Study on the Simulation Method of the Ground Test in the Arc-Heated Wind Tunnel

To analyze the effectiveness of the thermal assessment test, the simulation method of the ground test in the arc-heated wind tunnel is studied. Based on the solution of the thermochemical nonequilibrium Navier-Stokes equations, the flowfield around the spherical cylinder is simulated in the flight and ground test conditions, and the difference in the high enthalpy flowfield between the flight and ground test conditions is investigated. The flight parameters and ground test conditions are selected according to the criterion that the total enthalpy and the stagnation point heat flux of the fully catalytic cold wall (calibrated heat flux) are similar. The flowfield for different temperature boundaries and different catalytic walls is solved under the same free stream conditions, and the stagnation point heat flux and oxygen atom mass fraction are compared and analyzed. It is found that the heat flux on the fully catalytic wall for the radiation balance temperature boundary in the ground test is lower than that in the corresponding flight condition, but the difference is not obvious on the noncatalytic wall. In addition, the oxygen atom mass fraction after the shock wave in the ground test is higher than that in the corresponding flight condition. To make the stagnation point heat flux and oxygen atom mass fraction after the shock wave similar to those of the flight, the simulation method of the arc-heated wind tunnel test needs to be adjusted.

Aerothermodynamic correlations for high-speed flow

Heat flux and drag correlations are developed for high-speed flow over spherical geometries that are accurate for any Knudsen number ranging from continuum to free-molecular conditions. A stagnation point heat flux correlation is derived as a correction to the continuum (Fourier model) heat flux and also reproduces the correct heat flux in the free-molecular limit by use of a bridging function. In this manner, the correlation can be combined with existing continuum correlations based on computational fluid dynamics simulations, yet it can now be used accurately in the transitional and free-molecular regimes. The functional form of the stagnation point heat flux correlation is physics based, and was derived via the Burnett and super-Burnett equations in a recent article, Singh & Schwartzentruber (J. Fluid Mech., vol. 792, 2016, pp. 981–996). In addition, correlation parameters from the literature are used to construct simple expressions for the local heat flux around the sphere as well as the integrated drag coefficient. A large number of direct simulation Monte Carlo calculations are performed over a wide range of conditions. The computed heat flux and drag data are used to validate the correlations and also to fit the correlation parameters. Compared to existing continuum-based correlations, the new correlations will enable engineering analysis of flight conditions at higher altitudes and/or smaller geometry radii, useful for a variety of applications including blunt body planetary entry, sharp leading edges, low orbiting satellites, meteorites and space debris.

Heat flux correlation for high-speed flow in the transitional regime

An analytical correlation is developed for stagnation-point heat flux on spherical objects travelling at high velocity which is accurate for conditions ranging from the continuum to the free-molecular flow regime. Theoretical analysis of the Burnett and super-Burnett equations is performed using simplifications from shock-wave and boundary-layer theory to determine the relative contribution of higher-order heat flux terms compared with the Fourier heat flux (assumed in the Navier–Stokes equations). A rarefaction parameter ($W_{r}\equiv M_{\infty }^{2{\it\omega}}/Re_{\infty }$), based on the free-stream Mach number ($M_{\infty }$), the Reynolds number ($Re_{\infty }$) and the viscosity–temperature index (${\it\omega}$), is identified as a better correlating parameter than the Knudsen number in the transition regime. By studying both the Burnett and super-Burnett equations, a general form for the entire series of higher-order heat flux contributions is obtained. The resulting heat flux expression includes terms with dependence on gas properties, stagnation to wall-temperature ratio and a main dependence on powers of the rarefaction parameter $W_{r}$. The expression is applied as a correction to the Fourier heat flux and therefore can be combined with any continuum-based correlation of choice. In the free-molecular limit, a bridging function is used to ensure consistency with well-established free-molecular flow theory. The correlation is then fitted to direct simulation Monte Carlo (DSMC) solutions for stagnation-point heat flux in high-speed nitrogen flows. The correlation is shown to accurately capture the variation in heat flux predicted by the DSMC method in the transition flow regime, while limiting to both continuum and free-molecular values.