Influence of non-equilibrium on disturbance waves passing through a planar shock

Transcription

1 Center for rblene Researh Proeedings of the Smmer Program Inflene of non-eqilibrim on distrbane waves assing throgh a lanar shok By C. Stemmer, N. A. Adams AND N. N. Mansor he resent stdy investigates the behavior of harmoni waves assing throgh a strong shok in the resene of hemial reations and thermal non-eqilibrim. At a hyersoni Mah nmber (M=20), a lanar sinsoidal wave is eited at the inflow bondary of a steady strong lanar shok system. he amlitde and wave length of the distrbane is altered as it asses throgh the shok. As a referene ase, ideal gas onditions are allated. he distrbane amlitde and wavelength both derease by a fator of 1.6 for the freqeny of 100 khz. In a first stage, the behavior in the resene of hemial reations (eqilibrim) is shown. For the eqilibrim ase, the amlitde dereases twie as mh as for the ideal gas ase (by 3.3) and the wave length is dereased by 2.3. he non-eqilibrim ase ehibits ontrary behavior. he amlitde rises by 5.5 and the wave length inreases by a fator of 1.2. his shows the diret inflene of non-eqilibrim on the amlitdes and wave lengths of distrbane waves assing throgh a shok. 1. Introdtion Hyersoni re-entry vehiles from low-earth orbit (LEO) enter the atmoshere at seeds of abot 7.8 km/s, whih is in the Mah nmber range of abot 25. In the er layer of the atmoshere (h>100 km), free molelar flow is resent. As the vehile gets slowed down on its ath toward Earth, the density inreases sh that ontinm aroahes are jstified. he Mah nmber in an altitde of abot km is still abot 20, whih leads to high degrees of non-eqilibrim (hemially and thermally) behind strong shok waves (see also Miller 2005). As the density beomes higher, the qestion of transition of the laminar flow to a trblent state arises (Stemmer 2005). As the transition roess involves the eonential amlifiation of ertain waves and resonane between a gro of waves in the late stages of transition, the inflene of small shoks inside the bondary layer on the develoment of waves and their resonanes has to be investigated. he shoks inside the bondary layer (also alled shoklets) are a reslt of the veloity distrbanes of non-linear amlitdes in high-seed bondary layers. As the shoks are the sore of non-eqilibrim, the resent work attemts to break down that omle roess whih sally involves a whole setrm of distrbane waves into a model roblem. he resent work foses on the behavior of solitary waves as they ass throgh a strong shok wave. Single waves have been sed for the diret nmerial simlations (DNS) to identify individal hanges in freqeny and wave length as well as amlifiation or attenation in amlitde. If one were to investigate a white noise setrm, only global onlsions wold be ossible. he investigated freqenies lie in the freqeny domain, where instabilities or for the rrent flow onditions. he behavior of isotroi trblene in the resene of a weak shok (1.05 < M < Lehrsthl für Aerodynamik, ehnishe Universität Münhen, Germany

2 50 C. Stemmer, N. A. Adams & N. N. Mansor 1.2) for a thermal and hemial erfet gas has been investigated by Lee, Lele and Moin (1993). hey fond that trblene was enhaned dring interation with a shok wave as the trblent kineti energy and transverse veloity omonents were amlified. he trblent length sales were dereased. A loal raid inrease of trblent kineti energy jst downstream of the shok was also seen. In a stdy etending the investigation to strong shoks originating from higher Mahnmber flows, the inrease of the trblent kineti energy satrated for M>3 (Lee, Lele and Moin (1997)). Mahesh, Lee, Lele and Moin (1995) fond distint differenes between the interation of a vortial field (as in the stdies of Lee et al. (1993)) with a shok omared to aosti wave interation with the shok. A derease of kineti energy from the aosti waves de the interation with a weak shok wave (1.25 < M < 1.8) was observed. Bt at higher Mah nmbers eeeding 3, the behavior was reversed and an inrease in kineti energy was observed. his was aomanied by a generation of vortial distrbanes throgh the interation. his lead to an inrease of the far-field kineti energy with higher Mah nmbers. Work devoted to stdy the interation of entroy fltations in the resene of vortial fltations with shok waves for the range of 1.25 < M < 1.8 by Mahesh, Lele and Moin (1997) show a deendeny of the behavior on the orrelation of the two distrbanes. A ositive orrelation between and has a sressing effet on the amlifiation, whereas a negative orrelation an be fond to inrease the amlifiation of the trblent kineti energy, vortiity and thermodynami fltations. Using these findings as a base, we investigated the role of hemial non-eqilibrim on the aforementioned reslts. 2. Methodology he resent stdy was ondted sing DNS with the NSMB ode Vos et al. (1998), Vos, Dqesne, Lee (1999). NSMB is a finite volme higher-order method solving the Navier-Stokes eqations aable of handling eqilibrim, hemial non-eqilibrim and hemial and thermal non-eqilibrim. he method an handle shoks throgh an wind disretization sheme. A lanar shok wave satisfying the Rankine-Hgoniot relations was resribed as an initial soltion and the nmerial soltion was iterated ntil it reahed a steady state. In a seond ste, time-eriodi fltations at the inflow bondary were resribed and the simlation was ontined ntil it beame eriodi in the soltion. he distrbanes introded were of different natre. hree different ases are resented here. For referene reasons, a erfet gas soltion (Case I) is resented althogh the onditions wold not allow for that in a real flow. he temeratres of more than 20,000 K behind the shok are nrealisti withot the onsideration of dissoiation and reombination. In Case II, hemial eqilibrim is assmed where the hemial reation rates are assmed to ehibit a time sale that tends to infinity ths assring loal eqilibrim onditions for the resetive temeratres. Case III ses hemial non-eqilibrim where the seed of the hemial reation rates is in the same order of magnitde as the flow time sale. hs, the shok is a sore of non-eqilibrim and downstream of the shok, the hemial onentrations hange as the flow evolves (see fig. 1, disssed in the reslts setion)

3 Non-eqilibrim distrbane develoment throgh shok waves Figre 1. Seies onentrations for Case II and Case III. N 2 : ; N: ; NO: ; O 2 : ; O: For the inflow onditions, a M=20 flow at = K and = N/m 2 was assmed. his amonts to a seed of U = 6596 m/s. For Case II and Case III, an initial onentration of the seies of N2 = and O2 = was given. 3. Reslts 3.1. Basi shok roerties he erfet-gas shok soltion satisfies the Rankine-Hgoniot relations as well as the ideal-gas eqation = R, where is the ressre, is the density, is the temeratre and the ideal gas onstant is R = 287 J/(kg K). For Case I, the temeratre after the shok inreases to 2 = 21, K, the ressre to 2 = N/m 2 and the density to = 7.73 Kg/m 3. For Case II, the hemial reations (mostly the dissoiation of oygen and the bild of nitri monoide (NO); see fig. 5) take energy ot of the flow and the temeratre behind the shok inreases to only 2 = 7, K. he density inreases to = Kg/m 3 and the ressre inreases only to 2 = N/m 2. As the eat hemial omosition behind the shok is nknown at the beginning of the steady shok simlations, one starts with the ideal-gas simlation. herefore a transient eriod with the shok moving is eeriened. he simlations for Case II are in a moving frame of referene that moves at s = m/s, whih has to be added to the shown veloities in the fig. 3 and 4. he non-eqilibrim ase (Case III) ehibits thermodynami roerties that are in the same range one they reah a steady vale. he onentrations hange downstream of the shok (see fig. 5). It takes abot = 0.02 m ntil the eqilibrim state (Case II) is reahed again Distrbane develoment he distrbane onsidered is an entroi distrbane, i.e., the ressre remains onstant and the density distrbane satisfies the following relation = (γ 1) M 2 U.

4 52 C. Stemmer, N. A. Adams & N. N. Mansor E E E E () Figre 2. Case I: distrbane evoltion for an entroi distrbane after the shok. veloity, ressre, () density, temeratre. he freqeny hosen was F=100kHz and the veloity distrbane level was at A = 0.5%. For the ideal gas ase (Case I), the distrbane develoment after the shok at = 0.5m is shown in fig. 2 (the veloity (sbfigre a), ressre (sbfigre b), density (sbfigre ) and temeratre (sbfigre d) are resented). he entroi distrbane shows a harmoni behavior after it asses throgh the shok. he ressre also shows small osillations (not the sale in fig. 2d) that indiate an aosti distrbane being generated throgh the interation of the entroi distrbane with the shok. Note that the amlitdes remain onstant and no dissiation from the nmerial sheme sed is notieable. As the distrbane goes throgh the shok, the referene onditions hange to the onditions after the shok. In absolte nmbers, the distrbane amlitdes derease. he relative distrbane veloity amlitdes (the referene is the loal ū) derease for the ideal gas ase (Case I) by a fator of 1.6 and by the same fator in wavelength. For the eqilibrim ase (Case II), the reslting instantaneos distribtion after the distrbane int at the inflow bondary and before the shok at = is resented in fig. 3. he evoltion of the distrbane amlitdes after the shok is shown in fig. 4. It is obvios that the harmoni natre as in the ideal gas ase is lost and at least two different tyes of distrbanes with very lose wave lengths are resent. he ressre fltation is not small; an aosti distrbane has learly develoed. he relative distrbane

5 Non-eqilibrim distrbane develoment throgh shok waves () Figre 3. Case II: distrbane evoltion for an entroi distrbane before the shok. veloity, ressre, () density, temeratre. veloity amlitdes derease for the eqilibrim ase (Case II) by a fator of 3.3 and by a fator of 2.3 in wavelength. he inflene of the linear distrbane on the onentrations is as eeted (see fig. 5a). he distrbanes aear as small osillations in the onentrations. Most notieable is the osillation of the molelar nitrogen (solid line) bease it has the highest onentration. he hange in molelar nitrogen leads to a hange in atomi nitrogen onentration (dotted line). As molelar oygen (long dashes) is flly dissoiated, the nitri oygen onentration (dash-dot-dotted) and the atomi oygen are the most strongly inflened by the distrbanes. For the same distrbane, the non-eqilibrim ase (Case III) ehibits very different roerties. Before the shok, the distrbane is as resented in fig. 6. he distrbane veloity amlitde inreases by a fator of 5.5 and the wave length inreases by a fator of 1.2 behind the shok. he distrbane develoment downstream of the shok for Case III is resented in fig. 7. Only one to two distrbane wave lengths are shown sine the overall level of the resetive roerty moves ot of the shown range de to the hange of the thermodynami roerties and hemial seies. he develoment of the seies onentrations downstream of the shok is shown in fig. 5b. he small osillations in the onentrations an be notied in Case III as in the eqilibrim ase, bt the levels reahed frther downstream of the shok are different after the non-eqilibrim effet of the shok has sbsided. his is most notieable in the onentration of atomi nitrogen (dashed line), as it dros slowly to abot half the level

6 54 C. Stemmer, N. A. Adams & N. N. Mansor E E E E E+07 4E E () Figre 4. Case II: distrbane evoltion for a entroi distrbane after the shok. veloity, ressre, () density, temeratre Figre 5. seies onentrations for the distrbed Case II and Case III. N 2 : ; N: ; NO: ; O 2 : ; O: omared to Case II). he osillations an also be observed in all onentrations jst downstream of the shok. 4. Conlsions he behavior of harmoni entroi distrbanes as they move throgh a lanar shok wave are resented in this work. hree different ases are investigated. First, for referene

7 Non-eqilibrim distrbane develoment throgh shok waves () Figre 6. Case III: distrbane evoltion for a entroi distrbane before the shok. veloity, ressre, () density, temeratre E E E E () Figre 7. Case III: distrbane evoltion for a entroi distrbane after the shok. veloity, ressre, () density, temeratre.

8 56 C. Stemmer, N. A. Adams & N. N. Mansor roses, the ideal gas ase was resented, whih showed a derease in distrbane amlitde and wavelength downstream of the shok. With eqilibrim hemistry, the derease was even more rononed. In the third ase, the effet of the non-eqilibrim hemistry was investigated and fond to be adverse, leading to an inrease both in amlitde and wavelength. Chemial non-eqilibrim an lead to an inrease in distrbane levels downstream of a shok. he rrent work demonstrates the ossibility of an enhanement of the instability roess in transition where distrbane waves move throgh small shoks. Additional investigation is reqired. higher freqenies that lie in the instability range for hyersoni seeds and obliqe angles between shok and distrbane. REFERENCES Miller, J. H Comtational Aerothermodynami datasets for Hyersoni Heat transfer on Reentry Vehiles. AIAA Lee, S., Lele, S. K., Moin, P Diret nmerial simlation of isotroi trblene interating with a weak shok wave. J. Flid Meh., 251, Inlding Corrigendm 264, , Mahesh, K., Lee, S., Lele, S. K., Moin, P he Interation of an isotroi field of aosti waves with a shok wave. J. Flid Meh., 300, Mahesh, K., Lele, S. K., Moin, P he inflene of entroy fltations on the interation of trblene with a shok wave. J. Flid Meh., 334, Lee, S., Lele, S. K., Moin, P Interation of isotroi trblene with shok waves: effet of shok strength. J. Flid Meh., 340, Vos, J. B., Rizzi, A. W., Crojon, A., Chat, E., Soinne, E Reent advanes in aerodynamis inside the NSMB (Navier Stokes Mlti Blok) Consortim. AIAA Vos, J. B., Dqesne, N., Lee, H. J Shok wave bondary layer interation stdies sing the NSMB flow solver. Aerothermodynamis for sae vehiles, ESA SP-426, Proeedings of the hird Symosim on Aerothermodynamis for Sae Vehiles, Stemmer, C. Hyersoni ransition Investigations In A Flat-Plate Bondary-Layer Flow At M=20. AIAA