Preliminary study on heat flux measurement data of TT-0 flight test

Enwei LU, Linxun ZUO, Zheng GUO, Honggng ZENG,c, Wei ZHU,Feng QU

a National University of Defense Technology, Changsha 410073, China

b Shenyang Aircraft Design & Research Institute, Shenyang 110035, China

c Chinese Aeronautical Establishment, Beijing 100012, China

d School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

KEYWORDS Aerospace science;CFD;Drag reduction;Flight test;Heat reduction

Abstract With the explosive development of aerospace science, the design of the new generation airliner at higher speeds is attracting more attentions.To achieve this goal,it is necessary to achieve accurate prediction of the aerodynamic heating / force loads and successful reduction of drag and heat flux.As a remedy for the existing studies which are based upon the CFD and wind tunnel tests,this study presents a flight test for the drag and heat reduction spike technology.The principal goals of this flight test were to provide reference for verifying the accuracy of the prediction technology on ground and promote the development of the drag and heat reduction technology. By adopting the OS-X rocket, the TT-0 test vehicle designed by Shenyang Aircraft Design & Research Institute reached a maximum Mach number of 5.8 and a maximum altitude of 38 km.Hypersonic and supersonic pressure data by pressure scanning valves and heat fluxes by gauges at different locations were obtained successfully. Also, heat fluxes obtained by in-house CFD code are illustrated in comparison with the flight data.The results indicate that the numerical errors are large in most cases.More technologies,such as more CFD codes and more numerical procedures,should be adopted to conduct studies on this issue in the future.

1. Introduction

In the last decades, the design of the airliner which conducts cruising flight at around Mach number 0.85 has become mature.However,with the explosive development of the aerospace engineering and the rapid increasing frequency of global business communication,people’s desire for a quicker travel is stronger and stronger. For example, it should take up around 14 hours to travel from Beijing to New York if the existing widely used airliner is used. In comparison, if the airliner can conduct high-speed cruising flight, the traveling time consumed can be reduced significantly. As a consequence, it is attracting more and more attentions to study the design of the new generation airliner which is capable of carrying out high-speed cruising flight.1

Compared with traditional transonic airliner, the highspeed airliner encounters many severer aerodynamic loads,including the aerodynamic heating loads and the aerodynamic force loads.Therefore,it is in a high demand to accurately predict the aerodynamic heating / force loads and achieve the reduction of drag and heat at the same time.

In terms of the accurate prediction for the aerodynamics loads,the following three ways are usually adopted:Computational Fluid Dynamics (CFD),2-4wind tunnel test,5-7and flight test.8Among these three ways, the flight test can reveal the real flight condition by avoiding the limitation of the approximate mathematical physical model in CFD and the scale of the wind tunnel. Therefore, many flight tests for verification vehicles, such as X-43A,9X-51A,10Hifire series,11HYFLEX,12and X-37B,13have been conducted to help researchers study the aerodynamic loads at high speeds. In these tests, the wind tunnel experiment method is incapable of reproducing real flight environment in most cases. Also,the CFD technology cannot predict accurate pressure and heating distributions in cases where the flow is complex and the approximate mathematical physical model in CFD is limited. In comparison, the flight tests can easily help researchers dispel these defects.

In terms of the reduction of drag and heat,numerous techniques have been proposed. For example, spike,14-16energy deposition,17opposing jet,18-20and their combinations21-30are widely studied in recent years.Among them,the spike technology is becoming a hotspot because it is capable of reducing the heating load and the drag coefficient by splitting the bow shock into multiple weaker shock waves and inducing a large flow separation zone in the vicinity of the stagnation region.However,all studies on this issue are just conducted by numerical simulations or wind tunnel experiments, and few flight tests are conducted.Therefore,the conclusions drawn by these studies are with uncertainties.

To explore the efficiency of the spike technique and provide reference for verifying the accuracy of the prediction technology on ground, Shenyang Aircraft Design & Research Institute conducted a flight test called TT-0 by adopting the OS-X rocket on May 17th, 2018.31This manuscript will conduct a brief introduction to this flight test and illustrate the configuration,trajectory,pressure loads,and heating loads of the verification vehicle separately. Moreover, the comparison of the heat flux obtained by the CFD technology and the flight test is shown.

This manuscript is organized as follows. In Section 2, the governing equations and numerical procedures will be presented in brief. Section 3 will introduce the configuration of the model. Section 4 will illustrate the flight trajectory of the verification vehicles briefly.The pressure loads and the heating loads measured at different trajectory points will be presented in Section 5. Section 6 will show the comparison of the heat flux obtained by the CFD technology and the flight test.Conclusions will be drawn in Section 7.

2. Governing equations and numerical procedure

2.1. Governing equations

In this study, the three-dimensional steady Navier-Stokes equations are adopted to numerically solve the flow fields as follows:

where ρ indicates the density,uiis the ith component velocity,p indicates the static pressure, τijindicates the shear stress term,qjis the heat flux,E is the total energy,and H is the total enthalpy. More details can be found in Ref. 32.

2.2. Turbulence model

In this study,the SST RANS eddy-viscosity model is employed to simulate the effect of turbulence. As can be seen in Ref.32,the RANS equations are identical to the Navier-Stokes equations in Eqs. (1)-(3) except that μ is replaced by μ+μTand μ/Pr is replaced byμ/Pr+μT/PrT,and μTis the eddy viscosity which can be obtained by the turbulent kinetic energy k and the turbulent dissipation rate ω

In SST model,the terms k and ω are obtained with the following equations:

where Pkand Pωare the production terms,and μLdenotes the laminar viscosity.More details of these equations can be found in Ref. 32.

2.3. Numerical procedure

In this study,the Navier-Stokes equations illustrated above are discretized by the cell-centered finite volume approach based on the multi-block structured meshes.32For the inviscid flux,the Roe scheme which possesses a high resolution in capturing linear discontinuities is adopted in combination with the Muller’s entropy modification.33,34Moreover, the second-order Monotone Upstream-centered Schemes for Conservation Laws(MUSCL)reconstruction technology is used in combination with the minmod limiter.35For the viscous term, the second-order central difference scheme is employed. For time integration, the implicit Lower-Upper Symmetric Gauss-Seidel (LUSGS) technology with the Courant-Friedrichs-Le vy (CFL) number 5 is adopted.36Moreover, the grid strategy proposed in Ref. 37 is employed to guarantee the reliability of the analyses.

2.4. Code validation

In this section, the hypersonic viscous flow over the doubleellipsoid case, which was studied experimentally, to validate the code is adopted in this study. The model is the same as that in Ref.37The free stream conditions are Ma∞=7.8,Ptotal=5.7 MPa, T∞=66.59 K and Re=1.4×107. Fig. 1 illustrates the computational mesh for this case. As can be seen, the cells are clustered near the wall to make the cell Reynolds number equal to 8.

Figs. 2 and 3 compare the pressure and heating distributions obtained by our code and the experimental data.In them,the CFD code employed in this study shows its capacity of predicting the pressure loads and the heating loads in simulating hypersonic flows.

3. Introduction of verification vehicle

In this study,the verification vehicle which is assembled at the head of the OS-X0 rocket as depicted in Fig.4 is investigated.Also, a dimensioned drawing of this vehicle is displayed in Fig. 5 and the coordinate system is illustrated in Fig. 6.

This vehicle consists of a two-cone body,an aerospike,and a sphere at the head.In terms of the two-cone body,the length is 1357.4 mm.The first cone is with a base diameter of 300 mm and the second is with 850 mm.For the aerospike,the length is 600 mm and the diameter is 30 mm. In addition, the radius of the sphere at the head is 45 mm.

In terms of the construction of the vehicle,the 30CrMnSiA is adopted. After the vehicle is assembled, a profilometer is adopted to measure and guarantee the smoothness of the aeroshell. The primary aerothermal instrumentations are Gordon gauges and the pressure instrumentations are pressure scanning valves.

For the aerospike and the sphere at the head, the-22.5°line is the primary instrumented line. It contained thermocouples with the following distances between the axial position of these points and the vertex of the conical section:x=0.027 m,x=0.098 m, x=0.2 m, x=0.5 m, x=0.8 m, and x=1.1 m (Fig. 7). The other instrumented line, located in the 157.5°line,served as a secondary instrumented line.It also contained thermocouples at x=0.027 m, 0.098 m, 0.2 m,0.5 m, 0.8 m, and 1.1 m, to provide a symmetric check of the primary instrumented line. In addition,four different pressure transducers and thermocouples were installed at x=0.5 m as shown in Fig. 8 to provide an axisymmetric check.

Fig. 1 Computational grid for double-ellipsoid case.

Fig. 2 Pressure distribution along meridian.

4. Flight trajectory

In this case, the test vehicle used both the Global Positioning System (GPS) and the inertial navigation system IMU to permit cross-checks of the vehicle’s measured flight parameters by each instrument. Also, the IMU could provide the angles of attack and yaw by dealing with the flight path angles and azimuths measured by either the IMU or the GPS. Fig. 9 illustrates the altitude and velocity measured by the IMU in the climbing phase. As can be seen, the maximum altitude achieved by this flight test is around 38 km.Also,a peak Mach number of 5.8 was achieved with the altitude around 14.5 km during ascent.It should be reminded that the flight parameters obtained by the GPS are almost the same as those measured by the IMU. Therefore, only the parameters by the IMU are shown in this study.

Fig. 3 Heating distribution along meridian.

Fig. 4 Verification vehicle with OS-X0 rocket.

By differencing the vehicle’s instantaneous pitches and azimuths and the flight path pitches and azimuths measured by the IMU, the vehicle’s angles of attack and yaw during ascent between t=20 s and t=80 s are obtained as shown in Fig.10.As can be seen,the vehicle’s angles of attack and yaw saw oscillations during ascent. The largest absolute values of both the angles of attack and yaw approached 2°. It should be reminded that our private study shows that these angles of attack and yaw have little influence on the symmetry of the pressure and heating distributions in most cases.

5. Measured pressure and aerodynamic heating distribution

Fig. 5 Flight test vehicle drawing.

Fig. 6 Coordinate system (U∞ indicates freestream velocity vector).

Fig. 7 Locations of heat flux sensors.

In this study, the pressure results were obtained by adopting the pressure transducers as illustrated in Section 2. Fig. 11 displays the pressure measurements by different transducers at x=0.5 m. The trajectory shown in Section 3 indicates that the vehicle’s angles of attack and yaw are less than 3 degrees during ascent. Therefore, the pressure loads obtained by these four transducers at axisymmetric locations should be almost the same in theory. As can be seen in Fig. 11, all these four transducers obtain almost the same pressure loads along the ascent trajectory.It indicates that the angles of attack and yaw have little influence on the symmetry of the flow field.

Fig. 8 Distribution of pressure transducers and thermocouples at x=0.5 m.

Fig. 9 Measured trajectory of flight case during ascent.

Fig.10 Vehicle angle of attack and yaw along trajectory during ascent.

Fig. 11 Sample surface pressure measurement.

In terms of the heat transfer results, resolving the onedimensional inverse heat transfer problem was conducted to obtain the heat flux38. In addition, the obtained heat transfer rates were smoothed using a 25 point(0.03 s)moving average.Prior to the vehicle’s launch, the thermocouples were zeroshifted to make the heat flux equal to zero under the starting condition. According to the ground test, the heat generation within the payload has little influence on the thermal analysis.Therefore, all these excess powers were neglected.

Fig. 12 displays the heat fluxes measured at different locations along the-22.5°line and the 157.5°line in case the symbols‘I-IV’indicate different lines.As can be seen,the heat flux increases with the Mach number increasing before the Mach number approaches the maximum. After t=33.3 s, the heat flux decreases with the Mach number decreasing. However, it could be found that the heat flux at the surface of the vehicle is much lower at the later moments in cases that the Mach number is equal. It may be because the surface temperature at the later moments is higher and the air density is lower.On the other hand,the heat fluxes measured are nearly identical at most symmetric locations along the trajectory, besides the data at x=0.027 m and x=0.8 m. As can be seen in Fig. 5, the first gauging point at x=0.027 m is at the corner of the vehicle, where an unsteady recirculation zone exists.Because the flow structure of the recirculation zone is sensitive to the angles of attack and yaw, the heat fluxes measured at x=0.027 m are not symmetric along the trajectory. On the other hand, by comparing the data at x=0.5 m, x=0.8 m,and x=1.1 m, the following conclusion can be drawn: the trends of the heat fluxes’ distribution along the-22.5° line are different from those along the 157.5° line. In other words,along the-22.5°line,the fluxes at x=0.8 m are smaller than those at both x=0.5 m and x=1.1 m, while the fluxes at x=0.8 m are larger than those at both x=0.5 m and x=1.1 m along the 157.5°line.Therefore,the flow structures in the windward side along the trajectory should be different from those in the leeward side.Further studies should be conducted on this issue in the future.

Fig. 12 Heat fluxes measured at different gauging points along -22.5° line and 157.5° line.

It should be reminded that the gauge at x=0.027 m in the 157.5° line became invalid after t=36.6 s and the heat fluxes obtained are negative. However, this phenomenon has little influence on this flight test.

6.Comparison of heating distribution obtained by flight test and numerical simulations

As can be seen in Fig. 10, the vehicle’s angles of attack and yaw kept small during ascent and the largest ones were below 4°. Also, the measured data shown in Fig.12 indicate that the heat fluxes measured are nearly identical at the following locations: x=0.098 m, 0.2 m, 0.5 m, 1.1 m. Therefore, the comparison between the numerical simulations and the flight test at these locations could be objective by avoiding the uncertainty of the gauges.

Fig. 13 Computational mesh for verification vehicle.

Fig. 14 Grid independency test.

In order to conduct grid independency analysis, three different girds with the total number 1 million, 2 million(Fig. 13), and 4 million are adopted.

Fig. 14 shows the heating distributions at the head which are obtained in different grids. The origin of the horizontal ordinate is at the head of the aerospike as shown in Fig. 7.As can be seen,these three grids obtain almost the same distributions. Hence, the following study is conducted based on Grid2 which is with the total number 2 million.

Fig. 15 compares the heating distributions at different locations. It should be reminded that the wall temperature in Fig. 15(a) is measured by the thermocouples. As can be seen, the heat fluxes obtained by the CFD technology are much higher than the measured data in most cases.Also, the numerical errors as illustrated in Fig. 16 are large and the largest error is around 60%. It should be reminded that different RANS turbulence models and spatial reconstruction technologies are adopted and the conclusions obtained are similar. Further detailed studies will be conducted to explore the causes of the large numerical errors.

Fig.15 Average heat fluxes simulated and measured at different gauging points.

Fig. 16 Errors between the data measured and simulated at different gauging points.

7. Conclusions

In this paper, a flight test was conducted for the blunt vehicle with a drag and heat reduction spike. By adopting both the Global Positioning System (GPS) and the inertial navigation system IMU at the same time, the vehicle’s measured flight parameters are cross-checked to guarantee the accuracy of the measurement. By showing the measured pressure loads and heat fluxes along the flight trajectory at different locations,heat fluxes obtained by in-house CFD code are compared with the flight data.The results show a disappointing conclusion for CFD engineer. More technologies, such as more CFD codes and more numerical procedures, will be adopted to conduct studies on this issue in the future.

All in all, this study can provide reference for verifying the accuracy of the prediction technology on ground and promote the development of the drag and heat reduction technology for high-speed vehicles.

Declaration of Competing Interest

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

Acknowledgements

This study was co-supported by National Natural Science Foundation of China (Nos. 11902265 and 11972308), Natural Science Foundation of Shaanxi Province of China (No.2019JQ-376) and the Fundamental Research Funds for the Central Universities of China (Nos. G2018KY0304 and G2018KY0308).