enhanced mutually once cooperated. As mentioned in Section 4, the ablation on spike could only be resolved when combined with jet. In contrast, the opposing jet is capable of realizing self-aligning concept in combination to overcome its defect in flow with AoA.

Several schemes of injection have been put forward. Geng et al.66and Jiang et al.88tried to eject the coolant gas from the spike tip in axial and lateral directions respectively (see Fig. 1388,89), inducing higher drag reduction effect and greatly alleviating the aerodynamic heating on both spike tip and blunt shoulder according to the numerical results. Undoubtedly,the self-aligning spike and opposing jet concept also contributed to similar outcome as concluded by Geng et al.90Aimed at optimization for axial opposing jet and spike concept,Huang et al.91simulated a large number of cases to reveal the impact of spike shape and jet intensity on drag reduction,and Ou et al.92evaluated the influences of the nozzle diameter,the length-to-diameter ratio of the aerospike and the jet pressure ratio on the flowfield structures, the aerodynamic drag and heat properties numerically in a novel combinational opposing jet and spike concept based on a blunt cone.Another way of injection is from the spike root proposed by Gerdroodbary et al.93in hypersonic flow. The coolant jet reduced the temperature behind the aerodisk and the average heat load in the vicinity of the nose cone.

Naoki et al.94and Zheng95conducted numerical simulations after their respective experiment, but contradictory conclusions exist. For Naoki’s test conditions, relatively strong opposing jet and long extended nozzle reduced aerodynamic heating and drag simultaneously,while Zheng commented that an optimal pressure should be attained for an effective thermal protection at lower energy input.As considered,different conclusions may not necessarily contradict, since numerical code,simulation assumption and operating conditions may inevitably influence the results.Therefore,in order to exclude the discrepancy caused by numerical method, high-fidelity numerical codes, namely Large-Eddy Simulation (LES), Implicit Large-Eddy Simulation (ILES), Direct Numerical Simulation(DNS) and Detached Eddy Simulation (DES),96-98should be put into simulation of such complex flowfield in the future.

6.3.Combinational forward-facing cavity/counterflowing jet and energy deposition concept

Due to the difficulty in practice, energy deposition has now rarely been seen in combinational concept. Bazyma and Rashkovan99proposed the combinational forward-facing cavity and energy deposition concept in Mach number 3 freestream by two-dimensional CFD method (see Fig. 14, where the variables Ma∞symbolizes the freestream Mach number while s,x0,R,rcavand lcavdenote the respective length value).Several high-frequency pulses were added ahead the bow shock as the thermal spot.As mentioned before,both single concepts cause unsteady flowfield, while the combined scheme would eliminate the unsteadiness as aff irmed by the almost constant pressure evolution process inside the cavity with L/D ＞0.7.The authors believed that this concept was promising in controllability since no obvious pressure jump existed compared with single energy deposition scheme.

No typical combinational counterflowing jet and energy deposition concept shows up in open literature, but we prefer to classify the plasma injection for drag reduction into this category since the plasma jet possesses high energy. Shang et al.100-102set the hypersonic freestream as calorically perfect air, while for plasma injection, the non-equilibrium weakly ionized air changed the chemical composition and thermodynamic property of the injectant. The plasma injection would yield a range from 6.1% to 13.4% greater drag reduction due to the deployed energy.Also,the plasma injection reduced the amplitude of shock wave oscillation associated with the counterflowing jet and bow shock interaction.

Fig. 13 Typical combinational concepts of aerospike and counterflowing jet on nose tip in Refs.88,89.

Fig. 14 Schematic of forward-facing cavity with energy spot.99

6.4. Summary for combinational concept

As illustrated above, recent combinational concepts mainly center on counterflowing jet and its combinations,and geometric innovation has been the research hotspot for cavity and spike. We consider the importance of code reliability before numerical investigation and the necessity of introducing high-fidelity method for unsteady or non-equilibrium flow.The research information of this section is summarized in Fig. 15, where the main combinational concept textboxes are linked by lines from single scheme respectively, and several study-worth problems are also proposed around the outside circle for future investigators.

7.Design optimization theory applied to drag and heat reduction study

As illustrated in Section 1 and suggested by many scholars,optimization should be the core process of aircraft overall designs,103in which the drag and heat reduction scheme is included as well. Even though no optimization approach is introduced, numerical simulations for parametric analysis are conducted in many investigations,including the operating conditions and geometric scales.28,91,104In the strict sense, it is only the preclusion in optimization that performance parametric study helps to pick out the relatively inf luential factors.The orthogonal experimental and the Optimal Latin Hypercube design methods are frequently employed to improve the homogeneity and space-filling efficiency in test case selection.

Recent attempts from Ahmed et al.105,106and Seager and Agarwal et al.107-109for drag and heat reduction optimization have been reviewed in the section of introduction of Ref.104.It is worth noting that the Kriging model is commonly used to build a surrogate function,and NSGA-II multi-objective algorithm and genetic algorithm are recommended in optimization due to their efficiency and robustness.

The useful flowchart of whole optimization process proposed in Ref.110has been realized by Huang et al.110-114in supersonic internal flows. As commented in Section 6.1, we pushed forward the optimization process since the novel conf iguration failed to show superiority. The sampling points are obtained numerically by using the optimal Latin hypercube design method,and the multi-island genetic algorithm coupled with the Kriging surrogate model integrated in ISIGHT 5.5 was employed to establish the approximate model and solve the Pareto-optimal front. After optimization, higher efficiency of drag and heat reduction induced by the parabolic conf iguration could be obtained at a lower PR. Hence, it is advised to search an optimal working and geometric condition by multi-objective optimization method for each drag and heat reduction mechanism.115

8. Conclusions and outlook

Not only recent numerical simulation advances of drag and heat reduction concepts but also the design optimization theory are illustrated in this article. Finally, we provide several suggestions for future investigators who are interested in this field by CFD method.

(1) Verif ication of numerical method is the basic of followup study,including either comparison with experimental results or grid independent analysis, and the ability to predict heat flux tends to be essential in thermal protection research.

(2) The unsteady flow in forward-facing cavity has rarely been simulated, and obtaining the pressure fluctuation process contributes to revealing the heat reduction mechanism of both shallow and deep cavities.

Fig. 15 Research information of combinational concepts.

(3) Disagreements about the influence of various jet species on the efficiency of schemes related to opposing jet should be eliminated by future investigation,and numerical simulation might also shoulder the responsibility to uncover the steady-to-unsteady transition under varying PRs.

(4) Apart from novel geometric shape,aerospike is a simple and promising scheme to realize self-aligning, and further the dynamic characteristic researches coupling the Navier-Stokes equations with f ight equations are encouraged to display the whole dynamic process in the future.

(5) The disability of simulating high-energy flow has prevented the numerical investigation of energy deposition,and the solving heat increase and unsteady flow hitting on the vehicle surface at a small energy cost might be the main obstacle to its practice.

(6) The base flow is often ignored in simulation due to the theoretically inexistent effect from downstream flow to the upstream and the difficulty in controlling grid quality for blunt body,but the base drag contributes greatly to the whole resistance while hardly reported in open literature.

(7) Most scholars have aff irmed the advantage of combinational concept numerically,while high-fidelity numerical methods,namely LES,DNS and DES,are hoped to present more refined structures and reveal the intrinsic mechanism in such complex flows.

Acknowledgements

The authors would like to express their thanks for the support from the National Natural Science Foundation of China(Nos.11502291 & 11802340).