Homework 5

Problem 1

Derive Turns Eq. (15.6a) and Eq. (15.9a). Note, in the second of these equations, the term in brackets is the first equation. That is, get N in terms of a, y; and get a in terms of x, y, XO2. It should then be clear how the dry versions of these equations were found.

Problem 2

Turns 15.5

In using Table 15.6, use the value of 12 ppm as shown in the 3rd edition, instead of the value of 15 ppm as shown in the 2nd edition.

Problem 3

(a) This problem is similar to Turns 5.13. Run an isothermal stoichiometric PFR with methane/air fed at 300 K. Run the reactor at 2216 K. Run for 200 ms (the residence time in the primary combustion zone of the furnace). Report the NO concentration.

(b) Next, additional air is instantaneously added to the products of the first PFR and then reacted in a second PFR (the secondary combustion zone) such that the overall equivalence ratio is 0.9. Run the second PFR adiabatic. The secondary air is at 300 K. Report the NO concentration.

Problem 4

For methane/air combustion, beginning with adiabatic equlibrium products (but zero NO), run an adiabatic batch reactor and plot the NO concentration (ppmv) versus time. On the same plot, include the NO versus time curve obtained from using Turns Equation 5.7. Estimate an NO formation timescale from your curve. $$\tau = \frac{\Delta y_{NO}}{\left. \frac{dy_{NO}}{dt}\right|_{max}}$$

Problem 5

Plot the adiabatic PSR temperature as a function of $1/\tau$ for a stoichiometric syngas mixture. Go up to extinction. Take syngas to have a composition of 80% CO and 20% H2 by volume.