AME 436
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Assigned: 3/10/08 |
Problem Set #4
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Due: 3/24/08 at
12:00 noon in OHE 430 for on-campus students (scan and email to Dan Hong or
fax to me at 213-740-8071 if youŐre off campus); DEN students submit homework
through DEN |
For all problems, if useful,
you can use the AirCycles.xls spreadsheet to guide your answers but you need to
explain your results. Note: laptops or Pocket PCs running Excel
spreadsheets will NOT be permitted on the exams.
Problem #1
For an Otto cycle with constant-volume combustion
and the following parameters: r =
9, g = 1.3, M = 0.029 kg/mole, f = 0.062, QR
= 4.3 x 107 J/kg, T2 = 300K, P2 = 0.5 atm, Pexh
= 1 atm, h = 0, hcomp = hexp = 0.9 (in other words, ideal except
for the compression and expansion efficiency, and the throttling), 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
c)
Temperature (T5)
and pressure (P5) after expansion, and the expansion work per kg of
mixture
d)
Net work per kg of
mixture (donŐt forget about the throttling loss!)
e)
Thermal efficiency
f)
IMEP
Note in this case that we cannot simply use P2rg and T3 = T2rg-1; instead we have to use the
definitions of compression and expansion efficiency given in lecture 6 to get
the pressures and temperatures.
Problem #2 (a and b from last yearŐs
midterm)
Consider the ŇbaselineÓ ideal Diesel cycle shown on the P-V and
T-s diagrams. Sketch modified P-V
and T-s diagrams if the following changes are made. 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 Ňthis area = that area,Ó Ňthese two
temperatures are the same,Ó etc.
In some cases there may be no change to the P-V or T-s diagram.
a)
Part way through the
constant-pressure burn, knock occurs which causes the remainder of the burn to
occur instantaneously at constant volume
b)
A new lubricant is
used that decreases rubbing friction
c)
The compression
process is non-ideal (i.e. the entropy increases) but is still adiabatic. The rest of the cycle is still ideal.
Problem #3 (Cycle analysis) (from last
yearŐs midterm)
For parts (a) - (c) in problem 2, will the change
to the cycle cause the brake thermal efficiency to increase, decrease or remain
the same? Explain very
briefly. (You should be able to do
this even if your diagrams arenŐt right.)
Problem #4 (Engine performance) (from
last yearŐs midterm) The following 5 changes to a
premixed-charge engine are being considered:
1)
Increase the
displacement volume by a factor of 2
2)
Increase the compression
ratio by a factor of 2
3)
Increase the intake
pressure by a factor of 2
4)
Increase the engine
rotation rate (N) by a factor of 2
5)
Increase the
turbulence intensity by a factor of 2 using a different piston shape (N not
changed)
Briefly explain:
a)
Which of these would
decrease the tendency to
misfire the most? Assume knock is not a factor.
b)
Which of these would
decrease the tendency to
knock the most?
Problem #5 (reciprocating engine
performance) (similar to a problem on a previous final exam)
An engine designer claims to have developed a
naturally-aspirated (not turbocharged or supercharged) gasoline-fueled 4-stroke
engine with a 100 cubic inch displacement volume, compression ratio of 8,
operating at 4,000 rpm that produces 300 brake horsepower.
Possibly useful information: CP = 1400 J/kgK; g = 1.4; ambient air density 1.18 kg/m3;
QR (gasoline) = 4.5 x 107 J/kg; stoichiometric fuel mass
fraction in air (f) (gasoline) = 0.0622; 1 in3 = 1.64 x 10‑5
m3; 1 horsepower = 746 Watts.
a)
Do you believe this
claim? Why or why not? (Hint: your answer should be NO.) Support your answer with calculations.
b)
Would increasing
compression ratio from 8 to 24 (without changing displacement volume) make the
claim of 300 horsepower reasonable?
Assume that somehow knocking is not a problem even at this high
compression ratio. Again, support
your answer with calculations.
c)
Would increasing the
intake pressure to 3 atm (with compression ratio 8) using a turbocharger make
the claim of 300 hp reasonable?
Again, support your answer with calculations.
d)
Would changing the
fuel to hydrogen make the claim of 300 hp reasonable? Again, support your answer with calculations.
Problem
#6 (Combustion, miscellaneous) (from last yearŐs final exam)
Ronney Oil & Gas Company claims to have
developed a fuel, called PDR¨,
whose chemical formula is C8H18 (octane) and has all the
same thermodynamic properties, transport properties, etc. as C8H18. The only difference between C8H18
and PDR¨ is that using PDR¨ leads to 10% lower activation energy
(E) for all chemical reactions. If PDR¨ fuel were used instead of C8H18,
how would each of the following be affected? In particular, state whether the property would increase,
decrease or remain the same, and if there is a change, would it be by more
than, less than, or equal to 10%.
(Notice the operative words:
LOWER ACTIVATION ENERGY.) No
credit without explanation!
a)
Indicated thermal
efficiency of a premixed charge engine
b)
BMEP of a
nonpremixed-charge engine
c)
The equivalence
ratio at the lean misfire limit of a premixed-charge engine
Problem #7
Explain the experimental observations shown in the
figure below. For the premixed
charge engine, assume that the fuel mass fraction f = 1 and that the spark
timing is adjusted to that required for maximum power unless knock occurs, in
which case the spark is retarded until knocking just stops. For the non-premixed charge engine,
assume f (overall) = 0.7 = constant.
Hint: consider how intake
temperature affects
a)
Knock
b)
Spark timing
required to avoid knock
c)
Intake air density
d)
Burning velocity
e)
Misfire
f)
Cutoff ratio b (nonpremixed charge only)
