Zhi-tan Zhou,Chang-fang Zhao,Chen-yu Lu,Gui-gao Le

School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing,210094,China

Keywords: Four-engine rocket Afterburning Impinging flow field Different de flectors Numerical simulations

ABSTRACT This paper studies the four-engine liquid rocket flow field during the launching phase.Using threedimensional compressible Navier-Stokes equations and two-equation realizable k-epsilon turbulence model,an impact model is established and flow fields of plume impinging on the two different shapes of flame de flectors,including wedge-shaped flame de flector and cone-shaped flame de flector,are calculated.The finite-rate chemical kinetics is used to track chemical reactions.The simulation results show that afterburning mainly occurs in the mixed layer.And the region of peak pressure occurs directly under the rocket nozzle,which is the result of the direct impact of exhaust plume.Compared with the wedgeshaped flame de flector,the cone-shaped flame de flector has great performance on guiding exhaust gas.The wedge-shaped and cone-shaped flame de flectors guide the supersonic exhaust plume away from the impingement point with two directions and circumferential direction,respectively.The maximum pressure and temperature on the wedge-shaped flame de flector surface are 37.2%and 9.9%higher than those for the cone-shaped flame de flector.The results provide engineering guidance and theoretical signi ficance for design in flame de flector of the launch platforms.

1.Introduction

To explore the further deep space,many countries are developing new generation launch vehicles with more effective loads.Particularly,the heavy-lift capability launch vehicle is the focus of recent research in many space programs[1,2].To achieve a large carrying capacity,the propulsion systems usually use multiple engines working simultaneously to improve the launch power[3,4].The multi-engine rockets have certain advantages by comparing with the single-engine rocket,but the impingement flow field is more complex,which caused by the exhaust plume interaction[5].The jet flow impingement has been the vital factor for the launch safety.Since the rocket engines are close to the launch platform during launching phase,the exhaust jets of rocket engine not only disturb the attitude of rocket in the take-off,but also have a thermal impact on the rocket base and ground control system.Therefore,the jet flow characteristics of multi-engine rockets exhaust plume need to be studies carefully for the risk aversion and improvement of achievement ratio in launching[6-9].

During rocket launching,the exhaust gas impingement induces large aerothermodynamic and acoustic loads on the launch platform[10,11].To reduce the effect of thermal shock and dynamic of the rocket jet flow,flame de flectors have been installed under the rocket engine to guide the exhaust gas of high temperature and velocity away from the channel without recirculation.It is generally known that the shape of de flector surface is the main factor affecting the diversion performance of the flame de flector.The flame de flector structure should be designed to restrain the exhaust plume from backdraft inside the de flector and to protect the rocket from damage of discharged gas during launching[12].The poor ef ficiency of diversion can cause blockage of the de flector channel by the recirculation flow.The accumulation and reflection of the high temperature gas have a negative in fluence on the stability of the flame de flector and security of the launch process.Using the reasonable shape of the flame de flector can reduce the adverse effects caused by the recirculation or backdraft of rocket exhaust gas[13-15].For these reasons,studying the diversion ef ficiency of different shapes of flame de flector is important for the safety of launch.

With the rapid development of computational facilities and technology,numerical simulations have been utilized more widely in the aerospace science and technology.In addition,the signi ficant experimental cost savings can be realized.Extensive studies on shock characteristics of the launch vehicle exhaust gas have been conducted numerical simulations and launch tests in the past decades.Daniel and Vineet[16]obtained the structure of the ARES V exhaust jet flow and its impingement characteristics on the B-2 flame de flector by using a multi-element flow solver.The results showed that signi ficant reversed flows can be developed on the flame de flector surface due to the larger impingement angle and associated detached flame de flector shock wave.Sachdev et al.[17]investigated the temperature load on the flame de flector by numerical simulations.The ef ficiency and accuracy of the methodology was veri fied through its application in an actual sub-scale test facility.Tsutsumi et al.[18]developed a universal performance assessment and control system-large eddy simulation(UPACS-LES)computational code to study the effect of de flector shape on the plate and the tail shock waves.It showed that the magnitude of the plate shock and acoustic level around the vehicle were weakened by employing steeply inclined de flector plane.Jiang et al.[10]presented an overview on progresses and perspectives of the jet impingement research for rocket launching.A summary of the interactive mechanisms between impinging jets and the launch platform or the flame de flector system was provided.

The studies above have provided reference and help for the analysis of the engine exhaust impinging on the launch structures,and several dynamics mechanisms are studied separately or in a partially-coupled way.Still,there are many problems about the exhaust jet impingement on different flame de flectors remaining to be solved,especially when considering afterburning effect.This paper studies the in fluences of two shapes of flame de flector configurations which are designed for the four-engine liquid rockets.A comparison of the rocket motor exhaust jet impingement on the different de flectors can re flect the variation of flow field and provides reference for designs of the launch platforms.

2.Four-engine rocket model

2.1.Geometric model of the platform

The system of this study is a three-stage liquid rocket which utilizes kerosene/liquid oxygen(LOX)propellant as propulsion system for the first stage.Fig.1(a)and(b)show the structures of the four-engine rocket with the wedge-shaped and cone-shaped deflectors.Fig.1(c)displays the installation positions of four nozzles.The four Laval nozzles are identical in geometry.As shown in Fig.1(d),the Laval nozzle has an exit half-angle of 3°,a nozzle spacing ratio(Ds/De)of 1.82,and a nozzle expansion ratio(Dt/De)of 0.17.As shown in Fig.1(e),the structure of the two de flectors is identical except for the shapes of positive impulse area,which are the wedge and cone,respectively.The separation distance(Ls)between the nozzle exit and the de flector surface is 5d,whichdcorresponds to the nozzle exit diameter.The appropriate jet impingement angle shall minimize the induced thermal shock loading on the rocket.Therefore,an impingement angle(α1)of 30°is used in the de flector design[19].The exit radius of the cambered surface 1 and 2 are 2 and 1.5 times of the nozzle exit,respectively.More parameters of the de flectors are shown in the flame de flector pro files.

Fig.1.Computational fluid dynamics models.

2.2.Computational grids

Structured mesh with tensor product structure has better numerical ability than unstructured grids using a multi-block.Also structured mesh can improve the fidelity of the flow solutions and assure a good resolution of shock waves in the flow field,the computational mesh of this paper is shown in Fig.2.No-slip adiabatic temperature condition is applied for the solid walls of the rocket and de flectors.The inlet condition is set as the total temperature 3800 K and the total pressure 18.66 MPa.The species mole fractions of exhaust gas at inlet are given in Table 1.

Table 3 The parameters of freestream at 5,15,25,and 25 km.

Fig.2.Computational grid and boundary conditions.

Table 1 The composition and content of exhaust gas at the nozzle inlet.

3.Numerical method

3.1.Governing equations

The liquid rocket exhaust is considered as an ideal gas mixture with the continuum assumption.The numerical solution of the compressible,Reynolds-averaged Navier-Stokes(RANS)methods has been obtained by using second-order total variation diminishing(TVD)schemes with finite volume method[20].The simulations in this paper were performed using CFD++software.The multi-component conservation equation takes the following form

whereSiis the rate of creation by addition from the dispersed phase.The diffusion fluxJiis defined as

The governing equations for mass,momentum,and energy conservations for each species are given as follows:

whereUis the flow variables,F,G,Hare the flow flux vectors,andFv,Gv,Hvare the viscous flux vectors.

3.2.Turbulence model

The supersonic jet impingement on de flector was computed using the realizablek-?turbulence model,which has been used for solving the flow field near the wall[21].The transport equations for turbulence kinetic energy,kand its rate of dissipation,?in the realizablek-?model are given as

and

In Eqs.(7)and(8),Gkis the generation of turbulence kinetic energy due to the mean velocity gradients.The model constantsC1andC2are 1.44 and 1.9 respectively.

3.3.Reaction model

As the fuel burns,gases expand to fill the combustion chamber and create a high pressure.Meanwhile,the unstable components such as CO and H2are emitted.The fuel-rich exhaust gas from the nozzle exit mixes with the ambient atmosphere,and this may lead to afterburning reaction.To ensure the reliability and accuracy of the numerical result,the finite-rate chemical kinetics is used to track chemical reaction system.This method,which based on the Law of Mass Action[22],is applied to calculate the various steps of the chemical mechanism[23].

The general chemical reactionris given by

In Eq.(9),v’irand v’’irare the stoichiometric coef ficients of speciesiin reactant and product side of stepr,and the rate of production of speciesifrom the reaction steprcan be written as follows

whereKfrandKbrare the forward and backward rate constant for reactionrrespectively.The forward rate constant for each reaction stepris given by Arrhenius kinetics

Here,NTandNPare exponents of temperature in the rate constant of reactionr,the backward rate constantKbris computed from the equilibrium condition

The change in Gibbs free energyΔGfor reaction stepris given by

The exhaust gas in the afterburning reactions includes H2O,H2,O2,CO2,CO,and N2,with H,O,and OH as the free radicals of the intermediate products in combustion.Therefore,the 9-species and 14-step chemical mechanism is employed for H2/CO afterburning[24]as shown in Table 2.

Table 2Reaction mechanism of hydrogen and carbon monoxide.

4.Model validation

The Mach number contours on the symmetry plane at different flight altitudes are obtained by numerical method described above.The total pressure and temperature in the chamber are 18.66 MPa and 3800 K.The conditions of freestream at different altitudes are shown in Table 3.Various shock wave structures,including the barrel shock,plume induced shock,and plume boundary,can be observed in Fig.3.As the elevation gradually increases,the ambient pressure decreases,the Mach number increases and underexpanded plume becomes larger.Also the shock reflection gradually moves away from the nozzle.

Fig.3.Contours of Mach number of the liquid rocket exhaust plume at different altitudes.

Fig.4 shows the simulated and the measured heating rates at two calorimeters in the rocket base.The heat flux has two peaks with the maximum values at approximately 10 and 20 km.The simulated results are slightly different with the measured data,since governing equations of the model are discretized by using second-order TVD scheme rather than higher order method.In general,the heating rates show the similar trends.These comparisons suggest that our method can produce accuracy and reliable results for such systems.

Fig.4.Comparison of the heating rates between experiments and simulations.

To verify the performance of our model in solving the impact problems,the calculation of sonic jet impingement on the plate is carried out and is compared with the measured data from Alvi and Iyer[25].The under-expanded supersonic exhaust plume is based on the Laval nozzle with exit diameter(D)of 2.54 cm.The nozzle upstream of the throat was designed using a third order polynomial with a contraction ratio of approximately 5.Fig.5 shows the flow field structure of Ref.[25](left)and numerical result(right)with different nozzle pressure ratio(NPR)when the distance(h)between the ground plate and the nozzle exit is equal to 2D.The contours from numerical simulations are similar to the flow structure in the experiments.For the NPR is 3.7,the surface pressure coef ficient(Cp)distributions with the change of the radial location(r/D)ath/D=2 to 5 are shown in Fig.6.It is show from the case ofh/D=2 that the realizablek-?model may get better agreement with the experiment results than the SSTk-?model.A comparison between the results of calculations with the measured data veri fies the reliability and accuracy of the jet impinging model.

Fig.5.Flow field contours of different NPR.

Fig.6.Comparison of the Cp distributions on ground plate from measure data[25]and calculation results at different h/d radios.

5.Results and discussion

5.1.The exhaust plume flow field

Fig.7.Mach number(a),pressure(b)and temperature(c)contours of the exhaust plume impinging on the wedge-shaped de flector.

The Mach number,pressure,and temperature contours of the four-engine rockets exhaust plume impinging on the wedgeshaped and cone-shaped de flectors are shown in Figs.7 and 8.Two symmetry planes are cut off along the axis of nonadjacent nozzle respectively.Three shock cells are formed before the plume impacts the de flector surface.Under the combined effect of external air and high-unexpanded exhaust gas,a clear structure of the first shock cell can be observed near the rocket gas field.But the second shock cell-like structure is less clear due to the interaction of the four equal plumes.The plume radius increases gradually in the lower portions of the second shock cell.The third shock cell deforms after the engine exhaust plumes impact the de flector surface.A high temperature region is generated immediately on the de flector surface due to the impingement and accumulation of excessive high temperature gas.The core and developed region and boundary of plume are clearly visible downstream of flow field.Due to the afterburning reaction between exhaust gas and air,high temperature also occurs in the mixed layer and average slightly below accumulation region temperature.

Fig.8.Mach number(a),pressure(b)and temperature(c)contours of the exhaust plume impinging on the cone-shaped de flector.

Fig.9.Pressure contours and line charts of the de flector surface.

As shown by the calculated results,the third shock cell contains a Mach disk,a recirculation region with a wedge or conical shaped to form in front of the plate.Temperature in the accumulation region on the wedge-shaped de flector has increased signi ficantly compared with the cone-shaped de flector.However,due to the restriction of the sidewall of the cone-shaped de flector,part of exhaust gas exits the de flector channel through inlet rather than outlet.Improvements to the cone-shaped de flector design are useful for de flecting exhaust gas smoothly.As the spacing of the sidewalls increases,the cone-shaped de flector could prevent damage to the rocket due to the reverse exhaust plumes.

Fig.10.Temperature contours on the de flector surface(a)and distribution pro files along the X-axis(b).

5.2.The impingement surface flow field

Figs.9 and 10 show the pressure and temperature distribution on the wedge-shaped and cone-shaped de flector surface,respectively.As expected,the region of peak pressure appears under the rocket nozzle,which is the result of the direct impact of exhaust plume.However,since high velocity of the gas flow is unfavorable for the afterburning reaction,the maximum temperature areas are not formed at the impingement point.The temperature drops gradually from the center to the outlet of the flame de flector.Several cell-like shocks are formed along the plate due to the interaction of four plumes.

Fig.11.Planar static temperature contours of the exhaust gas impingement on wedge-shaped de flector.

As shown in Fig.9,the wedge-shaped de flector has a peak pressure of 471.4 kPa in the impingement point,well above the 343.5 kPa in the same position on the cone-shaped de flector.Fig.9(b)displays the pressure distributions along the Y-axis and the projection line which connecting the projection of the nonadjacent nozzle centers on the de flector surface.The pressure changes abruptly in the projection line andY-axis of the wedge surface.As the conical surface has bigger impact area and better flow capacity,the pressure in the projection line of the wedge surface is higher than those on the conical surface,with the biggest difference about 37.2%at the impingement point.

Fig.10 displays the temperature distributions on the wedgeshaped and cone-shaped de flector surface,where the maximum values are 3182 K and 2896 K,respectively.Meanwhile,a larger high-temperature region appears in the wedge-shaped de flector.Different diversion orientation of the flame de flectors is a prime cause of the difference in temperature distribution.The supersonic exhaust plume was diverted into outlet with two directions in the wedge-shaped de flector.The high temperature jet impingement on the de flector plate produces large thermal loads and possible ablation on the de flector.On the other hand,the cone-shaped de flector can de flect the exhaust gas towards the circumferential direction,which will cause a smaller thermal shock effect.Fig.10(b)displays the temperature distributions along theX-axis andY-axis of the de flector surface.The temperature distribution along theYaxis of the conical surface is smaller than those in the wedge surface.The high temperature region on the wedge surface is much higher and more focused than in the conical surface,which will more easily lead to a signi ficant ablation and damage in the wedgeshaped de flector.Instead,the wedge plate is underutilized.The conical plate has relatively uniformly distributed in temperature and higher utilization ratio with better anti-ablation performance.One of the weaknesses with the conical plate is that the higher temperature regions occur on both sides of theX-axis.The exhaust gas in the cone-shaped de flector is obstructed by the sidewalls and the obstruction enforces the heating effect at the higher temperature regions.The de flecting performance of the cone-shaped de flector could be improved by reforming the sidewalls structure and increasing the sidewalls spacing.

5.3.Planar static temperature contour

Figs.11 and 12 show the planar static temperature contours for the rocket motor exhaust gas impinging on wedge-shaped and cone-shaped de flectors at Z/d=3,4,and 5 in axial plume direction,where Z/d=0 corresponds to the nozzle exit.For the supersonic jet impinging on the wedge-shaped de flector,the in fluence of the plume interaction and exhaust gas circulation are weak since the relatively stable individual shock unit can be observed at Z/d=3 and 4.The planar static temperature contour at Z/d=5 is blurred and a circular high temperature region is occurred in the core,which mainly caused by the interaction between exhaust and reverse flow.The exhaust gas inlet of the wedge-shaped de flector has the same temperature as atmosphere except for jet flow region,and not affected by the reverse flow.As shown in Fig.12,a part of gas flow is discharged from the exhaust gas inlet due to the resistance in sidewalls.The temperature in edge region of planar,as well as the central region,is much higher than ambient temperature.The temperature in the edge at Z/d=3,which is closest to the exhaust gas inlet,may reach up to 1000 K.Increasing the distance between the sidewalls of the cone-shaped de flector could be helpful to prevent the damage of the rocket afterbody from high temperature reverse flow.

Fig.12.Planar static temperature contours of the exhaust gas impingement on cone-shaped de flector.

6.Conclusion

Numerical simulations have been performed to investigate the exhaust gas impinging on the wedge-shaped and cone-shaped de flectors.By comparative analysis between the four-engine rockets impinging jet on different de flector,the following conclusions can be made:

(1)The peak pressure on the de flector surface appears at the intersection of the nozzle axis and the de flector plate,and the temperature drops gradually from the center to the outlet of the de flector.

(2)The wedge-shaped and cone-shaped de flectors have different diversion directions.The maximum pressure and temperature in the wedge-shaped de flector are,respectively,37.2%and 9.9%higher than those in the cone-shaped flame de flector.

(3)Compared to the wedge-shaped de flector,the cone-shaped de flector could achieve better performance for de flecting with sufficient distance of the sidewalls.

Declaration of competing interest

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