ANALYSIS OF HEAT TRANSFER IN HYPERSONIC FLOW OVER RE-ENTRY CONFIGURATIONS

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1 IJATSE Volume 3 Number 1 January-June 2012, pp ANALYSIS OF HEAT TRANSFER IN HYPERSONIC FLOW OVER RE-ENTRY CONFIGURATIONS R. Balu 1 and L. Prince Raj *2 ABSTRACT: Inter planetary space mission involves the re-entry of the space modules through the dense layer of surrounding atmosphere at very high Mach number of the order of 30 to 50. This implies very high temperatures. At these high temperatures, the surrounding gas dissociates and sometimes even becomes ionized. The boundary layer surrounding these bodies is also at very high temperature and the heat transfer from boundary layer to the body is predominantly by radiation. Present work focuses on the analysis of heat transfer occurring at hypersonic and hyper velocity flow regimes over reentry configurations. To gain knowledge about these flow fields, FIRE II re-entry capsule was taken as an example. Geometry modeling and meshing were done using GAMBIT software and the flow analysis was done FLUENT code. Both convective as well as radiative heating has been modeled using appropriate correlations. Convective heating involves estimation of heat flux at the stagnation point and its distribution in the stagnation region. Radiative heat transfer is estimated using empirical correlations proposed by V.P.Stulov[9]. A radiation parameter is defined in terms of which, the heat transfer coefficient is evaluated. Necessary software codes have been developed using FORTRAN for this purpose. These codes have been validated against published experimental and flight data of FIRE II and MUSES - C space missions. The properties of air at high temperatures, taking in to account the dissociation of oxygen and nitrogen, have been formulated using the correlations proposed by Roop N. Guptha [5], These give air properties like enthalpy, viscosity, specific heat capacity, Prandtl number, etc at a given pressure and density. These properties are used in an iterative fashion for shock calculations taking into account the real gas nature of the air at high temperatures. Necessary software codes for these calculations also have been developed as a part of the present work. The comparisons with the both flight and experimental data show good agreement with the present proposed methodology. Keywords: Hypersonic flows, Re-entry vehicle, FIRE II, Aerodynamic heating, Heat transfer, Molecular dissociation, Real gas effect 1 Dean, Inter Disciplinary Studies, Noorul Islam Center for Higher Education Kumaracoil balshyam2003@yahoo.com 1. INTRODUCTION Atmospheric re-entry is the movement of man-made or natural objects as they enter the sensible atmosphere of a planet, from outer space. In the case of Earth, this extends up to an altitude of 100 km. Vehicles that undergo this reentry process include, those returning from earth orbits (like spacecrafts) and those from suborbital trajectories ( like ICBMs ). Typically these vehicles require special thermal protection systems to protect against the severe heating environment. 2. AERODYNAMIC HEATING Aerodynamic heating refers to the heating of a solid body produced by the flow of a fluid (such as air), over the body such as a meteor, missile, or airplane. The heat transfer essentially occurs at the vehicle surface, where the viscous force ensures that the flow is at finite viscosity of air brings the flow velocity to zero, relative to the body in a very small layer of molecules at the surface. Because the flow has slowed to zero velocity, a significant part of its kinetic energy from the free-stream is converted to heat. In high speed flows especially, large amount of energy is possessed by the mean motion of the flow. As the flow is slowed to zero speed, its temperature is increased. But the gradient in the speed in the direction normal 2* Post Graduate Student, Anna University Tirunelveli (Corresponding author lpraero@gmail.com)

2 2 IJATSE to the surface allows small scale mass transport effects to dissipate the temperature in the outward direction and thus the temperature at the surface is less than the stagnation temperature. The actual temperature is referred to as the recovery temperature. These viscous dissipative effects to neighboring sub-layers make the boundary layer slow down via a non-isentropic process. Heat then conducts into the surface of the material from the higher temperature air. The result is an increase in the temperature of the material and a loss of energy from the flow. The forced convection ensures that hot gases are replenished the gases that have cooled to sustain the process. The stagnation and the recovery temperature of a flow increase as the square of the flow speed and are very high at hypersonic speeds. The total thermal loading of the structure hence is a function of both the recovery temperature and the mass flow rate of the flow. Aerodynamic heating is greatest at high speed and in the lower atmosphere where the density is greater. In addition to the convective process described above, there is also radiative heat transfer from the flow to the body and vice versa with the net direction set by the relative temperatures of each. Aerodynamic heating increases with the speed of the vehicle and is continuous from zero speed. It produces much less heating at subsonic speeds but becomes more important at supersonic speeds. At these speeds it can induce temperatures that begin to weaken the materials that compose the object. The heating effects are greatest at leading edges. Aerodynamic heating is dealt with by the use of high temperature alloys for metals, the addition of insulation of the exterior of the vehicle, or the use of ablative material 3. HYPERSONIC FLOW PROCESS In aerodynamics, hypersonic speed refers to highly supersonic flow. The term has generally been assumed to refer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime is a subset of the supersonic regime. The precise Mach number at which a body can be said to be flying at hypersonic speed is vague, since physical changes in the airflow (molecular dissociation, ionization) occur at quite different speeds. Generally, a combination of chemical changes becomes important around Mach 5. A vehicle flying through the atmosphere at hypersonic speeds generates a shock layer. This is defined as, the region between the bow shock wave and the vehicle surface, in which the pressure, the temperature, and the density change by more than two orders of magnitude. Because the kinetic energy associated with hypersonic flight is converted into high temperatures within the shock layer, lot of parameters will affect the flow. A few important factors are 3.1. Compressibility Effects The compressibility of a fluid is a measure of the change in density that will be produced in the fluid by a specified change in pressure. Gases are generally highly compressible whereas most liquids have very low compressibility. Now in a fluid flow, there are usually changes in pressure due to changes in the velocity in the flow. These pressure changes will induce density changes which will have an influence on the flow. If these density changes are important, the temperature changes in the flow that arise due to the kinetic energy changes associated with the velocity changes also influences the flow. A shock wave is a type of propagating disturbance. Shock waves are characterized by an abrupt extremely rapid rise in pressure, temperature and density of the flow Real Gas Effects At high temperatures, the molecules of gases that consist of two or more atoms can start to break down into simpler molecules causing dissociation of molecules. Oxygen dissociation starts at around 2000 K and is completed at about 4200 K at which about 1 percentage of the nitrogen is dissociated. The dissociation of nitrogen is completed at 9000 K. The dissociation reactions are: N 2 N + N O 2 O + O 2H 2 O 2H 2 + O 2

3 Analysis of Heat Transfer in Hypersonic Flow Over Re-Entry Configurations 3 As illustrated in the Figure.1 the dissociation occurs over the wide range of temperatures. Figure 1: Effect of Temperature on Composition of Oxygen at 1 Atmosphere In Figure 1, the dissociation of O 2 into O + O is illustrated. At low temperatures the gas essentially consists of O 2 molecules. As the temperature further increases, the number of O 2 molecules decreases and the number of O atoms increases until at high temperatures the gas essentially consists entirely of O atoms. The amount of O 2 and O molecule depends up on the pressure and temperature of the gas. If very high temperatures are involved in the flow, ionization of the atoms can occur. Ionization is the physical process of conversion of an atom or molecule into an ion by adding or removing charged particles such as electrons or other ions. For example, in case of air flow, the following ionization reactions become important: N N + + e O O + + e The ionization of N and O starts at about 9000 K. This will occur at free stream velocities of around km/s. The effects of dissociation and ionization of the gas on its thermodynamic properties are often referred to as real-gas effects. In an ideal gas the compressibility factor is assumed to be unity, it becomes important to know the various thermodynamic properties as functions of a pair of independent state variables. These data are correlated as polynomials and are used along with few constants to find the thermodynamic properties as function of two known state variables. By using these curves the real gas effect is taken into account. 4. THERMODYNAMIC PROPERTIES OF HIGH TEMPERATURE AIR Under subsonic flight conditions, air can be treated as an ideal gas composed of rigid rotating diatomic molecules. The thermodynamic properties of such a gas are well known. However, under hypersonic flight conditions air may be raised to temperatures at which the molecules can no longer be treated as rigid rotators. Thus, there is a very real need for the thermodynamic and transport properties of equilibrium air for the computation of flow fields around bodies in high-speed flight.

4 w i t h h i g h a c c u r a c y i s u n i v e r s a l f u n c t i o n o f p a r a m e t e r Γ 4 IJATSE Thus curve fits proposed by Roop N. Guptha are used to find the fluid properties such as enthalpy, viscosity, Prantl number,etc. The normal shock relations are used in an iterative fashion by using a curve fit to take care of the real gas effect. 5. ESTIMATION OF CONVECTIVE AND RADIATIVE HEAT TRANSFER RATES: The convective heat transfer through the equilibrium stagnation point boundary layer can be computed accurately by a simple correlation given by J.A. Fay and F.R. Riddell [1] as, Where, (du e /dx) s = ( ) q = 0.94()() ρ µ 1ρ µ 1() { + ( )( )}( ) L h h h h du dx (1) w w s s D s s w e s 1/ R 2()/ P s P P s To calculate the convective heat transfer the above equations are used and a FORTRAN code is developed. In the above equation q is the heat transfer rate, ρ is the density, L is the Lewis number (L = 1.42), h is the enthalpy, P is the pressure and R is the nose radius. The subscripts w indicates the properties at the wall condition, s indicates the properties at the stagnation point respectively. h D is the dissociation energy, of oxygen and is taken as KJ/Kg and the wall temperature T w is taken as 300 K 5.1. Surface Heat Transfer Rate Distribution By using Fay and Riddell equation the convective heat transfer at the stagnation point is calculated and it is necessary to know the heat transfer distribution in the remaining portion of the nose. To calculate the heat transfer rate in the surface Lester Lees [4] surface heat transfer rate distribution equation is used, which is given below, q () q w w 0 = 1 2θsinθ 1 cos θ + Y M D( θ) Y M (2) where, D(θ) = 1 θsin 4θ 1 cos 4θ 4 1 cos 2θ 1 θ + + θ θsin 2θ + Y M Y M where (q w ) 0 is the heat transfer rate at the stagnation point, M is the mach number. By using the above equations the heat transfer distribution is calculated At velocities above 10 km/s, the radiative heating becomes significant along with convection. At still higher velocities, the radiative heating will dominate the convection. In case of re-entry vehicles the effect of radiation on the flow field will be an important consideration. The presence of a radiating flow field adds the radiation mode of heat transfer to the vehicle surface. Along with convective heating, radiative heat transfer must also be considered to make an accurate heating prediction. Research studies have shown that the radiation heat transfer coefficient to the stagnation point ch0 = q is /0.5ρV 3 where qis is a radiation flux from a homogeneous shock layer before a stagnation point of the blunt body with the assumption that the output of radiation does not change parameters of gas along the stagnation line. For air the law of similarity is expressed by the formula c h0 = 0.111Γ 0.53 (3) Universal dependence (c h0 ) in case of the air flow is shown in figure by a continuous line. Points show results of numerical calculations. For determining the required function c h = c h (R, V,ρ) on the basis of expression (3), first, it is necessary to connect parameter Γ with arguments R,V, ρ and, second, to express parameter of heat exchange for all frontal part of a body c h through parameter of heat exchange in a

5 Analysis of Heat Transfer in Hypersonic Flow Over Re-Entry Configurations 5 Values of radiation parameter Γ can be determined, if there are tables of equilibrium shock waves and degrees of blackness of a flat layer for considered mixture of gases. Then calculation of the value Γ, in turn, can be broken on two stages. At the first stage, at preset values of speed and density of incident stream, under tables of equilibrium shock waves, thermodynamic functions of gas behind shock wave Ts, Ps, ρ are determined. Figure 2: Radiation Heat Transfer Co-efficient Into Stagnation Point Finally the radiation parameter Γ is calculated under the formula. Γ = 4 2εσT5 0.5ρ V 3 (4) On the basis of the above mentioned scheme, the following analytical approximation of parameter? for air is offered. (1) ρ 0.2E 6g/cm 3 At At n () R i /2 V 2 Γ = Ci()( R 10 ρ) R KW/ cm (5) 10 C 1 (R) = ( R ) 1/4 n 1 (R) = 10 (0.0079R ) 1/4 10 B 13Km/s; C 2 (R) = (0.3215R ) 1/4 n 2 (R) = 10(0.4355R ) 1/4 13 < V < 20 Km/s; (2) 0.2E 6 < ρ 1.3E 6g/cm 3 (3) 1.3E 6 < ρ g/cm 3 n () R i /2 V Γ = Ci() R R (6) 10 n () R i /2 V Γ = Ci() R R (7) 10

6 6 IJATSE Approximations (5)-(7) pertains to the following range of the characteristics body size: 30 R 300 cm. In last two ranges of density (6) and (7) expressions for C i (R), n i (R) it is necessary to take from (5). Here R is expressed in cm, V is expressed in km/s. It is very important to calculate the distribution along the frontal part with high accuracy. The expression q θ /θ is = cos n θ is used, the parameter n = 3 for large speeds. 6. APPLICATION TO FIRE II AND MUSES-C RE-ENTRY VEHICLES: The purpose of FIRE is to determine the hot-gas radiative heat flux and the total heat- transfer rates on a blunt-nosed body of fairly large scale at a velocity of approximately 11.3 kilometers per second. The data resulting from the flight are intended to provide anchor points for comparison with data obtained from ground facilities and theoretical prediction methods. The project FIRE II ballistic reentry to Earth at a nominal velocity of km/s 37 years ago remains one of the best sources of aero thermal heating data for the design of sample return capsules. The data from this flight experimental encompass both the thermochemical non-equilibrium and equilibrium below regimes and include measurements of both radiative and total heating on the fore body and aft-body. Because of the quality of these data, a number of researchers have performed computational fluid dynamics (CFD) simulations of the fore body of the FIRE II re-entry vehicle, with generally good results. Figure 3: Relevant Dimensions (in Centimeters) of the Fire II Reentry Vehicle Uncertainties in aft-body heating predictions can have a significant impact on thermal protection system material selection and weight. Conservatism in the aft-body heat shield design will shift the center of gravity backward, reducing stability and in some cases necessitating ballast in the nose. The configuration and dimensions of the FIRE II re-entry vehicle as modeled in the CFD simulation is as in Figure. 3. To know about the flow fields it s very important to model and analysis in CFD commercial packages. GAMBIT is used to model and grid generation and by using FLUENT analysis has been done. Heat flux value is evaluated using the procedure described above for the FIRE II and Muses-C.

7 Analysis of Heat Transfer in Hypersonic Flow Over Re-Entry Configurations 7 7. RESULTS AND DISCUSSION The comparison of convective and radiative heat flux is shown in the following figures. Figure, 4 shows result of total heat flux at an altitude of 76km, velocity = 11.36km/s, which corresponds to a Mach number 42. Where the P = 1.93 N/m, T = 179 K, ρ = E-5. The results of FIRE II, Taylor et.al, Direct Monte Carlo Method, 11 species chemistry and 5 species chemistry models are also included for comparison. Figure 4: Heat Transfer at Capsule Nose Surface for Both the 11 Species and 5 Species Chemistry Sets, 85km Case. Square Data Point is the Measured Heat Transfer from FIRE II Experiment. Circular Data Point is the DSMC Results Including the Radiative Component are Shown with the Present Work Figure 5 shows the total heat flux at an altitude of 85km, velocity = km/s, which corresponds to a mach number 44. Where the P = N/m, T = 165 K, ρ = E-6.The results of FIRE II, Taylor et.al, Direct Monte Carlo Method, 11 species chemistry and 5 species chemistry models are also included for comparison. Figure 5: Heat Transfer at Capsule Nose Surface for Both the 11 Species and 5 Species Chemistry Sets, 76 km Case. Square Data Point is the Measured Heat Transfer from FIRE II Experiment. Circular Data Point is the DSMC Results Including the Radiative Component are Shown with the Present Work

8 8 IJATSE The Muses-C reentry capsule is part of an asteroid sample return mission and reenters the Earth's atmosphere at approximately 12 km/s. The peak heat loading to the vehicle is predicted to be at an altitude of 65 km when its velocity is 11.6 km/s. At the reported altitude of 65 km, the atmospheric density is kg/m 3 and the temperature is K. The predicted convective heat transfer is 7.5 MW/m 2 and radiative heat transfer is 0.94 MW/m 2. By using the above methods convective and radiative heat flux value is evaluated. The trajectory of Muses-C is as in Figure 6. The predicted heat flux values for various instants in the trajectory is shown in Figure 7 and Figure 8. The variation in radiative heat flux is due to the variation of wall temperature. The comparison for both these missions seems to be quite reasonable. Figure 6: Re-entry Trajectory Model of MUSES-C Capsule Figure 7: Time History of Stagnation Point Convective Heating Rate of MUSES-C Capsule Nose Surface for Both the 11 Species and 5 species Chemistry Sets are Shown with the Present Work

9 Analysis of Heat Transfer in Hypersonic Flow Over Re-Entry Configurations 9 Figure 8: Time history of Stagnation Point Convective Heating Rate of MUSES-C Capsule Nose Surface for Both the 11 Species and 5 Species Chemistry Sets are Shown with the Present Work 8. CONCLUSION Heat flux by convection and radiation have been estimated taking into account the real gas properties of air at high temperatures. These properties have been taken from the curve fits available in the literature. The flight measured values for FIRE II and Muses-C missions show good comparison of the heat flux histories, so the present procedure is validated and can be used for inter-planetary as well as re-entry module thermal design. REFERENCES [1] Fay, J.A and Riddell, F.R Theory of Stagnation Point Heat Transfer in Dissociated Air Journal of Aeronautical Science, 25, February [2] Gollan, R. J, Jacobs, P. A, S. Karl, Smith, S. C Numerical Modelling of Radiating Superorbital Flows, Division of Mechanical Engineering Report, the University of Queensland, Brisbane, Febraury C248 [3] Kojiro Suzuki, Kazuhisa Fujita and Takashi Abc Chemical Non Equilibrium Viscous Shock-Layer Analysis Over Ablating Surface of Super-Orbital Re-Entry Capsule, The Institute of Space and Astronautical Science, Report SP No. 17, March [4] Lester Lees Laminar Heat Transfer Over Blunt-nosed Bodies at Hypersonic Flight Speeds Jet Propulsion. April pp [5] Roop N. Gupta, Kam-Pui Lee, Richard. A. Thompson, Jerrold. M. Yos Calculations and Curve Fits of Thermodynamic and Transport Properties for Equilibrium Air to 30,000 K Nasa RP-1260, 1991 [6] Takashi ABE, Overview of Research for Prediction of Aerodynamic Heating Environment During a Super- Orbital Reentry Flight of MUSES-C Reentry Capsule, The Institute of Space and Astronautical Science, Report SP No. 17, March 2003.

10 10 IJATSE [7] Tannehill. J.C and Mohling, R.A, Development of Equilibrium Air Computer Programs Suitable for Numerical Computation Using Time-Dependent or Shock-Capturing Methods, NASA CR-2134 (September 1972). [8] Tannehill. J.C and Mugge, P.H, Improved Curve Fits for the Thermodynamic Properties of Equilibrium Air Suitable for Numerical Combination Using Time-Dependent or Shock-Capturing Methods NASA CR ( october 1974). [9] Stulov, V.P Radiating Heat Transfer at the Entrance of Space Bodies to the Earth s Atmosphere European Conference For Aerospace Sciences (Eucass).