COMPUTATIONAL STUDY OF CHEMICALLY REACTING HYPERSONIC FLOW

Transcription

1 COMPUTATIONAL STUDY OF CHEMICALLY REACTING HYPERSONIC FLOW Yoshiuru Funahashi Department o Aeronautics and Astronautics, Graduate School o Engineering, The University o Tokyo, Tokyo, JAPAN Keywords: Hypersonic low, Chemical equilibrium, Thermal protection Abstract Because space vehicles reentering the Earth s atmosphere are exposed to immense aerodynamic heating, so some kinds o thermal protection systems are indispensable. Computational analysis o two kinds o thermal protection systems, that is, the ilm cooling and the transpiration cooling, was conducted, taking real gas eects into account. General Introduction. Thermal Protection Systems Because space vehicles reentering the Earth s atmosphere are exposed to immense aerodynamic heating, so some kinds o thermal protection systems are indispensable. Currently, various types o thermal protection have been contrived. Among them, the ones that involve mass transer are listed below: Film cooling Transpiration cooling Ablation cooling Film cooling is a method o injecting coolant gas through some slits and making a thin ilm on the surace. The irst injection point is usually set to the stagnation point, where the aerodynamic heating is the most severe. And in many cases, the second injection point is set to the point where the inluence o the irst injection becomes weak. Transpiration cooling is a method to transpire a coolant air through a porous media in a wide area. Like as ilm cooling, the coolant air orms a thin ilm on the surace and makes the boundary layer thicker. The coolant air exchanges the heat with a material also in the matrix. Film cooling and transpiration cooling have the advantage o reusability and saety, but the systems are so complicated and hence costly. Ablation cooling is a method that makes use o the sublimation o the resin called ablator. This method can save cost and weight and has high reliability, but the disadvantage is that the system cannot be reused.. Real Gas Eects The gas temperature in the nose region o the vehicles is extremely high, so real gas eects such as chemical reactions occur. Under the

2 YOSHIFURU FUNAHASHI constant pressure o atm, the vibrational energy o the molecules becomes signiicant at about K. When the temperature reaches about K, O begins to dissociate. At K, N begins to dissociate. At 9 K, the oxygen and nitrogen ionization occurs. These phenomena make a great impact on the properties o the gas, and hence, on the low. Thereore, the proper inclusion o real gas eects is vital to the calculation o the low around the hypersonic vehicles.. Classiication o the Flows Chemically reacting lows can be classiied into three types depending on the two characteristic times, that is, the characteristic time o the low and the one o the chemical reaction. The characteristic time o the low can be deined as the time it takes or a luid element to traverse the low ield o interest. And the characteristic time o the chemical reaction can be deined as the time it takes or the chemical reactions to reach equilibrium. So, we can assume: τ τ τ τ c τc :FrozenFlow : Nonequilibrium Flow τ : Equilibrium Flow c In this study, the present author analyzed the low under the condition in which the assumption o the chemical equilibrium is valid. ππ q q C T = κ n N = ρ d h D i i i i () () q = Iν( θ, φ )cos θ sin θ d θ d φ dν () R Conductive heating is caused by the temperature gradient and governed by Fourier s law. For a chemically reacting mixture, there is also an energy transport due to diusion. As species diuse through the gas, the enthalpy o the species is carried with them. The heating caused by this phenomenon is called diusive heating. Moreover, when the temperature o the gas is extremely high, radiation becomes signiicant. For air, this threshold temperature is about, K. The radiation interacts with the low ield and creates the immense heating or the space vehicles. For example, or the Apollo reentry, the radiative heating was more than percent o the total heating. But under the condition o this study, where the assumption o the chemical equilibrium holds, radiative heating can be neglected compared to conductive heating and diusive heating. Computational Method. Aerodynamic Heating. Governing Equations Aerodynamic heating consists o three kinds o The governing equations or the external low heating, that is, conductive heating, diusive are the two dimensional axisymmetric heating, and radiative heating: Navier-Stokes equations: q= qc + qd + qr () Q E F Ev F H v = + + H v t x y x y ()

3 COMPUTATIONAL STUDY OF CHEMICALLY REACTING HYPERSONIC FLOW For the analysis o transpiration cooling, we must solve the internal low and heat conduction o the porous media simultaneously with the external low. Like as Navier-Stokes equations, the equations or the internal low in the porous media also consist o the equation or mass conservation, the equations or motion and the equation or energy conservation. To model the low in the porous media, we must deine the porosity,φ, as the volume o the pore in the unit volume o the porous media. Then, the equation or mass conservation is: ρ φ t ( ρ V ) + i = () The equation or motion is: p = ( αµ + βρ V ) V () O, N, O, NO, N, NO, e, N, O, Ar, Ar O O () N + O NO () N N + NO + e NO + N + e N + O + e O + Ar + e Ar equilibrium equations mass-balance equations charge neutrality equation () () () () () The chemical equilibrium composition is governed by simultaneous equations.. Numerical Scheme The above equation is the empirical law called Darcy s law. α, β is the constant. [] And the equation or the energy conservation is: T Cpρ Vi T C pρ + t φ p Vi T hv = + + i( κ T ) + ( Ts T) t φ φ () Speciic heat ratio h in the above equation is called the volumetric Speciic heat v heat transer coeicient. Finally, the heat conduction equation o the porous media is: c T t h = i( κ v s Ts) ( T T φ s sρs s ). Chemical Model (9) In this study, species and chemical reactions were considered:.. External Flow For the external low, we adopted the Harten-Yee s upwind TVD scheme to evaluate the numerical lux o the convective terms and used the nd order central dierence. To take real gas eect into account, the correction was made or the thermodynamic properties and the transport properties listed below. [],[] Sound speed Temperature Viscosity Thermal conductivity To calculate the chemical equilibrium composition, we have to solve the simultaneous equations, but the equilibrium equations are nonlinear, so they cannot be solve analytically. Thereore, the iterative method

4 YOSHIFURU FUNAHASHI developed by Prabhu [] was adopted. The Prabhu s method can save computational time by dividing the density-temperature domain into our regions and identiying the major species, the species that are ound in abundance in each o these regions. Finally, the Baldwin-Lomax model was adopted as the turbulence model. The transition rom laminar to turbulence can occur even at hypersonic speeds and cause an increase in aerodynamic heating, hence it is important to take it into account. Baldwin-Lomax model is in the class o what is called the eddy viscosity model, where the eects o turbulence in the governing equations are included simply by adding an additional term to the transport properties. µ = µ l + µ t () µ lcp µ tcp κ = κl + κt = + () Pr Pr.. Internal Flow and Porous Media For the internal low and the heat conduction o the porous media, the present author used the nd order central dierence to evaluate the partial derivative, and introduced the relaxation parameter to suppress the numerical instability. l t external low. The green and blue grids are or the porous material. Coolant air is transpired only in the region o the blue grids.. Code Validation.. Turbulence model The present author calculated the low on the adiabatic wall and checked the velocity proile in the boundary layer. Fig. shows its results. Its agreement with the law o the wall, which was conirmed by the experiment, is quite well... Real Gas Eects The temperature behind the shock wave is lower under the condition o chemical equilibrium than in the case where the gas is assumed calorically perect. This is because the kinetic energy o the low is shared across the all molecular modes o energy and goes into the zero point energy o the product o the chemical reaction. And the lower the pressure is, the more remarkable this eect is. This is because increasing the pressure tends to inhibit the dissociation and the ionization. The code was checked by calculating the low around the blunt body. Fig. shows its results. The result agrees very well.. Computational Grid In the computational grid or the external low, there are grid points normal to the surace, and grid points along the surace. In the computational grid or the internal low and porous media, there are grid points normal to the surace and grid points along the surace. Hence, there are, grid points in total. Fig. shows the grid system. Red grids are or the.. Chemical Composition Chemical equilibrium composition under the constant density was solved. Fig. shows its results. We can see that the dissociation and the ionization occur as the temperature increases. The present author checked that its result agrees very well quantitatively with Prabhu s results.. Computational Results and Discussions

5 COMPUTATIONAL STUDY OF CHEMICALLY REACTING HYPERSONIC FLOW. Without Thermal Protection Systems First o all, the low around the blunt body without a thermal protection system was calculated. Table shows the computational conditions. The assumption o the chemical equilibrium is valid under this condition. Fig. shows the temperature distribution o the low ield. And Fig. shows the one under the same condition but in the case where the gas is assumed to be calorically perect. We can see the dierence in the shock stand-o distance and the temperature decrease. Fig. shows the mole ractions on the stagnation streamline. We can see that atomic oxygen and nitric oxide are produced as the low passes through the shock. Fig. shows the aerodynamic heating on the surace. We can see that diusive heating is about % o the total.. Film Cooling In this study, the present author assumed that the coolant air chokes in the converging nozzle and reaches to sonic speed at the exit. And the position o the second injection point is changed as a parameter. Table shows the computational condition. Fig. 9 shows the pressure distribution. We can see that low ield is changed by the injection. To study the eects o ilm cooling, the decrease in the aerodynamic heating and the one per unit mass low was calculated. Fig. shows the ormer, and Fig. shows the latter. For each, we can see that there is the optimal position or the second injection point. Finally, the present author calculated the increase o the drag and compared its results with that o the case without thermal protection system. Fig. shows the percentage o the increase o the drag. We can see that not only aerodynamic heating but also the drag can be decreased in the case where the second injection point is set near the stagnation point.. Transpiration Cooling The transpiration cooling has the disadvantage o the mass low near the stagnation point becoming insuicient i the coolant air is transpired at the same constant pressure in all areas. This is because the pressure o the external low is high near the stagnation point. To avoid this, the present author combined ilm cooling and transpiration cooling, and assumed part o the coolant air is injected through the slit at the stagnation point and the rest is transpired through the porous media in the limited regions on the surace. Table shows the computational condition. Fig. shows the temperature distribution o the media and the velocity vector plot o the transpiring coolant air. We can see that the temperature o the media is cooled down by the transpiration, and the coolant air is transpired almost normal to the surace. Fig. shows the decrease o the average surace temperature o the media per unit mass low. The less the mass low is, the more eective the cooling is.. Comparison between the Cooling Systems To compare the eects o the ilm cooling and the transpiration cooling, the present author

6 YOSHIFURU FUNAHASHI removed the isothermal condition or the analysis o ilm cooling and recalculated it under the same condition o the transpiration cooling. Fig. shows the surace temperature o the media. The transpiration cooling system can keep the surace temperature low in the wide region o the transpiration. Fig. shows the decrease in the average surace temperature o the media. We can see that the transpiration cooling is more eective than the transpiration cooling under the condition o this study.. Conclusion Numerical analysis o the chemical equilibrium low was conducted. The temperature behind the shock is decreased by real gas eect, and atomic oxygen and nitric oxide are in the majority o the chemical composition under the condition o this study. In the analysis o ilm cooling, there is an optimal position or the second injection point. And not only aerodynamic heating but also the drag can be decreased when the second injection point is set near the stagnation point. Regarding the transpiration cooling, the less the mass low is, the greater the decrease o the average surace temperature per unit mass low is. Finally, two cooling systems were compared. The transpiration can cool down the surace temperature in a wide region and is more eective than ilm cooling under the condition o this study. Reerences [] Ishii I, Kubota H. Two-Dimensional Material Response o a Transpiration-Cooled System in a Radiative/Convective Environment, AIAA Journal, Vol., No., pp -, 9 [] Srinivasan S, Tannehill J.C. Simpliied Curve Fits or the Thermodynamic Properties o Equilibrium Air, NASA RP, 9 [] Gupta R.N, Lee K, Thompson R.A, Yos J.M. Calculation and Curve Fits o Thermodynamic and Transport Properties or Equilibrium Air to K, NASA RP, 99 [] Prabhu R.K, Erickson W.D. A Rapid Method or the Computation o Equilibrium Chemical Composition o Air to K, NASA TP 9, 9 Table. : Computational condition or the case o no thermal protection system Table. : Computational condition or ilm cooling Table. : Computational condition or transpiration cooling

7 COMPUTATIONAL STUDY OF CHEMICALLY REACTING HYPERSONIC FLOW.. y x Fig. : Computational grid Fig. : Temperature behind the shock - N O N + - e O + u+ x=. x=.9 x=. Lawo the Wall log (σ i / σ) Ar NO NO + Ar + N O y+ Fig. : Velocity proile in the boundary layer - T[K] Fig.: Chemical composition o air

8 YOSHIFURU FUNAHASHI y... T σ i / σ.... O NO x Distance [m] Fig. : Temperature distribution: chemical equilibrium Fig. : Mole raction on the stagnation streamline y x T q[mw/m ] q C q D q C +q D 9 θ [deg] Fig. : Temperature distribution: calorically perect Fig. : Aerodynamic heating on the surace

9 COMPUTATIONAL STUDY OF CHEMICALLY REACTING HYPERSONIC FLOW y..... p Q /m..... =. [MPa] =. [MPa] =. [MPa] x m[kg/sec] Fig. 9: Pressure distribution Fig. : Decrease in aerodynamic heating per unit mass low Q [MW]..... m[kg/sec] =. [MPa] =. [MPa] =. [Mpa] Fig. : Decrease in aerodynamic heating D/D [%] =. [MPa] =. [MPa] =. [MPa] - - m[kg/sec] Fig. : Increase o drag 9

10 YOSHIFURU FUNAHASHI y.... Ts x T[K] Point Film θ = [deg] Point Film θ =. [deg] Point Film θ =. [deg] Transpiration φ =. Transpiration φ =. Transpiration φ = 9 θ [deg] Fig.: Temperature distribution: transpiration cooling Fig.: Surace temperature o the media =. [MPa], φ =. =. [MPa], φ =. p jet =. [MPa], φ = =. [MPa], φ =. =. [MPa], φ =. =. [MPa], φ = =. [MPa], φ =. p jet =. [MPa], φ =. =. [MPa], φ = Point Film Point Film θ = [deg] Point Film θ =. [deg] Point Film θ =. [deg] Transpiration φ =. Transpiration φ =. Transpiration φ = T /m 9 T ave /m.... m[kg/sec].... m[kg/sec] Fig. : Decrease in average surace temperature o the media per unit mass low Fig. : Decrease in average surace temperature o the media per unit mass low