AME 436
|
Assigned: Thursday
2/12/09 |
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Problem Set #2 |
á
Due Friday
2/20/09 at 4:30 pm in OHE 430J á
Email to the
grader (Thada Suksila, suksila@usc.edu) or fax to 213-740-8071 if youÕre off
campus á
DEN students
submit through the usual channels |
Problem
#1 (15 points)
Using the Zeldovich equation for burning velocity
(SL), and typical ÒbaselineÓ values of ambient temperature (T°),
adiabatic flame temperature (Tad), order of reaction (n) and
activation energy (E), answer the following questions:
a) How does the reactant temperature T°
affect SL, everything else (including the product temperature Tad)
held constant? That is, will a 10%
increase in T° cause a more or less than 10% increase/decrease in SL?
b)
How does Tad affect SL, everything else (including
T°) held constant? That
is, will a 10% increase in Tad cause a more or less than 10%
increase/decrease in SL?
c)
How does the concentration of fuel in the reactants affect SL,
everything else (including T° and Tad) held
constant? That is, will a 10% increase
in the concentration of fuel in the reactants cause a more or less than 10%
increase/decrease in SL?
d)
How does the pressure of the reactants affect SL? That is, will a 10% increase in
pressure cause a more or less than 10% increase/decrease in SL?
Problem #2 (15 points)
For the homogeneous reaction/ignition problem
discussed in class, write a short computer program to solve the differential
equation that results. You can use
the simple Excel sheet I created (or you build your own in Excel,
Matlab, etc.) Using your program,
and taking into account the definitions of the dimensionless input parameters f (phi), b (beta) and H answer the following:
a) How
does the reactant temperature T° affect the dimensional time for ignition to occur (arbitrarily defined as
90% completion of reaction), everything else (including the product temperature
Tad) held constant?
That is, will a 10% increase in T° cause a more or less than
10% increase/decrease in the dimensional time for ignition to occur? How does the activation energy affect
your conclusion, that is, will a 10% increase in E change the sensitivity of
ignition time to T°?
b) How does Tad affect the dimensional time for ignition to occur, everything else
(including T°) held constant?
How does the activation energy affect your conclusion? How does the activation energy affect
your conclusion, that is, will a 10% increase in E change the sensitivity of ignition
time to Tad?
c) How does the concentration of fuel in
the reactants affect the dimensional time for ignition to occur?
d) How does the pressure of the reactants
affect the dimensional time
for ignition to occur?
Problem #3 (15
points)
a) Calculate and plot
the homogeneous ignition time (default definition is time to reach initial
temperature + 400K) at constant pressure as a function of temperature for a
stoichiometric H2 - O2 mixture at 1 atm over the initial
temperature range 800K - 1500K using the on-line chemical kinetics calculator
at http://navier.engr.colostate.edu/tools/homkin.html.
Use for 800K the following parameters: integration time 10 seconds, time
interval 0.1 seconds, HydrogenOxygen mechanism. For higher initial
temperatures the time to ignition will decrease and you'll have to decrease the
integration time and time interval.
b) From this
information, estimate the effective activation energy of H2 - O2
combustion from a plot of ln(ignition time) vs. 1/T° (the slope of
this plot is E/R). (Note: the slope wonÕt be very constant; there
will be a ÒkinkÓ near 1000K because of a change in the dominant chemical
reactions at that temperature.)
c) Calculate and plot the ignition time at
constant pressure as a function of pressure for a stoichiometric H2
- O2 mixture at 800K over the pressure range 1 atm - 10 atm using
the on-line chemical kinetics calculator.
d) From
this information, estimate the effective order of reaction (n) of H2
- O2 combustion from a plot of ignition time vs. pressure (the slope
of this plot on a log-log scale is 1–n)
Problem #4 (15
points)
Using the d2
law for droplet burning, explain following.
a) How
does the reactant temperature T° affect the total droplet burning
time, everything else (including the product temperature Tad) held
constant? How does the activation
energy affect your conclusion, that is, will a 10% increase in E change the
sensitivity of droplet burning time to T°?
b) How does Tad affect the
total droplet burning time, everything else (including T°) held
constant? How does the activation
energy affect your conclusion, that is, will a 10% increase in E change the
sensitivity of droplet burning time to Tad?
c) How does the concentration of oxygen in
the atmosphere affect the total droplet burning time?
d) How does the pressure of the reactants
affect the total droplet burning time?
Problem #5 (from a previous midterm exam,
continued from Homework #1) (10 points)
On Jupiter is an atmosphere of 60% hydrogen (H2)
and 40% helium (He) (60%/40% on a molar basis) at a pressure of 0.2 MPa (2
earth atmospheres) total pressure at 200K . Deep underground are deposits of pure O2 that the
Jovians (residents of Jupiter) pump out of the ground. Unfortunately, most of the O2
wells are located in politically unstable regions of Jupiter, so this O2
is a valuable resource which they call Òfuel.Ó The hydrogen/helium mixture in the atmosphere, which they
call Òair,Ó is ÒfreeÓ as far as Jovians are concerned.
Thermodynamic data: average mixture properties g = 1.3, R = 300 J/kgK, CV = 1000 J/kgK
|
|
H2 |
O2 |
He |
H2O |
|
Dhfo (kJ/mole) |
0 |
0 |
0 |
-241.83 |
|
Molecular weight (g/mole) |
2 |
32 |
4 |
18 |
Estimate the BMEP of stoichiometric
premixed-charge naturally-aspirated Jovian engines at wide-open throttle, with
compression ratio 8. To do that, use
the relationship IMEP = BMEP + FMEP, where IMEP is calculated from the formula
in lecture 5, slide 27, and assume a typical FMEP = 2 atm (weÕll discuss that
in lecture 8).
Problem #6 (from a previous midterm exam)
(15 points)
Ronney Oil and Gas Company
claims to have developed a fuel, called PDR¨, that has all the same
thermodynamic properties, transport properties, chemical reaction rate
parameters, etc. as octane except that PDR¨ has 10% higher heating value per
unit mass than octane. If PDR¨ fuel were used instead of
octane, how would each of the following be affected? In particular, state whether each of the above will increase
or decrease or remain constant, and by less than 10%, more than, or exactly 10%
and briefly explain why.
a)
The
laminar burning velocity (SL) of a premixed flame in a
stoichiometric mixture (hint: how does the 10% higher heating value change the
adiabatic flame temperature?)
b)
The
burning rate constant (K) of a liquid fuel droplet
c)
BMEP of
a premixed-charge engine burning a stoichiometric mixture
Problem #7 (from a previous final exam)
(15 points)
A four-stroke gasoline engine with a
displacement of 3.05 liters is tested in the laboratory at 3000 RPM and found
to have the following performance characteristics: net IMEP 107.9 pounds per
square inch, 70.32 brake horsepower, fuel flow rate 16.66 kg/hr, and air flow
rate 269.6 kg/hr. The fuel is
iso-octane, C8H18 (heating value 4.3 x 107
J/kg.) The ambient air temperature
is 295K. The intake pressure gauge is broken, so the intake pressure is not
known. Determine the following
performance parameters.
(Possibly useful information: 1000 liters = 1 m3; 1 hp =
746 Watts; 1 atm = 1.01325 x 105 N/m2; 1 pound = 4.448
Newtons = 4.448 kg m/s2; 1 inch = 0.0254 m; 1 hour = 3600 seconds.)
a)
BMEP
b)
c)
friction
MEP
d)
equivalence
ratio
e)
brake
thermal efficiency
f)
indicated
torque
g)
Is this engine
throttled, turbocharged or neither?
Explain. (Hint: compute the volumetric efficiency.)