Download Part C : Cylinder Pressure Measurements

Part C : Cylinder Pressure Measurements
Introduction
Direct measurement of engine cylinder pressure is necessary to obtain accurate estimates
of the indicated mean effective pressure and indicated power. Other quantities such as the
peak pressure and the peak rate of pressure rise are also useful.
Accurate measurement of cylinder pressure requires three things: a pressure transducer
that can survive the engine environment, a means for synchronizing the pressure
measurements with the engine and some way to record the pressure measurements. In this
laboratory we will use a piezoelectric pressure transducer to measure the cylinder
pressure, an incremental shaft encoder to time the measurements to the engine and a high
speed data acquisition system to record the pressure data. A detailed description of the
equipment follows.
Equipment
Figure 1 Equipment set-up
Pressure Transducer - AVL GU12P
The pressure transducer is a AVL Model GU12P Quartz Pressure Transducer. The
transducer operates on the principle that a quartz crystal, when mechanically stressed,
produces an amount of electrical charge that is proportional to the magnitude of the
stress. The transducer has a thin diaphragm welded to its body that, when subjected to
pressure, deflects inward, pushing on the crystal. The transducer is intended to be
mounted in the head of the engine so that the diaphragm is flush with the surface of the
combustion chamber.
The GU12P is very linear. The linearity is rated at better than 0.3% of full scale. The
natural frequency of this transducer is greater than 100 kHz. Most of the information in
the cylinder pressure signal is contained at frequencies less than 10 kHz, so we should
have no problem with frequency response.
A major source of error for this type of transducer is "transient temperature error." When
the transducer is exposed to combustion processes in the engine, the pressure is not the
only thing, which causes the diaphragm to deflect. The convective and radiative heat
transfer from the hot gases cause the surface of the diaphragm to expand and the resulting
deformation is recorded as a false pressure. For the purposes of this experiment, we will
assume the transient temperature error is negligible.
One difficulty with piezoelectric transducers is they do not hold a constant baseline
output during use. Even when used with a charge amplifier (set to long time constant) the
output voltage corresponding to a fixed pressure will change slowly with time. This can
be due to variation in tightening torque used during installation, variation in temperature
of the transducer and either physically damaged or contaminated cables and connectors.
The usual procedure is to assume the baseline drift is slow with respect to a single engine
cycle and then to reference each cycle to a known pressure. Data is collected starting at
BDC before compression. The first point is therefore taken at the end of the intake stroke
when the piston is momentarily stationary. At this point it is assumed that the pressure in
the cylinder is equal to the pressure in the intake manifold which can be measured with a
technique that is resistant to baseline drift. All the following data points are adjusted by
adding or subtracting the amount required to get the first point to be the intake manifold
pressure.
Shaft Encoder - Kistler Model 2613B
To time the data acquisition process to the engine, a Kistler Instruments Corporation
Model2613B. Optical Encoder is directly coupled to the engine crankshaft. This device
consists of a rotating disc with very fine lines etched onto it to provide alternating dark
and transparent spaces. A light source illuminates the disc and an optical sensor measures
the alternating signal produced as the disc rotates and the lines block the light. Two
outputs are available; one is based on a single fine line blocking the light per revolution
and the other is based on 1800 lines blocking the light per revolution (one every one-fifth
of a degree). Signal conditioning is built into the encoder so that the sinewave-like signal
from the optical sensor is converted into a clean, sharp square wave.
The figure shows what the output looks like. The one pulse per revolution (ppr) signal,
called the 'Z' signal, is timed to occur at Bottom Dead Center. This is done by using the Z
pulse to trigger a strobe light which then flashes onto a degree wheel on the engine
showing the current timing of the pulse. The encoder is then rotated in its mount so that
the pulse occurs at BDC. The Z pulse will then be used to trigger the data acquisition
system so that it starts to take data at BDC. The 1800 ppr signal, called the 'A' signal, will
also be used to trigger the data taking process. Once the process is started by the Z pulse,
the A pulses tell the system when to actually make a pressure measurement. As shown in
Figure 2, whenever the A pulse undergoes a low-to-high transition, the system measures
the pressure. The output of the data acquisition is thus a list of pressure measurements
with the first point on the list corresponding to the pressure at BDC and the succeeding
points corresponding to the pressure every 1/5° after that.
Figure 2 Timing of data collection.
Instruments Data Acquisition Unit
An Instruments data acquisition unit is designed to plug into a computer. It can record
input signals at a maximum rate of 8x100,000 measurements per second. It has a 12 bit
analog to digital converter. This means that it converts an analog voltage input to a 12 bit
binary number. The lowest 12 bit binary number is 000000000000 which equals a
decimal zero and the highest number is 111111111111 which is equal to a decimal 4095.
So, if we set the input range of the board to +/- 5 Volts, this 10 volt range is divided into
4096 parts and the digit corresponding to the voltage closest to the signal voltage is
stored in the memory of the computer. The numbers will be converted to pressures and
stored in a data file that can be loaded into Excel.
Laboratory Exercise
The equipment in the laboratory has been set up following the schematic given in Figure
1. We will operate the engine at the following five operating conditions.
1. 1400 RPM, 100% of full load torque
2. 1400 RPM, 50% of full load torque
3. 1400 RPM, 25% of full load torque
A set of pressure data will be taken at each operating condition while the engine is firing.
The data will be made available for your use in doing the calculations assigned below.
The files will be stored on the computer using the naming convention given below.
P14_20.dat
where P designates that this is cylinder pressure data, 14 designates that this data was
taken at 1400 rpm, and 20 designates the percent of the full load torque.
Data Analysis Techniques
The three most common ways to display cylinder pressure data are: pressure vs. crank
angle, pressure vs. volume and log(pressure) vs. log(volume). Examples of each of these
plots are presented in Figure 3. The first type is obviously useful because it shows the
way the pressure varies through-out the combustion event. The pressure vs. volume plot
is useful because the area enclosed by the process lines corresponds to the indicated
work.
Figure 3
Plot of cylinder pressure data: pressure vs. crank angle, pressure vs.
volume and log(pressure) vs. log(volume)
The log(p) vs. log(v) plot is also useful. Since the compression and expansion are
essentially polytropic processes, they follow the relation PVn = Constant. Taking the log
of this equation gives:
log(P) + n log(V) = log(constant)
or
log(P) + (-n)log(V) + log(constant)
which has the general form of y = mx + b, a straight line.
On a log-log plot, a polytropic process will plot as a straight line with a slope of -n, the
polytropic exponent. You will have a chance to test this yourself with the data taken in
this experiment.
Now that we have a set of pressure data, we can calculate the actual IMEP for this
engine. To review, remember that the IMEP is defined as the integral of PdV for the
cycle divided by the displacement volume. We can partition this into two parts
corresponding to the two revolutions of the four-stroke cycle. The MEP based on the
compression-expansion revolution is called the Gross Indicated MEP, or GIMEP. The
second revolution, when the exhaust and intake processes occur, we can define as the
PMEP (Pumping MEP). If the GIMEP is the indicated work per unit displacement
volume that is produced in the engine, then part of it goes out the shaft (BMEP), part
goes to pump the air and exhaust into and out of the engine (PMEP) and the rest goes to
overcoming friction (FMEP).
GIMEP + PMEP = BMEP + FMEP
or
BMEP = GIMEP + PMEP - FMEP
This equation can be evaluated for either a firing cycle or motoring cycle although we
would expect the GIMEP for a motoring cycle to be a very small number. For isentropic
conditions it would be zero, but with heat transfer it will probably be a small negative
number.
Calculations
1. Write a computer program to calculate the value of the polytropic exponent as a
function of crankangle for the full load data set corresponding to the speed used in your
section. Plot this exponent vs. crankangle from -180° to 180°. Estimate the start of
combustion from this plot.
To determine the polytropic exponent, you should recognize that from, say, one degree (5
data points) to the next
P(i) * V(i)**n = P(i+4) * V(i+4)**n
Therefore,
You may find that there is considerable noise in your results. The curve will be
progressively smoother if you use data over 2 degrees (8 data points), 3 degrees (12 data
points) and so forth. However, you lose detail when you do this. Try several values to see
the effect and choose a value which you feel is the best compromise between noise
rejection and loss of detail.
In the above approach, although the procedure is technically correct, the random
fluctuations (noises) in the measured pressure data make it difficult to use. A more
satisfactory method which overcomes the random noise problem will be used, as
described in the following.
(a) Convert the crank position vs. transducer voltage data recorded from each test to
cylinder pressure and volume. The P-V diagram can be plotted from this data and the
gross indicated work (GIMEP) and the pumping work (PMEP) can be computed.
(b) Next, calculate log P and log V and plot on large scale (full page) for the
compression-expansion revolution only. Visually examine the Log P vs. Log V plot and
select the region of both the compression and expansion strokes which appear to be linear
(a straight edge is useful). Perform a linear least squares best fit for each of these visually
linear regions and add these best fit curves to the plot along with the polytropic exponent
(slope) values. You may find that initially you include points too near TDC when
combustion has started during compression or is still going on during expansion that will
affect the linearity and n values. Adjust by omitting some points until good linearity is
obtained. You can also estimate when combustion begins and ends from this plot.
2. Write a computer program to calculate the IMEP and PMEP for each of the operating
conditions studied, both firing and motoring. You will need to integrate PdV. This can be
done simply by converting the integral to a summation as shown below.
where the volume can be obtained from engine geometry. Prepare a table showing the
IMEP, BMEP, PMEP and FMEP for all four operating conditions. (Note: IMEP, PMEP
are calculated, BMEP is measured and FMEP is obtained by subtraction.) Comment on
the validity of the assumption that FMEP = MMEP.
Write up:
Your write-up should contain:
1. A full page plot of Pcyl vs. Vcyl for the two complete recolutions for the 100%load run.
2. A full page plot of Log Pcyl vs. log Vcyl for the 100% load run including the linear best
fits and n values for the compression and expansion processes.
3. A table of the determined values of ploytropic exponents (n) for compression and
expansion and the various MEP values for all the firing and motoring tests. Remember,
GIMEP and PMEP are calculated from P-V data, and BMEP are determined from
dynamometer torque and engine speed data,
FMEP = GIMEP + PMEP - BMEP,
4. Plot of FMEP vs. BMEP.
5. Plot of PMEP vs. BMEP.
6. Discussion of this laboratory exercise. Discuss the n values obtained in relation to
expected values.