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SAE TECHNICAL
PAPER SERIES
2007-01-1052
A Crevice Blow-by Model for a Rapid
Compression Expansion Machine Used
for Chemical Kinetic (HCCI) Studies
S. Scott Goldsborough
Marquette University
Reprinted From: CI and SI Power Cylinder Systems, 2007
(SP-2073)
2007 World Congress
Detroit, Michigan
April 16-19, 2007
400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-0790 Web: www.sae.org
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2007-01-1052
A Crevice Blow-by Model for a Rapid Compression Expansion
Machine Used for Chemical Kinetic (HCCI) Studies
S. Scott Goldsborough
Marquette University
Copyright © 2007 SAE International
ABSTRACT
A crevice blow-by model has been developed for a
Rapid Compression Expansion Machine. This device
can be used to study chemical kinetics with application
to Homogeneous Charge Compression Ignition and
other alternative combustion processes. In order to
accurately resolve the ignition conditions and
understand the oxidation process, accurate models for
heat transfer and crevice flow, including blow-by past the
ringpack, must be utilized. Crevice flows are important
when high compression ratio or boosted operation is
investigated.
In previous work the heat loss
characteristics of the RCEM were characterized; this
study concerns the crevice flows within the RCEM. A
ring-dynamic model, first developed at MIT and recently
modified at UIUC to account for circumferential flow pas
unlubricated rings, was employed. The 0-D model was
coupled to a four-zone heat release code and tuned so
that good agreement could be achieved between a
computed ‘modified-entropy’ pressure and the
experimentally measured pressure for a number of high
compression ratio (20-50:1) ‘motored’ runs. The model
was then used with two ‘fired’ cases (natural gas / air) to
understand how the crevice dynamics change and how
the model affects the understanding of the combustion
process. In a companion paper the ringpack model is
incorporated into an integrated chemical kinetics /
computational fluid dynamics (CFD) code to investigate
the influence of the crevice flows on the in-cylinder
charge motion and temperature profiles that develop
during the compression and expansion strokes of the
RCEM.
INTRODUCTION
Rapid Compression Machines (RCMs) and Rapid
Compression Expansion Machines (RCEMs) are often
used to study low and intermediate temperature
(<1100K) autoignition characteristics of fuel-air mixtures
[1-24]. These devices are usually configured with
piston-cylinder geometries where an initially quiescent
fuel / air or air-only charge is rapidly compressed by the
piston(s) to a desired temperature and pressure;
compression times are on the order of 15-80ms. In this
arrangement the combustion process can be isolated
from typical in-cylinder engine phenomena like the
turbulent fluid dynamics which result from the gas
exchange processes. The chemical kinetics, which play
a predominant role in homogenous charge compression
ignition (HCCI) and many low temperature combustion
(LTC) schemes, can thus be studied and evaluated.
The data collected from these machines have been used
to develop and correlate detailed and reduced kinetic
models for various fuel species [25-33].
RCMs operate with a locking piston so that the
compressed temperature / pressure environment can be
sustained for long times (up to 130ms). ‘Ignition delay’
(IJD) is usually reported, where this is typically defined as
the residence time required at the elevated temperature
& pressure before autoignition occurs. The ignition time
is often taken as the point of maximum pressure rise, or
maximum light emission observed. RCEMs are a
variant of the RCM where a non-locking piston is used.
In these devices, the influence of the expansion process
on the ignition and heat release events can be studied;
the dynamic piston behavior more closely approximates
the time-varying pressure and volume conditions found
in IC engines. Even though an elevated temperature /
pressure environment cannot be maintained with this
design, and ignition delay times may not be directly
comparable to RCM results, the adaptation can be
useful since the ignition and combustion process,
including the formation of pollutants, can be affected by
the dynamics of the piston. Regimes of partial or late
(after top dead center (TDC)) oxidation can be
investigated. Additionally, useful characteristics such as
rate of heat release (ROHR), mass burned fractions (F),
and cycle thermal efficiencies (KTH) can be used as
additional means to validate kinetic and other HCCI
modeling techniques.
RAPID COMPRESSION EXPANSION MACHINE
A free-piston RCEM has been constructed by Sandia
National Laboratories, California to investigate the
autoignition characteristics of various fuel-air charges.
The primary interest of previous studies was to assess
the energy conversion efficiency and emissions potential
of HCCI, with the intent to incorporate a rapid
combustion system into a free piston based powerplant
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[7]. The objective of the current work is to develop a
framework
to
accurately
determine
additional
parameters such as autoignition temperature (including
temperature distributions within the device (see Ref. [34]
which is a detailed kinetic / CFD study of the RCEM
utilizing the 0-D crevice model described here)), ignition
delay, ROHR and F of different fuel-air charges.
The RCEM’s design and operation has been described
in detail previously [7,35], however its principal operating
characteristics are reviewed here. An illustration of the
SNL RCEM is presented in Figure 1; its primary
specifications are listed in Table 1. The RCEM consists
of a double ended free piston that is enclosed in a
double ended cylinder (there is a combustion chamber
and a driver chamber on either end of the piston). The
piston crown on either end is flat (as can be seen in
Figure 2) creating a pancake chamber at TDC.
Stainless steel caps are used for the cylinder heads,
while cylinders of steel and cast iron have been used.
The cylinder is wrapped with Briskheat electric heating
tape and covered with Fiberfrax insulation, which is
visible in the photo, to enable investigation of preheated
charges (up to 75C).
The SNL RCEM is pneumatically driven using high
pressure helium (near 45-65MPa). The helium pressure
is adjusted based on the compression heating desired;
higher driving pressures yield greater compression of
the cylinder charge. (RCM studies generally vary the
diluent composition to achieve different compression
temperatures since the compression ratio is not fixed.
The gas is dumped to the driver (or back) side of the
double ended piston where the volume is initially
evacuated. A specially modified Nupro bellows valve
allows rapid gas transfer for the driving process. The
combustion side is initially charged with a homogeneous
mixture of fuel and oxidizer / diluent (‘air’). (For some
liquid fuels the combustion chamber can be filled with
‘air’ only (at atmospheric pressure) and then fuel is
injected directly into the chamber using a stainless steel
syringe. If this procedure is followed, time is allotted for
the fuel to evaporate and mix with the air, usually on the
order of 30 minutes.) The fuel / air charges, whether
premixed or directly injected, are assumed to be uniform
and quiescent at the start of the compression process.
The cylinder pressure is recorded using two
piezoelectric effect transducers (Kistler types 7061A,
7063A, 7061B, 607L, and AVL Type QC42D-X with
Kistler Type 5010 and 5026 charge amplifiers have been
used) at a sampling frequency of 500kHz.
The
transducers are coated with a 0.25mm-thick layer of
Silastic J silicone compound to prevent against thermal
shock during the fired runs. The piston position is
recorded using a Data Instruments FASTAR Model
FS5000HP inductive transducer with a sampling
frequency of 200kHz. For the data presented here the
pressure traces were filtered using an FFT low-pass
filter where the cutoff frequency was set to 4kHz for the
‘motored’ (air-only) runs and 30kHz for the ‘fired’ runs.
Lower cutoff frequencies tend to significantly alter the
Figure 1 – SNL Rapid Compression Expansion Machine.
Bore
76.2 mm
Stroke
254 mm (max)
234 mm (average)
Bore to Stroke Ratio @ TDC
5.1 @ CR = 16:1
9.6 @ CR = 30:1
16.9 @ CR = 50:1
Piston Mass
2.89 kg
Compression Time
13 - 15 ms
Expansion Time
10 - 12 ms
Compression Ratio
Variable; utilized 16-50:1
Pressure Capacity
>30MPa
Table 1 – SNL RCEM Specifications
perceived ignition point and the ROHR calculations (as
illustrated in Ref. [35]).
Noise from the position trace was removed by the
following method. The position data was first smoothed
using a binomial routine with the number of smoothing
passes set to 200; the trace was then differentiated to
obtain the piston velocity. The velocity trace was
smoothed, again using the binomial routine (this time the
number of passes was set to 1000); the trace was then
differentiated to obtain the piston acceleration. The
acceleration trace was smoothed, again using the
binomial routine (this time the number of passes was set
to 6000). The velocity trace was then integrated to
recover the piston position. Examples of this procedure
and the effects that this can have on the data can be
found in Ref. [35].
The SNL RCEM has been designed to operate at high
pressures, measured up to 30MPa; this design
parameter is important since some charges, such as
lean natural gas / air mixtures shown here, can require
significant compression heating (up to 45:1, 17MPa)
before the autoignition process is initiated. Additionally,
accurate ignition/oxidation data is needed for high
pressure environments. In order to achieve this level of
pressurization with minimal piston and head blow-by, a
custom ringpack and head sealing system have been
designed. Three ringpack configurations have been
utilized, each using different in ring types and groove
geometries; for more detail see Ref. [7]. One
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Combustion End
Driver End
Figure 2 – RCEM free piston and detailed ringpack.
configuration, which was used in this study, is illustrated
in Figure 2. This ringpack consists of two seals on the
combustion chamber end and one on the driver end.
The combustion or top-land seal is a C. Lee Cook ZGS
compression ring (graphite reinforced polyimide), and
behind that a Furon elastomeric lip seal (lubricated
glass-filled PTFE) with an o-ring expander ring (this ring
is a continuous piece). On the driver end a Furon lip
seal is used in conjunction with a stainless steel
expander spring. Two C. Lee Cook bronze-impregnated
Teflon rider rings are used to ease the piston’s motion
within the cylinder. The head uses a plain o-ring which
is fitted into a rectangular cross-section groove cut into
the cylinder body. A 45˚ bevel is cut around the
circumference of the interior cylinder and the piston
crown to enable easy insertion of the free piston into the
cylinder. The head is fastened to the cylinder body
using 12 bolts positioned around the circumference.
AUTOIGNITION PARAMETERS
RCM and RCEM data sets can include autoignition
temperatures, ignition delays, rates of heat release and
mass
burned
fractions;
sometimes
specie
concentrations (temporally varying, or at a single time)
are available.
However, in order to correctly
characterize the data sets an accurate quantification of
the in-cylinder temperatures through the compression
and delay, or expansion processes is required;
temperature is the predominant driver of the chemical
kinetics and thus it is extremely important to accurately
determine this. Various experimental and computational
techniques have been employed to evaluate this
parameter, including the use of fine-gage thermocouples
[18], planar laser induced fluorescence [35,37], Rayleigh
scattering [38], 1-D gas dynamic calculations [39] and
multi-dimensional computational fluid dynamics software
[38,40,41]. Recent RCM designs have incorporated
features that seek to minimize the thermal gradients
within the charge; the objective is to create a uniform
charge with a single representative temperature. This is
important with regard to interpreting the rates of
reaction, especially in regimes where significant
negative temperature coefficient (NTC) behavior can be
observed. In addition, the ability to use 0-dimensional
Figure 3 – RCM piston with machined crevice volume [46].
Figure 4 – RCF piston utilizing a nose-cone geometry [18].
(0-D) modeling of the system is preferred due to lower
computational costs. Finally, substantial stratification
within the reaction chamber and the resulting gradients
in the heat release time can lead to the development of
resonant acoustic waves which can alter the heat loss
characteristics of the charge and emissions formation
within the system. These are not indicative of the bulk
gas kinetics themselves and should be avoided.
Modern RCM designs have utilized machined piston
crevice volumes or nose-cone piston geometries
[18,38,41,42] (for examples see Figures 3 and 4) which
work to swallow, or exclude the cold gases that are
adjacent to the cylinder walls during compression, and
prevent their reintroduction into the bulk charge during
the delay period; the vortex roll-up behavior that is
usually seen in reciprocating engines [43,44] is
suppressed or excluded entirely. O-rings are typically
used to seal the reaction chamber during the
experiment.
RCEMs are precluded from using
significant crevice volumes as this can enable large
quantities of cold gas to reemerge into the bulk charge
on the expansion stroke; crevice flows should thus be
minimized. In some studies the piston(s) have been
coated with silicon-based thermal barriers to reduce the
heat losses that result from the “vortex roll-up” and thus
decrease the degree of thermal stratification that
develops during compression [7,35].
Engine-like
ringpacks are often used in RCEMs to seal the reaction
chamber [35,45].
The bulk charge temperature in RCMs is typically
computed using a 0-D, isentropic compression
approximation; variations in specific heats are
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considered and either the geometric compression ratio
or the experimental pressure ratio used. Heat loss has
been incorporated into the analysis through the use of
either a time-varying cylinder volume [24,31,38], an
effective compression pressure [18,19,22], or a global
heat transfer correlation [28,29].
The charge
temperature in RCEMs has been computed using an
equation of state (EOS) (e.g., ideal gas (similar to IC
engine analyses)); a ‘modified-entropy’ approach has
also been used in conjunction with a global heat transfer
correlation [35,45,47]. Another method is to replace the
isentropic coefficient with a polytropic coefficient.
Mass transfer to and from the crevice region, including
blow-by past the rings, can significantly alter the
experimental pressures achieved, as well as the incylinder temperature distributions, and the emissions
recorded during the experiment. This is especially true if
high compression ratios are utilized since a greater
fraction of the bulk charge can enter and leave the
crevice volume; boosted charge operation can have a
similar effect. Calculations of the ROHR can also be
skewed if the crevice flows are substantial but not taken
into account. Because of these issues it is important to
appropriately quantify the crevice flows for the RCEM
studies; this is the primary objective of this paper.
The remainder of this manuscript is organized as
follows. First an overview is presented of the two
prominent crevice modeling techniques; this is followed
by a detailed description of the ring-dynamic model
explored in this study. The specifics of the bulk charge
modeling are presented along with some notes
concerning the solution methodology. Finally, results of
the RCEM modeling are presented, illustrating both
‘motored’ and ‘fired’ conditions, with conclusions drawn
concerning the significance of the crevice flows in the
RCEM.
CREVICE FLOWS
Two approaches are typically utilized to account for
crevice mass transfer in piston-cylinder arrangements.
The first, a relatively simple method, assumes a single
aggregate, fixed-volume to which all of the crevice
charge is transferred; this is assumed to be in pressure
equilibrium with the main cylinder gases, and in thermal
equilibrium with the piston and cylinder wall. Surface
area to volume ratios are generally large enough to
satisfy this latter condition, enabling adequate rates of
heat transfer between the crevice gases and the solid
engine surfaces to achieve isothermality. (This was
demonstrated by Furuhama and Tada [48] to be a good
approximation in operating IC engines.) This volume
could be considered as the top land crevice volume, that
region just above the top compression ring. Calculating
mass flow to and from this region using this method is
fairly straightforward and computationally inexpensive;
as such, it is often used for real-time engine ROHR
calculations [49,50].
A second, more complex, and more computationally
expensive approach employs a series of disparate
volumes which represent the various ‘pockets’ within a
piston ringpack. The pressures of these volumes are
not assumed to be in equilibrium with the main cylinder
gases, but are based on the time varying flow rates into
and out of these ‘pockets’ and the size of the ‘pockets’.
In this model, as with the former, thermal equilibrium
with the solid surfaces is usually assumed. This ‘ringdynamic’ crevice model, as it is termed since it also
accounts for the dynamic movement of the rings within
the grooves of the ringpack, was initially proposed by
Namazian [51] and Namazian and Heywood [52]. This
model has been used for analyses of emissions and the
influence of the crevice flows on the in-cylinder fluid
dynamics [51-59].
Figures 5a & 5b are presented to illustrate the
differences between these two approaches, as applied
to the SNL RCEM. In these figures computed and
measured pressure traces, and computed temperature
traces are shown for a ‘motored’ shot, versus
instantaneous compression ratio. Much of the data in
this work are plotted versus instantaneous geometric
compression ratio (i.e., Vmax / Vinst) to eliminate the slight
variations in piston compression - expansion times (for
varying driver pressures, i.e., maximum compression
ratios), and to accentuate the region near TDC, where
the largest rates of mass transfer occur. Arrows indicate
the direction of the traces; here along a clockwise path.
For this run the cylinder contained air only and a
maximum geometric compression ratio of about 50:1
was used. The initial pressure and temperature were
0.099MPa and 300K, respectively.
The computed
pressures are calculated using a ‘modified-entropy’
approach where the cylinder charge is assumed to be
compressed and expanded with constant specific
entropy (between each time step (i.e., the intervals of
piston motion data)) with the specific entropy modified to
account for heat losses. Details of this procedure can
be found in the Bulk Charge Model section of this paper.
The crevice model parameters have been adjusted to
achieve fairly good agreement with the peak pressures,
and, for the ring-dynamic model, with the cylinder
pressure along the piston’s trajectory.
For this comparison, and throughout the rest of this
paper, the combustion chamber volume is computed by
assuming a right-circular cylinder configuration defined
by the bore and the measured stroke; a ‘free-volume’ is
added to account for slight variations that may occur as
the piston position is initialized. ‘Free-volume’ values
were within r2.0cm3 (about 0.2% of the initial cylinder
volume); this parameter was adjusted for each run in
order to enable good agreement between the measured
pressure trace and the ‘modified-entropy’ pressure.
As can be seen in the figures, the ring-dynamic model
gives significantly better agreement with the
experimentally measured pressure and computed massaverage temperature both on the compression stroke
and the expansion stroke. In Fig. 5b it can be seen that
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18
Pressure [MPa]
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
Significant discrepancy through compression
and expansion strokes for single zone model
12
Slight departure on expansion
stroke for ring dynamic model
6
a1_17
Experimental pressure
Computed pressure, ring dynamic model
Computed pressure, single zone model
0
0
10
20
30
40
50
Instantaneous Compression Ratio
Figure 5a – Cylinder pressure vs. instantaneous compression
ratio; comparison of experimental data to calculations using singlevolume crevice model and ring-dynamic model, with maximum
geometric compression ratio of 50:1.
1200
Temperature [K]
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
900
Slight departure on expansion
stroke for ring dynamic model
Significant discrepancy through compression
and expansion strokes for single zone model
600
Modified-entropy Temperature
Mass averaged temperature, ring dynamic model
Mass average temperature, single zone model
a1_17
300
0
10
20
30
40
50
Instantaneous Compression Ratio
Figure 5b – Computed temperature vs. instantaneous
compression ratio; comparison of modified-entropy temperature to
mass-average temperature computed using single-volume crevice
model and ring-dynamic model; a maximum geometric
compression ratio of 50:1 is used.
the mass-average temperature using the single-zone
crevice model is substantially greater than the ‘modifiedentropy’ temperature, which is not realistic; this would
indicate greater-than isentropic compression.
(The
mass-average temperature is computed using an EOS
with the measured pressure, and the cylinder masses
determined from the associated crevice model, e.g., Tavg
= f (Pavg, ȣ); ȣ = Vcyl /(mcyl R).) Because of the better
agreement achieved with the ring-dynamic model, this is
the focus of this paper.
RING-DYNAMIC MODEL
A description of the ring-dynamic model is presented
next. The ring-dynamic model attempts to account for
the pressurizing and depressurizing of the ringpack
pockets, the mass transfers from the main cylinder and
between these pockets, the variations in the forces
acting on the rings, and the kinematics of the rings within
the grooves, with this generally limited to axiallyconstrained movements. Namazian and Heywood [52]
coupled this 0-D model to experimental, in-cylinder
pressure measurements to investigate the influence of
the ringpack parameters on a number of factors,
including the mass entering the crevice, the mass
trapped within the ringpack, the mass lost to blow-by,
and the contribution of the ringpack gas flow to the
engine-out emissions. Kuo et al [53] coupled this model
to a ring-friction model which interactively computed the
lube-oil-film thickness; they conducted validation tests
over a range of operating conditions and performed a
sensitivity study of the model’s parameters. Reitz and
Kuo [54] integrated the 0-D ring-dynamic model into a
computational fluid dynamics (CFD) code (KIVA [55]),
assuming uniform, axisymmetric behavior of the crevice
flows, in order to investigate the influence of this gas
motion on the bulk-charge fluid dynamics, as well as the
in-cylinder temperature fields and the engine-out
emissions for three different operating points of a sparkignited (SI) engine. Tonse [56] integrated the ringdynamic model into KIVA as well, also assuming
axisymmetric behavior, in order to study the crevice flow
induced fluid dynamics and the effects on a sparkignited propagating flame. Huynh et al [57] used a
coupled 0-D / CFD (KIVA) formulation to study the
influence of various engine operating parameters on the
crevice flows and the resulting hydrocarbon emissions.
Roberts and Matthews [58] modified the original
formulation of the 0-D model to account for thermal
expansion of the rings and piston, variations in gas
composition within the ringpack, as well as azimuthal
variations in the crevice flows, which result from the
location of the ring end gaps.
They compared
calculations with spatially resolved, in-cylinder HC
measurements, and investigated the influence of a
number of engine operating parameters on the HC
emissions. More recently, Zhao and Lee [59] modified
the original ring-dynamic model to account for
circumferential flows that occur in unlubricated engine
configurations; their application was a small-bore directinjection (DI) optical engine. They integrated the 0-D
model into KIVA to investigate the crevice flow induced,
in-cylinder fluid dynamics and the blow-by emissions
encountered in their engine.
Finally, Potokar and
Goldsborough [34] incorporated the 0-D model
developed in this paper into an integrated chemical
kinetic / CFD solver to investigate charge motion and
temperature profiles within an RCEM.
The ring-dynamic crevice model is presented here in two
parts: first the mass transfer to and from the crevice and
between the ringpack pockets is described, then the
movement of the rings within the ringpack is discussed.
The formulation used in this study is similar to the
development by Namazian and Heywood [52], along
with the modifications of Zhao and Lee [59]; additional
details can be found in those references. Differences
with previous approaches will be highlighted.
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dm 3
dt
dm 4
dt
13 m
23 m
13 c m
34 m
35 m
3 5c
m
(2)
34 m
45
m
(3)
In these expressions the mass flow rates between zones
i j ; the “c”
‘i’ and ‘j’ are designated by subscripts, e.g. m
subscript denotes the circumferential flow path.
Figure 6 – Pathways for gas motion within the ringpack.
GAS MOTION
The
ringpack
pockets
are
pressurized
and
depressurized as mass travels from the bulk charge into
the top-land crevice and then through various pathways
within the pack. Due to the small size of the pathways
the flow is restricted, and this results in a lag between
the pressurization/depressurization of the main charge
and the changing pressure of the ringpack gas. The
primary passages for the gas motion are illustrated in
Figure 6; these include the ringside clearance (between
the inner diameter of the ring and the grooves of the
piston), the end gaps of the rings (used for ring
installation and removal), and the circumferential
passage (between the outer ring diameter and the
cylinder wall). The pockets within the ringpack are
labeled 1 through 5 in the figure. For this work, these
volumes are assumed to be discrete but azimuthally
contiguous within the ringpack, with each zone
independently homogeneous in temperature, pressure
and composition. The gas in volume 1, the top-land
crevice, is assumed to be at the cylinder pressure, which
is consistent with previous studies. The gas in volume 5
is assumed to be at atmospheric pressure, which is
consistent with previous work. As well, the gas within
the pockets is assumed to quickly equilibrate to the wall
temperatures. However, the effects of ring heating (due
to sliding friction) on the flow rate and temperature of the
charge passing through the circumferential gaps are
taken into account. A discussion of the ring heating is
presented in the Ring Heating sub-section.
The mass conservation for each pocket can be
expressed as in Equations (1) through (3). Previous
publications have reduced these equations to rates of
pressure change by assuming isothermal, ideal gas
behavior within the pockets.
In this work the
expressions are kept in their generalized form so that an
arbitrary EOS can be applied with the intent to account
the effects of non-ideal gas behavior. (This will be more
fully investigated in a future publication.)
dm 2
dt
12 m
23
m
(1)
To determine the mass flow rates the flows between the
zones are modeled as either channel (Poiseuille) flow, or
orifice (isentropic) flow; these are described next. The
flows into and out of volumes 2 and 4, the ringside
clearance volumes, are modeled as compressible,
laminar channel flows; the channel clearance heights
are ct and the channel lengths (i.e., the ring radial
lengths) are L. The flow rates using these assumptions
can be determined by
m
A
ct 2 U dP
12 P dx
(4)
With an assumed linear drop in pressure across the
channel length this can be rewritten as
m
A
ct 2 1 u dP
U
dx
12 P L ³ d dx
(5)
In this equation the upstream and downstream
conditions are denoted by the limits ‘u’ and ‘d’; A is the
cross-sectional area normal to the flow based on the
clearance height and the circumference of the ring. The
gas viscosity, µ, is assumed to be only a weak function
of the pressure drop, and thus it is left outside the
integral.
The gas viscosity is evaluated at an average
temperature, between entering and exiting conditions,
where the formulation
P
CP T 0.7
(6)
is used. The constant CP is set to 3.3e-7 kg/m-s, as per
the discussion in Ref. [60]; this equation, though it was
developed for hydrocarbon/air charges also fits data for
dry air very well over the temperature range considered.
The second set of flows, those through the ring end
gaps, can be modeled as compressible, laminar,
isentropic flow through an orifice. The 1-D flow rate can
be written as
m
A
Cd Us v s
Cd Us
2 h o h s (7)
where Cd represents the discharge coefficient, Us the
downstream density (after the isentropic expansion), and
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vs the throat velocity of the orifice. The velocity is
rewritten in terms of the upstream, or stagnation
enthalpy, ho, and the downstream, or throat (isentropic)
enthalpy, hs, based on the isentropic condition.
If the flow is choked the throat velocity approaches the
sonic velocity where this can be expressed as,
c
§ wP ·
¨
¸
© w U ¹s
(8)
The sonic velocity, c, at a particular pressure and
temperature can be determined through an arbitrary
EOS. (For ideal gas, this reduces to J R T .)
It is noted here that previous publications used the ideal
gas approximation to reduce Eq. (6) to the following,
m
A
­ 2 ª § P ·2
°
«¨ d ¸
Cd Uu c ®
°¯ J 1 «¬ © Pu ¹
J
§P ·
¨ d¸
© Pu ¹
J 1 J
1 2
º ½°
»¾
»°
¼¿
(9)
Figure 7 – Free body diagram of the compression ring within the
ringpack; the elastomeric ring is identical.
of motion to yield the second derivative of the ring’s axial
position within the ring groove; this is an inertial
reference frame fixed to the piston. This is the same as
the second derivative of the ringside clearance height
can thus be expressed as,
m r acr
mr
d 2 zcr
dt 2
mr
d 2 ct
dt 2
FP Ff Fi Foil
(10)
where ȡ is the upstream density, Ȗ the ratio of specific
heats (assumed constant), and the subscripts ‘u’ and ‘d’
represent the upstream and downstream conditions.
However, references [52,53,59] have mistakenly written
this expression without the square root of the 2/(Ȗ-1)
term.
In this equation the subscript ‘r’ denotes the ring, ‘p’
pressure, ‘f’ friction and ‘i’ inertia; the variable h is the
clearance height, as in Eq. (5). These forces are
determined using the following equations. The pressure
force can be computed using the pocket pressures,
The third set of flows, those through gaps between the
cylinder wall and the outer ring surface (the
circumferential flow that occurs due to the absence of a
lubricating oil) are also modeled as compressible,
laminar, channel flows, as per the discussion given in
Ref [59]. Eq. (5) is used where it is also assumed that
the temperature gain due to ring heating is linear along
the length of the channel. The gas is heated to an
average of the ring surface temperature and the
temperature of the cylinder wall.
FP1
A r1
P P3
P1 P2
A r1 2
2
2
(11)
where the numeric subscripts denote the ringpack
volumes; Ar1 is the ring-side surface area. The friction
force as the ring slides along the cylinder wall is
determined by
Ff1
C f1 P2 A f1
C f1 P2 S d r1 t r1
(12)
where C f1 is the coefficient of sliding friction. Again, the
RING MOTION
In a typical ringpack, the ring dynamics can contribute
significantly to the flow through the crevice region,
accounting for as much at 50% of the blow-by mass [51].
As the rings shift position within the grooves the
pathways for the flow through the ringpack change and
as a result the cylinder charge can more easily escape
through the ringside clearance volumes, 2 and 4, from
volumes 1 to 3, and 3 to 5.
The kinematics of the rings are generally governed by a
number of forces including contributions due to
pressure, friction, inertia and the oil film; in the RCEM
however, there is no lubricating fluid so the film force is
absent. A free body diagram of the rings and their
forces is presented in Figure 7; only axial dynamics are
considered here, which is consistent with previous work.
The forces shown can be combined using Newton’s law
friction does not consider any twisting of the rings which
could be important. Af1 is the surface area of the ring in
sliding contact with the cylinder wall; this is given by the
outer diameter of the ring and its axial length. The
inertial force is the mass of the ring, mr, multiplied by its
acceleration, ar, as in
Fi
mr ar
(13)
The acceleration of the ring in the non-inertial reference
frame is generally governed by the piston motion,
excepts when it floats freely within the piston groove,
and for the purposes of this model it is assumed to be
accurately approximated by the acceleration of the
piston. (As is seen later in Figure 11, the inertial force is
extremely small relative to the pressure and friction
forces, and therefore any errors associated with ring
acceleration term are negligible.)
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BULK CHARGE MODEL – HEAT RELEASE
ANALYSIS
Figure 8 – Schematic of ring material for unsteady energy
equation.
RING HEATING
As the piston traverses the cylinder length in the RCEM,
the rings slide along the unlubricated wall. Due to the
single-shot nature of the RCEM, some amount of
transient friction heating is expected to occur. This
effect may be more pronounced if rings of low thermal
diffusivity are used. In order to consider the ring heating
due to friction, especially at the ring surface, and any
effect this might have on the flow rates or emerging gas
enthalpies, the time varying temperature distribution
within the ring is computed by applying the onedimensional, unsteady heat diffusion equation to the
solid ring material. This is expressed as
w Tr
wt
Dr
w 2 Tr
w x2
(14)
and is assumed to be constant with respect to
temperature.
The heat flux into the ring surface due to sliding friction
can be calculated by
f fric
Ff1
A f1
vr
The methodology used here is multi-zonal: within the
cylinder the charge is assumed to consist of three
zones: a fresh zone, a burned zone, and a mixed zone;
a crevice zone exists separate from the main charge and
the mixed zone contains fresh and burned gases that
reemerge from the crevice. The cylinder zones are
assumed to be compressed through successive time
steps with constant specific entropy and the partial
pressure of each zone in the main charge is summed to
give the total cylinder pressure. The cylinder pressure
can be represented by
Pcalc
where Tr is the ring temperature, t is time, and x the
radial direction into the ring, as seen in Figure 8. A
cartesean formulation is used here as an approximation
to the cylindrical arrangement since the diameter of the
rings is large compared to the depth of heat penetration.
The thermal diffusivity of the ring is represented by D r ,
qccf1
The ring-dynamic crevice model is integrated with a
model for the bulk cylinder charge so that the effects of
the crevice flows on the cylinder dynamics can be
characterized. The model for the bulk charge is based
on an energy balance approach that has been used
extensively for the analysis of heat release in IC
engines. This approach was originally described by
Kreiger and Borman [61], Gatowski et al [62], Heywood
[63] and Heywood and Chun [64] for SI engines, and is
similar to more recent work by Jensen and Schrammof
[65], and others [66-70].
(15)
where f fric is the fraction of the friction power that is
absorbed by the ring; the remainder of this friction
heating should be absorbed the cylinder wall. Since the
rings travel along the length of the cylinder wall, and
because the cylinder wall has a relatively high thermal
diffusivity, it is expected that there is no appreciable rise
in the surface temperature of the wall.
For the
calculations presented here, the friction fraction is
assumed to be 0.35. Larger values (to 0.5) give
unrealistically high peak surface temperatures; smaller
values (to 0.0) do not allow the computed bulk cylinder
pressure to be accurately matched to the experimental
pressure (see Fig. 13, and its discussion).
Pfr Pbr Pmx
(16)
where the subscripts ‘fr’, ‘br’ and ‘mx’ indicate the fresh,
burned and mixed zones, respectively. Pcalc is the total
calculated cylinder pressure. The mass of each zone is
allowed to vary through the compression / combustion
(for a ‘fired’ run) / expansion processes as mass is
‘transferred’ between the cylinder and the crevice zone;
for the ‘motored’ calculations there is no burned mass.
In general, the fresh, burned and mixed charges are all
allowed to enter the crevice, with the fraction from each
based on the mass fraction of the zones within the
cylinder. While it may be true that more of the unburned
charge lies near the cold cylinder walls, and mass from
this zone is more likely to enter the crevice, this
assumption is used here anyway; this approach may
need to be revisited for cases where slow burning fuel
charges are investigated.
The zones are assumed to be homogeneous and no
inter-zonal heat transfer is allowed, however heat loss to
the combustion chamber walls is incorporated into the
analysis by modifying the zonal specific entropy at each
time step, as dictated by the second law of
thermodynamics (thus the term, ‘modified-entropy’
approach). For this work the total heat loss to the
cylinder walls is calculated based on a modified Woschni
model, which was correlated to the RCEM heat flux data
[35]; the zonal heat loss is apportioned based on each
zone’s representative volume fraction.
The zonal specific entropy at a particular time step can
be calculated as
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1
s fr ,t ' t
m fr ,t ' t
m
ª¬ m fr s fr m fr , i s fr ,i
m fr , e s fr , e q
w
Aw
T fr
m fr T fr m br Tbr m mx Tmx
0
The heat loss from the fresh zone is approximated by
w
Aw
V fr
fr
V cyl
q
w
Aw
3.82
P 0.8
ª 2.28S p 3.61×10 -3 0.73 ¬
H 0.2 Tcalc
V ref Tini
Pini Vini
P
calc
Pmotor
0.8
º¼ T
calc
Tw
m
fr
u fr
0
(21)
0
where the burned specific internal energy, ubr is a
function of the zonal temperature, and pressure,
generally. The integrated heat loss to the walls, the
boundary work and total heat lost within the crevice
volumes, Qcr, are included in this expression. The total
crevice heat loss is calculated by applying the energy
conservation equation to the crevice volume,
Q cr
m
cr
u cr
m
t
cr
u cr
0
³
t
0
cr,ex h ex dt
m
t
(22)
cr ,in h in dt
³ m
0
where the integrated enthalpy flows into and out of the
crevice used.
(19)
This formulation differs from previous heat release
analyses due to the generalized equation of state
employed. The advantage however, is that the effects of
non-ideal gas behavior, which may be important in the
crevice volume and in the main bulk charge for boosted
or high compression ratio, low temperature combustion
(LTC) operating schemes, can be taken into account.
(20)
SOLUTION METHODOLOGY
For reference, the modified Woschni model is
q w
t
t
t
dt Q
³ q w A w dt ³ W
cr
(18)
m fr m br m mx
m br u br m mx u mx m cr u cr
@t
't
zonal temperature is T.
The zone-averaged, or
‘modified-entropy’ temperature is Tcalc, where this is
computed by
q
u fr m br u br m mx u mx m cr u cr
(17)
fr
This expression describes the fresh zone, as noted by
the subscript, ‘fr’. The subscripts ‘t’ and ‘t+ǻt’ indicate
the state of the system at different times separated by
ǻt. The specific entropy is given by s, the rate of heat
transfer to the wall by q w and the wall area by Aw. The
Tcalc
fr
where the leading coefficient and the coefficient
corresponding to the combustion generated portion (the
second term in the brackets) have been changed from
the original formulation [71] to match the RCEM data. In
Eq. (20) H is the instantaneous height of the combustion
chamber when this dimension is less than cylinder
radius (otherwise this characteristic dimension is the
bore), and the subscript ‘ini’ refers to the cylinder
conditions at the beginning of the single-shot
experiment.
Pmotor for this analysis refers to an
uncombusted pressure trace, taking into account heat
and mass losses. Tw is the wall temperature.
For the ‘fired’ runs the mass fractions burned are
determined by matching the computed pressure as
expressed in Eq. (16), to the measured pressure. It is
assumed that any departure from the modified-entropy,
or ‘polytropically’ computed pressure, after already
accounting for heat transfer to the walls and mass
transfer to or from the crevice, must come from a heat
releasing reaction converting fresh or mixed charge to
burned charge. The temperature of the burned zone,
which is assumed to be of frozen composition (complete
combustion with no dissociation), is determined by
applying the energy conservation equation, written as,
Some notes regarding the solution methodology are
discussed here; details concerning the fitting of the
crevice model parameters are provided in the next
section and in the Appendix.
The crevice and bulk charge models presented earlier in
this paper are formulated in a generalized form; an
arbitrary equation of state can be applied in their
numerical solution. However, some of the calculations
will require an iterative loop (for instance, using a
Newton method to determine the sonic velocity at a
particular pressure and temperature) as opposed to a
simple algebraic equation.
This results in a
computationally more intensive solution. A forthcoming
article will provide additional details of the methodology,
and to illustrate the notable differences between the
application of real gas equations of state and the ideal
gas approximation. For the results presented here
however, the RCEM dynamics are solved using the ideal
gas EOS.
The surface temperatures of the rings in the ringpack
are computed using the unsteady energy equation (Eq.
(14)) with a 4000 node mesh, just to the inside diameter
of the rings. An explicit formulation is used with the
node spacing chosen to satisfy the Fourier number
criterion. The heat flux due to the friction is assumed to
be uniform across the ring surface and a constant
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temperature condition is applied to the inner boundary of
the ring.
Topland crevice height
0.254 cm
Topland crevice volume (vol1)
0.100 cm3
The trapped ringpack charges, especially the one in
volume 3, are all assumed to quickly lose any
heating/cooling effects from the gas flow process and
thus achieve isothermality within the pockets between
time steps. The exception to this is the reemerging
circumferential flow (from volumes 3 to 1), where the
heat absorbed from the circumferential ring is carried
through to the bulk charge.
Volume behind compression ring (vol2)
0.040 cm3
Volume between the rings (vol3)
0.500 cm3
Volume behind elastomeric ring (vol4)
0.420 cm3
Compression ring thickness (t r1)
0.437 cm
Compression ring width (rw1)
0.478 cm
Compression ring mass (m r1)
11.23 g
Compression ring ring-gap clearance (A 13)
0.000 mm2
Compression ring clearance height (ct1)
0.005 mm
Compression ring circumferential area (A 13c)
2.500 mm2
Compression ring friction coefficient [72]
0.24
Compression ring density [73]
1412 kg/m3
Compression ring thermal conductivity [73]
0.536 W/m-K
Compression ring heat capacity [73]
1100 J/kg-K
Elastomeric ring thickness (t r2)
0.495 cm
Elastomeric ring width (rw2)
0.508 cm
Elastomeric ring mass (m r2)
6.09 g
Elastomeric ring ring-gap clearance (A 35)
0.000 mm2
Elastomeric ring clearance height (ct2)
0.700 mm
Elastomeric ring circumferential area (A 35c)
1.0-1.5 mm2
RCEM MODELING / ANALYSIS
The goals of this modeling and analysis effort were to
first demonstrate that the integrated crevice and bulk
charge models can accurately interpret the RCEM
experimental data, using the bulk charge parameter of
average cylinder pressure for comparison. The effects
of various modeling parameters (e.g., the accounting for
ring heating, etc) on the computed results were also of
interest. In addition, some understanding was to be
gained with regard to the crevice flows, and the effects
these may have on accurately quantifying the
autoignition data, including the average cylinder
temperature, the ignition delay, rate of heat release and
mass burned fraction.
The RCEM data set considered for this work included
air-only ‘motored’ runs and natural gas / air ‘fired’ runs.
The air-only experiments utilized geometric compression
ratios ranging from 25-50:1, where the initial
temperature and pressure of the charges were 25C and
0.099MPa, respectively. The natural gas / air shots
were compressed to about 40:1 from an initial
temperature and pressure of 67C and 0.1MPa,
respectively. The natural gas consisted of 93.13%
methane, 3.2% ethane, 0.7% propane, 0.4% butane,
1.2% carbon dioxide, and 1.37% nitrogen by volume.
Driving pressures near 60MPa were utilized.
Table 2 lists the parameters for the ring-dynamic model.
The single-zone model has a single parameter, the
volume of the zone; this was set to 0.60cm3 to match the
experimental peak pressure of a 50:1 shot (see Fig. 2).
The ring-dynamic model parameters are based on
geometric values of the RCEM ringpack, however they
have been modified to give reasonable agreement
between the computed and experimental pressure
profiles.
Discussions of the ‘motored’ runs are
presented first; the results of the ‘fired’ runs are
presented after that. A sensitivity analysis of the model
parameters is included in the Appendix for reference.
‘MOTORED’ RUNS
Figure 9 illustrates the effectiveness of the ring-dynamic
model towards accurately matching the experimental
RCEM pressure; the major energy flows seem to be
properly taken into account. In this figure the ratio of the
experimental pressure to the ‘modified-entropy’ pressure
is plotted versus the cylinder volume. This metric seems
Elastomeric ring friction coefficient [74]
0.09
Elastomeric ring density [75]
2260 kg/m3
Elastomeric ring thermal conductivity [75]
0.560 W/m-K
Elastomeric ring heat capacity [75]
1000 J/kg-K
Table 2 – Ring-dynamic model parameters
to provide a more rigorous means of evaluating the
modeling effort compared to the traditional metric of
comparing pressure traces with respect to time. Three
maximum compression ratio cases are shown (25, 37
and 50:1). There are two sets of curves, the top set
incorporates the ring-dynamic model into the
calculations, while the bottom set does not include any
crevice sub-model; the performance of the single-zone
model is shown in a later plot. The curves are plotted
from the experiment initialization through the first
compression and expansion stroke, moving from right to
left and back again on the graph. The bottom set of
curves run along a counter-clockwise path through the
experiment, as is indicated by the arrows. There is a
slight shift in both sets of curves at the experiment
startup. This is consistent throughout most of the RCEM
data (with some shifts indicating experimental pressures
higher than the ‘modified-entropy’ pressures), and could
be due to some electrical noise in the system, but this is
not yet understood.
The bottom set of curves indicate the extent of the
crevice flow in this experiment. It is apparent that as the
charge is compressed to higher compression ratios
more of the charge will be forced into the ringpack (up to
20%), thus the experiment pressure drops relative to the
‘modified-entropy’ pressure. The lag time for the return
of the charge into the bulk volume is also visible. Not all
of the mass reemerges from the ringpack by the end of
Author:Gilligan-SID:12426-GUID:27843746-134.48.93.192
20
1.15
Initial shift in experimental pressure
(due to noise?)
1.00
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
1.10
0.90
1.00
Drop in experimental pressure
due to heat / mass transfer to ringpack
0.90
End of
experiment
a1_11, CR=25:1
a1_14, CR=37:1
a1_17, CR=50:1
0.70
0.65
0
200
400
0.85
Air-only Charge
Compression Ratio 25,37,50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
600
800
1000
2
10
3
1
4
5
Elastomeric ring
does not slip
0.80
3
Volume [cm ]
Figure 9 – Ratio of experimental to modified-entropy pressure vs.
cylinder volume illustrating the issue of crevice flows and the
capability of the tuned ring-dynamic crevice model; ‘motored’ aironly shot, showing three maximum geometric compression ratios.
the stroke, and there is substantial heat loss when the
compressed gases come in contact with the crevice
walls; these issues result in cumulative losses of about
10% for all of the runs. It is also clear that the pressure
ratio is fairly stable through most of the compression
stroke, indicating that the majority of the crevice flows
don’t occur until after a compression ratio of about 5.5:1
(where the volume is 200cm3) is achieved.
The top set of curves illustrates the capability of the ringdynamic sub-model to reasonably account for the
crevice flows in the RCEM. The model parameters have
been adjusted so that the pressure ratio is maintained at
about 0.98 through both strokes of the piston. There is
some fluctuation/noise in the trace, but the overall
agreement is very good. One issue still unresolved
however, is the slight drop in the pressure ratio on the
expansion stroke for the higher CR runs; this was also
apparent in Figs. 5a and 5b during the expansion from a
compression ratio of 48:1 to 22:1. The drop seems to
indicate that there is unpredicted ringpack charging /
discharging on the expansion stroke.
5
0
0.75
1200
0
10
20
30
40
50
Instantaneous Compression Ratio
Figure 10 – Ringpack pocket pressures vs. compression ratio for a
‘motored’ air-only shot, using a maximum geometric compression
ratio of 50:1.
1000
Forces [kgf]
0.75
/P
0.80
calc
0.95
exp
0.85
Pressure [MPa]
1.05
Slight discrepancy for higher CR runs on
expansion stroke, even with ring dynamic model.
Cross-over of pressure leads
to reemergence of charge,
(from volume 3 to 1)
15
P
P
0.95
Compression ring
slippage
2500
'Fired' run, 29_06, Natural Gas / Air
Equivalence Ratio 0.365
Initial Temperature 67C
Initial Pressure 0.1MPa
500
2000
0
1500
-500
1000
-1000
500
-1500
0
-2000
-500
Friction force (F )
Forces [kgf]
1.05
exp
/P
calc
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f1
'Motored' run, a1_17, Air-only
Initial Temperature 25C
Initial Pressure 0.099MPa
Pressure force (F )
-2500
p1
Inertial force (Fi1)
Net force (F +F +F )
-3000
f1
0
10
p1
-1000
i1
20
30
40
50
-1500
Instantaneous Compression Ratio
Figure 11 – Forces on the compression ring vs. compression ratio
for a ‘motored’ air-only and a ‘fired’ (natural gas / air) shot.
Maximum compression ratios of 50:1 and 42:1, respectively, were
used.
0.20
Air-only Charge
Compression Ratio 25,37,50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
Crevice Mass Fraction
Figure 10 illustrates the behavior of the ringpack pocket
pressures, for the model parameters used. This case is
a high CR ‘motored’ run (the same as that shown in
Figs. 5a & 5b) and the pressures are plotted versus
instantaneous compression ratio; again arrows indicate
the direction of the curves. The individual pocket
pressures are labeled by the volume numbers. It is
immediately clear that there is a lag in the
pressurization/depressurization of the ringpack, as all of
the curves are different from volume 1 which is at the
bulk volume pressure. This is due to the narrowness of
the transfer gaps available to the flow. Two points of
interest are the drop in the volume 2 pressure as the
compression ring shifts in the groove, and the cross-over
point where the volume 3 pressure becomes greater
than the pressure in volume 1, thus leading to the
reemergence of the charge from the ringpack. The shift
Rollover indicates point of
reemergence from ringpack
back into bulk charge
0.15
a1_17
Crossover at
end of stroke
for the 3 runs
0.10
a1_14
a1_11
0.05
0.00
0
10
20
30
40
50
Instantaneous Compression Ratio
Figure 12 – Mass fraction of cylinder charge in the crevice and
ringpack volumes vs. compression ratio for ‘motored’ air-only runs,
using three different maximum geometric compression ratios.
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Two other featuress are evident from these calculations.
First, the reemergence of the crevice charge begins
shortly after TDC has been reached. This is slightly
earlier than the crossover of pressures between volumes
1 and 3, and is led by the transfer of the top-land charge
back to the main volume. This early reemergence may
be important if the chemical kinetics are slow and they
occur on the expansion stroke; the reemerging cooler
charge could significantly influence the bulk charge
chemistry or the interpretation of it. Secondly, there is a
cross-over in the mass fraction traces for the three runs
presented. This cross-over is at the end of the runs and
indicates that the operation with higher CR conditions
results in a return of more charge to the cylinder on the
expansion stroke of the experiment.
In order to
accomplish this with the 0-D model the circumferential
area of the elastomeric ring needed to be adjusted over
the range of CR conditions investigated (from 1.5mm2 to
1.0mm2); this was the only ringpack parameter that was
adjusted. This issue seems to indicate that there is
some inconsistency within the model that still needs to
be resolved. One possibility which may explain this is if
volume 5 is not at atmospheric conditions, but is
pressurized during the run due to the presence of the
rider ring. Higher CR runs will result in higher pocket
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
1.10
Drop in computed pressure at end of
experiment due to too much heat /
mass transfer to ringpack
/P
calc
1.05
1.00
0.95
Initial shift in experimental
pressure (due to noise?)
exp
Figure 11 illustrates the component forces (from Fig. 7)
on the compression ring for both a ‘motored’ case and a
‘fired’ case. The inertial force is clearly the smallest of
the forces for both cases and is negligible. In addition, it
can be seen that the friction forces are much higher than
those reported in previous studies (Refs. [51-53,59]).
The behavior of the combined forces results in almost
instantaneous slippage of the ring at TDC.
This
behavior is seen in both the ‘motored’ case and a ‘fired’
case presented here.Figure 12 shows the mass fraction
of the cylinder charge that is driven into the top-land
crevice and ringpack volumes for various ‘motored’ runs;
three different maximum geometric compression ratio
cases are presented. As was seen earlier in Fig. 9, less
than 0.5% of the charge is forced into the
crevice/ringpack before a compression ratio of 5.5:1 has
been reached. As greater and greater compression is
utilized (to achieve greater levels of compression
heating), substantially more charge is driven into the
ringpack. For the 50:1 run nearly 15% enters these
volumes; this has a significant impact with regard to
interpreting the cycle thermal efficiency, as a large
fraction of the thermal energy is lost to the ringpack
surfaces. A better option to achieve charge heating in
future work might be to replace some of the nitrogen
with a diluent like argon which has a higher specific heat
ratio.
1.15
P
in the compression ring position is interesting here since
it occurs at nearly TDC and very quickly. This is due to
the high friction forces on the ring (as can be seen in
Fig. 11) which result from the unlubricated conditions,
and the high friction coefficient for this ring (Cf1 = 0.24).
This is different from the results reported in previous
studies (e.g., [52,53,57]).
End of
experiment
0.90
0.85
ring dynamic model, with ring heating
no crevice model
ring dynamic model, no ring heating, circum. area (A35c ) =0
0.80
0.75
ring dynamic model, no ring heating, circum. area (A35c ) =1.1mm
single-zone model
0
200
400
600
800
1000
2
1200
3
Volume [cm ]
Figure 13 – Ratio of experimental to computed pressures vs.
cylinder volume illustrating the effects of various modeling
parameters for a ‘motored’ air-only shot, using a maximum
geometric compression ratio of 50:1.
pressures and more charge will be returned to the
cylinder.
Figure 13 is presented to illustrate some of the effects
that various modeling parameters have on the computed
‘modified-entropy’ pressure. Here the pressure ratio is
shown again versus cylinder volume. A maximum
geometric compression ratio of 50:1 is used for this
example. Traces are presented for the tuned ringdynamic model (parameters listed in Table 2), the case
with no crevice sub-modeling (for reference), a
calculation using the single-zone crevice sub-model, and
two cases that do not include ring heating (for the ringdynamic model). It can be clearly seen that the singlezone model cannot accurately replicate the dynamics of
the crevice flows (as was evident earlier in Figs. 5a &
5b). In addition, it evident that although the ringdynamic model without ring heating can accurately
predict the cylinder pressure on the compression stroke,
this model option results in a computed ‘modifiedentropy’ pressure
that is lower than the experimentally measure pressure
on the expansion stroke. Modifying the circumferential
area, A35c to 0.0 seems to improve the match but there is
still a discrepancy. These results indicate that in order
to match the compression pressure, a certain fraction of
mass and energy must be removed from the cylinder.
However if all of the sensible enthalpy of this mass is
transferred to the walls then the computed pressure will
be too low. Thus, it is thought that ring heating is an
important parameter that can account for this.
To illustrate the extent of the friction heating, examples
of selected temperature profiles within the compression
and elastomeric rings are presented in Figures 14a &
14b; the computed temperature profiles are plotted
versus time for different locations within the grid that are
close to the ring surface. ‘Motored’ conditions have
been used for illustration at two different compression
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1100
Air-only Charge
Compression Ratio 25:1
Initial Temperature 25C
Initial Pressure 0.099MPa
800
1000
700
900
Ring Surface
10 Pm from surface
50 Pm from surface
100 Pm from surface
600
500
Compression
Ring
TDC
800
700
Into ring
400
600
300
500
Into ring
200
100
400
Elastomeric
Ring
0
5
10
15
20
25
30
300
Temperature [K]
Temperature [K]
900
Time [ms]
Figure 14a – Temperature profiles within the rings of a ‘motored’
air-only shot, using a maximum geometric compression ratio of
25:1.
1100
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
800
Compression
Ring
1000
700
900
Ring Surface
10 Pm from surface
50 Pm from surface
100 Pm from surface
600
Into ring
800
500
700
TDC
400
300
500
Into ring
Elastomeric
Ring
200
100
600
0
5
10
400
15
20
25
30
300
Temperature [K]
Temperature [K]
900
pressures are still high on the expansion stroke (as seen
in Fig. 10) and this results in high friction forces.
Uncertainties exist in the calculated ring temperatures;
these may be associated with the evaluation of the ring
thermal diffusivity (there could be substantial changes as
the temperature increases) and the fact that as the ring
surface becomes significantly hot, a higher fraction of
the heat will be transferred away from the colder ring to
the cylinder wall and not to the ring’s interior (the
constant value of the friction fraction may not be
realistic).
‘FIRED’ RUNS
The integrated ring-dynamic crevice model and multizonal heat release code has been demonstrated to
provide a reasonably good match between the
computed ‘modified-entropy’ and experimental cylinder
pressures for a number of ‘motored’ cases.
The
purpose of this section is to apply this integrated code to
two ‘fired’ cases to illustrate how the crevice dynamics
change under the ‘fired’ conditions, and how these
overall dynamics can influence the accuracy and
interpretation of the autoignition/HCCI data.
Figures 15a & 15b present the computed ringpack
pocket pressures for two ‘fired’ natural gas / air runs
where the ignition occurs before TDC (early) and after
TDC (late), respectively. These plots are schematically
similar to Fig. 10. One notable feature is that the model
predicts that a significant amount of mass can be driven
into crevice and ringpack as the autoignition process
occurs (this is observable from the volume 1 and volume
3 pressure traces). The pressure in volume 3 more than
doubles in Fig. 15a as the main charge autoignites.
Time [ms]
Figure 14b – Temperature profiles within the rings of a ‘motored’
air-only shot, using a maximum geometric compression ratio of
50:1.
ratios; higher compression ratios will result in higher
ringpack pocket pressures and thus higher friction forces
on the rings. The heating will be more significant for
high CR and boosted cases, as well as for ‘fired’ runs.
The computed temperature rise at the ring surface is
substantial due to the low thermal diffusivity of the rings
used in these experiments (Įcomp ring = 0.35x10-6m2/s);
there is little (slow) penetration of the heat into the ring,
leaving it concentrated at the ring surface. Conventional
metal rings are more effective at diffusing the friction
heat away from the ring surface (Įsteel = 15x10-6m2/s).
On a typical lubricated surface a maximum temperature
rise of less than 20K for typical compression rings would
be predicted for the pressure profiles in the RCEM; less
than 60K would be seen on an unlubricated surface.
In Figs. 14a and 14b it can be seen that there is a slight
drop in the ring surface temperatures near TDC as the
piston comes to rest, and then there is additional heating
as the piston reverses direction. The ringpack pocket
Another interesting aspect can be interpreted from Figs.
15 and 16, which shows the crevice mass fraction for the
two ‘fired’ runs versus instantaneous geometric
compression ratio. It appears that for both cases,
whether the charge ignites before TDC or after TDC, the
crevice mass does not reemerge into the main charge
until after the autoignition event is essentially complete
(for these natural gas / air runs). This point, if real, is
beneficial with regard to accurately characterizing the
bulk charge temperature, especially for late-firing
conditions (there would not be a significant mass of cold
reemerging crevice charge during the ignition process;
more investigation is needed to see if similar behavior is
seen for very-late ignition or slower reacting fuel / air
charges.
Also seen in Fig. 16 is the crossover issue that was
discussed for the ‘motored’ runs.
Again, the
circumferential gap area (A35c) of the elastomeric ring
was adjusted so that agreement could be achieved for
the pressure ratio (Pexp / Pcalc) late in the expansion
stroke; as with the ‘motored’ cases, this was the only
ringpack parameter adjusted between these runs.
Figure 17 is presented next to illustrate the importance
of accurately characterizing the crevice flow behavior in
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Compression ring
slippage
Tempertature [K]
Cross-over of pressure leads
to reemergence of charge,
(from volume 3 to 1)
15
Ignition
Elastomeric ring
does not slip
10
1
2
5
1500
2800
Discrepancy
through expansion
1000
Discrepancy
at ignition
500
10
20
30
-1000
40
Instantaneous Compression Ratio
29_11
Compression ring
slippage
Cross-over of pressure leads
to reemergence of charge,
(from volume 3 to 1)
Ignition
2
1
3
4
10
20
30
Instantaneous Compression Ratio
Figure 15b – Ringpack pocket pressures vs. compression ratio for
a ‘fired’ natural gas / air shot, using a maximum geometric
compression 32:1.
0.20
Natural Gas / Air
Equivalence Ratio 0.365
Initial Temperature 67C
Initial Pressure 0.1MPa
29_06
29_11
0.10
25
30
35
40
0.1
0.0
29_11
-0.3
-0.1
ignition after TDC
-0.4
0.0
-0.5
-0.1
-0.6
-0.2
-0.7
-0.2
29_06
-0.3
Greater crevice loss due
to more crevice flow
ignition before TDC
-0.4
heat loss to walls (modified Woschni)
heat loss in crevice
combined heat loss (wall + crevice)
0
5
10
15
-0.5
20
25
Time [ms]
Figure 18 – Calculated heat loss from the bulk charge for a
‘motored’ run and two ‘fired’ runs. The issue of ring heating is
observable.
crevice flow accounts for difference
in RCEM KTH and ideal
calculations close
to emissions data
thermodynamic cycle
1.00
2.00
0.75
1.75
0.50
29_11
ring-dynamic
0.25
29_06
ring-dynamic
0.00
behavior matches
crevice flow dynamics
1.50
1.25
discrepancy with
emissions data
burned fraction in cylinder
burned fraction overall
1.00
0.75
-0.50
-0.75
0.05
0.50
29_11
single-zone
-1.00
29_06
single-zone
negative burned fraction
behavior does not
match single-zone
crevice flows, or
current HCCI
understanding
0.25
0.00
-1.25
-2
0.00
0
10
20
30
300
0.2
Positive heat transfer
from heated ring
-0.25
Rollover indicates point of
reemergence from ringpack
back into bulk charge
Crossover at
end of stroke
20
-0.2
40
0.15
15
-0.1
-0.8
0
10
a1_17
Elastomeric ring
does not slip
5
0
Cumulative Heat Loss [kJ]
15
Mass Fraction Burned
Pressure [MPa]
29_11
5
5
0.0
Natural Gas / Air
Equivalence Ratio 0.365
Initial Temperature 67C
Initial Pressure 0.1MPa
10
0
Figure 17 – Mass-average temperature versus effective
compression ratio for two ‘fired’ natural gas / air charges,
illustrating the effects of using the ring-dynamic and single-zone
models.
25
Crevice Mass Fraction
800
Average temperature, ring dynamic model
Average temperature, single zone model
Instantaneous Effective Compression Ratio
Figure 15a – Ringpack pocket pressures vs. compression ratio for
a ‘fired’ natural gas / air shot, using a maximum geometric
compression 42:1.
20
1800
1300
-500
0
2300
29_06
5
0
3300
0
3
4
2000
40
Instantaneous Compression Ratio
Figure 16 – Mass fraction of cylinder charge in the crevice and
ringpack volumes versus compression ratio for ‘fired’ natural gas /
air charges, using two different maximum compression ratios.
Cumulative Heat Loss [kJ]
29_06
3800
Natural Gas / Air
Equivalence Ratio 0.365
Initial Temperature 67C
Initial Pressure 0.1MPa
0
2
4
6
0
8
2
10
4
12
6
14
Mass Fraction Burned
20
Pressure [MPa]
2500
Natural Gas / Air
Equivalence Ratio 0.365
Initial Temperature 67C
Initial Pressure 0.1MPa
Temperature [K]
25
Time (arbitrary) [ms]
Figure 19 – Calculated mass fraction burned versus time for two
‘fired’ natural gas / air charges, illustrating the effects of using the
ring-dynamic and single-zone crevice models.
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the RCEM. The mass-average temperatures of two
‘fired’ runs are shown versus instantaneous effective
compression ratio; the effective compression ratio is the
ratio of the mass-specific volumes, as opposed to the
ratio of the geometric volumes ( CR eff X ini X inst ). This
takes into account the mass transfer to and from the
bulk charge (from & to the crevice/ringpack volume).
The temperature curves have been modified slightly to
correct for the shift in the pressure data that occurs at
the experiment initiation, which was discussed in
reference to Fig. 9. Calculations using the tuned ringdynamic model and the single-zone model are
presented in Fig. 17. From this plot it is apparent that
both the autoignition temperature and the temperature
on the expansion stroke are significantly impacted by the
crevice modeling. The accuracy of the autoignition
temperature is extremely important with regard to kinetic
modeling. The expansion temperature is related to the
mass fraction burned calculations; lower computed
temperatures will indicate less charge oxidation, and this
will lead to discrepancies between the calculations and
any emissions measurements that are taken.
Figure 18 plots the cumulative heat loss for three runs,
one ‘motored’ and two ‘fired’ cases. The bulk charge
(modified Woschni correlation) and the crevice heat
losses are shown independently, the combined heat loss
is also plotted. It is apparent that the crevice losses are
significantly greater than the bulk charge losses; the
crevice losses are on the order of 15% of the fuel energy
while the main cylinder losses are only about 3% for the
fired cases (~1% for the ‘motored’ case). The effect of
the ring heating modeling is also visible in the ‘motored’
case, as there is apparently a decrease in the magnitude
of the crevice heat loss as the crevice charge reemerges
into the main cylinder. Finally, it can be seen that the
case where ignition occurs before TDC seems to have
greater heat loss in the crevice due to the increase in
crevice flow (as was seen in Fig. 16). An increased loss
of about 4% of the fuel energy is observed. However,
this result does not necessarily match the thermal
efficiency trends presented in Ref. [7] where there
seemed to be little variation in the computed thermal
efficiency with increased compression ratio.
More
investigation of this point is required.
Finally, Figure 19 presents the results of the mass
fractions burned calculations for the two ‘fired’ natural
gas / air cases. Comparison is made between the ringdynamic model and the single-zone models. Two
curves are shown for each case, one is an overall value
of the mass fraction burned, and the other for the
fraction of the charge that is within the bulk volume that
is determined to be oxidized. Again, this is calculated by
matching the ‘modified-entropy’ pressure to the
experimental pressure; the heat released from
combustion is required to account for the pressure
change not associated with piston compression &
expansion, heat loss to the walls, or mass transfer
to/from the crevice.
The discrepancies of the single-zone approach are
again evident. First, there is a computed negative
burned fraction just before the main heat release; this
could be interpreted incorrectly as an endothermic preignition period. Secondly, there appears to be a spike
and then a drop in the mass fraction burned, especially
for the over-compressed case (29_06); the charge then
appears to oxidize more as the time progresses. This
might be interpreted (again incorrectly) as a high
pressure effect, since the cylinder pressure is
significantly greater for this run. Finally, the computed
burned fractions indicate that only 80% of the charge
has oxidized, while the emissions measurements for
these runs indicate that close to 98% of the of the fuel
has burned. This discrepancy may be due to blowby
mass however.
The ring-dynamic model seems to provide more
plausible results compared with the single zone model,
and the effects of the crevice flows can be clearly seen
(especially for the 29_06 case). The computed mass
fractions burned (for the main cylinder charge) much
more closely match the emissions data, and the overall
values seem to account for the amount of mass that is
calculated to be trapped in the ringpack at the end of the
stroke, as well as the heat that is lost to the
crevice/ringpack walls. The difference between the
thermodynamic cycle efficiency of the RCEM
experiments, 56% as presented in Ref. [7], and the ideal
Otto cycle efficiency for these compression ratios (up to
68%) is more understandable with the use of the ringdynamic model.
SUMMARY AND CONCLUSIONS
A ring-dynamic crevice model has been modified and
integrated with a multi-zonal heat release code to
investigate the effects of crevice flows on the
interpretation of autoignition (HCCI) data from a Rapid
Compression Expansion Machine.
The model
parameters have been tuned so that reasonable
agreement could be achieved for a number of ‘motored’,
air-only compression – expansion runs. The ratio of the
experimentally measured pressure to the computed,
‘modified-entropy’ pressure provides a rigorous metric
for evaluating the performance of the crevice sub-model.
It was found that the heating of the low thermal diffusivity
rings due to sliding friction as the piston traverses the
unlubricated walls of the cylinder, may significantly
influence the mass flow rates and the enthalpy of the
reemerging crevice flows. A significant fraction of the
cylinder charge is computed to be driven into the
crevice/ringpack (15%) (since there is no wet seal) as
high compression ratios (50:1) are achieved.
The modified ring-dynamic model has been able to
provide useful insight with regard to the interpreting
‘fired’ runs as well.
The characteristics of the
autoignition (HCCI) process, including the autoignition
temperature, the rate of heat release and the computed
mass fraction burned are much better understood and
the experimental results seem to better correlate with
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current HCCI understanding.
Additional studies,
including the development and refinement of various
kinetic models will now be possible. An improved
ringpack for the RCEM, which could minimize crevice
flows and/or prevent the cooler crevice charge from
reentering the bulk volume on the expansion stroke,
might improve the capabilities of this experimental
apparatus.
This study has also provided some understanding with
regard to the discrepancies between the ideal Otto cycle
performance, and the efficiencies that have been
computed for this experiment. If the crevice flows can
be controlled, along with the associated heat losses
within the crevice and ringpack, through sufficient
sealing, it appears that even better cycle performance
could be achieved.
ACKNOWLEDGMENTS
The author is grateful to Peter Van Blarigan and Nick
Paradiso of Sandia National Laboratories, California who
provided the raw data and experimental details used for
this work.
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CONTACT
S. Scott Goldsborough
Department of Mechanical Engineering
Marquette University
Milwaukee, Wisconsin 53201-1881
Scott.Goldsborough@mu.edu
DEFINITIONS, ACRONYMS, ABBREVIATIONS
Roman letters
A , Area (m2)
a c , acceleration in inertial reference frame (m/s2)
BDC , bottom dead center
c , speed of sound
Cd , discharge coefficient
Cf , friction coefficient
CP , constant for viscosity fit
CR , compression ratio
ct , clearance height (m)
d , diameter of ring (m)
Ff , friction force (N)
Fi , inertia force (N)
Foil , oil film force (N)
FP , pressure force (N)
f fric , friction power factor
H , cylinder characteristic dimension (m)
h , specific enthalpy (kJ/kg)
k , thermal conductivity (W/m-K)
L , length (m)
m , mass (g)
, mass flow rate (g/s)
m
P , pressure (kPa)
q w , convective heat flux (W/m2)
R , universal gas constant (kJ/kg-K)
S p , mean piston speed (m/s)
s , specific entropy (kJ/kg-K)
T , temperature (K)
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t , time (s)
TDC , top dead center
't , time step (s)
v , velocity (m/s)
V , volume (m3)
, rate of work transfer (kJ/s)
W
x , spatial dimension (m)
z c , axial position in inertial reference frame (m)
Greek letters
D , thermal diffusivity (m2/s)
J , ratio of specific heats
U , density (kg/m3)
P , dynamic viscosity (N-s/m2)
X , specific volume (m3/kg)
Subscripts
0 , beginning of experiment
1 , crevice zonal index
1 2 , from zone 1 to zone 2
br , burned zone
c , combustion
calc , calculated, “modified entropy method”
conv , convective
cr , crevice zone
d , downstream
eff , effective
ex , exiting
exp , experiment
fr , fresh zone
g , gas
in , incoming
ini , conditions at start of experiment
inst , instantaneous conditions
motor , motored
mx , mixed zone
o , stagnation conditions
r , ring
ref , reference condition
s , isentropic
t , previous time step
t + 't , new time
u , upstream
w , wall
APPENDIX
This section discusses briefly the fitting of the ringdynamic model and the sensitivity of the adjusted
parameters. The model consists of a number of physical
dimensions and an empirical constant (the friction power
factor), all of which were described earlier. The values
used in the tuned model are listed in Table 2 of the main
text. The parameters tuned for this study were the
ringpack volumes, the ringside clearance heights and
the circumferential areas. The endgap areas were set to
0.0 since there is no gap for the elastomeric ring (this is
a continuous piece) and the circumferential flows seem
to dominate in this configuration (much better fitting of
the model to the data is possible using this assumption).
In the model the ringpack volumes determine the
amount of charge that can leave the main cylinder;
larger volumes are able to capture more mass. The flow
areas determine the rate of ringpack pressurization.
Insufficient areas restrict the flow and do not allow
sufficient charging of the pockets; areas too large result
in pressure equilibrium with the bulk gas – there is no
lag in the pocket pressurization. The friction power
mainly affects the reemerging charge temperature; the
computed flow rates are also affected, but these can be
modified by slightly adjusting the circumferential areas.
In tuning the model the objective was to match both the
compression and expansion stroke pressures; the
former is critical to characterizing the ignition conditions
for early firing, the latter impacts late cycle ignition /
oxidation and overall heat release from the charge.
The performance of the model was assessed by
analyzing the ratio of the experimental to calculated
pressures (Pexp / Pcalc) with respect to time, volume and
instantaneous compression ratio; it is critical that the
conditions near TDC are well matched.
A fitness
parameter was defined in order to quantify the capability
of the model; this is expressed in Equation A1. The
absolute value of the relative difference between the
experimental and calculated values is integrated over
the compression and expansion strokes. A low value of
the fitness is desired.
fitness
³
0.75
CR exp
³
0.25
1.0
³
CR exp
1.0
V exp
Vini
³
Pexp
1 dCR
Pcalc
dCR
Pexp
Pcalc
V exp
Vini
1 dV
(A1)
dV
Figure A1 plots this fitness parameter with respect to
time for a typical ‘motored’ shot; the 50:1 CR case
discussed earlier is used as the example. This provides
a rigorous test of the model since higher CR runs result
in more crevice flows and are therefore more difficult to
match. Three features are evident in this plot. First, the
fitness is poor during the experiment initiation; this is due
to the low signal-to-noise ratio at low pressure. Next, it
can be seen that the fitness improves along the
compression stroke to TDC indicating good agreement
during the critical part of the experiment. The fitness
then decreases just after TDC (significantly for this high
CR case) due to the departure of the experimental trace
from the calculated trace (as seen in Fig. 5); this shift in
fitness is not as significant for the low CR shots.
The sensitivities of the adjustable model parameters are
presented in Figure A2. These are graphed as a
percent where this is defined by Equation A2. The
percent sensitivity is the relative difference in fitness with
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0.030
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
0.025
Low signal-to-noise ratio at
experiment initiation
Fitness
0.020
0.015
0.005
0.000
1
vol2
2
vol3
3
vol4
4
ct1
5
A
6
ct2
7
A
8
f
9
13c
Departure from experimental pressure
on expansion for high CR cases
0.010
vol1
35c
TDC
-5
0
5
10
15
20
25
30
Time [ms]
Figure A1 – Fitness of ring-dynamic model vs. time based on
fitness definition.
the base fitness compared to the new fitness; the base
value is used in the numerator to give a positive
sensitivity for better fits and a negative sensitivity for
worse fits. Each of the parameters is individually
changed by 15 percent (increased and decreased)
about the base value and the fitness of the model is
recalculated. Values at TDC and at the end of the
experiment are graphed.
sensitivity
ª fitness base
º
1»
100 «
«¬ fitness new
»¼
(A2)
fric
Air-only Charge
Compression Ratio 50:1
Initial Temperature 25C
Initial Pressure 0.099MPa
Negative sensitivity indicates
a drop in fitness relative to the
tuned ring-dynamic model.
+15%, TDC
+15%, Full Cycle
-15%, TDC
-15%, Full Cycle
-75
-60
-45
-30
-15
0
15
Percent Sensitivity
Figure A2 – Sensitivity of crevice modeling parameters based on
fitness definition. TDC and full cycle fitnesses shown.
provides a good combination to match the experimental
data. Additionally, some parameters are more sensitive
at either TDC or at the end of the experiment. An
example is the value of the circumferential area of the
elastomeric ring, A35c; this is more critical at the end of
the experiment where this determines how much blowby there is past the ringpack.
The most critical
parameters in the model are the primary flow path (A13c)
and the primary volumes that capture the crevice charge
(vol3 & vol4). There is no sensitivity for ct2 since this
clearance height is set large enough so that volumes 3
and 4 are in pressure equilibrium (as was seen in Figs.
10 and 15).
It can be seen that most changes result in a drop in the
fitness parameter, indicating that the set of crevice
model parameters chosen for the ringpack model
Author:Gilligan-SID:12426-GUID:27843746-134.48.93.192