AME 436
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Assigned: 2/29/08 |
Problem Set #3
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Due: 3/7/08 at 4:30
pm in OHE 430 for on-campus students; 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 (Cycle analysis)
For a Diesel cycle engine 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 of course check your answers with
aircycles4recips.xls, but I want to see that you know the equations behind
them. For example, for 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)
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 #3 (engine performance) (similar to
a problem 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
increase the thermal
efficiency the most? Assume knock is not a factor.
b)
Which of these would
increase the volumetric
efficiency the most? Assume knock is not a factor.
c)
Which of these would
increase the brake power the most?
Assume knock is not a factor.
Problem #4 (P-v and T-s diagrams) (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) The compression ratio is increased (same maximum
volume)
Same max. volume for modified
cycle
b)
The intake valve
closes late (i.e. after part of the compression stroke has started; the
pressure stays at ambient pressure and no compression occurs until after the
intake valve closes) in such a way that the pressure after the expansion is
ambient (i.e. the cycle has been converted to a complete-expansion cycle).
Same max. and min. volumes
for modified cycle
Problem #5 (Cycle analysis) (from last
yearŐs midterm)
For part (a) and part (b) in problem 4, 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 6. (Miscellaneous) (from last yearŐs midterm). Answer each of the following in a couple of sentences. Note that the choices (i) – (v)
are the same for each part.
a) If
the heating value of a fuel
were increased by a factor of
2, the adiabatic flame temperature
would
i.
stay the same
ii.
increase by less
than a factor of 2
iii.
increase by exactly
a factor of 2
iv.
increase by more
than a factor of 2
v.
decrease by less
than a factor of 2
b) If
the activation energy of a
fuel were decreased by a
factor of 2, the adiabatic flame temperature would
i.
stay the same
ii.
increase by less
than a factor of 2
iii.
increase by exactly
a factor of 2
iv.
increase by more
than a factor of 2
v.
decrease by less
than a factor of 2
c) If
the intake pressure in a
premixed-charge internal combustion engine were increased by a factor of 2, the brake thermal efficiency would
i.
stay the same
ii.
increase by less
than a factor of 2
iii.
increase exactly a
factor of 2
iv.
increase by more
than a factor of 2
v.
decrease by less
than a factor of 2
d) If
the intake pressure in a premixed-charge internal combustion engine is were increased by a factor of 2, the maximum brake power would
i.
stay the same
ii.
increase by less
than a factor of 2
iii.
increase exactly a factor
of 2
iv.
increase by more
than a factor of 2
v.
decrease by less
than a factor of 2