ME 475/675 Introduction to

CombustionLecture 26

Plug flow reactor, Problem X5:Constant area and pressure equations

Announcements• Midterm 2, November 13, 2015 (2 weeks)• HW 8a, Due now, Example 6.2 Equations• HW 8b, Due Monday, Numerical solution• HW 9 Due Monday, 10/26/15, Problem X5• Friday, 10/30/2015, Holiday

• Student, Alumni, and Faculty Research Opportunities at ORNL• hands-on research in a-real world setting with award winning scientists• Visit: http://www.orau.org/ornl[orau.org]• Or contact: ORNL Education Programs at ornledu@orau.org, or Leslie Fox at (865)

576-3427

Broader Impact Assignment• Two important ABET Student Learning Objectives:• Students will show:

• A recognition of a need for, and an ability to engage in, life long learning (graduate school, continuing education, short courses, technical training, self instruction by reading articles or textbook)

• A knowledge of contemporary issues

• Two choices, Both due November 6, 2015• Attend and write a two paragraph summary of this seminar: • Used Nuclear Fuel: Storage, Transportation, and Disposal – Technical, Political and Other

Issues• John Wagner, Director, Reactor & Nuclear Systems Division, Oak Ridge National Laboratory• Noon, November 2, 2015, DMS 102 • Hosted by UNR American Nuclear Society’s Student Chapter

• President: Kodi Summers klsummers92@gmail.com

• Read and write a two paragraph summary of this article• Dependence of Fire Time of Concern on Location of a One-assembly Transport Packages

Plug-Flow Reactors• Assumptions• Quasi-one dimensional

• All quantities are • Steady state, • No-viscosity • Axial turbulent and molecular diffusion are small

compared to advection (high enough axial velocity)• If velocity is “constant” then pressure is “constant”

• Integrate to find • At each location also need to calculate

• Like the transient constant-pressure reactor, but varies with location instead of time.

Stationary Reaction

Zone

What do we expect? (flow from left to right)

• Reaction take place is a “small” region

Problem X5 (homework)

• Consider a constant-area plug flow reactor. It has an axially-varying heat flux applied to the wall, mass flow rate , and operates a constant pressure (velocity variations are small).

• The following mass-based reaction is taking place within the reactor with a stoichiometric air/fuel ratio of :• ;

• Assume • The mass flow kinetic energy per mass is much less than its enthalpy (• The fuel F, Oxidizer Ox, and products Pr, have the same and (and )• The oxidizer and product heat of formation are zero, and that of the fuel is • The inlet equivalence ratio and temperature are and

• Use conservation of species and energy to find equations that can be used to find the axial variation of

h Yi

h Yi

h + (dh/dx)dx Yi + (dYi/dx)dx

dx

m

x

�̇�} ( 𝑥 ¿

�̇�

End 2015

General Plug-Flow Reactor

• What’s different from problem X5?• Area • Flow kinetic energy is not small compared to enthalpy

• • Species can have different, temperature-dependent properties

Conservation Laws• Mass

• Momentum

• Energy (including kinetic)

• Species

Manipulate ….• Use

• ; ;

• Need and • Assume and are given• Find … (page 209)

Problem 6.11 (Homework)• Develop a plug-flow-reactor model using the same chemistry and

thermodynamics as in Example 6.1. Assume the reactor is adiabatic. Use the model to:

A. Determine the mass flow rate such that the reaction is 99 percent complete in a flow length of 10 cm for , and The circular duct has a diameter of 3 cm.

B. Explore the effects of , and on the flow length required for 99 percent complete combustion using the flow rate determined in Part A.

• Constant volume, constant pressure, well-stirred, plug-flow?

Excel Solution Method

mdot phi dx x Yfuel Yox Ypr rho T P u Wf Wox Wpr d[Yfuel]/dx d[Yox]/dx d[Ypr]/dx d[rho]/dx dT/dx completionkg/s m m kg/kg kg/kg kg/kg kg/m3 K Pa m/s kmole/m3s kmole/m3s kmol/m3s 1-Yf(0.1m)/Yf(0)

0.00125 1 0.0001 0 0.058824 0.941176 0 0.070669 1000 20260 25.02362 -0.002826921 -0.045230736 0.048057657 -0.046359 -0.74174399 0.788102987 -0.109386259 1479.404 0.9906069790.0001 0.058819 0.941102 7.88E-05 0.070658 1000.148 20259.86 25.0275 -0.002832083 -0.045313333 0.048145416 -0.0464437 -0.7430985 0.789542155 -0.109552871 1482.092

mdot phi dx x Yfuel Yox Ypr rho T P u Wfkg/s m m kg/kg kg/kg kg/kg kg/m3 K Pa m/s kmole/m3s

0.00125 1 0.0001 0 0.058824 0.941176 0 0.070669 1000 20260 25.02362 -0.0028269210.0001 0.058819 0.941102 7.88E-05 0.070658 1000.148 20259.86 25.0275 -0.002832083

Wf Wox Wpr d[Yfuel]/dx d[Yox]/dx d[Ypr]/dx d[rho]/dx dT/dx completionkmole/m3s kmole/m3s kmol/m3s 1-Yf(0.1m)/Yf(0)-0.002826921 -0.045230736 0.048057657 -0.046359 -0.74174399 0.788102987 -0.109386259 1479.404 0.990606979-0.002832083 -0.045313333 0.048145416 -0.0464437 -0.7430985 0.789542155 -0.109552871 1482.092

• Starting Point• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH.475.675.Combustion/Prob.6.11.start.xlsx

• Pay attention to• Integration step size• Avoiding raising negative numbers to a non-integer power