Speaker
Description
Space exploration has become a stronghold in aerospace engineering. Understanding the dynamic behind hypersonic flows is crucial for the design of thermal protection systems of space vehicles. The extremely high flight velocities of such bodies while entering in the atmosphere induce the formation of strong shock waves in front of them: in the downstream region, non equilibrium takes place due to chemical activity and vibrational excitation. One of the most interesting aerodynamic shape object of current efforts is the double-wedge or the double-cone. These shapes present two wall deflections that promote a complex shock structure, resulting in a complicated shock wave/boundary layer interaction. The attached shock generated near the leading edge interacts with the detached shock propagating in front of the second wall, inducing the boundary layer separation near the compression corner. By the years, these geometrical configurations got interest since they represent simplified models of more complex aerodynamics components (wings or fuselage) and their study is currently a major topic.
Given the chemical activity occuring in hypersonic flows, the problem is stiff: at high enthalpy regime, the assumption of perfect gas deteriorates due to molecular dissociation induced by the strong shock waves forming near the body. Also, most of the kinetic energy is converted into internal energy (translational, rotational, vibrational and electronic), leading to thermochemical non equilibrium. In this work, electronic contribution is neglected since the temperature does not exceed 9000 K, threshold value for ionization phenomena. In order to properly treat the non equilibrium, the multitemperature Park model (mT) is employed: it accounts for 5 species neutral air mixture and 17 chemical reactions; furthermore, a Boltzmann distribution governs the population of the vibrational levels. This approach is an affordable compromise between computational cost and accuracy. Nevertheless, when dealing with strong non equilibrium phenomena, the assumption of a Boltzmann distribution is not acceptable and one should reformulate the problem accordingly. In this view, a detailed state-to-state model (StS) is employed. It takes into account all the vibrational levels for molecular oxygen and nitrogen: since each of them is treated as a single species, this model leads to a relevant increment of the total number of species. To overcome such an issue, an MPI-CUDA approach is implemented in the solver to allow for multi-GPU executions.
In order to simulate the hypersonic flow around a double-cone, 2D axis-symmetric Navier-Stokes equations are solved for an oxygen reacting mixture. Steger-Warming flux vector splitting is employed for inviscid fluxes, along with a MUSCL reconstruction ensures second order accuracy; diffusive fluxes are discretized through the generalized Gauss' theorem. Finally, time integration is performed through an explicit third order Runge-Kutta scheme, such that potential unsteady behavior is well captured. Source terms are evaluated through a splitting approach. In the first step, homogeneous equations are solved; in the second step, source terms are computed through an iterative Gauss-Seidel scheme to update the mixture composition. In such a way, the overall time-step size preserves reasonable values and is not affected by the stiffness of the chemistry terms.
In this work, two different flow regime are investigated. The first one presents a low free stream enthalpy value (4 MJ/kg): indeed, it is found that non equilibrium phenomena are not relevant. Also, the flow reaches a steady state. The results obtained through the simulations are in a good agreement with those reported in literature and with experimental measurements in terms of surface heat flux and pressure.
On the contrary, when dealing with a higher enthalpy regime (10 MJ/kg) non equilibrium becomes relevant. Chemical phenomena are very strong since oxygen dissociation starts occurring for temperature values above 2000 K. Numerical results have shown a poor agreement with experiments, as also found by other researchers: in particular, the predicted separation region is much smaller than those evinced during the experiments. In order to assess possible influence of wall chemical activity, a fully catalytic model has been also implemented: the results are still in poor agreement with experimental measurements.
However, it is evident from the simulations that the computed wall pressure presents an important deviation from experimental measurements also downstream of the attached shock generating near the leading edge, where the calculation should be straightforward. This led the authors to investigate the influence of non equilibrium in the free stream conditions: for this reason, simulations of the flow expanding through a nozzle have been performed. It has been found out that the mT model provides different conditions at the exit of the nozzle (namely the free stream conditions of the double-cone flow) with respect to those calculated through the StS model. The new simulations performed starting from the mT nozzle conditions and the StS nozzle conditions highlighted a different shock wave/boundary layer interaction over the double-cone. Specifically, the wall quantities computed through the StS simulations predicted a larger separation region, as expected from the experiments, leading to consider that a StS calculation of the free stream quantities (nozzle expansion) would bring the results much closer to experimental measurements.
Summary
This work deals with numerical simulations of hypersonic flows and thermochemical non equilibrium modeling. The hypersonic flow over a double-cone is investigated.
