ME 475/675 Introduction to

CombustionLecture 18

Hypothetical chain reaction steps, Global rate calculation, Example 4.3

Announcements• HW 7, Due 10/12/15 (problem list next lecture)

• Midterm I, Average 74

Hypothetical Chain reactions (example)• Globally: ( and are general atoms) • Find rate of product production in terms of reactant molar concentrations• • Find and for a proposed mechanism

• Until you have more experience, you can’t yet know how to propose these mechanisms • Based on global (observed) reaction

• So if we can any one of these three time-derivatives, then we can find the other two

Proposed intermediate steps• For the Global (observed) reaction • Someone has postulated four steps:• Slow creation of free radicals (and ),

• • Chain-initiating step. creates radicals

• Fast consumption of and (neglect reverse because and are small)•

• Chain-propagating step (consumes and creates radical, net zero)• De-energization ter-molecular reaction is slow

• Chain-terminating step (consumes radicals)• Assume and are much greater than and • Number of species ( N = 6

• 5 differential equations, 1 algebraic equation (M)

Product Production• Products: (eventually want this in terms of and , alone)• (need to eliminate )

• But remember

• So if it’s easier to find or in terms of and , then that works also

• Reactant consumption, , •

• So if we can in find terms of and (and , which is constant), then we will be successful

Production - Consumption equations• Intermediates , (fast, so becomes algebraic, not differential)• Steady state approximation

Solve for [A]

• Divide by -2

• (quadratic in )

• Use + since ; also simplify knowing and and ≫

•

• Plug into

Production

Consumption

Production

• We were trying to find and for • So

Example 4.3 page 125• As mentioned previously, a famous chain mechanism is the Zeldovich, or thermal,

mechanism for the formation of nitric oxide from atmospheric nitrogen:

• Because the second reaction is much faster than the first, the steady-state approximation can be used to evaluate the N-atom concentration. Furthermore, in high-temperature systems, the NO formation reaction is typically much slower than other reactions involving and . Thus and can be assumed to be in (partial) equilibrium:

• Construct a global mechanism

• Represented as

• i.e. determine , , and . Using the elementary rate coefficients, etc., from the detailed mechanisms.

End 2015

Example 4.4 page 127• Consider the shock-heating of air to 2500 K atm 3 atm. Use the results of

Example 4.3 to determine:• A. The initial nitric oxide formation rate in ppm/s• B. The amount of nitric oxide form (in ppm) in 0.25 ms.

• The rate coefficient, is [reference 10 from book]