Comtations of the Shock Waves at Hyersonic Velocities aken into Accont the Chemical Reactions that Aear in the Air at High emeratres Mihai Leonida NICLESC*,, Maris Gabriel COJOCAR Mihai Victor PRICOP, Dmitr PEPELEA *Corresonding athor INCAS National Institte for Aerosace Research Elie Carafoli, Flow Physics Deartment, Nmerical Simlation nit, B-dl Ili Mani 0, Bcharest 066, Romania niclesc.mihai@incas.ro*, cojocar.gabriel@incas.ro, rico.victor@incas.ro eelea.dmitr@incas.ro DOI: 0.3/066-80.05.7.3. Received: 5 Jly 05 / Acceted: 3 Agst 05 Coyright 05 Pblished by INCAS. his is an oen access article nder the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-nd/4.0/) 3 rd International Worksho on Nmerical Modelling in Aerosace Sciences, NMAS 05, 06-07 May 05, Bcharest, Romania, (held at INCAS, B-dl Ili Mani 0, sector 6) Section Flight dynamics simlation Abstract: he temeratre in the nose region of a hyersonic vehicle can be extremely high, for examle, reaching aroximately 000 K at a Mach nmber of 36 (Aollo reentry). he bow shock wave is normal, or nearly normal, in the nose region of a blnt body, and the gas temeratre behind this shock wave can be enormos at hyersonic seeds. In this case, the assmtion of a calorically erfect nonreacting gas with the ratio of secific heats of.4 gives an nrealistically high vale of temeratre. herefore, the roer inclsion of chemically reacting effects is vital to the calclation of an accrate normal shock wave temeratre. Key Words: Hyersonic flow, shock waves, chemical reactions, CFD, casle reentry.. INRODCION It is well known that at high temeratres, the air become to dissociate and ionize. For examle, for air at one atmoshere, the moleclar oxygen become to dissociate at abot 500 K and it is essentially totally dissociated at 4000 K. At this temeratre, moleclar nitrogen begins and it is essentially totally dissociated at 9000 K. Above this temeratre, ions are formed and the gas becomes a artially ionized lasma []. nfortnately, the kinetics of these chemical reactions (cr) is qite, not very well nderstood and reqires hge comtational resorces. For examle, only the air dissociation reqires at least 5 chemical reactions with third body efficiency and five secies (O, O, N, N, NO) [, 3]. For this reason, the resent aer resents a simlified CFD method for comting the casle reentry, which takes into accont both the released or absorbed heat Q de to the chemical reactions and the modification of global gas constant R. INCAS BLLEIN, Volme 7, Isse 3/ 05,. 9 33 ISSN 066 80
Mihai Leonida NICLESC, Maris Gabriel COJOCAR, Mihai Victor PRICOP, Dmitr PEPELEA 30. GOVERNING EQAIONS FOR OBLIQE SHOCK WAVES WIH CHEMICAL REACIONS he conservation laws of continity, momentm and energy for obliqe shock waves with chemical reactions cold be written as follows [4]: () n n n n () () nt nt t t (3) cr c c cr R - cr cr R Q cr cr c Q (4) Combining the above eqations, one obtains the following link relation between the shock angle and the flow deflection angle [] INCAS BLLEIN, Volme 7, Isse 3/ 05 M sin β tanθ cotanβ (5) M cosβ for calorically erfect nonreacting air while for reacting air, the link relation is [] tan β n n n - θ tanβ t n 3. NMERICAL SIMLAIONS AND RESLS he main difficlty in the imlementation of eqations for shock waves with chemical reactions in an in-hose code consists in obtainment of reliable data for the released or absorbed heat Q de to the chemical reactions. sally, one gives the sedo secific heat ratio cr instead of released or absorbed heat Q becase it is more convenient and efficient to imlement it from the nmerical oint of view. nfortnately, there are very few available works that give data for sedo secific heat ratio cr, which is clearly a fnction of temeratre and ressre. For examle, the reference [] recommends to se [5] to comte the secific heat ratio cr =f (, ) and temeratre =f(, )= / /R (, ). hese fnctions are qite comlex becase they have to take into accont the chemical reactions (dissociation and ionization) that aear in the air at high temeratres. nfortnately, or simlations have shown that the fnction =f(, ) given in [5] is not enogh accrate and the fnction cr =f(, ) given in [5] is rone to srios nmerical oscillations that can indce the divergence of iterative nmerical algorithm. For this reason, we refer to se the formlas given in [6] that are more comlex bt they fix the above mentioned deficiencies. In order to nderline that the roer inclsion of chemically reacting effects is vital to the calclation of an accrate normal shock wave temeratre, one resents the case of Aollo reentry, in able. t (6)
3 Comtations of the shock waves at hyersonic air velocities taken into accont the chemical reactions = 0 97.8 m/s H = 5 86 m able Comtation of normal shock wave for Aollo reentry for calorically erfect nonreacting air, =.4 for eqilibrim chemically reacting air (CAL Reort AG-79-A- [7]) for eqilibrim chemically reacting air (INCAS code) / 33 387 463 / 5.97 5.9 5.40 h /h 06.35.8 3.0 / 06.35 4.64 4.65 R [J/(kg.K)] 87.9 x 87.3 x 87 (kg/kmol) 8.96 8.96/.9 8.96/.3 From able, one clearly sees that the chemical reactions have the strongest effect on temeratre. Moreover, the calorically erfect nonreacting model considerably overredicts the temeratre behind the normal shock wave by nearly 5 times, given a highly nrealistic vale of 55 377 K. For this reason, it is imossible to se the calorically erfect nonreacting model even in the early stages of design becase it is imossible to size the thermal shield of reentry vehicles. Instead, the ressre is governed mainly by the flid mechanics of the flow, and not so mch by the thermodynamics. Frthermore, there is a good agreement between the INCAS reslts and those blished in [7]. De to the dissociation of oxygen and nitrogen (O O, N N), the air weight decreases. When the dissociated air weight becomes times smaller than that of the air at room temeratre (8.96 kg/kmol), the air is ractically totally dissociated. In the examle resented in table, the vale of temeratre behind the normal shock wave is abot 300 K and air weight is aroximately 8.96/. kg/kmol; therefore, the air is comletely dissociated downstream to normal shock wave. he bow shock wave is ractically a normal one in the nose region of hyersonic reentry vehicles, after which it becomes an obliqe shock wave. For this reason, it is very imortant and sefl to stdy the obliqe shock waves at hyersonic regime. Fig. Inflence of stream ressre on obliqe shock waves INCAS BLLEIN, Volme 7, Isse 3/ 05
Mihai Leonida NICLESC, Maris Gabriel COJOCAR, Mihai Victor PRICOP, Dmitr PEPELEA 3 In order to nderline the imortance of chemical reactions at hyersonic regime, even for obliqe shock waves, Fig. clearly shows the difference between the traditional calorically erfect nonreacting air model and eqilibrim chemically reacting air model, esecially for the maximm (detachment) flow deflection angle. Moreover, there is a qite good agreement between or reslts obtained with in-hose INCAS codes and those blished in [8]. Frthermore, one sees that the stream ressre has a small inflence on chemical reactions becase the reslts for stream ressre of 0.atm and 0.0atm are almost identical. his observation is very imortant becase it sggests that it is ossible to assme that the sedo secific ressre heat c cr is fnction of temeratre only in certain ressre ranges. nfortnately, there are very few available works that give data for sedo secific ressre heat c cr. Moreover, or simlations have shown that the relations for c cr =f() given in [9] are not enogh accrate becase the nmbers that aear in these relations have too few digits. Even the reliminary simlations of Earth reentry vehicles reqire a lot of comtational work [0]. For this reason, it is sefl to have a fast CFD method bt it has to be enogh accrate. he real gas model reqires more comtational effort than the ideal gas model bt it is more accrate. For this reason, we roosed a method based on ideal gas model that takes into accont the chemical reactions throgh introdction of sedo secific ressre heat c cr =f() given in [9] or in another work, instead of classical secific ressre heat c and throgh the modification of classical air constant R air = 87 J/kg/K: Comte the normal/obliqe shock wave with chemical reactions sing eqations (- 6) se as global air constant R the average mean of R and classical air constant R air = 87J/kg/K, see able se sedo secific ressre heat c cr =f() given in [9] or in another work, instead of classical secific ressre heat c Some reslts sing this methodology are given in Figs. and 3. Fig. Mach nmber distribtion for a reentry casle, M = 0, = 0.867 Pa, c cr are taken from [9] sing ANSYS Flent 5 [] and ASM scheme INCAS BLLEIN, Volme 7, Isse 3/ 05
33 Comtations of the shock waves at hyersonic air velocities taken into accont the chemical reactions Fig. 3 Pressre distribtion for a reentry casle, M = 0, = 0.867 Pa, c cr are taken from [9] sing ANSYS Flent 5 [] and ASM scheme 4. CONCLSIONS he resent aer resents a CFD methodology that has been sccessflly imlemented in Ansys Flent to comte the hyersonic vehicles reentry. he chemically reactions that aear in the air at high temeratres are taken into accont only throgh the introdction of sedo secific ressre heat c cr () and the globally changing of air constant R, see able. Frther work is necessary to be done in order to diminish the srios nmerical oscillations that aear, see Figs and 3. Moreover, the athors of this aer has scceeded in develoing in-hose codes written in Fortran that comte normal and obliqe shock waves at hyersonic regime taking into accont the chemical reactions that aear in the air at high temeratres. Frthermore, there is a good concordance between the reslts obtained with in-hose codes and those blished in [7, 8], see able. REFERENCES [] J. D. Anderson, Hyersonic and high temeratre gas dynamics, McGraw-Hill Book Comany, 989. [] C. Park, A review of Reaction rates in high temeratre air, AIAA aer, Vol. 89, 989. [3] V. Carandente, Aerothermodynamic and mission analyses of deloyable aerobraking Earth re-entry systems, Ph. D. hesis, niversity of Nales Federico II, 04. [4] V. N. Constantinesc and S. Găletşe, Mecanica flidelor şi elemente de aerodinamică (only in Romanian), Editra Didactică şi Pedagogică, Bcharest, 983 [5] J. C. annehill and P. H. Mgge, Imroved crve fits for the thermodynamic roerties of eqilibrim air sitable for nmerical comtation sing time-deendent or shock-catring methods, NASA CR-470, 974. [6] S. Srinivasan, J. C. annehill and K. J. Weilmenster, Simlified crve fits for the thermodynamic roerties of eqilibrim air, NASA RP-8, 987. [7] P. V. Marrone, Normal Shock Waves in Air: Eqilibrim comosition and flow arameters for velocities from 6,000 to 50,000 ft/s, Cornell Aeronatical Laboratory (now CALSPAN), Reort no. AG-79-A-, 96. [8] W. E. Moeckel, Obliqe shock relations at hyersonic seeds for air in chemical eqilibrim, NACA N 3895, 957. [9] R. N. Gta, K. P. Lee, R. A. homson and J. M. Yos, Calclations and crve fits of thermodynamic and transort roerties for eqilibrim air to 30 000 K, NASA-RP-60, 99. [0] M. V. Prico, M. G. Cojocar, M. L. Niclesc and M. Boscoian, Earth reentry tool for reliminary mission analysis, INCAS Blletin, (online) ISSN 47 458, (rint) ISSN 066 80, ISSN L 066 80vol. 7, Isse, DOI: 0.3/066-80.05.7.., g. 3-8, 05. [] * * * Ansys Flent, heory Gide, release 5, 03. INCAS BLLEIN, Volme 7, Isse 3/ 05