I would like to thank the Department of Mechanics and Aerospace of IITH and the entire IIT Hyderabad system for providing us with an excellent computational facility to work on. In this paper, numerical simulations are performed in a discontinuous hypersonic regime to analyze the flow properties in the shock layer of a blunt body. Simulations involving chemical reactions for high-temperature gases are performed for the atmospheres of Earth and Mars.
Therefore, the integration of radiation along with all non-equilibrium effects in the rarefied hypersonic regime is imperative.
Literature Review
Another approach is to measure the shock distance, which depends on the roughness of the geometry, the degree of rarefaction and the radiative heat transfer. Radiant heat transfer has been studied for the Stardust capsule for non-equilibrium ground reentry conditions [7][8][9]. OpenFOAM provides a number of C++ libraries that can be manipulated to add new features to existing solvers.
The sparse HypersonicFoam solver is developed in the present work by combining a number of features of two existing solvers rhoCentralFoam and reactingFoam.
Objectives of Present Work
OpenFOAM is integrated with many flow solvers that have been validated by a large number of users for a wide range of problems related to heat transfer, combustion and fluid mechanics. The reactingFoam provides a number of functions such as species transport, chemical kinetics and thermodynamic properties based on chemkin format and data. Therefore, the OpenFOAM thermodynamic library was updated with data from Gordan and Mcbride [15], which provides polynomial fits for thermodynamic properties of a wide range of species, and is valid up to 20,000 K.
The main goal is to develop and validate a solver within OpenFOAM capable of solving problems related to high-temperature gas flows (M a >10) and an altitude of 40 to 70 km.
Governing Equations
Transport Properties
Mixture values of µ and k are calculated as the weighted average of µi andki based on the mole fraction of species. The simulations are done for laminar cases if the Reynolds number <2000 because density is very low.
Boundary Conditions
Radiative Modeling
The total radiation flux can be obtained by integrating the radiation intensity in all possible directions and at all possible points.
Algorithm for rarefiedHypersonicFoam
Blunted Flat Plate
In Figure 3.2, the grid independence study is performed for four different meshes ranging from coarse to fine near the wall. A slight difference in the prediction of the shock layer thickness between the coarse and fine meshes is observed. In Figure 3.3a, the distribution of normalized temperature along the stagnation streamline is compared with that of the DSMC obtained by OpenFOAM [12] and the internal N-S solver (UNS) of Massimi et al.
However, the shock thickness obtained by the solver is slightly lower than the DSMC result since the Knudsen number is 0.1 and continuous decay occurs within the shock layer. The shock layer turns out to be more prevalent in sparse hypersonic foam compared to UNS due to the inclusion of non-equilibrium effects. In Figure 3.3b it can be seen that the shock layer and the boundary layer merge into each other, which makes it very difficult to distinguish between the two.
In Figure 3.4, the temperature profile along the stagnation currents is plotted for the coupled radiation solver using the P1 and fvDOM approximations. The shock layer loses heat to the surroundings by radiation, so a difference of about 750 K between the peak values is seen for the cases with and without radiation. Heat loss also reduces the thickness of the shock layer. For fvDOM, we observe a 127% increase in inlet temperature along the stagnation stream because.
The stagnation zone is very important because the temperature and pressure in this zone increase immeasurably. Blunt bodies are preferred in hypersonic flows because separate shocks are formed for such cases as if there is a sharp angle, an oblique attached shock will form and the temperature at the stagnation point will be very high. Figures 3.6a and 3.6b show how the shock temperature and thickness decrease when the solver is coupled to radiation, although the shock pattern remains the same.
Blunted Wedge Geometry
When the temperature in the shock layer region reaches above 2500 K, O2 dissociates to form O and when the temperature goes further above 4000 K, N2 begins to dissociate to form N. The simulation is first done on a coarse mesh and to get better results, mesh is made finer near the wall and over the shock region. The peak temperature predicted by raref iedHypersonicF OAM is also less than that of Tchuen and Zeitoun.
The reason behind this is the inclusion of two temperature models from Tchuen and Zeitoun. However, in this case, Tchuen and Zeitoun use a single temperature model assumption to simulate this case using rare hypersonic FOAM. Behind the shock, the translational temperature quickly reaches its peak value, while the vibrational temperature takes more time to reach its equilibrium value.
Therefore, a model driven only by translational temperature will tend to overestimate the dissociations taking place in the shock layer region. That is why in the rare case of HyperpersonicF OAM0s, an underprediction of the temperature peak value is observed. In addition, a uniform character of the temperature profile can be seen in the boundary layer region, because the chemical reactions are endothermic and they extract heat from the shock layer, resulting in a decrease in temperature and shock distance.
Tchuen and Zeitoun have used Park's model for forward reaction rates and backward reaction rates are calculated using the equilibrium constant Keq. Since the stroke thickness for the rare iedypersonicF oam is smaller than Tchuen and Zeitoun, therefore dissociation starts early for this case.
Blunted Cone
The box is first run without radiation, then the P1 model is used with Marshak's edge conditions at the inlet, outlet and wall. The fvDOM model coefficients are defined as nP hi= 4 and nT heta= 0, the convergence criteria for radiation iteration is 10−3 and maxIter = 4 for the maximum number of iterations. Only nP hi is considered in this case since it is a 2D geometry and the direction of the beam is on the x-y plane.
For the fvDOM model, a diffusely emitting and radiating surface boundary condition is applied at the inlet, outlet and wall. In Figure 4.2, the temperature profiles along the stagnation stream are plotted to see the effect of coupled radiation on the case. The peak temperature predicted by the P1 model and fvDOM is slightly lower than that without radiation, as radiative heat transfer causes radiative cooling in the shock region.
A difference in peak temperature prediction of about 1.47% for P1 and 2.037% for fvDOM without radiation case is observed. There is some disagreement between fvDOM and P1 and no radiation is observed in the boundary layer region. This is due to the assumption of gray gas which in this case is considered as a constant value of the absorption and emission coefficient, while for such cases of hypersonic flow it depends on pressure, temperature and wavelength.
As soon as the flow hits the bow shock, the value of Cp increases sharply and then remains constant in the boundary layer region.
Blunted Wedge Geometry
The enormous amount of kinetic energy of the flow in a hypersonic free stream is converted into internal energy of the gas over the strong bow shock wave, creating very high temperatures in the shock layer near the nose. Furthermore, downstream of the nose region, where the shock layer around the body has expanded and cooled, we have a boundary layer with a Mach number at the outer edge that is still high, hence the intense friction dissipation within the hypersonic boundary layer. causes high temperatures and causes the boundary layer to become chemically reactive. This lowers the temperature to even lower values near the stagnation point because the gas molecules have more time to dissociate as the velocity decreases as the flow approaches the point.
When ionization is present in the shock layer, a large number of electrons are supplied throughout the layer. The free electrons can cause a communication disruption to and from the vehicle during parts of the entry route, because it absorbs the radio frequency radiation. Therefore, it is a high priority to determine the electron number density in the shock plasma region around the body.
Since the boundary layer is chemically reactive, dissociation and ionization reactions cause the concentration of N2 and O2 to initially decrease, then near the stagnation region a recombination reaction takes place for N2 and its concentration increases again to 0.67. The contours for temperature, pressure, electron density and mass fractions for N2 and O2 are presented below. The absorption coefficient in this case should be a function of temperature, pressure, mass fraction and frequency, but for clarity a constant value is considered for this case [1].
In Figure 4.9, the temperature profiles along the stagnation line are compared for the no-radiation model and the P1 model. There is a large difference of about 2700 K between the maximum values with and without radiation.
Crew Exploration Vehicle
Also, in this case a two-equation Mentor Shear Stress Transport (MSST) is used as the turbulence model. The presence of N2, even in small amounts, can significantly affect the flow field, therefore a more accurate chemistry model consisting of 9 species and 11 reactions is considered in this case since the martian composition is 98.07% of CO2 and 1.93% of N2 be taken by mass [6]. In Figures 4.15a and 4.15b the temperature profile and pressure coefficient are plotted along the stagnation streamline.
Most of the CO2 in this case is dissociated, and some other species include undissociated CO2 and some O2. To calculate the absorption and emission coefficients in this case, the gray absorption-emission polynomial means as a function of temperature given by Centeno et al. The recirculation zone formed due to the sharp edge of the vehicle geometry can be clearly seen in the velocity contour (Figure 4.18a) and the temperature contour (Figure 4.18b). A recirculation length of 4.7 m is observed in this case.
The same previously used air chemistry model is extended and in this case ionization reactions are also taken into account; therefore, 11 species and 40 reactions are used in this case [3]. In this case, a more realistic study is made of Crew Exploration Vehicles driving through the Martian atmosphere at a speed of 5 km/s [11]. Because CO2 acts as the primary gas in the Martian atmosphere, a completely different chemical model is required.
Analysis and Model Validation of Airborne Shock Layer Radiation,” in 46th AIAA Aerospace Sciences Meeting and Exhibit, 2008, p. Johnston, “Examining Coupled Continuum Fluid Dynamics and Radiation in Hypersonic Simulations,” at the 7th AIAA Aerospace Sciences Meeting, including The New Horizons Forum and Aerospace Exposition, 2009, p.
