Defence Science Journal, Vol. 61, No. 4, July 2011, pp. 364-369, DOI:10.14429/dsj.61.1089
© 2011, DESIDOC
Received 23 March 2010, published online 25 July 2011
Viscous Shock Layer Method to Predict Communication Blackout during Re-entry Phase
Communication blackout generally occurs during the re-entry at high velocities through the atmosphere. Air ahead of the re-entry vehicle dissociates and then ionises, leading to the production of electrons. These electrons may reflect or attenuate the communication signals. Electron densities with plasma frequency exceeding the communication frequency lead to blackout. Electron density is a function of the body shape, velocity and altitude. The viscous shock layer method is used to predict the electron density, and thereby the plasma frequency for various configurations. This method is successfully implemented for analytic and non-analytic geometry configurations available in the literature. The electron densities computed for the RAM-C configuration agree well with the flight results. The onset of blackout during the re-entry phase is also predicted reasonably well by this method. The method performs well at high altitudes, where nonequilibrium conditions prevail.
|Ci||Concentration of species i, ρi/ρ|
|Cp||Specific heat at constant pressure|
|FVSL||Fully viscous shock layer|
|kbr||Backward reaction rate constant|
|kfr||Forward reaction rate constant|
|m||Mass of electron|
|M1,M2,M3||Catalytic third bodies|
|nj||Number of species plus catalytic third bodies|
|nr||Number of chemical reactions|
|r||Body radius, r*/Rn*|
|Rn*||Body nose radius|
|s||Coordinate measured along body surface, s*/Rn*|
|Tref*||Reference temperature, u∞*2/Cp∞*|
|TVSL||Thin viscous shock layer|
|u||Velocity component tangent to body surface, u*/u∞*|
|u∞*||Free stream velocity|
|v||Velocity component normal to body surface, v*/u∞*|
|Xi||Chemical species and catalytic third bodies|
|y||Coordinate measured normal to the body, y*/Rn*|
|z||Coordinate measured along body axis, z*/Rn*|
|αri||Forward stoichiometric coefficient|
|βri||Backward stoichiometric coefficient|
|ε||Permittivity of vaccum|
|*||Indicator for dimensional quantities|
|sh||Value behind the shock|
|∞||Free stream value|
Communication blackout generally occurs during reentry at high velocities through the atmosphere. The ionised gas forms a layer of plasma over the re-entry vehicle. The frequency of oscillation of the electrons about their mean position is called plasma frequency. If the plasma frequency exceeds the communication frequency, it attenuates the communication signal, leading to communication blackout.
The plasma frequency, ƒp in Hz is obtained from Eqn (1), where Ne is the electron density per cc, e is the electronic charge, ε the permittivity of vacuum, and m is the mass of electron.
Viscous shock layer (VSL) approach is one of the methods to estimate the electron density in the shock layer. Communication is restored at lower altitudes due to reduction in vehicle velocity and increase in collision frequency of electrons with neutral particles in high density air.
At atmospheric pressure, dissociation of oxygen and nitrogen molecules start at 2000 K and 4000 K, respectively. Molecular oxygen is completely dissociated at 4000 K. Molecular nitrogen is totally dissociated at 9000 K. Above these temperatures, the gas becomes a partially ionised plasma consisting of O, O+, N, N+ and electrons1. In the temperature range of 4000 K to 6000 K, small amount of NO is formed, some of which ionise to form NO+ and electrons. The electron density due to NO ionisation may be sufficient to cause communication blackout. The mechanism by which free electrons in the plasma affect the electromagnetic wave signals has been explained in literature2.
Viscous shock layer approach can be used to compute viscous, hypersonic flows over blunt bodies. The entire flow-field, from the body to the shock, is treated in a combined manner. One of the pioneers in the development of viscous shock layer method was Davis3. The VSL equations hold across the entire shock layer, and hence are more powerful than the boundary layer equations1. These equations are parabolic, and hence, a downstream marching solution can be obtained using finite difference method. The perfect gas viscous shock layer method of Davis was extended for chemically reacting nonequilibrium flow4 and for nonanalytic blunt bodies with multi-component, ionising air or dissociated oxygen5.
The VSL code described here was developed6 to predict hypersonic, low Reynolds number flows over nonanalytic blunt bodies. The first nonequilibrium gas chemistry model is for dissociating oxygen and the second is for ionising, multi-component air. The aim of this study is to implement the VSL code, named Viscous Shock Layer-Advanced Systems Laboratory (VSLASL) for different nonanalytic blunt bodies like the 20° blunted cone, radio attenuation measurements-C (RAM-C) and space capsule recovery experiment (SRE) configurations to predict the electron density.
The governing equations include the continuity equation, s-momentum equation, y-momentum, energy equation, species conservation equation in addition to the equation of state. Since these equations are given in literature3, 4, these are not presented here. The y-momentum equation is solved in the first iteration assuming thin viscous shock layer (TVSL) and subsequent iterations use either TVSL or fully viscous shock layer (FVSL). The VSL equations are second order accurate in the Reynolds number parameter.
The independent and dependent variables were normalised by their local shock values to transform the shock-layer equations. Solutions of continuity and y-momentum equations were obtained by integration with the trapezoidal rule. The transformed equations for the remaining governing equations were expressed in the standard form of a parabolic partial differential equation. Finite difference method3 was used for solving the governing equations.
Species enthalpy and specific heat were computed by second-order Lagrangian interpolation from the tables included in the program. The viscosity of each individual species was calculated by curve fit relations in the program. The mixture viscosity and thermal conductivity were evaluated using semi-empirical relations.
At the body, no-slip boundary conditions were specified. The species concentrations in the free stream were specified as CO = 0, CN = 0, CO2 = 0.23456, CNO = 0, CNO+ = 0, CN2 = 0.76544.
A fully catalytic wall leads to recombination of all atoms at the wall. The recombination reactions release heat and increase the heating of the surface. If the surface is non-catalytic, the recombination does not take place and heating of the surface is relatively low7.
The chemical reactions are assumed to proceed at a finite rate. The chemical reaction equations are written in the general stoichiometric form as in Eqn. (2), where r = 1,2,… nr (nr = number of reactions) and nj is equal to sum of the number of species and catalytic third bodies. Xi represents the chemical species and catalytic third bodies, and αri and βri are the stoichiometric coefficients for reactants and products. The reaction rate constants, kfr and kbr are the forward and backward reaction rate constants.
For multi-component air, the reactions and chemical reaction rates have been taken from literature8. The seven reactions for the seven species (O2, N2, NO, O, N, NO+ and e−) are given in Eqn. (5) through Eqn. (11) where M1, M2 and M3 are the catalysts.
The VSL programme is written in Fortran. This programme is applicable to nonanalytic blunt bodies in addition to analytic bodies like the paraboloid and hyperboloid. The first global iteration is for TVSL only. Subsequent global iterations may be for TVSL or FVSL. The altitude and body nose radius, free stream density, body wall temperature, free stream temperature and free stream velocity were specified. At each stream-wise ‘s’ location, the shock-layer equations are solved in the order of species, energy, s-momentum, continuity, and y-momentum. For spherically blunted cones, the pressure distribution being highly non-Newtonian, an initial shock shape was input to the program.
The limitations of VSL method are as follows:
- The VSL method, being a space-marching scheme, cannot be applied to separated flows.
- For solving flow past a spherically blunted cone, the discontinuity in surface curvature at the sphere-cone tangent point creates difficulties in solving the equations in a stable manner.
- For conditions approaching equilibrium, there is increased difficulty in obtaining a converged solution at the stagnation point.
The present VSL code is run for both analytic and nonanalytic bodies. The implementation of this code is checked by running it for the sample cases6. On successful implementation of these sample cases, the code is examined for spherically-blunted cones such as 20° blunted cone, RAM-C 9° blunted cone and SRE configurations.
8.1 Sample Cases
The first analytic geometry considered is the 31° hyperboloid sample case6 at an altitude of 74.6 km with a free stream velocity of 7.6 km/s. The temperature profile in the stagnation region, with the maximum temperature at the shock, is shown in Fig. 1. The results obtained match perfectly with results available in the literature6.
8.1.2 140B Orbiter
The second sample geometry considered is the 140B Orbiter, for which the geometry is specified in a tabular form. The electron density at the stagnation point of this body matches extremely well with value of electron density as available with literature6 as shown in Fig. 2. It is observed from this figure that the peak electron density occurs within the shock layer. Since the sample cases are implemented successfully, the VSL code is extended to spherically-blunted cones.
8.2 Spherically-blunted Cone Geometries
8.2.1 20° Blunted Cone
The blunted cone geometry considered9 is a cone of 20° half angle with a nose radius of 38.1 mm. The nondimensional pressure on the body wall in the nose region is compared with literature9 and plotted in Fig. 3. The pressure drop due to expansion of the flow over the spherical portion and almost constant pressure over the conical portion is clearly observed from the above figure. The nondimensional temperature at the stagnation point extending from the body to the shock is shown in Fig. 4. The mass fraction of various species in the stagnation region is compared in Fig. 5. It is observed that the mass fraction profiles match reasonably well with the the mass fraction profiles available in the literature9. The small variations in the mass fraction profiles might be due to differences in the thermodynamic properties. The degree of nonequilibrium in the flow field is evident from the mass fraction profiles.
8.2.2 RAM-Series C-9° Blunted Cone
The radio attenuation measurements (RAM) project consisted of spherically-blunted cones used to study the plasma characteristics during re-entry10. The RAM-series C consists of flight experiments in a higher velocity regime (about 7.6 km/s)11. The RAM-Series C configuration consists of a 9° cone with a bluntness radius of 152.4 mm.
The change in curvature at the sphere-cone junction of the RAM-Series C geometry causes problems in obtaining the shock shape properly. Hence the shock shape computed from a code based on inviscid shock layer12 is given as an input to the viscous shock layer code. This helps in better resolution of the shock shape. The runs are carried out assuming no shock slip as in the literature5. The electron density at the antenna location for altitudes varying from 61 to 76 km computed from the present code are compared with literature5, 13. As shown in Fig. 6, the order of the electron density at the antenna location obtained from this code matches fairly well with what is available in the literature. It is observed from the above figure that with decrease in altitude, the electron density increases.
The shock layer thickness at an altitude of 70 km compares reasonably well with what is available in the literature5 as shown in Fig. 7. The temperature profile at the antenna location obtained from the present code also compares well with what is available in the literature5 for the same altitude as shown in Fig. 8. It is observed from the above plot that the maximum temperature occurs within the shock layer. The temperature distribution behind the shock at 70 km altitude also matches well with what is available in the literature as presented in Fig. 9. As expected, the temperature behind the shock decreases along the surface as the shock strength reduces downstream of the stagnation point.
8.2.3 SRE Configuration
The SRE configuration consists of a blunted double cone. The bluntness radius is 508.8 mm while the cone angles are 20° and 25°. Since the antenna is located on the 20° cone, only this part was considered as the SRE geometry in the present VSLASL code. The walls were assumed to be catalytic and at a temperature of 1000 K as in the VSL results reported in the literature14. Shock slip boundary condition was applied to enable comparison with literature. The electron densities at the stagnation and antenna location at an altitude of 80 km are plotted in Fig. 10. The viscous shock layer code is able to predict the electron density levels quite well as compared with the literature14. The maximum electron densities along the axial direction for 80 km and 85 km are shown in Fig.11. A fairly good match is obtained in predicting the maximum electron density level. The kinks in the plot could be due to the change in curvature near the sphere-cone junction. The plasma frequency, obtained from the electron density, at altitudes varying from 70 km to 85 km at the stagnation and antenna locations are plotted in Fig. 12. The communication signal frequency is 2.25 GHz. The present code predicts the onset of blackout to be at about 82 km which matches very well with flight, where the onset of blackout was at 81 km14.
The present Viscous Shock Layer-Advanced Systems Laboratory is implemented for both analytic and nonanalytic body geometries. The results from the present code for spherically-blunted cones like the 20° cone, RAM-Series C and SRE configurations compare favourably with available literature. Various parameters such as the temperature, pressure, species mass fraction, electron density, and plasma frequency are found to match well with literature. A good comparison is obtained between the electron densities for the RAM-Series C configuration predicted by the present code and the measured flight electron densities. Hence, the present code can be used to compute the electron densities for similar spherically blunted cones. Since this code is meant for nonequilibrium flows, it functions well at higher altitudes. But convergence problems arise at lower altitudes, which aid in achieving the equilibrium state. Consequently this code can be used to compute the electron density over bodies during re-entry phase and predict the altitude corresponding to the onset of communication blackout.
The authors thank Shri Avinash Chander, Director, Advanced Systems Laboratory (ASL), Hyderabad, for granting permission to publish this work. The efforts of Shri Rahul Chopde, formerly working at ASL is also gratefully acknowledged.
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