Tham khảo tài liệu 'thermodynamics kinetics of dynamic systems part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Shock Structure in the Mixture of Gases Stability and Bifurcation of Equilibria 199 the system of governing equations 46 to the following set of ODE s which determine the shock structure d Pu 0 d d pu2 p J A 0 d Pc 1 -c d 1 .2 uJ 1 pu2 pi p u -33 - J 0 dn 2P p p pc 1 - c PJ 1 d Pcu J 0 52 d d pcu2 pc 2uJ vj mil d fl L . J A L . J a pq u pce V u dQ V2 k Pc PcJ J ni1 u év where u v s is x-component of the relative mixture velocity with respect to the shock wave and J and nil are x-components of diffusion flux and source term. Due to change of variables we shall have a standing shock profile with upstream unperturbed state U0 limp . TO u ỉ and downstream perturbed state U1 liny .TOu ỉ . In view of equilibrium conditions discussed above we adjoin the system 52 with following boundary conditions upstream downstream p P0 c C0 p Pl c Ci u u0 J 0 u ui J 0 T tT0 0 0 T T1 0 0. 53 Downstream boundary conditions u1 will be determined in the sequel. Stability and bifurcation of equilibria in shock structure problem Further analysis will be performed in dimensionless form using the following dimensionless variables p p u u T T J 0 0 ỉ - M0 dp P0 csE T0 P0c0 csE T0 TD csE csE We shall also assume that both components have the same ratio of specific heats equal to the average one 7. Upstream boundary data thus read p0 1 u0 M0 T0 1 J0 0 001 0 54 while c0 is already a dimensionless quantity. For convenience hats will be dropped in the sequel. To reduce the order of the system as well as computational effort conservation laws for mass and momentum of the mixture 52 1 2 and conservation law for mass of the component 52 4 200 Thermodynamics - Kinetics of Dynamic Systems will be used to express p J and T in terms of c and u p ĩ J M0C - cổ 55 T m-u 11 YM0 mo M0 I 0 1 - u 1 . c 2 AU I M0 V c 1 - c JJ Ỉ where m0 denotes the average atomic mass evaluated in upstream equilibrium state. There will remain three equations which will finally determine the shock structure. Although still .
