SAE TECHNICAL

PAPER SERIES 2008-01-0093

A New Technique for Residual Gas Estimation

and Modeling in Engines
James F. Sinnamon and Mark C. Sellnau
Delphi Corp.

2008 World Congress

Detroit, Michigan
April 14-17, 2008

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 2008-01-0093

A New Technique for Residual Gas Estimation

and Modeling in Engines
James F. Sinnamon and Mark C. Sellnau
Delphi Corp.

Copyright © 2008 SAE International

ABSTRACT affect the gas flows through the engine valves that
determine the residual content of the trapped charge.
This paper addresses the longstanding problems of
residual gas measurement during engine dynamometer Because of the complexity of the process, various
testing, and of real-time residual modeling for engine experimental techniques have been applied to measure
control applications. residuals in engines. These can be broadly classified
into a) optical, and b) gas-sampling methods.
A new method is described which is simple to apply,
requiring only currently standard calibration test cell Optical methods include CARS (coherent ant-Stokes
instrumentation. Experimental validation against Raman spectroscopy), LIF (laser induced fluorescence),
measurements using direct in-cylinder CO2 sampling is Raman scattering and infrared absorption [1-10]. These
presented, and a comprehensive error sensitivity require much tedious calibration and analysis to be
analysis is included. numerically accurate, and also generally require optical
access to the combustion chamber. Some recent work
A real-time capable, controls-oriented model is also has focused on small, spark plug sized, infrared
described. Its accuracy is assessed by comparison to absorption sensors [9,10], but accuracy in a firing engine
engine-simulation-generated residual values after using has not been demonstrated.
these values to determine the model parameters.
Gas sampling methods include several approaches.
One approach is nitrous oxide or hydrocarbon sampling,
INTRODUCTION either directly from the cylinder or from the exhaust port,
in combination with skip firing [11-14]. Another
The importance of internal residual to engine approach, the oldest and most widely used, is direct
combustion quality has long been recognized. cylinder sampling with CO2 measurement [15-21].
Historically, the motivation for developing residual Recent developments have enabled sample extraction
estimation methods comes from the fact that it is needed through a capillary tube for relatively easy access to the
as input to a heat release rate analysis. More recently, it cylinder [22-24]. Cylinder CO2 sampling was chosen for
has been recognized that the use of variable valve the engine validation experiments reported in this paper.
actuation to control and maximize internal dilution All of the gas sampling techniques require elaborate and
enables the elimination of external EGR systems, along expensive instrumentation, and may not be feasible for
with significant fuel economy and NOx control routine engine calibration work, especially if
improvement. More recently the role of internal dilution measurements from all cylinders of a multi-cylinder
in the control of advanced-mode combustion systems, engine are needed in order to obtain an engine average
such as HCCI, has been explored. Due to the above residual value.
factors, there has been a surge of interest, both in
methods of measuring or estimating engine residuals In view of the difficulty of residual measurement, there
during engine tests, and in the formulation of real-time has been significant effort toward modeling the residual
capable residual models for use in production engine generation process [12, 13, 15, 18, 19, 21, 25-33].
management systems. These models may be classified into two groups: a)
models that require iteration and/or numerical
RESIDUAL MEASUREMENT – The physical process of integration, and b) empirical or semi-empirical models
residual generation is complex. During the gas suitable for real-time control applications. The former
exchange process pressure and velocity pulsations are will be called “on-line estimators” since their primary
generated in the intake and exhaust manifolds due to application is to generate residual values during engine
fluid inertia and wave action. These pulsations strongly dynamometer testing. The later will be called “real-time
capable” models, since their primary application is
engine control. These modeling approaches are NEW ON-LINE RESIDUAL ESTIMATION
summarized in the following two sections. METHOD
ON-LINE RESIDUAL ESTIMATION –There are two CONCEPT – To explain the new residual estimation
basic approaches to on-line residual estimation. The method [34] we start with the ideal gas equation of state
first approach uses detailed, 1-D, multi-cylinder applied at the time of intake valve closing.
simulation. An engine model may be constructed and
carefully calibrated against engine test data (airflow,
Mtrap = Mair + Mfuel + Megr + Mresid =
temperatures and combustion rates) over the entire (1)
operating range of interest. This approach is predicated (Pcyl * Vcyl) / (R * Tcyl)
on the fact that volumetric efficiency and residual
fraction are both a result of the same gas exchange The trapped mass consists of air, fuel, EGR and
process, so a simulation that is accurate for one should residual. It is assumed that air, fuel and EGR are
be accurate for the other as well [33, 38]. The accurately measured. The residual estimator
disadvantage is that creation and calibration of a determines total burned gas dilution, so if EGR is
sufficiently accurate model is a rather difficult task, so a present in the test engine, then EGR must be measured
substantial time investment by an engineer highly skilled to determine residuals. EGR is typically measured by
and knowledgeable in the field of engine simulation is intake manifold CO2 sampling. Cylinder volume, Vcyl,
required. can be accurately calculated from engine geometry and
crank position. Therefore, if cylinder gas temperature,
The second approach which also uses detailed process Tcyl, can be determined with sufficient accuracy,
simulation, is referred to in this paper as the “port- residuals could be calculated by substituting the
pressure method”. It requires a much simpler single- measured cylinder pressure, Pcyl, at intake valve closing
cylinder simulation. Measured crank-angle-resolved into the above equation. The problem is that Tcyl is
intake and exhaust pressures are applied as boundary difficult to determine, and it also depends on residuals.
conditions, while cylinder pressure data are used to This problem has been addressed by coupling an
derive the combustion rate inputs [18,25,26]. A more optimizer to a simple single-cylinder engine simulation.
thorough discussion of this technique is presented in When the optimizer completes its tasks as described
Appendix B. While this method is coming into fairly below, the estimated residual is then the value
common use, a disadvantage is that the instrumentation calculated by the simulation.
required on multi-cylinder test engines is somewhat
elaborate, costly, and time consuming. Residual Estimator

This paper presents a simpler on-line estimation method Pint_meas

that requires only standard engine test instrumentation, Pexh_meas
Mair_meas
namely time or cycle average intake and exhaust

Optimizer

Single Cylinder
pressure and temperature, and crank-angle resolved Tair

Simulation
cylinder pressure. Texh_meas

REAL-TIME CAPABLE RESIDUAL MODELS –

Motivated by engine control issues, much effort has Airflow
Meter Pcyl_meas
recently been exerted toward this type of model [8, 12,
13, 21, 27-30]. The model must be simple enough to
Multi-Cyl
execute between cylinder events over the operating
speed range of a multi-cylinder engine. It therefore must Test Engine Residual
be empirical or semi-empirical, involving a limited
number of arithmetic operations. CAD
Crank
Encoder
An early attempt is the semi-empirical model of Fox, et
al. [27], and most subsequent attempts are refinements Figure 1. Schematic of the test engine and residual
or extensions of the Fox model. To date, these have not estimator system.
demonstrated the desired accuracy over the full range of
engine operating conditions for all types of variable valve Figure 1 is a simplified schematic of the residual
actuation systems. In view of the complexity of the gas estimation system showing the required transducer
exchange process, the prospects for semi-empirical signals from the multi-cylinder test engine. Intake
models seem rather dim. Consequently, an empirical manifold pressure, exhaust manifold pressure, air mass
modeling approach has been pursued, and the general flow, intake air temperature, and exhaust temperature,
structure of a model having sufficient speed and are time average (or engine cycle average) values.
accuracy is described in this paper. Intake and exhaust pressures do not need to be highly
accurate since they are used only as initial values in the
optimizer. The only crank-angle-resolved input is
cylinder pressure, which is a standard measurement in accuracy of the simulated temperature value.
modern engine test cells. Alternatively, a radiation-shielded exposed-junction
thermocouple may be used during engine test.
Figure 2 shows more detail concerning the residual
estimator itself. The engine simulation is highly 4) Determination of a cylinder pressure pegging offset
simplified, with constant pressures imposed at the using values of compression polytropic exponent,
upstream and downstream sides of the intake and polyC, calculated by the simulation. This procedure
exhaust valves, respectively. There is no need to will be referred to as “auto-pegging”, and will be
compute pressure fluctuations in the intake and exhaust discussed in greater detail later.
pipes, but “imaginary” pipes are needed to store
backflow gas and perform a wall heat transfer Three approaches to modulating the simulated trapped
calculation. The cylinder model includes Woschni heat residual have been successfully demonstrated in the
transfer and a simple, approximate combustion model. course of this work.
A highly accurate combustion model is not required
because the calculated residual is relatively insensitive 1) A burned gas source/sink can be connected at the
to combustion duration. A fast, approximate heat upstream side of the intake valve, or directly to the
release calculation using the measured cylinder cylinder, depending on the mode of residual
pressure record is sufficient. generation. When the source of residual is intake
valve backflow, the optimizer modulates the
Pint Mb HTmult source/sink flow rate at the intake valve during the
intake backflow period. For negative valve overlap
Single-Cyl
(NVO), a source/sink connected to the cylinder is
Mair_meas activated during the negative overlap period. For
Simulation
both of these cases, the temperature of burned gas
Optimizer

Pcyl_meas added is set equal to the instantaneous cylinder

Pint Mresid
temperature. In the case where residual is generated
Tair Mair Cyl
primarily by backflow of exhaust into the cylinder,
Texh_meas such as for late-exhaust-valve-closing, a source/sink
Thermocouple
Model connected to the cylinder is activated during the
intake stroke, with source temperature set equal to
exhaust port gas temperature.
Mair_sim Pcyl_sim PolyC Texh_sim
2) Both intake and exhaust valve effective flow areas
Figure 2. Schematic of the optimizer and simulation. can be modulated during their periods of backflow.
This approach still requires a burned gas source/sink
at the cylinder to handle the negative valve overlap
The optimizer performs four functions:
case.
1) Determination of intake pressure, Pint, such that
3) Exhaust port pressure may be modulated. This
simulated airflow equals the measured airflow. Since
method is simple and robust – covering all modes of
manifold pressure pulsations are ignored, this
residual generation. Adjusting Pexh affects intake
pressure will differ somewhat from the measured
and exhaust valve backflows in roughly equal
average manifold pressure.
proportions, as well as affecting the mass of burned
gas trapped at the start of a negative overlap period.
2) Determination of the mass of burned gas trapped at
The disadvantage is that temperature conditions may
intake valve closing such that simulated cylinder
become unrealistic if a large shift in Pexh relative to
pressure matches the measured pressure, which is
the measured value is required.
averaged over a crankangle window early in the
compression stroke. Depending on how residuals
In practice, a combination of methods 2 and 3 is the
are generated in the engine, there are several options
most accurate and robust implementation.
for simulation input parameters that can modulate
trapped residual into the cylinder, as described
below. Thus after the optimizer completes its task, the
simulation has calculated all the quantities needed to
satisfy equation-1 while providing the most realistic
3) Determination of exhaust pipe heat transfer multiplier
possible estimate of temperatures. Note that this
such that measured and simulated exhaust
method uses only the early compression portion of the
temperatures are equal. This feature was found to
measured cylinder pressure data, where errors due to
improve the accuracy of the residual estimate for
transducer thermal shock are a minimum, and where
cases where a large portion of the residual is
cylinder gas temperature can be simulated most
generated by exhaust backflow. A thermocouple
accurately.
model may be included in the simulation to improve
CYLINDER PRESSURE PEGGING – At this time the and then coupled to a GT-Power [37] single-cylinder
only pressure transducers capable of surviving in- simulation. Multi-cylinder engine “test data” was
cylinder temperature conditions are of the piezoelectric generated using a GT-Power simulation model of the
type, which measure only relative pressure change, and GMPT 4.2L L6 light truck engine. This model had been
require “pegging” by some independent means in order constructed and carefully calibrated to support previous
to yield absolute pressure. In the next section dealing work [38, 39]. The output from the multi-cylinder
with error analysis we will see that pegging of the simulation was used as input to the residual estimator,
cylinder pressure is one of the most critical and the resulting residual values were compared to
considerations. The difficulty of accurately pegging is evaluate the error.
well recognized and several methods have been
proposed [35]. Several methods use an independent Estimator error may be categorized into two types. The
reference obtained using an absolute pressure first are “intrinsic” errors, which are due to the single-
transducer. These are: a) setting Pcyl at BDC-intake cylinder approximation and assumptions in the basic
equal to average intake manifold pressure, b) setting estimator technique. This error is due to the neglect of
Pcyl at BDC-intake equal to intake port pressure manifold flow pulsations, which cause the air and
measured by an absolute pressure sensor (usually residual gasses to undergo a somewhat different heat
piezoresistive) mounted as close as possible to the transfer history. To determine sensitivity to these errors,
intake valve, c) setting Pcyl averaged over a specified simulations were conducted to compare the estimator to
crankangle window during the exhaust stroke equal to detailed simulation. All the optimizer inputs are made to
average exhaust manifold pressure, and d) setting Pcyl be perfectly accurate and all the engine simulation
at BDC-intake equal to pressure measured using an parameters (such as compression ratio, burn rates, heat
absolute transducer mounted through the cylinder wall transfer multipliers, port and cylinder wall temperatures,
just above the piston BDC position. For purposes of etc.) are correct, that is, the same as used in the multi-
residual estimation, methods a), b) and c) are not cylinder simulation.
sufficiently accurate. Method d) seems most promising,
but requires elaborate preparation. The second type of errors are “input-induced’. These
are caused by inaccuracies in the inputs to the
An alternative indirect method, here referred to as estimator. To determine sensitivity to these errors,
“polyC-pegging”, was first proposed by Matekunas [36]. perturbations were introduced in both optimizer input
It relies on the fact that the polytropic exponent, polyC, and the single-cylinder simulation setup. The errors
calculated using cylinder pressure data during the were evaluated by comparing the resulting residual
compression stroke depends on pegging, so if an values with those calculated by the estimator without
accurate value for the exponent is known, then the input error. In practice, of course, test engine data will
corresponding pegging pressure can be calculated. The have errors, and many of the simulation setup
difficulty is that the value of polyC depends on gas parameters will have significant uncertainty.
temperature, composition (air, fuel, burned gas), heat
transfer, and leakage - none of which can be accurately To evaluate the intrinsic error, simulations were
determined a-priori. This difficulty has been addressed performed to generate a wide range of residual values
by using the value of polyC calculated by the simulation using various cam phaser positions over a range of
to peg the measured cylinder pressure data. PolyC is engine speeds and loads of interest for a typical driving
continually fed back to the optimizer, so cylinder test cycle. A variety of variable valve actuation (VVA)
pressure is dynamically pegged as simulated gas strategies for generating residual are represented. The
temperature and composition vary during convergence, operating conditions are listed in Table-1.
to finally yield a self-consistent set of airflow-pressure-
temperature-residual values. Cases 1–13 pertain to early-intake-valve-closing (EIVC)
with dual-independent-cam-phasing (DICP) using a
PolyC is evaluated by averaging over a 30 crank degree short-duration low-lift cam. The intake and exhaust
interval starting at 90 degrees BTDC. This interval was valve opening times (IVO, EVO) were chosen so that
chosen primarily to minimize the effect of cylinder wall residual was generated with various proportions of
heat transfer and cylinder leakage, which are both low intake and exhaust backflow. Note that in most of these
during early compression. In addition, the rate of cases the intake manifold pressure is high for low
pressure rise is high enough to reduce the effect of pumping loss while the valve overlap is large for high
noise in the measured pressure signal to tolerable residual gas fraction (RGF). This is a particularly
levels. An error sensitivity study was performed, and demanding situation for a residual estimator because
results are presented in Appendix A. small perturbations in port or cylinder pressures produce
a large change in residual. It is also an important
scenario because VVA systems provide greatest
pumping work reduction in this operating regime.
ERROR ANALYSIS – An initial assessment of the
potential accuracy of the method was performed using Cases 14 and 15 pertain to DICP with conventional long-
simulation. The optimizer was programmed in Simulink, duration cams, using very low overlap (case 14) and
high overlap (case 15). Here the residual is generated 1.0
primarily by intake backflow. Cases 16-22 use dual-

Error (%Estimated - %Actual)

equal-cam phasing to generate residual primarily by
exhaust backflow into the cylinder. Cases 23-26 use
negative valve overlap to trap residual without 0.5
backflows.

Figure 3 shows the estimation error (estimated RGF –

actual RGF) plotted against actual RGF, that is, the 0.0
multi-cylinder GT-Power value. All residual errors
reported in this paper are difference in %residual as
defined here. The intrinsic errors are quite low, within -0.5 EIVC + DICP
+/-0.5 %. DECP
Neg Overlap
DICP + Conv Cam
Case NMEP RPM IVO EVO MAP RGF
-1.0
# (bar) (bar) (%)
0 10 20 30 40
EIVC+DICP RGF Actual [%]
1 2.00 750 308 386 0.47 20.38
2 2.75 1400 292 419 0.89 31.87
3 3.26 1400 299 431 0.90 30.14 Figure 3. Intrinsic residual estimator error.
4 4.25 1400 322 456 0.90 30.18
5 6.00 1400 333 456 0.89 19.81 It is of interest to compare port pressures and valve flow
6 10.0 1400 350 406 0.89 4.19 rates during the gas exchange process as shown in
7 3.50 1000 301 423 0.90 30.47 Figure-4 for case-8. Figure 4a shows that manifold
8 3.50 1400 308 443 0.90 32
pressure pulsations produce large valve flow rate
9 3.50 2000 310 449 0.89 29.79
10 3.50 2600 313 456 0.90 29.81 pulsations in the multi-cylinder engine, and there are
11 3.50 3200 314 456 0.93 25.86 large differences from the single-cylinder simulation
12 3.50 4000 315 456 0.91 18.16 used in the residual estimator. As shown in the cylinder
13 2.00 1600 285 446 0.97 41.67 pressure plot (fig. 4b), the optimizer converges to the
correct pressure at IVC. In spite of the fact that details
DICP with Conventional Cams of the gas exchange process are drastically different, the
14 3.50 1600 340 406 0.40 8.47
residual fractions differ by only 0.24%.
15 2.00 1200 290 406 0.55 43.89

DECP
0.06
16 3.50 1400 330 390 0.42 10.69 Estimator
17 3.50 1400 350 410 0.42 9.03 Intake
18 3.50 1400 370 430 0.50 12.45
Valve Flow Rate [kg/s]

19 3.50 1400 380 450 0.61 19.3

0.04 Multi-Cyl
20 3.50 1400 380 460 0.67 23.56
Intake
21 3.50 1400 380 470 0.74 28.04
22 3.50 1400 380 480 0.82 32.37

Negative Valve Overlap

0.02
23 2.00 1200 410 360 0.42 31.18
24 2.00 1200 395 375 0.33 20.6
25 2.00 1200 360 365 0.40 27
26 2.00 1200 420 350 0.50 38.38
0.00
Estimator
Table 1. Engine operating conditions for error analysis Exhaust
Multi-Cyl
using simulation. Exhaust
-0.02
180 270 360 450 540
Crank Angle

Figure 4a. Valve flow comparison between the multi-

cylinder simulation and the single-cylinder residual
estimator.
 2.0 Nominal
Cylinder Pressure [bar] Parameter Error +/- Value
Airflow Rate 1.0 %
Multi-Cyl Pressure Transducer Pegging 1.0 kPa
1.5 Pressure Transducer Gain 1.0 %
Estimator Crank Encoder Error 0.5 deg
Intake Air Temperature 5C 25 C
Exhaust Temperature 20 C 610 C
1.0 Intake Cam Timing 1 deg
Exhaust Cam Timing 1 deg
Effective Valve Lash 0.04 mm 0.08 mm
0.5 Intake Exhaust Pressure 1.0 kPa 100 kPa
Opens Exhaust Combustion Phasing (CA50) 2 deg 9 deg
Intake
Closes Combustion Duration (10-90 % MBF) 10 deg 30 deg
Closes
Intake Port Surface Temperature 20 C 120 C
0.0 Intake Port Heat Transfer Coef 0.5 1.0
Cylinder Wall Temperature 10 C 150 C
180 270 360 450 540 Cylinder Heat Transfer Coef 0.1 1.0
Crank Angle Intake Port Cd (at low valve lift) 0.1 0.7
Exhaust Port Cd (at low valve lift) 0.1 0.7
Compression Ratio 1.0 10.0
Figure 4b. Cylinder pressure comparison between the Blowby 2.0 % 2.0 %
multi-cylinder simulation and the single-cylinder residual Air-Fuel Ratio 1.0 ratios 14.5
estimator.
Table 2. Estimator input errors for error sensitivity
Now consider estimator input errors. Table 2 is a list of
analysis.
the parameters considered, the amount of error
introduced, and the baseline value where appropriate.
The input error ranges were chosen to reflect an The results are plotted in Figures 5a and 5b. For
estimate of what might be realistically achieved. To legibility the x-axis has been spit into two plots. The
preserve sensitivity to pegging error, the auto-pegging responses to positive and negative errors were fairly
was turned off. Case 8 in Table 1 was chosen as the symmetric, so only the absolute values are plotted.
baseline operating condition because: a) intake manifold Although the results are generally quite favorable, a few
pressure and valve overlap are high which makes it are somewhat worrisome. An airflow measurement
sensitive to cylinder pressure measurement error, b) accuracy of 1% is achievable, but requires close
early intake valve closing makes it sensitive to valve flow attention by the test engineer. In particular, air/fuel
and cam timing parameters, and c) residual is high and ratios based on measured air and fuel flow must match
cam phasing is such that there is large backflow for both the emissions-base value well within this 1% tolerance.
intake and exhaust, so factors that affect either one will The 1.0 kPa tolerance on cylinder pressure pegging is
cause error. In other words Case 8 represents a worst- more stringent than is achievable by pegging methods in
case scenario. common use, which is the motivation for introducing the
polyC auto-pegging procedure described above.

When exhaust temperature “optimization” was disabled

in the estimator, relatively large errors were obtained for
exhaust port heat transfer coefficient, cylinder wall
temperature and cylinder heat transfer coefficient (0.78,
.046 and 0.58, respectively). This shows that this
feature improves accuracy significantly (Figure 5b).

In view of the intrinsic error and the input parameter

sensitivities, an overall residual estimation accuracy of
about +/-1.5 % may be reasonably expected.
 0.6 where [CO2] is measured CO2 molal concentration on a
Residual Error [%]
0.5
wet basis, W is molecular weight of sampled gases, and
subscripts, cyl and exh, refer to gas samples taken from
0.4 the cylinder during compression and from the exhaust
stream, respectively. A derivation of Equation 2 is
0.3
presented in Appendix C, along with a discussion of
0.2 alternative definitions of RGF for various types of
engines.
0.1

0 IN-CYLINDER SAMPLING SYSTEM - The Cambustion

CSV500 uses a small sample tube with two GDI

Intk Cam Timing

Pcyl Pegging

Pcyl Gain

Intake Air Temp

Valve Lash
Exh Cam Timing

Exh Pressure
Exhaust Temp
Crank Encoder
Airflow

injectors operating as valves to precisely extract gases

from the cylinder [24]. In a timed sampling scheme, one
GDI injector was used to first purge the sample tube,
and the other was used subsequently to extract the
desired gas sample. Specifications of the sample valves
are shown in Table 3. For testing on a single-cylinder
diesel engine, the sample tube was inserted in a dummy
Figure 5a. Estimator input error sensitivity. glow plug as shown in Figure 6. Installation on the test
engine is shown in Figure 7.
0.6
Parameter Value Units
Residual Error [%]

0.5
OD Sample Tube 3.2 mm
0.4 ID Sample Tube 0.92 mm
0.3 Effective Flow Area 0.75 mm2
Length Sample Tube 300 mm
0.2
Min. Pulse Width 600 us
0.1 Open Duration 250 us
0 Close Duration 250 us
Max. Cyl Pressure 100 bar
Air-Fuel Ratio
Comb Duration
Comb Phasing

Intake Port Cd
Exhaust Port Cd
Intk Port HT Coef
Cylinder Wall Temp
Cyl HT Coef
Intk Port Surf Temp

CR
Blowby

Heater Temp 200 deg C

Table 3. Specifications for CSV500 Sample Tube and

Valves

Glow
Figure 5b. Estimator input error sensitivity. Plug
Adapter
RESIDUAL MEASUREMENT

In order to validate the residual estimator, an in-cylinder

CO2 sampling technique was developed using the Figure 6. CSV500 sample valves and sample tube
Cambustion CSV500 Sample Valve System [24]. Small installed in dummy glow plug for diesel tests.
gas samples were extracted from the cylinder after
intake valve closing and prior to combustion. The
samples were analyzed for CO2 concentration and
compared to CO2 measurements in the exhaust stream
for the same cylinder.

The residual gas mass fraction, RGF, is defined as

follows:

RGF = ([CO2]cyl * Wexh ) / ([CO2]exh * Wcyl) (Equ. 2)

 The procedure minimized the amount of sampled gases
Sample while insuring ample flow for the analyzers.
Valves The test procedure involves opening the purge valve just
after intake valve closing (IVC) and performing a series
of tests with increasing purge duration until the sample
CO2 concentration is invariant. It is important to verify
sufficient purge flow in this manner. The sample valve
Sample duration is adjusted to achieve desired analyzer flow.
Figure 9 shows an example of a sample timing diagram
Tube with purge valve timing, sample valve timing, and
approximate timing of sample extraction from the
cylinder. Figure 10 shows measured CO2 concentration
Figure 7. CSV500 sample system on single-cylinder during one test at 1500 rpm, 3 bar load, and low internal
diesel engine. residuals. For all tests, the sample valve closed prior to
combustion. The interval between purge valve closing
In this study, the sample valves were used in a and sample valve opening was constant at 10 CAD.
continuous-flow mode with timed sampling from the
cylinder for consecutive cycles. The sample tube and
Sample 7.E+06

......
injectors were heated to prevent fuel or water from 800
Purge

crank angle degrees

6.E+06
condensing. A heated sample line carried the in-cylinder

cyl press. (bara)

Analyzer
gas sample to both a micro gas chromatograph (GC) 600 5.E+06

and a Fourier transform infrared (FTIR) analyzer. An 4.E+06

400
additional heated sample line was used for exhaust 3.E+06

sampling. Emphasis was placed on highly accurate CO2 200

2.E+06

measurements using these analyzers. The analyzers 1.E+06

required low flow rates of about 50 cc/min (minimum) at 0 0.E+00

900 930 960 990 1020 1050 1080 1110
about 920 mmHg with maximum sample duration of a crank angle

few minutes. A schematic of the complete test

apparatus is shown in Figure 8. Figure 9. Sample Timing Diagram (typical) showing
purge valve timing, sample valve timing, and timing of
Cambustion Fast
sample extraction from
Sampling System cylinder.
Back
Pressure 0.35
Timing Sample Closing: 50 btdc
PC & Transducer
Control Temp
Software Sample Closing: 40 btdc
Unit (TCU) Controller 0.3
In-Cyl [CO2] (%)

& Drivers
3-Way 4-Way
Heated
BP
Heated
CSV-
Purge
CSV- Heated
Sample Fuel
Valve
1/8”-20ft Heated
Sample Line
Valve FTIR Regulator 0.25
Valve Valve Trap 110 C Vent Analyzer
Sample Chamber:200 cc
Block Temp: 165 C
Pres: 900 Torr
0.2
7 um
Sintered N2 Purge Increasing Purge Flow
Vac Pump
Sample Filter
Flow
Tube
Exhaust
Micro Calib Meter 0.15
Spark Plug Heated GC &
OR Boost
Shut-off Zero
GP Adapter Pump
Metering
Valve
1/4”-20ft Heated
Sample Line
Gases
0.1
Combustion 110 C
Chamber

7 um Vent
0.05 Purge Opening: 140 btdc
Engine
Sintered
Filter Purge Close-to-Sample Open: 10 CAD
Bottle Rack
Encoder
0
50 70 90 110 130
Figure 8. Sampling system showing heated lines and Purge Valve - Close Time (CAD btdc)
sample analyzers.

Leakage of the valves (GDI injectors) was not a problem Figure 10. Measured in-cylinder CO2 concentration as
during these tests. A precision MKS flow meter function of purge duration, 1500 rpm, 3 bar and low
indicated zero flow when the valves were turned off. internal residuals.
Gases sampled from the cylinder were much less than
1% of the total charge and had negligible effect on
engine processes.
VALIDATION RESULTS
MEASUREMENT PROCEDURE – A test procedure was
developed to insure that the sampled gas from the Experimental validation data has been acquired on two
cylinder was not diluted by either burned gas from the different test engines. The first test engine was a 0.5L,
prior cycle nor combustion gases from the current cycle. direct-injection, single-cylinder diesel in a research-
grade test facility capable of highly accurate data
acquisition under well-controlled conditions. Residuals the estimator model expected from error analysis.
were measured using in-cylinder timed-sampling of CO2 However, the validation dataset is limited. The difficult
as described above. Significant valve overlap could not case of EIVC+DICP, and the DECP (exhaust reverse
be used on this diesel engine without valve-piston flow) modes of residual generation have not been
interference, but by varying the ratio of intake to exhaust validated. Additional experiments are planned to cover
pressure, and advancing the exhaust cam for negative these types of VVA systems.
overlap, a very wide range of residuals up to 60% could
be generated. Table 4 lists the test conditions and the 60
resulting residual values as measured by CO2 sampling. Homogeneous DI Gasoline

Estimated Residual [%]

50
Single-Cyl Diesel, Neg Overlap
GIMEP Exh Cam Pint Pexh RGF
RPM (bar) Advance (bar) (bar) (%) 40

1500 3.0 0 1.1 1.2 6.9 30

1500 6.0 0 1.5 1.6 5.7
1500 3.0 34 1.1 1.2 22.2 20
1500 6.0 34 1.5 1.6 18.5
1500 3.0 49 1.1 1.2 31.4 10
1500 3.0 64 1.1 1.2 39.2
1500 3.0 64 1.1 1.6 47.3 0
1500 3.0 64 1.1 1.9 59.9 0 10 20 30 40 50 60
Measured (CO2) Residual [%]

Table 4. Engine test conditions for residual

measurement from negative valve overlap on single- Figure 11. Validation results for residual generation by
cylinder diesel engine. negative valve overlap and intake cam phaser advance.

The second test engine was a 4-cylinder, 1.6L,

turbocharged, early-injection (homogeneous) gasoline
direct-injection engine. This engine was equipped with REAL-TIME-CAPABLE RESIDUAL MODEL
an intake cam phaser having 65 crank degrees
authority, which permitted residual values ranging from A primary purpose of a residual measurement is the
10% to 40%. Residuals were measured from cylinder 4 generation of data for calibration of real-time capable
only by continuous cylinder sampling using a residual models. The model may then be embedded in
Cambustion fast CO2 analyzer. Phaser sweeps were the engine management controller to control dilution
performed at nine speed-load combinations, at 1000, during vehicle operation. Residual models are needed
1500 and 2500 RPM, and 2.0, 3.5 and 4.5 bar NMEP. for steady state operation, transient operation, and for
advanced combustion systems that require precise
The single cylinder diesel results constitute a more control of in-cylinder residuals.
rigorous validation because both airflow and CO2
measurements were highly accurate - within 1.0% of A model formulation that is both simple enough for real
reading. For the multi-cylinder engine, however, the time control and sufficiently accurate is shown
CO2 measurement was less accurate, giving a schematically in Figure 12. The model consists of a
repeatability of +/- 0.5 percentage points of RGF. In combination of lookup tables and regression equations.
addition, for the multi-cylinder engine, total engine At each of several discrete RPM values there is a set of
airflow was measured, but CO2 samples were taken three tables that contain values of the regression
from cylinder-4 only. This means that any cylinder-to- coefficients A0, A1 and A2. The first step of the
cylinder airflow maldistribution, which may vary with algorithm, as shown in the overall model schematic in
speed and load, will produce additional error, since Figure 12a, is to identify the two sets of tables,
measured airflow is an input to the estimator model. A corresponding to a high and low RPM (RPM_H and
more ideal validation would use data from all cylinders in RPM_L, respectively) that bracket the input RPM value.
order to compare engine-average residuals, but the test Two residual values, RGF_H and RGF_L, are then
time would have been prohibitive. calculated at each at each RPM, and linear interpolation
produces the final RGF.
The estimated residuals from the on-line model for both
test engines are plotted against measured values in RPM_H Calculate RGF
Figure 11. Error bands are shown at +/-1.5 % residuals. Determine @ RPM_H RGF_H
All the single-cylinder diesel points, and most of the RPM (see Fig 7b) RGF
RPM_H Interpolate
multi-cylinder points lie within the +/-1.5% band.
RPM_L
Considering the additional uncertainty in the multi- RPM_L Calculate RGF RGF_L
cylinder measurement described above, it appears that @ RPM_L
these results are consistent with +/-1.5% accuracy for
Figure 12a. Overall residual model structure. cylinder simulation values. The model errors are plotted
in Figure 13. These errors are due to the basic form of
Figure 12b shows more detail about the RGF calculation the model and do not include interpolation error. The
performed within the shaded box in Figure 12a. The axis spacing of the lookup tables must, of course, be
regression coefficient tables have intake and exhaust chosen to avoid excessive interpolation error. Nearly all
cam phaser position as inputs. The RGF calculation the points show less that +/-2% error, and the standard
uses the coefficients, along with the intake and exhaust deviation is 0.53%.
pressures, to calculate a RGF using an analytic function.
The tables are populated with values determined by 10

Error (%RGF_model - %RGF_actual)

regression on experimentally measured RGF data.

Calculate RGF @ RPM_H

0
Coefficient
Tables @ RPM_H
Intake
Phase 2-D Table -5
A0
A0

Exhaust 2-D Table A1 Calculate RGF_H

Phase A1 -10
RGF_H
0 10 20 30 40
A2
2-D Table Actual RGF
A2
Figure 13. Real-time residual model error.

Pint Pexh

Figure 12b. Calculation of RGF at a given RPM. CONCLUSION

The accuracy of the model was evaluated using GT- A residual estimator has been developed for
Power multi-cylinder simulation of the GM 4.2L L6 (the reciprocating engines, which requires only currently
same model used for residual estimator error analysis) standard engine test instrumentation, namely:
to generate a “test engine” map of residual as a function measurements of airflow, cylinder pressure and mean
of RPM, NMEP and intake and exhaust phaser pressure and temperature in the intake and exhaust
positions. Mapping was performed over a very wide manifolds.
range of conditions as shown in Table 5.
The method basically consists of using an optimizer
coupled to a simple single-cylinder engine simulation to
• Intake Cam: Low-lift, EIVC iteratively determine correct conditions at intake valve
Lift= 7.0 mm, Duration= 210 crank deg
closing. Intake pressure, trapped residual and exhaust
• RPM = 500, 750, 1000, 1200, 1400, 1600, 1800, heat transfer coefficients are adjusted so that airflow,
2000, 2400, 2800, 3200 cylinder pressure early in the compression stroke, and
exhaust temperature calculated by the simulation are
• IVO = 280 to 360 deg ATDC (0 - 80 deg advance, 5 deg steps)
equal to values measured on the test engine. The
• EVO = 90 to 165 deg ATDC (0 to 75 deg retard, 5 deg steps) simulated residual value is then outputted.
• Pint = 0.07 to 0.99 bar
A cylinder pressure auto-pegging routine using
• Pexh = 1.0 bar simulated and measured values of the polytropic
exponent has been implemented to improve accuracy
• Residual Range = 4 to 40 %
and robustness.

Table 5. Engine operating conditions for real-time An extensive error sensitivity analysis indicates that an
residual model error study (using simulation). accuracy of +/-1.5 percent residual should be
achievable. Validation testing using in-cylinder CO2
Regression was performed on this data to produce the sampling to measure residual was performed on two
coefficient values. The residual values calculated by the different engines. The residual estimator gave values
real-time model were then compared to the multi- within the expected 1.5% error band over a very wide
range of residuals.
For the alternative port-pressure-based method of 10. Kakuho, A., “Simultaneous Measurement of In-
residual estimation, an error sensitivity analysis indicates Cylinder Temperature and Residual Gas
that similar accuracy should be achievable. However, Concentration in the Vicinity of the Spark Plug by
the instrumentation and data handling requirements are Wavelength Modulation Infrared Absorption,” SAE
much more complex, costly, and time consuming to use. Paper 2007-01-0639.
11. Galliot, F., et al., “In-Cylinder Measurements of
A relatively simple real-time-capable residual model is Residual Gas Concentration in Spark-Ignition
described, and good accuracy is demonstrated. Engines,” SAE Paper 90485, 1990.
12. Giansetti P., et al., “A Model for Residual Gas
Fraction in Spark Ignition Engines,” SAE Paper
2002-01-1735.
ACKNOWLEDGMENTS 13. Cho, H., et al., “Measurements and Modeling of
Residual Gas Fraction in SI Engines,” SAE Paper
The authors would like to thank Craig DiMaggio, Ken 2001-01-1910.
Rahmoeller, Daniel Trytko, Jan Holmskov, Jean-Baptiste 14. Ford, R. and Collings, N., “Measurement of Residual
Terpreau, and Hanho Yun for their support for engine Gas Fraction Using a Fast Response NO Sensor,”
testing during the residual measurements. Thanks also SAE Paper 1999-01-0208.
to Nick Collings of Cambustion, LLC for his support for 15. Miller, R., et al., “Comparison of Analytically and
the experimental residual measurements Experimentally Obtained Residual Fractions and
NOx Emissions in Spark-Ignited Engines,” SAE
REFERENCES Paper 982562, 1998.
16. Quader, A.A. and Majkowski, R.F., “Cycle-By-Cycle
1. Lebel, M. and Cottereau, M.J., “Study of the Effect of Mixture Strength and Residual-Gas Measurements
Residual Gas Fraction on Combustion in a S.I. During Cold Starting,” SAE Paper 1999-01-1107.
Engine Using Simultaneous Cars Measurements of 17. Westin, F., Grandin, B. and Angstrom, H., “The
Temperature and CO2 Concentration,” SAE Paper Influence of Residual Gases on Knock in
922388, 1992. Turbocharged SI Engines,” SAE Paper 2000-01-
2. Nakada, T., Itoh, T. and Yakagi, Y., “Application of 2840.
Cars to Development of High Compression Ratio 18. Schwarz, F. and Spicher, U., “Determination of
Spark Ignition Engine,” SAE Paper 932644, 1993. Residual Gas Fraction in IC Engines,” SAE Paper
3. Grunefeld, G., et al., “A Major Origin of Cyclic 2003-01-3148.
Energy Conversion Variations In SI Engines: Cycle- 19. Karagiorgis, S., et al., “Residual Gas Fraction
By-Cycle Variations of the Equivalence Ratio and Measurement and Estimation on a Homogeneous
Residual Gas of the Initial Charge,” SAE Paper Charge Compression Ignition Engine Utilizing the
941880. Negative Valve Overlap Strategy,” SAE Paper 2006-
4. Johansson, B., et al., “Residual Gas Visualization 01-3276.
With Laser Induced Fluorescence,” SAE Paper 20. Shayler, P.J. and Alger, L., “Experimental
952463. Investigations of Intake and Exhaust Valve Timing
5. Hinze, P.C. and Miles, P.C., “Quantitative Effects on Charge Dilution by Residuals, Fuel
Measurements of Residual and Fresh Charge Consumption and Emissions at Part Load,” SAE
Mixing in a Modern SI Engine Using Spontaneous Paper 2007-01-0478.
Raman Scattering,” SAE Paper 1999-01-1106. 21. Giansetti, P. and Higelin, P., “Residual Gas Fraction
6. Schuette, M., et al., “Spatially Resolved Air-Fuel Measurement and Estimation in Spark Ignition
Ratio and Residual Gas Measurements by Engines,” SAE Paper 2007-01-1900.
Spontaneous Raman in a Firing Direct Injection 22. Collings, N., et al., “Cycle Resolved Measurements
Gasoline Engine,” SAE Paper 2000-01-1795. of In-cylinder NOx Concentration in a Gasoline
7. Hall, M.J., Zuzek, P., and Anderson, R., “Fiber Optic Engine,” JSAE Paper 20065423, 2006.
Sensor for Crank Angle Resolved Measurements of 23. Collings, N., et al., “In-Cylinder Sampling of IC
Burned Gas Residual Fraction in the Cylinder of an Engines using Modified GDI Injectors – the CSV,”
SI Engine,” SAE Paper 2001-01-1921. JSAE Paper 20055401, JSAE Annual Congress
8. Alger, T. and Woodbridge, S., “Measurement and 2005.
Analysis of the Residual Gas Fraction in an SI 24. User Manual – Cambustion CSV 500 Sampling
Engine with Variable Valve Timing,” SAE Paper Valve System (Version 2.4), Cambustion LLC,
2004-01-1356. Cambridge, UK.
9. Kawahara, N., Tomita, E. and Tanaka, Y., “Residual 25. Mladek, M. and Onder, C.H., “A Model for the
Gas Fraction Measurement Inside Engine Cylinder Estimation of Inducted Air Mass and Residual Gas
Using Infrared Absorption Method with Spark Plug Fraction Using Cylinder Pressure Measurements,”
Sensor,” SAE Paper 2007-01-1849. SAE Paper 2000-01-0958.
26. Liu, J.P., et al., “A Model for On-Line Monitoring of DEFINITIONS, ACRONYMS, ABBREVIATIONS
In-Cylinder Residual Gas Fraction (RGF) and Mass
Flowrate in Gasoline Engines,” SAE Paper 2006-01- BDC: Bottom dead center
0656. CA50: Crank Angle at 50% Mass Burned
27. Fox, J.W., Cheng, W.K., Heywood, J.B., “A Model CO2: Carbon Dioxide
for Predicting Residual Gas Fraction in Spark– Cd: Discharge Coefficient
Ignition Engines,” SAE Paper 931025, 1993. DECP: Dual-equal Cam Phasing
28. Senecal, P.K., Xin, J. and Reitz, R.D., “Predictions DICP: Dual-Independent Cam Phasing
of Residual Gas Fraction in IC Engines,” SAE Paper EIVC: Early Intake Valve Closing
962052. EVC: Exhaust Valve Closing (crank degrees ATDC
29. Koehler, U. and Bargende, M., “A Model for a Fast expansion)
Prediction of the In-Cylinder Residual Gas Mass,” EVO: Exhaust Valve Opening (crank degrees ATDC
SAE Paper 2004-01-3053 expansion)
30. Cavina, N., Siviero, C. and Suglia, R., “Residual Gas GDI: Gasoline Direct Injection
Fraction Estimation: Application to a GDI Engine GIMEP: Gross Indicated Mean Effective Pressure (bar)
with Variable Valve Timing and EGR,” SAE Paper HTmult: Heat Transfer multiplier
2004-01-2943. IVC: Intake Valve Closing (crank degrees ATDC
31. Amer, A.A. and Zhong, L., “A Semi-Empirical Model expansion)
for Fast Residual Gas Fraction Estimation in IVO: Intake Valve Opening (crank degrees ATDC
Gasoline Engines,” SAE Paper 2006-01-3236 expansion)
Mair: Trapped air mass
32. Payri, F., et al., “A Simple Model for Predicting the
Mfuel: Trapped fuel mass
Trapped Mass in a DI Diesel Engine,” SAE Paper
Mresid: Trapped residual mass
2007-01-0494, 2007.
NVO: Negative Valve Overlap
33. Mueller, M. and Pfeiffer, J., “Method of Estimating
Pcyl: Cylinder Pressure (bar)
Residual Exhaust Gas Concentration in a Variable
Pexh: Exhaust Pressure (bar)
Cam Phase Engine,” U.S. Patent 6,550,451, 2003.
Pint: Intake Pressure (bar)
34. Sinnamon, J.F., US Patent Applied For.
PEG: Cylinder Pegging Pressure (bar)
35. Davis, R. and Patterson, G., “Cylinder Pressure PolyC: Polytropic Exponent Compression
Data Quality Checks and Procedures to Maximize PolyE: Polytropic Exponent Expansion
Data Accuracy,” SAE Paper 2006-01-1346. RGF: Residual Gas Fraction (% mass)
36. Matekunas, F.A., “Engine Combustion Control With RPM: Revolutions per Minute
Ignition Timing by Pressure Ratio Management,” VVA: Variable Valve Actuation
U.S. Patent 4,622,939, 1986. W: Molecular Weight
37. GT-Power Software, Version 6.2, Gamma
Technologies Inc, Westmont, Illinois.
38. Sellnau, M., et al., “2-Step Valve Actuation: System APPENDIX A
Optimization and Integration on an SI Engine,” SAE
Paper 2006-01-0040. ERROR ANALYSIS OF POLYTROPIC AUTO-
39. Sinnamon, J.F., “Co-Simulation Analysis of PEGGING
Transient Response and Control for Engines with
Variable Valvetrains,” SAE Paper 2007-01-1283. Polytropic auto-pegging can improve the accuracy of
residual estimation by minimizing the effect of pegging
error in the measured cylinder pressure input data.
CONTACT However, any other input errors that affect the polytropic
exponent calculated from either the measured or
For additional information, simulated cylinder pressure profiles will affect the
calculated pegging, and thereby cause a corresponding
James Sinnamon error in the residual estimate. These include
james.f.sinnamon@delphi.com temperatures, air-fuel ratio, blowby and any errors in the
Delphi Powertrain Systems measured cylinder pressure. The variables of interest
Advanced Powertrain are shown in Table A1, along with the range of error
3000 University Drive introduced and the baseline value where appropriate.
Auburn Hills, MI 48326 The procedure was the same as used to obtain the error
sensitivity results shown in Figure 5, except the auto-
Mark Sellnau pegging feature was activated.
mark.sellnau@delphi.com
Delphi Powertrain Systems
Advanced Powertrain
3000 University Drive
Auburn Hills, MI 48326
The results are listed in Table A1. In most cases both to the simulation. Usually, an optimizer is employed to
the pegging error and the residual error are quite small. adjust the average intake pressure so that simulated and
However, the two highlighted cases for crank encoder measured airflow match.
and air-fuel ratio merit comment. First, note that auto-
pegging amplifies the effect of crank encoder error,
Air Meter
although the sensitivity is still acceptable since encoder

Simulation
phasing within +/- 0.2 degrees is not difficult to achieve. Pressure Transducer
Nevertheless, it is recommended that the most accurate
Intake
phasing technique, described by Davis and Patterson Pint
[35] be employed as a test standard. In this method the

Test Engine
signal from a piston position sensor is plotted against
cylinder volume while the engine is motored, and the Heat Release Xb
Analysis
encoder is adjusted so that the compression and
expansion lines overlay. IRG_sim
Pexh
Peg RGF
Base Error Error Exhaust
Parameter Error +/- Value (kPa) (%)
Pressure Transducer Gain 1.0 % -- 0.033 0.40
Crank Encoder Error 0.2 deg -- 0.400 0.29
Intake Air Temperature 5C 25 C 0.032 0.17
Figure B1. Port-pressure method of residual estimation.
Exhaust Temperature 20 C 610 C 0.060 0.30
Combustion Phasing 2 deg 9 deg 0.015 0.03
This method relies on accurate simulation of the
Combustion Duration 10 deg 30 deg 0.015 0.04
pulsating pressures and valve flows during gas
Intake Port Surface Temp 20 C 120 C 0.036 0.19
exchange, and is therefore sensitive to several
Intake Port Heat Transfer Coef 0.5 1.0 0.015 0.03
simulation setup parameters to which the cylinder-
Cylinder Wall Temperature 10 C 150 C 0.160 0.20
pressure method is relatively immune. An input error
Cylinder Heat Transfer Coef 0.1 1.0 0.020 0.29
sensitivity study was performed using the same
Compression Ratio 1.0 10.0 0.058 0.15
procedure described previously, except that several
Blowby 2% 2% 0.015 0.02
parameters were added, namely, port pressure
Air-Fuel Ratio 1.0 ratio 14.5 0.240 0.10
transducer sensitivity and pipe geometry. Table B1 is a
list of the parameters and the errors imposed. The
Table A1. Error sensitivity results for polyC auto- parameters associated with cylinder pressure
pegging. measurement are irrelevant because in this method the
cylinder pressure data are only used to calculate the
The second notable feature is that auto-pegging reduces burn parameters, and these are retained.
the sensitivity to air-fuel ratio. It appears that the affect
on polyC and the resulting error in pegging is offset by
the effect on simulated cylinder pressure.

APPENDIX B

ERROR ANALYSIS OF THE PORT-PRESSURE-

BASED RESIDUAL ESTIMATION METHOD

The method referred to as the “port-pressure” method is

an alternative approach to of estimating residual. As
illustrated in Figure B1, it consists of acquiring crank-
angle-resolved pressure measurements either in the
intake and exhaust ports or somewhere in the intake and
exhaust pipes. These data are then input as boundary
conditions to an engine gas-exchange simulation, which
calculates the trapped air and residual gas masses. A
single-cylinder simulation is used in which only those
portions of the intake pipes between the pressure
transducers and the valves need be included. A heat
release analysis is performed using the cylinder
pressure data to derive combustion parameters for input
 Nominal requires more elaborate test engine instrumentation, and
Parameter Error +/- Value second, it relies on several input parameters that are
rather difficult to obtain with the required accuracy.
Airflow Rate 1.0 %
Overall, its accuracy potential is similar to that of the
Intake Pressure Transducer Gain 1.0 %
cylinder-pressure method.
Exh Pressure Transducer Gain 1.0 %
Intake Air Temperature 5C 25 C
0.6
Intake Cam Timing 1 deg

Residual Error (%)

Exhaust Cam Timing 1 deg 0.5
Valve Lash 0.04 mm 0.08 mm
Exhaust Pressure 1.0 kPa 100 kPa 0.4
Combustion Phasing (CA50) 2 deg 9 deg
0.3
Combustion Duration (10-90 % MBF) 10 deg 30 deg
Intake Port Surface Temperature 20 C 120 C 0.2
Intake Port Heat Transfer Coef 0.5 1.0
0.1
Exhaust Port Surface Temperature 20 C 120 C
Exhaust Port Heat Transfer Coef 0.5 1.0 0
Cylinder Wall Temperature 10 C 150 C

Intake Air Temp

Valve Lash
Intk Pressure Gain

Intk Cam Timing

Exh Pressure Gain

Exh Cam Timing

Exh Pressure
Airflow Rate
Cylinder Heat Transfer Coef 0.1 1.0
Intake Port Cd (at low valve lift) 0.1 0.7
Exhaust Port Cd (at low valve lift) 0.1 0.7
Compression Ratio 1.0 10.0
Blowby 2.0 % 2.0 %
Air-Fuel Ratio 1.0 ratios 14.5
Intake Pipe Length 10 mm 105 mm
Intake Pipe Diametr 5 mm 47 mm
Exhaust Pipe Length 10 mm 75 mm Figure B2a. Input error sensitivity of the port-pressure
Exhaust Pipe Diameter 5 mm 40 mm residual estimation method.

Table B1. Error sensitivity parameters for the port 0.6

pressure residual estimation method.
0.5
Residual Error (%)

The results are shown in Figure B2. When compared to

0.4
the results for the cylinder-pressure method, two main
features are evident: 0.3

1) The sensitivity to airflow measurement accuracy is 0.2

similar. In principle, if the port pressure measurement is
accurate, an airflow-matching optimizer is unnecessary. 0.1
However, an error sensitivity analysis performed without
this optimization revealed a very high sensitivity to port 0

Cyl Wall
Intk Port
Surf Temp

Surf Temp

Cylinder
Duration

Exh Port
Phasing

HT Coef
HT Coef

HT Coef
Exh Port
Intk Port

pressure measurement error, so it is concluded that this

Comb

Temp
Comb

feature is required.

2) As expected, the port-pressure method has significant

sensitivities to the valve-related parameters, especially
lash and low-lift port Cd. In practice, it is somewhat Figure B2b. Input error sensitivity of the port-pressure
difficult to determine these input values within the error residual estimation method.
ranges shown in Table B1.

Additionally, it is seen that the sensitivities to the thermal

parameters (port and cylinder surface temperatures and
heat transfer coefficients) are significant. However, this
error study was performed without an exhaust
temperature optimizer. When the cylinder-pressure
method is evaluated with the exhaust temperature
optimizer disabled, similar sensitivities are obtained.

In summary, the port-pressure method has the

advantage that it is less reliant on the quality of the
cylinder pressure data. Its disadvantages are, first, it
 Residual Error (%) 0.7 MCO2 / Mtrap = (nCO2 / ntrap) * (WCO2 / Wtrap), (Equ. C2)
0.6
where nCO2/ntrap is the CO2 molal concentration (volume
0.5 fraction) on a wet basis, and W is molecular weight. It is
0.4 this concentration that is measured by the Cambustion
0.3
instrument.

0.2 Similarly for the exhaust gas,

0.1
0 MCO2 / Mexh = (n CO2 / nexh) * (WCO2 / Wexh) (Equ. C3)

Air-Fuel Ratio
CR
Exh Port Cd

Intk Pipe Diam

Intake Port Cd

Exh Pipe Length

Exh Pipe Diam

Intk Pipe Length
Blowby

Since

MCO2/Mtrap = (Mresid / Mtrap) * (MCO2 / Mexh),

it follows, for EGR=0, that the mass fraction of residual

on a wet basis is:
Figure B2c. Input error sensitivity of the port-pressure
residual estimation method. RGF = ([CO2]trap / [CO2]exh) * (Wexh / Wtrap) (Equ. C4)

where [CO2] is CO2 molal concentration on wet basis,

the subscript, trap, refers to the trapped gas sampled
APPENDIX C from the cylinder during compression, and the subscript,
exh, refers to an exhaust gas sample.
DEFINITIONS OF RESIDUAL GAS FRACTION (RGF)
AND DERIVATION OF RGF BASED ON IN-CYLINDER This definition of RGF applies to PFI engines and early-
CO2 MEASUREMENTS injection GDI engines for which fuel and air are well
mixed in the cylinder by time of combustion.
For homogeneous engines in which fuel is premixed with
air in the cylinder, the residual gas fraction is defined as For late-injection DI engines, such as conventional
the ratio of residual mass to total trapped mass, diesel or stratified charge gasoline engines, the fuel and
including fuel: air are not uniformly mixed in the cylinder, and the
cylinder gas sample contains no fuel. In this case, an
RGF = Mresid / Mtrap, (Equ. C1) alternative definition of RGF, which may be more
appropriate, is proposed as follows:
Where, Mtrap = Mair + Mfuel + Mresid
RGF = Mresid / Mtrap,
Mair = air mass
Where Mtrap = Mair + Mresid (fuel not included).
Mfuel = fuel mass
Derivation of RGF yields the same expression (Equ C4)
as for homogeneous PFI engines, however, the
Mresid = residual mass.
molecular weight, Wtrap, is different due to absence of
fuel during gas sampling. The difference between RGF
For conditions in the cylinder prior to combustion, the
values from the two definitions is of order 1% residual.
mass fraction of CO2 is