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BAROCLINIC TURBULENCE OF DISSOCIATING GAS AS A REASON FOR INSTABILITY OF BOW SHOCK WAVE A.S.Baryshnikov Physico-Technical Institute of RAS, Russia,

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The history The gases with great molecular weight is often used for high Much number modeling in free flight of body in ballistic ranges. One of them is gaseous CF 2 Cl 2, which has very high energy of dissociation what is impotent for modeling flight in ideal not reacting gas.

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Scheme of ballistic range Powder gun One of visualization windows with Shlieren set up receiver

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Problem When velocity of body riches the amount at which Chemical dissociation (not exothermic reaction) takes the place Just a disturbances on bow shock wave are arising. The flow behind body becomes disturbed in such manner as for turbulent flow. Its important that such turbulence is outside the wake flow region

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Fig.1. Instability of bow shock wave in front of segmental body. Flow Mach number: М 0 =3,9; Gas: CF 2 Cl 2. Pressure in flow: Р 0 =3,8·10 4 Pа. Wake turbulence Single vortex Disturbance on bow shock wave

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Fig.2. Instability of bow shock wave in front of segmental body. Flow Mach number: М 0 =3,9; Gas: CF 2 Cl 2. Pressure in flow: Р 0 =4,3·10 4 Pа.

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Applications Reducing a drag of air vehicles ( destabilization and destruction of bow shock wave), At dropping of Temperature and so of heat flux to surface!!! Controlling a flight of them, Without any energy deposition ( Compare with case of plasma control ),

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Usual study region

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Fig.3. Estimation of one dimension spectrum of density fluctuations in investigated region of turbulent flow behind segmental body higher than axis. Body diameter d=27 mm, CF 2 Cl 2 ; М 0 =6,8, Р 0 =3,8·10 4 Pа, length of realizations Θ =18 mm. I(ξ) Db ξ bin -20 -40 100200 ξ is normalized wave number of fluctuations

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Fig.4. Estimation of one dimension spectrum of density fluctuations in investigated region of turbulent flow behind sphere body higher and lower than axis. Body diameter d=27 mm, CF 2 Cl 2 ; М 0 =6,1, Р 0 =8·10 4 Pа, length of realizations Θ =41 mm. I( ξ) Db 15010050 -10 -20 -30 -40 200 ξ bin

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Estimation of energy spectra For isotropy turbulence we have

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Fig.5. Estimation of three dimension energy spectrum of turbulence in investigated flow region behind segmental body higher than axis. Body diameter d=27 mm, CF 2 Cl 2 ; М 0 =6,8, Р 0 =3,8·10 4 Pа, length of realizations Θ =18 mm. 1/r c

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Fig.6. Estimation of three dimension energy spectrum of turbulence in investigated flow region behind sphere body higher and lower than axis. Body diameter d=27 мм, CF2Cl2; М0=6,1, Р0=8·10 4 Па, Θ =41 mm. 1/r c

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Some conclusions from spectral estimations Maximum amount of three dimensional spectrum in the investigated region of waves numbers (Fig.5-6) corresponds to vortexes with character size 2r c θ ξ max, r c 0,3 mm (θ - length of realization, ξ max - wave number corresponds to maximum of spectra intercity) This size is local dimension of investigated turbulence. It can be used for obtaining estimations of energy of turbulent pulses near 100 kDj/kg [experiment]. As it will be shown this energy is well compared with character energy of physical-chemical processes determining the turbulence pulses 90,8 kDj/kg which is the energy of dissociation of molecule of CF 2 Cl 2.

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The baroclinic term is conditioned by change the entropy - grad S How to explaine the turbulence arising? Lets write equation for vorticety = B

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Estimation of energy amount conditioned the flow instability For this aim the relation connected entropy changing, -ΔS, with a vortices in gas particle in homogeneous stationary flow. The amount of energy participated in thermal exchange, - q, for chemical processes is simply the same as T·S. Stationary equation of fluid dynamics will be:

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This situation is just realized for 1. large Damkeler number ratio of reacting time to the time of flow ( so called almost frozen flow) and 2. for such polyatomic gas as CF 2 Cl 2 with high energy of dissociation Deposition of chemical processes in change of entropy ΔS for great dissociation energy ΔH, little concentration lnζ k and great grad ζ k of products becomes very large: H k, M k, ζ k – creation energy, molecular weight and concentration of spesies; R Γ - gas constant

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Use the model of rolling swirl q =6 10 2 Here is V m 250 - the middle flow velocity near the lateral surface m/s. [ found from estimation of full mass consumption of gas stream ( 3,4 kg/s) between the shock wave and lateral surface]. S = almost (consider that vortex of characteristic size r is moving along the surface as if it is rolling along the surface without slide)

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The second step in turbulence investigation, which could give the answer for a question about a nature of phenomena, could be made, consider the dissipation function: Maximum of it corresponds to dimension of vortexes, on which main part of pulses energy in gas is dissipated energy diffusion due to the dissipation take the place if their dimension about of order of amount or larger than Kolmogorov's micro dimension of turbulence: ε x - mass density of power of dissipation, ν - the viscosity of gas

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Table 1. η - Kolmogorov's microdimension. η d - Dimension of vortexes which is most intensely dissipated ξ d - amount of wave number at which dissipation function have an absolute maximum, ε - mass density of power of dissipation. ηηdmηηdmη ηηmηηm ξ d bin ε W/kg Usual viscose stationary turbulence (estimation) 6 10 -5 6 10 -6 7 10 2 2 10 7 Estimation found from experimental data and data of energy release at dissociation 1 10 -6 1 10 -7 4 10 4 5 10 10 Estimation from equilibrium energy of oscillatory degrees of freedom. 2 10 -6 2 10 -7 2 10 4 7 10 9

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Some conclusions estimation of power of dissipation of investigated turbulent flow (second row) is close and almost higher than estimation made for the case of release of all equilibrium energy of oscillatory degrees of freedom third row (accuracy of ε in frames of order of value). Then its amount is greater than estimation for usual viscose stationary turbulence in three orders of value.

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So appearance of turbulent flow in experiments is not conditioned by viscose dissipation of flow energy on the lateral surface and is connected with excitation of more energy capable degrees of freedom than oscillatory one. Such degrees of freedom can be, for instance, the chemical degrees or degrees of electron excitation.

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Fig.8. Scheme of flow around blunt body at the transformation to reacting regime. Dashed region is high entropy layer of gas flow. grad S is not coincides with vector of V, so rotV is not zero Reactions are only at stagnation point and products flow near the surface of body

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The gradient is conditioned by difference of entropy between its value on surface and on shock wave – ΔS, and by the depart of shock wave from surface - δ. Assume once more the following model of rolling swirl: let's consider that vortex of characteristic size is moving along the surface as if it is rolling along the surface without slide alike cylinder of radius – r(t). Then: =2V/r

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1. Interaction of vortex with shock wave takes the place if r0,5 δ ; i.e. at 2. On the other hand for perturbation of shock wave it's necessary that VVsound γ*, μ – effective ratio of specific thermo capacities of gas and its molecular weight in compression zone

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Two conditions take the place if: this criteria is valid for regime at which first (at shock wave Mach number arising) disturbances on shock wave were observed at flow of CF 2 Cl 2 around the blunt body. ( M =4, P =0,04 MPa ) INDEED: Temperature and pressure in critical point will be: T=750 K, P=0,1 MPa

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There is experimental data of equilibrium chemical composition of dissociation of CF 2 Cl 2 about at this temperature and pressure: Trenwith A.B., Watson R.H. Thermal decomposition of chlorofluoromethanes.// J.Chem.Soc. (London). 1957. N 5. P.2368-2372 Using it we can find TS=90,8 kDj/kg. Then (Т S)=150,7 m/s. Since sound speed in CF 2 Cl 2 at this regimes 239 m/s (at γ* 1,1) criterion (14) take the place. At rising of M and P they reach the values at which criterion (14) is not available (for instance for P =0,04 MPa it is M =6) and center of disturbances creation is moving from region of lateral flow to region of bottom flow.

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Comparison with experiment In experiments we observe that perturbations of shock wave front (and of the flow behind it) indeed at P =0,04 MPa at M =4 is of find scale 0.3 mm But at M =6 they are almost neglected.

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Summary We can say from experimental study and made estimations that effect of so called instability of bow shock wave and flow behind it Is conditioned by the baroclinic type of flow of reacting gas in compression zone between bow shock wave and bow surface I am very thanks for collaboration first of all to A.Bedin, then to V.Derevyanko, V.Maslennikov, I.Basargin and M.Chistyakova. Thank you for attention

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