1 / 12

ME 475/675 Introduction to Combustion

ME 475/675 Introduction to Combustion. Lecture 19. Announcements. HW 7, Problems ?; Due ? Return midterm. Midterm 1. Before Scaling Average 70 Max 100; Min 37 After Scaling Average 82 (UG: 80, Grad: 95) Max 100; Min 61 Problem 1a was intended to help with 1b

venus-holman
Download Presentation

ME 475/675 Introduction to Combustion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ME 475/675 Introduction to Combustion Lecture 19

  2. Announcements • HW 7, Problems ?; Due ? • Return midterm

  3. Midterm 1 • Before Scaling • Average 70 • Max 100; Min 37 • After Scaling • Average 82 (UG: 80, Grad: 95) • Max 100; Min 61 • Problem 1a was intended to help with 1b • Many people didn’t attempt much of problems 2 or 3 • Solutions posted outside PE 215

  4. Chemical Time Scales • How long does it take for the reactant with the smaller initial amount to significantly decreases? • Uni-molecular Reaction • ; (separable) • Units • Assume T changes slowly, so that • ; • At time (chemical time scale)

  5. Bi-molecular Reaction • ; • assume A has smaller initial amount • But and are related (decrease from initial concentrations are the same • so • Where is a positive constant (initially more B than A)

  6. Bi-molecular Reaction Chemical Time • At (find this) • and • For , , and

  7. Ter-molecular • ; • For , , and • Time scale increases as increases, but only by 67%

  8. Example 4.5page 131 • Work in Excel, conclude: • Time scale t decreases at temperature T increases • Ter-molecular reaction is slow

  9. Partial Equilibrium • Some reactions of a mechanism are much faster in both directions (forward and reverse) than others (as described in Example 4.3) • Usually chain propagating (or branching) reactions are bi-molecular and faster than ter-molecular recombination reactions • Treat fast reactions as if they are equilibrated • This allows them to be treated using algebraic equations and reduces the number of differential equations that must be solved.

  10. Example: Shuffle Reaction (Stable , , ) • 1f • 1r • 2f • 2r • 3f • 3r • 4f (ter-molecular recombination) • , need and = fn(, , ) • Assume reactions 1, 2 and 3 are all in partial equilibrium • Species , , , N=7 • Stable: , , • Intermediaries:

  11. Find intermediary concentrations () • ; 1 • ; 2 • ; 3 • Goal: find , , and = fn(, ) • From 3: 4 • Plug into 1: ; 5 • Plug 4 and 5 into 2: • 6 • Plug 6 into 4:

  12. Problem 4.20 page 148 • In the combustion of hydrogen, the following reactions involving radicals are fast in both the forward and reverse directions: • Use the assumption of partial equilibrium to derive algebraic expression for the molar concentrations of the three radical species, , and , in terms of the kinetic rate coefficients and the molar concentrations of reactant and product species , , and .

More Related