AME 436
|
Assigned: Thursday
2/26/09 |
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Problem Set #3 |
á Due Friday 3/6/09 at 4:30 pm in OHE 430J á Email to the grader (Thada Suksila,
suksila@usc.edu) or fax to 213-740-8071 if youŐre off campus á DEN students submit through the usual
channels |
Problem #1 (Cycle analysis) (15 points)
For an ideal Diesel cycle with the following
parameters: r = 20, g = 1.3, M = 0.029 kg/mole, f = 0.05, QR
= 4.45 x 107 J/kg, initial temperature T2 = 300K, initial
pressure P2 = 1 atm, Pexh = 1 atm, h = 0, hcomp = hexp = 1 (in other words, an ideal
cycle), determine the following:
a)
Temperature (T3)
and pressure (P3) after compression, and the compression work per kg
of mixture
b)
Temperature (T4)
and pressure (P4) after combustion, and the work output during
combustion per kg of mixture
c)
Cutoff ratio
d)
Temperature (T5)
and pressure (P5) after expansion, and the expansion work per kg of
mixture
e)
Net work per kg of
mixture
f)
Thermal efficiency
g)
IMEP
You can check your answers with
aircycles4recips.xls, but I want to see that you know the equations behind
them. For example in part a, P3
= P2rg = (1 atm)(20)1.3 = 49.1 atm and T3 = T2rg-1 = (300K)(15)(1.3-1) =
737K.
Problem #2 (Cycle analysis) (15 points)
For an ideal complete expansion (Atkinson) cycle
with the following parameters: r =
20, g = 1.3, M = 0.029 kg/mole, f = 0.05, QR
= 4.45 x 107 J/kg, initial temperature T2 = 300K, initial
pressure P2 = 1 atm, Pexh = 1 atm, h = 0, hcomp = hexp = 1 (in other words, an ideal
cycle), determine the following:
a)
Temperature (T3)
and pressure (P3) after compression, and the compression work per kg
of mixture
b)
Temperature (T4)
and pressure (P4) after combustion, and the work output during
combustion per kg of mixture
c)
Temperature (T5)
and pressure (P5) after expansion, and the expansion work per kg of
mixture
d)
Net work per kg of
mixture
e)
Thermal efficiency
f)
IMEP
Again you can check your answers with
aircycles4recips.xls, but I want to see that you know the equations behind
them.
Problem #3 (Cycle analysis) (15 points)
a)
Repeat Problem 1
using a fuel-air cycle analysis (using GASEQ, as outline in the Lecture 7
notes) with an iso-octane air mixture.
b)
Explain why the peak
temperature, work done and efficiency are all lower for the fuel-air cycle as
compared to the air cycle analysis of Problem 1. (Remember, GASEQ is a adiabatic equilibrium solver; it
doesnŐt compute the effects of slow burn, heat loss or friction.)
Problem #4 (P-v and T-s diagrams) (30
points) (from last yearŐs midterm exam)
Consider the "baseline" ideal Otto cycle
shown on the P-V and T-s diagrams (next page). Sketch modified P-V and T-s diagrams if
a)
Knocking occurs and
all of the fuel-air mixture burns instantaneously before the piston reaches Top
Dead Center (minimum cylinder volume)
b)
A new fuel with 10%
higher heating value is used (fuel mass fraction not changed), but to avoid
overheating the engine, the compression ratio is changed so that the peak
temperature is the same for the baseline cycle and the modified cycle.
c)
The vehicle drives
into a dense fog where the air contains much more moisture, thus CV
increases and g decreases.
Unless otherwise noted, assume in each case the
initial temperature and pressure, compression ratio, fuel mass fraction,
heating value, etc. are unchanged.
Where useful for clarity, label plots with phrases like "this area
= that area," "these two temperatures are the same," etc. In some cases there may be no change
to the P-V or T-s diagram. Unintelligible scribbles on P-V and
T-s diagrams donŐt get much credit!
a) 
Same
peak T for baseline and modified cycles
b)
c)
Problem
#5 (10 points) (from last yearŐs midterm exam)
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
thermal efficiency of an ideal Diesel cycle
b)
BMEP of
a premixed-charge engine burning a stoichiometric mixture
Problem
#6 (Miscellaneous) (5 points)
(from last yearŐs final exam)
On Planet X the constant-pressure specific heats
(Cp) of air and all other gases are 10% higher than they are on earth. All other properties of the atmosphere are exactly the same
as on earth, in particular the mole-based ideal gas constant (ĺ), molecular weight (M), thermal conductivity (k),
density (r), mole fraction of O2
in the atmosphere, etc. In
particular, state whether each of these properties will be higher, lower or the
same on Planet X, and if different, by less than, more than, or exactly a
factor of 10%.
a)
Brake thermal
efficiency of a nonpremixed-charge engine
Problem #7 General cycle knowledge (10 points) (from last yearŐs final exam)
Answer the following questions (T-s diagrams will
be much appreciatedÉ)
a)
Why do internal
combustion engines need to compress the air or fuel-air mixture before
burning? What would happen if
there were no compression, could work still be generated?
b)
Why is it necessary
to add heat to generate work?