Thermodynamics filled in class notes_Part_126

Thermodynamics filled in class notes_Part_126 - 259 7.1....

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7.1. ISOTHERMAL, ISOCHORIC KINETICS 259 Evolution on these two time scales is predicted in Fig. 7.8. This in fact a multiscale problem. One of the major di±culties in the numerical simulation of combustion problems comes in the e²ort to capture the e²ects at all relevant scales. The problem is made more di±cult as the breadth of the scales expands. In this problem, the breadth of scales is not particularly challenging. Near equilibrium the ratio of the slowest to the fastest time scale, the stifness ratio κ , is κ = τ 2 τ 1 = 4 . 691 × 10 7 s 3 . 181 × 10 8 s = 14 . 75 . (7.231) Many combustion problems can have sti²ness ratios over 10 6 . This is more prevalent at lower temperatures. We can do a similar linearization near the initial state, ³nd the local eigenvalues, and the the local time scales. At the initial state here, we ³nd those local time scales are τ 1 = 2 . 403 × 10 8 s, (7.232) τ 2 = 2 . 123 × 10 8 s. (7.233) So initially the sti²ness, κ
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This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Park-sou during the Fall '11 term at FSU.

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Thermodynamics filled in class notes_Part_126 - 259 7.1....

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