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Orr, F. M. - Theory of Gas Injection Processes Episode 4

Tham khảo tài liệu 'orr, f. m. - theory of gas injection processes episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4.2. SHOCKS 51 shock at T Ci cn shock at t At I I I I I I I I I I I I Ci cl ệ Aệ Figure 4.6 Motion of a shock. original conservation equation. In other words it is a statement that volume is conserved across the shock just as Eq. 4.1.1 states that volume is conserved at locations where all the derivatives exist. Eq. 4.2.2 says that the velocity at which the shock propagates is set by the slope of a line that connects the two states on either side of the shock on a plot of Fl against C1 such as that shown in Fig. 4.1. Now we apply the jump condition to determine what happens at the leading edge of the displacement zone where fast characteristics the characteristics in Fig. 4.5 that have high values of dFi dSi intersect the characteristics for the initial composition. Point a in Fig. 4.7 is the initial composition which is the composition on the downstream side of the leading shock and points b c d e f and g are possible composition points for the fluid on the upstream side of the shock. Any of the shock constructions shown in Fig. 4.7 satisfies Eq. 4.2.2. Hence some additional reasoning is required to select which shock is part of a unique solution to the flow problem. Two physical ideas play a role in that reasoning. The first is simply an observation that compositions that make up the downstream portion of the solution must have moved more rapidly than compositions that lie closer to the inlet. If not slow-moving downstream compositions would be overtaken by faster compositions upstream. The idea is frequently stated 31 as a Velocity Constraint Wave velocities in the two-phase region must decrease monotonically for zones in which compositions vary continuously as the solution composition path is traced from downstream compositions to upstream compositions . When the velocity constraint is satisfied the solution will be single-valued throughout. Composition variations that satisfy the velocity constraint are sometimes described as compatible waves and the velocity