Cooling of rocket plume using aqueous jets during launching

With an increase in rocket motor thrust, the thermal loads on the launch platform by the impingement exhaust jet are significantly increased, this poses serious safety risks to rocket launch. Therefore, a water cooling system should be designed to improve the thermal environment. In this study, the cooling effects of a water spray system with different injection velocities were analyzed through numerical simulation of high precision, and the afterburning effect of the exhaust gas was also considered to improve the calculation accuracy. The results showed that afterburning primarily occurred in the mixing layer, leading to a larger high-temperature region in the impingement plate. The water cooling system realized thermal protection for the launch platform, which was achieved by decreasing the temperature and velocity of impingement jet. With an increase in the aqueous jet velocity, a more significant cooling effect of the water spray system was obtained. However, the guiding performance of the deflector was decreased owing to the large amount of water vapor formed in the channel. It is suggested that the water spray system design should adopt an aqueous jet velocity of 20 m/s as a parameter after considering the cooling effect and guiding performance of the deflector.


Introduction
During rocket launching, the deflector plate under the Laval nozzle is easily ablated and destroyed because the extremely hot supersonic rocket exhaust gas directly impinges on the flame deflector. This leads to a low repeated utilization of the deflector, and the launching cost is increased significantly (Ciottoli et al., 2017;Zhou et al. 2020a). Meanwhile, a high-temperature reverse flow is produced by jet impingement, and then strong recirculation is formed in the deflector channel and near the rocket base, creating a harsh thermal environment of at launch platform (Sakaki et al., 2018). Excessively high temperature may cause malfunctioning of electronic control equipment, thereby threatening the launch success and normal operation of the heavy launch vehicle. To enhance the safety of the rocket launch, the spray cooling system is installed at the launch platform to control the thermal environment, as shown in Figure 1. The water spray system was originally designed to suppress noise caused by the rocket exhaust jet (Ignatius et al., 2015;Krothapalli et al., 2003). Recently, with the wide application of heavy launch vehicles in a space mission, the water spray system has become essential equipment for the rocket launch. It suppresses the reflection CONTACT Zhitan Zhou ztzhou93@nchu.edu.cn and superimposition of the rocket noise, and reduces the thermal shock of the impinging jet (Giordan et al., 1999;Yang & Sun, 2013). As an important facility of the launch pad, the rational arrangement and design of water spray systems are vital for improving the thermal environment. However, the existing literature lacks in analyzing the optimum design parameters of the spray cooling systems. Therefore, research on the cooling effect under different spray parameters should be conducted for an optimized design of water cooling systems to provide the most favorable thermal environment during rocket launching (Ruan et al., 2019).
Owing to the diversity of the water spray systems, the heat and noise reduction efficiencies depend on several design parameters, including spray angles, aqueous jet velocity, injection pressure (Ahmed et al., 2021). It is infeasible and difficult to improve the water spray system only through experimental trials, which is a long and significantly expensive procedure (Ghalandari et al., 2019;Salih et al., 2019). Meanwhile, because the interaction between the exhaust gas and water involves complex coupling multi-phases and afterburning reactions, the related parameters cannot be optimized through conventional theoretical analysis. Therefore, the flow fields of the rocket impinging jets under water injection have been studied by coupling between experiment and numerical simulation in several countries, and most of the researches have focused on the noise suppression effect caused by water spraying (Jiang et al., 2019;Panda & Mosher, 2013;Sankaran et al., 2012). For instance, Ignatius et al. (2008) carried out experiments to assess the reduction in noise levels under different water injection angles. The results showed that the relative water injection location was crucial for noise reduction during rocket lift-off. They observed that the water injection at an angle of 60°was more effective in noise suppression than that at 90°. Henderson (2010) reviewed the progress in jet noise reduction through water injection over a period of approximately five decades. The velocity of the main jet decreases owing to the momentum transfer between the water spray and exhaust gas, resulting in a reduction in jet noise. The important factors in noise reduction include the mass flow rate and injection pressure of the water spray system.
With an increase in the rocket thrust, the launch thermal environment becomes more rigorous under exhaust jet impingement. Improving the conventional water spray systems has attracted significant attention, and several researches have studied heat reduction by aqueous jet injection (Raoult et al., 2019;Sachdev et al., 2010). For instance, Vu et al. (2013) simulated the interaction between Space Launch System (SLS) vehicle exhaust and water jet from a spray cooling system. They concluded that the spray nozzles should be designed with a larger inclination angle to provide a better cooling effect on the flame deflector. Similarly, Lamini et al. (2018) investigated the heat transfer in spray cooling with a moving nozzle, and the cooling effects using moving and fixed nozzles were compared. Zhou et al. (2019) investigated the heat reduction of the launch platform under different spray hole locations using the Eulerian disperse phase (EDP) model.
During rocket launching, the interaction process of extremely hot exhaust gas having a high velocity with aqueous jet is very complex, which is accompanied by vaporization of liquid water and condensation of water vapor (Gai et al., 2019;Marchewicz et al., 2019). Moreover, momentum and energy exchange occurs in the gas and liquid phases when water is sprayed into the exhaust jet (Lu et al., 2020). Owing to all these factors, it is significantly difficult to study the cooling effect of water spray systems. Compared with studies on noise suppression by aqueous jet injection, research on heat reduction by water spraying is relatively rare. Existing research on the thermal environment of rocket launch platform under aqueous jets is mostly qualitative. Quantitative analysis of the cooling effect of water injection is insufficient. Meanwhile, owing to limitations of computational resources, conventional numerical simulations in multiphase flow ignore the afterburning reactions which have a significant effect on the thermal environment (Zhou et al., 2020b;Zhou et al., 2021).
In this study, a three-dimensional numerical model was developed to analyze the interaction between the rocket exhaust plume and aqueous jet, and the afterburning effect was simulated by the finite-rate chemical kinetics. The cooling effect of water spray under different injection velocities and its influence on the supersonic exhaust plume flow field are compared using a numerical method, which provides a theoretical reference for improving the water cooling system. The geometric and mesh models of the rocket exhaust jet impinging on the deflector under water spray are presented in Section 2. Section 3 introduces the numerical methods for simulating the gas-fluid two-phase flow field. In Section 4, the accuracy and validity of the numerical model are verified by comparing the numerical results with the experimental data. In Section 5, the afterburning effect on the thermal environment is discussed, and the cooling effects on the rocket and deflector under different aqueous jet velocities are compared. Finally, a summary of this study and conclusions are presented in Section 6.

Geometric model
As shown in Figure 2, a three-dimensional geometric model of the water spray into the rocket exhaust gas was established to simulate the interaction between impinging and aqueous jets. The flame deflector was installed under the rocket nozzle with an exhaust gas inlet area of 10 × 10 m 2 . The impinging angle between the exhaust jet and deflector surface was set as 30°to minimize the induced pressure and temperature of the launch vehicle (Hwayoung et al., 2017). The exit diameter (D e ) and length (L n ) of the Laval nozzle were 1.46 and 2.04 m, respectively. The diameters of the nozzle inlet (D i ) and throat (D t ) were 0.30 and 0.17 times of the exit diameter, D e . The water spray system was designed with two cylindrical nozzles having diameter and height of 0.24 and 0.18 m, respectively. The spray angle between the exhaust and aqueous jets was 60°. To compare the thermal environment of the flame deflector under different spray conditions, four temperature monitoring points were selected along the deflector surface centerline. Among these, monitoring point T 2 was located at the impinging point. Three-dimensional coordinates of four monitors are shown in Table 1, where the center of the Laval nozzle exit corresponds to the coordinate origin.

Mesh model
In comparison with an unstructured mesh, the structured mesh has the advantages of high precision, easy calculation, and good convergence (Blazek, 2005). Therefore, structured grids were used as the grid topology to ensure a high-resolution two-phase flow field, as shown in Figure 3. In addition to the mesh type, the grid density has a significant effect on the calculation accuracy. A high mesh density can improve the accuracy of numerical   results. However, an excessive quantity of grids requires substantial computational time and memory resources. Local grid refinement was adopted to provide a clear shock structure around the main jet and near the impinging surface. Further, five structured grids with different quantities were compared to determine a rational mesh model. Figure 4 shows the pressure coefficient (C p ) distribution along the deflector surface centerline, where, C p , is defined as the ratio of surface pressure to the ambient pressure. The calculated results varied with an increase in the grid density when the number of mesh cells was less than 12.21 million, whereas it was stabilized when the number of mesh cells increased to 12.21 million. Therefore, a three-dimensional mesh model of 12.21 million hexahedral cells was used in the simulation, which showed sufficient accuracy and reduced the computational time and memory requirement. Four types of boundary conditions were applied to simulate the interaction between the exhaust and aqueous jets. All solid walls were defined as adiabatic walls. The exhaust gas outlet of the flame deflector was defined as the pressure outlet, which had the same pressure as that of the ambient environment. The Laval nozzle inlet was defined as a pressure inlet with a total pressure of 18.66 MPa and temperature of 3800 K. The mole fractions of the rocket gas in the Laval nozzle inlet are listed in Table 2. The initial particle diameter of the water spray was 1.6 × 10 −5 m, and the aqueous jet velocities were varied between 10 and 40 m/s.

Numerical methods
In the numerical simulation, a hybrid RANS/LES turbulence model and the finite-rate chemical kinetics are used to establish the impinging model of supersonic exhaust gas on the flame deflector. The Eulerian disperse phase (EDP) model is applied to simulate the evaporation of the liquid water and condensation of the water vapor. These equations are briefly described in this section.

Governing equations
For a multi-species rocket gas, the conservation equations in three-dimensional Cartesian coordinates can be expressed as: where U is the conservative variable based on the density of the mass, momentum, and energy. F 1 , F 2 , F 3 are the flow flux vectors, G 1 , G 2 , G 3 are the viscous flux vectors. These are given as: where Y i is the mass fraction of species i, and D is the diffusivity constant, u, v, and w are the velocity components in the x, y, and z directions, ρ, p, e, τ are the fluid density, pressure, total energy, stress.

Turbulence model
A hybrid RANS/LES method avoids the Reynolds number restrictions typical of traditional LES by blending to a RANS-type method where the local mesh is too coarse to support calculations in the LES method, which can overcome the shortcoming of the low precision of the RANS and high computational cost of the LES. The combined effects of Leonard-, Reynolds-and cross-stress terms are treated using a non-linear extension to the Boussinesq hypothesis, and the RANS/LES blending is achieved by damping the modeled stress tensor according to a given latency parameter, α.
where αu i u j M is the Reynolds-stress tensor calculated by the RANS method, the latency parameter, α, is determined by: in which LV LES and LV RANS are the norms for the effective viscosity of LES and RANS methods, which are calculated by the characteristic length-scale/velocity-scale product. k is the kinetic energy, is the turbulent dissipation rate, and the δ is a small parameter to overcome singularities in low Reynolds number regions as α approaches 1.

Reaction model
During rocket launching, the afterburning reaction of the exhaust gas cannot ignore which has a significant effect on the thermal environment. In this paper, a nine-species and ten-step chemical mechanism is employed to simulate the afterburning reactions of the exhaust gas and air. The kinetic parameters for the chemical reaction are listed in Table 3 (Frey & Tien, 1979;Tsang & Hampson, 1986;Varga et al., 2016).
where v ir and v ir are the stoichiometric coefficients of species i in reactant and product of chemical reaction r, and M i is the chemical symbol. The rate of production ω ir is given by: In which W i is the molecular weight. The forward reaction rate, K fr , is determined from: where A is the frequency factor, N T and N P are the exponents for the temperature and pressure, E A is the activation energy, and R 0 is the constant of universal gas. The rate of change of the product concentrations is given by K fr multiplied by the product of the reactant concentrations raised to that reactant exponent.  (7) Notes: Units: m, kmol, s, J.The number in parentheses is the exponent of 10 (for example, 5.17(8) = 5.17×10 8 ).

Gas-liquid two phases flow model
When the water cooling system starts up, a lot of evaporation of the liquid water can be seen near the rocket exhaust jet, and the condensation of the water vapor occurs near the deflector exit. The Eulerian disperse phase (EDP) method couples the particle dynamics with the fluid dynamics to simulate the heat and mass transfers of the aqueous and exhaust jet. The mass, momentum and energy equations of the gas-liquid two phases flow can be written as: where the subscript pi represents the particles of species i, the subscript f represents the fluid, Q is the heat transfer rate to a unit volume. The evaporation term,ṁ i , is given by: where the r is the average particle radius, N is the number density, the evaporation rate, r i dr i /dt, is solved by coupling between Hertz-Knudsen and Boiling equations. When the temperature is below 373.15 K, the evaporation rate is solved by the Hertz-Knudsen equation (Young, 1993): where a v is a correction factor, R is the gas constant of the water vapor, p sat is the saturation pressure. The boiling equation is used to calculate the evaporation rate when the temperature exceeds the boiling point as follows: where L V is the latent heat of evaporation and λ is the heat conductivity. The condensation of water vapor occurred as far away from the exhaust jet core, the condensation rate can be written by: In Equation (13), the first and second terms represent the condensation rate due to the formation of criticallysized nuclei and molecular condensation onto existing nuclei.

Model validation
The numerical simulation of water spray into the impinging jet during rocket launching involves two physical processes: an inclined jet impinging on a plate and the coupling of the gas and liquid phases. The numerical and experimental results were compared to verify the validity of the proposed numerical methods.

Inclined impinging jet flow
To verify the validity of the numerical methods for the simulation of the inclined impinging jet, the flow fields of the under expanded jet impinging on the ground plate were calculated and compared with the experimental results (Lamont & Hunt, 1980). The Laval nozzle had a throat and exit (d) diameter of 21.4 and 30 mm, respectively. The semi-angle of the nozzle conical exit section was 15°, and the Mach number of the nozzle exit was 2.2. The distance between the nozzle exit and impinging point on the plate (h), impinging angle (θ ), and the ratio of the nozzle exit pressure to the ambient pressure (NPR) were varied from 2d to 3d, 30°to 45°, and 1.2 to 2.0, respectively. All parameters for the four cases are listed in Table 4. Figure 5 shows the Mach shock cell of the experimental shadowgraphs and the numerical results. The impinging jet structures of the simulation were highly consistent with the experimental shadowgraphs under different nozzle conditions. Figure 6 shows the comparison between experiments and simulations results for the pressure distribution along the impinging plate midline. The s and r of the X-axis are the distances from the pressure tapping to the nozzle axis and exit radius, respectively. The dimensionless parameter, P s /P r , represents the surface pressure to the chamber pressure. It was observed that the qualitative trends and quantities of the pressure of the calculated results were in good agreement with the measured data, which proves the accuracy and validity of the numerical model.

Multiphase flow
A comparison between the simulation results and experimental data (Jiang et al., 2010;Li et al., 2015) was performed to verify the accuracy and reliability of the multiphase model. The side and bottom views of the injection water device are shown in Figure 7(a). The nozzle exit diameter was 76 mm, and the impingement angle between the water and jet flows was 60°. The total pressure and temperature of the rocket engine were 7 MPa and 3000 K, respectively. The mass flow rate and velocity of water injection were 3.6 kg/s and 16 m/s, respectively. Four temperature monitors were installed on the impingement plate. The distance from the first monitoring point to the center of the impingement plate was 0.2 m, and the distance between the monitoring points was 0.1 m. Figure 7(b) shows the flow field of the rocket jet flow with water spray. The shock cell structures from the simulation were compared with the experimental result, and good agreement was observed. The structure of the exhaust gas tail in the high-speed photography image was blurred because of the substantial amount of water vapor. Moreover, the temperatures of the four monitors in the numerical simulation were consistent with those in the experiment. The maximum error between the experimental and calculated results was less than 6%, which demonstrates the accuracy and reliability of the multiphase model (Table 5).

Effect of afterburning on the impingement jet
Owing to the entrainment effect, the incomplete combustion exhaust gas interacts with the air, which leads to secondary combustion in the mixing layer. Therefore, the afterburning effect cannot be neglected in the numerical simulation of the exhaust flow field. Figure 8 shows the impingement flow field with (reaction flow) and without afterburning reactions (frozen flow). As shown in Figure  8(a), the afterburning has an insignificant effect on the Mach number of the impingement flow. Three shock cells    can be observed before the exhaust jet impinges on the deflector. The first and second Mach cells showed stable and clear structures, such as jet boundary, jet core, and shock reflection. Owing to the exhaust gas impinging on the deflector, the jet core of the third shock cell was blurred, and its plume radius became larger. Figure  8(b) shows the temperature contours of the symmetry plane and deflector surface. Considering the afterburning effect, the area of the high-temperature region increased significantly, and the peak temperature of the reaction flow increased 7.55% compared with that in the frozen flow. The temperature contours of the symmetry plane show that the exothermic reactions between incomplete combustion gas and oxygen in the air occur in the mixing layer, resulting in an evident change in its temperature. The temperature iso-surfaces of 2200 and 2800 K are shown in Figure 8(c). Two hot zones on the deflector surface can be clearly observed, as well as the impingement jet dynamics, as it impacts the plate. The thermal shock on the deflector by the rocket exhaust gas was stronger in the reacting flow than that in non-reacting flow. For more precise numerical results, the afterburning effect cannot be ignored in the simulation.

Flow fields under different aqueous jet velocities
To investigate the cooling effect of the water spray system on the thermal environment, the impingement flow fields of water spray into the exhaust gas considering afterburning under eight different velocities were compared. The aqueous jet velocity represents the mass flow rate of water injection. The aqueous jet mass flow was normalized with respect to the mass flow of the rocket gas jet. The mass flow rate of the aqueous-gas jet (AMR) and water injection velocities for the eight cases are listed in Table 6, where Case 1 represents the exhaust jet flow without water spray. Figure 9 shows the Mach number contours of the symmetry plane under different water spray velocities. Because the pressure at the Laval nozzle exit was higher than the ambient pressure, the exhaust plume expanded initially until its pressure was balanced with the environmental pressure. Then, the flow became over-expanded and induced a compression wave, which was converged to form the shock reflection. It can be seen clearly that three shock cells were established before the exhaust jet impacted the deflector. A series of shock cell-like structures were produced on the deflector surface. The first and second shock cells were insensitive to the varying water injection velocity, however, the aqueous jet with high velocity can cause severe deformation in the third barrel shock cell deformation much more severe. For Cases 1-3, the structures of the shock wave were similar with and without water spray. Because the water injection velocity was smaller, significant evaporation of the liquid water occurred before the aqueous jets were injected into the exhaust gas. For Case 4, the interaction between the aqueous-gas jet occurred in the exhaust plume boundary layer. The impingement jet structure showed insignificant change in comparison with Case 1, except for the radius of the third shock cell being slightly reduced. For Cases 5-8, significant deformation and serious failure of the barrel shock occurred below the intersection point, particularly in Cases 7 and 8. Under a higher velocity aqueous jet impingement, the exhaust gas at the right side of the third Mach cell in Case 8 was less than that in Case 7. The deflection angle of the third Mach cell in Case 7 appeared greater than that in Case 8 but was the same in reality. Because the aqueous jets of high-momentum were injected into the core region of the impingement gas, the jet core of the third Mach cell was blurred and almost disappeared, and a significant decrease was observed in its radius, which may have an adverse effect on the impingement jet stability. It was concluded that the greater the impulse of the aqueous jet, the deeper the interaction point between the aqueous-gas jet, and the stronger the deformation of the rocket exhaust jet structure. In addition to influence on the Mach shock structure, an aqueous jet results in a change in the impingement jet velocity, as shown in Figure 10. Figure 10(a) presents the velocity of the exhaust jet distribution along the nozzle axis. When the distance to the nozzle exit was less than 5.75 m, which corresponds to the upper part of the jet flow (above the interaction point), the nozzle axial velocities of the exhaust gas with and without the water cooling system were equal. With an increase in the aqueous jet velocity, the reduction rate of the exhaust gas velocity below the interaction point was increased. Owing to the significant evaporation before the aqueous jet reached the exhaust gas, the nozzle axial velocity for Case 2 remained unchanged compared to Case 1. For Case 4, the intersection between the liquid water and exhaust gas was occurred at the plume boundary, leading to a slight downward trend in the nozzle axial velocity. For Cases 6 and 8, the jet velocity along the nozzle axis decreased sharply with a further increase in the aqueous jet velocity, which can reduce the impact loads on the deflector. When the distance to the nozzle exit was 11.2 m, the exhaust jet velocity in Case 8 was 64.57% lower than that in Case 1. Figure 10(b) shows the radial velocity of the exhaust jet at the second Mach cell tail (the intersection region between water and gas). With an increase in the aqueous jet velocity, the rocket gas velocities and jet diameters decreased gradually. Compared with Case 1, the peak velocity of the exhaust gas was reduced by up to 20.81% for the case of 40 m/s. The Mach number contours can only reflect the impingement jet structure, and the coupled characteristics of the aqueous-gas jet cannot be presented. Therefore, density contours under different water spray velocities were created to investigate the interaction between the exhaust gas and aqueous jet. As shown in Figure 11, with an increase in the water spray velocity, the aqueous jet can be easily injected into the exhaust plume. Meanwhile, the interaction effect between the exhaust gas and water injection becomes strong. For Cases 2 and 3, the liquid water cannot reach the exhaust gas of high temperature due to insufficient momentum. The water cooling system with low spray velocity could not remove the heat from the impingement jet and improve the thermal environment during rocket launching; on the contrary, the guiding performance of the flame deflector decreases, which is caused by the formation of large quantities of water vapor in the deflector channel. For Cases 4 and 5, one part of the liquid water evaporated quickly before being injected into the impingement jet, and the other interacted with the exhaust gas in the plume boundary. Therefore, the total energy of the rocket gas is reduced before the exhaust jet flow with water impinging on the deflector surface, resulting in a decrease in the thermal loads on the deflector. With a further increase in aqueous jet velocity, the intersection point of the gas-liquid flow moved into the impingement jet core. For Cases 6-8, a liquid film was produced on the deflector surface owing to the strong interaction effect between the aqueous-gas jet, which avoids the exhaust gas of high-temperature impact on the plate directly. Compared with the flow field without an aqueous jet, more mixture gas of the exhaust and water vapor was formed near the deflector exit after the activation of the water cooling system. It was unfavorable to guide the exhaust gas throughout the deflector channel smoothly without recirculation. Figure 12 shows the temperature contours of the symmetry plane under different aqueous jet velocities. The   peak temperature of the symmetry plane without water spray was 3192 K, where the impingement region was created. Further, the maximum temperature for Case 2 was decreased by 0.38% as compared with Case 1. Moreover, the temperature distribution along the deflector centerline under an aqueous jet velocity of 10 m/s was higher than that without water injection. It can be concluded that the water cooling system with low injection velocity failed to avoid damage to the deflector from high-temperature gas, and caused a negative effect on the thermal environment. The peak temperature for Case 3 was 2965 K, which was 7.66% lower than that of 'dry plume' (without water injection). The aqueous jet of 15 m/s showed a slight cooling effect on the thermal environment of the deflector. With a further increase in the water injection velocity, the temperature at the impingement point and deflector centerline decreased more than 600 K for Case 4, which shows a significant cooling effect. Because the evaporation of water absorbed heat, the thermal environment of the deflector channel was improved. Meanwhile, the interaction between aqueous-gas jet occurred in the mixing layer, which inhibited the afterburning reactions effectively. Subsequently, the thermal shock on the deflector surface by the rocket exhaust gas was decreased. It is noteworthy that the value and area of the high-temperature region of the impingement plate depend on the radius and length of the impingement jet core. For Cases 5-8, the aqueous jet of high-instantaneous impulse can widely reduce the radius of the jet core, leading to a better cooling effect on the deflector. Considering Cases 7 and 8, the temperature in the impingement region was significantly closer to the ambient temperature. However, the impingement jet structure was already twisted, and even destroyed by aqueous jet of high velocity, which decreases the stability of the rocket jet.
As expected, the thermal loads on the deflector surface decreased gradually with an increase in the aqueous jet velocity, as shown in Figure 13. For a water injection velocity of 10 m/s, the peak temperature in the deflector surface decreased by only 0.38% compared with that of the dry plume. However, the temperatures near the deflector exit for Case 2 are higher than those for Case 1, owing to the poor guiding performance of the deflector channel. For Case 4, an evident cooling effect was observed on the impingement surface by the water spray. The maximum temperature of the dry plume was dropped from 3192 to 2535 K, reducing by 20.58%, which satisfies the thermal protection design of the launch platform in practical aerospace engineering. For Case 6, the average temperature of the impingement region decreased by more than 60% than that of the dry plume due to the strong interaction between water and exhaust gas. When the aqueous jet velocity further increased to 40 m/s, a liquid film was formed on the deflector surface. The thickness of the liquid film on the deflector surface depends on the liquid flow rate. With an increase in the flow rate, smaller droplets with higher velocities will be produced (Estes & Mudawar, 1995;Zhen et al., 2013). Therefore, the temperature of the impingement region for Case 8 was almost equal to the ambient temperature. In summary, the interaction effect between the aqueous-gas jet becomes stronger and the liquid film on the deflector surface becomes thicker with an increase in the water injection velocity, resulting in a significant cooling effect on the deflector.
In the numerical simulation, four temperature monitoring points were defined on the deflector surface, and the temperature curves under different aqueous jet velocities with respect to the time are shown in Figure 14. The monitor temperatures of the 'dry plume' reached steadystate after 0.12 s, however, it took 0.25 s for the monitor temperatures of the 'wet plume' (with water injection) to stabilize due to the interference of the water vapor. The stable temperatures of Cases 1 and 2 were similar, which indicates a poor cooling effect on the deflector by the water spray system with low injection velocity. For the temperature of monitor T 1 near the deflector inlet, the stable temperature was similar to the ambient temperature in Cases 4, 6, and 8. It turns out that the water spray system can suppress the backdraft of the rocket gas at a high temperature to the deflector inlet when the aqueous jet velocity was greater than 20 m/s. For monitors T 2 , T 3 , and T 4 , the higher the water injection velocity, the faster and more significant was the decrease in the stable temperature.
It is widely accepted that an improvement in the thermal environment is vital for the launching success of the rocket. Meanwhile, the guiding performance of the deflector, which plays an important role in launching safety, should not be neglected. The water spray system can cause a cooling effect on the launch platform, but the large amounts of water vapor formed by aqueous jet evaporation are detrimental for guiding the exhaust gas into the air from the deflector channel. The air ejector coefficient of the deflector inlet, λ, is an important standard for measuring the guiding performance of the deflector, which can be calculated as  follows: where m in and m out are the total mass flow rate of the deflector inlet and exhaust gas at the nozzle exit, respectively.
The parameters for different aqueous jet velocities are listed in Table 7. The air ejector coefficient was reduced by more than half after injecting water owing to a significant amount of water vapor produced in the deflector channel. With an increase in the aqueous jet velocity, the air ejector coefficient decreased gradually. For the dry plume, the air ejector coefficient was 6.09, and the deflector can guide the exhaust gas of high temperature and velocity away from the channel smoothly without recirculation and backdraft inside it. For Cases 2-4, the air ejector coefficients varied between 2.59 and 2.96. The deflector exhibited good guiding performance when the aqueous jet velocity was less than 20 m/s. For Cases 5-8, the air ejector coefficients were less than 1.98, which indicates poor guiding performance of the deflector. The formation of water vapor causes obstruction and blocks the exhaust gas throughout the deflector channel because of the strong interaction between the exhaust gas and the water jet.
In summary, the maximum temperature of the deflector for an aqueous jet velocity of 20 m/s was 2535 K, which was reduced 20.58% lower than that of the dry plume. This satisfies the requirement of the cooling standard and, also saves the design cost of the high-pressure sprinkler nozzle. Meanwhile, the air ejector coefficient in Case 4 was 2.59, which was insufficient to significantly affect the guiding performance of the deflector. Therefore, it is suggested that the water spray system design should adopt an aqueous jet velocity of 20 m/s as a parameter after considering the cooling effect and guiding performance of the deflector.

Conclusion
In this study, the rocket impingement jet flow field under eight different water injection velocities while considering the afterburning effect was compared by numerical simulation and the main conclusions can be drawn as follows: (1) Afterburning reaction primarily occurred in the mixing layer of the exhaust plume, resulting in an increase in the peak temperature of the impingement flow by 7.55%. Compared with the frozen flow, the high-temperature region formed by the exhaust gas impingement became larger in the reaction flow.
(2) Water cooling system can decrease the temperature and velocity of the exhaust jet, thus reducing the thermal loads on the impingement plate and achieving effective thermal protection for the deflector.
(3) Aqueous jet velocity is an important factor that influences the cooling effect of the water spray system. On the one hand, the aqueous jet velocity affects the total amount of water injection; a large amount of liquid water evaporates in a unit of time, which removes the heat from the exhaust jet flow. On the other hand, a higher velocity of water injection can cause a larger instantaneous momentum when the liquid water reaches the exhaust gas. The impingement jet is sheared by a high-impulse aqueous jet, which can reduce the thermal shock on the deflector. (4) With an increase in the aqueous jet velocity, the cooling effect of the water injection becomes evident, whereas the guiding performance of the deflector decreased. The water injection velocity of 20 m/s corresponds to the mass flow rate of the aqueous-gas jet of 4.4, for this velocity, the water cooling system can significantly improve the thermal environment of the launch platform and causes a good guiding performance of the deflector.
In this study, the cooling effects of different aqueous jet velocities on rocket exhaust plumes were analyzed. In addition, there are some elements that affect the thermal environment of the rocket launch platform. For future research, it is recommended to study the cooling of rocket plumes using multi-plane water injection configurations.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
The fourth author want to acknowledge the financial support from the National Natural Science Foundation of China [grant number 12002144].