Modeling for Control of HCCI Engines
Gregory M. Shaver J.Christian Gerdes Matthew Roelle
P.A. Caton C.F. Edwards
Stanford UniversityDept. of Mechanical
Engineering
DDL
ynamicesign
aboratory
Outline
� What is HCCI?
� Experimental test-bed at Stanford
� Motivation for modeling and control
� Proposed model
� Conclusion
� Future work
Stanford University Modeling for Control of HCCI Engines - 2 Dynamic Design Lab
What is HCCI?
� Homogeneous Charge Compression Ignition: combustion due to uniformauto-ignition using compression alone.
• Main Benefit: Low post-combustion temperature → reduced NOx emissions.
• Requires: A sufficient level of inducted gas internal energy
� Approaches to increasing inducted gas internal energy:
• Pre-heating the intake
• Pre-compressing the intake
• Throttling exhaust/intake → promotes hot exhaust gas re-circulation
Stanford University Modeling for Control of HCCI Engines - 3 Dynamic Design Lab
Another Approach: Variable Valve Actuation (VVA)
� with VVA:
• Exhaust reinduction achieved us-ing late EVC
• Load variation achieved by lateIVO coupled with late EVC
� Benefits:
• No pumping penalty
• More control over presence of re-actant/exhaust products in cylin-der at any time
� Challenges:
• Currently no VVA systems on pro-duction vehicle
• R&D: ongoing by many
220 490
220 4900
intakeexhaust
VBDC
VTBC
IVO EVC
EVOIVC
crank angle [deg.]
cylin
der
volu
me
valv
e op
eing
Stanford University Modeling for Control of HCCI Engines - 4 Dynamic Design Lab
Emissions characteristics of HCCI with VVA
2 3 4 5 60
500
1000
1500
2000
2500
net IMEP (bar)
Nitr
ic O
xide
(pp
m d
ry)
0
10
20
30
40
50
Indi
cate
d E
ffici
ency
(%
)
NO (SI)
NO (HCCI)
ηth (SI)
ηth (HCCI)
Experimental results from Stanford single-cylinder research engine
Stanford University Modeling for Control of HCCI Engines - 5 Dynamic Design Lab
Experimental Testbed
� Single cylinder research en-gine
� Fuels:
• Propane
• Hydrogen
• Gasoline
� Comp. Ratio: 13:1 (ad-justable)
� Engine rpm: 1800
Stanford University Modeling for Control of HCCI Engines - 6 Dynamic Design Lab
Motivation for Modeling and Control
� Challenge: Combustion Phasing
• No direct combustion initiator (like spark for SI or fuel injectionfor Diesel combustion)
� Combustion phasing depends on:
• Concentrations of reactants and re-inducted products
• Initial temperature of reactants and products
� Initial Concentrations/temperature directly controlled withVVA system
Stanford University Modeling for Control of HCCI Engines - 7 Dynamic Design Lab
Modeling Approach
� Assumptions
• Homogeneous mixture
• Uniform combustion
• Complete combustion to major products
� States
• volume, V
• temperature, T
• concentrations: [XC3H8], [XO2
], [XCO2], [XN2
], [XH2O], [XCO]
• mass of products in exhaust manifold: me
• internal energy of products in exhaust manifold: ue
Stanford University Modeling for Control of HCCI Engines - 8 Dynamic Design Lab
Modeling Approach
� Volume Rate Equations
� Valve Flow Equations
� Concentration Rate Equations
� Temperature Rate Equations
� Exhaust Manifold Modeling: Mass Flows and InternalEnergy
� Combustion Chemistry Modeling
• Temperature threshold approach
• Integrated Arrhenius rate threshold approach
Stanford University Modeling for Control of HCCI Engines - 9 Dynamic Design Lab
Volume Rate Equations
V = Vc +πB2
4(l − a − acosθ −
√
l2 − a2sin2θ)
V =π
4B2aθsinθ(1 + a
cosθ√
(L2 − a2sin2θ))
θ = ω
� where:
• ω - the rotational speed of the crankshaft
• a - is half of the stroke length
• L - connecting rod length
• B - bore diameter
• Vc - clearance volume
Stanford University Modeling for Control of HCCI Engines - 10 Dynamic Design Lab
Valve Flow Modeling
for un-choked flow (pT/po > [2/(γ + 1)]γ/(γ−1)):
m =CDARpo√
RTo
(
pT
po
)1/γ[
2γ
γ − 1
[
1 −(
pT
po
)(γ−1)/γ]]
for choked flow (pT/po≤[2/(γ + 1)]γ/(γ−1)):
m =CDARpo√
RTo
√γ
[
2
γ + 1
](γ+1)/2(γ−1)
� where:
• AR - effective open area forthe valve
• po - upstream stagnation pres-sure
• To - downstream stagnationtemperature
• pT - downstream stagnation
pressure
INTAKE VALVE
EXHAUST VALVE
m1.
EXHAUST VALVE
m3
.
INTAKE VALVE
m2.
Stanford University Modeling for Control of HCCI Engines - 11 Dynamic Design Lab
Temperature Rate Equation
� The first law of thermodynamics for an open system is:
d(mu)
dt= Qc − W + m1h1 + m2h2 − m3h3
• u - internal energy
• Qc - heat transfer rate
• W = pV - piston work
• h - enthalpy of species
using the definition of enthalpy, h = u + pv:
d(mh)
dt= mpV/m + pV + m1h1 + m2h2 − m3h3
with:Qc = −hcAc (Tc − Twall)
� Assuming ideal gas and specific heats as functions of temperature, can re-write equa-tion as a temperature rate expression
Stanford University Modeling for Control of HCCI Engines - 12 Dynamic Design Lab
Concentration Rate Equations
˙[Xi] =d
dt
(
Ni
V
)
=Ni
V−
V Ni
V 2= wi −
V Ni
V 2
wi = wrxn,i + wvalves,i
where:
• wrxn,i - combustion reaction rate for species i
• wvalves,i - volumetric flow rate of species i through the valves
• Ni - number of moles of species i in the cylinder
wvalves,i = w1,i + w2,i + w3,i = (Y1,im1 + Y2,im2 − Y3,im3)/(V MWi)
where:
• Y1,i - mass fraction of species i in the intake (constant)
• Y2,i - mass fraction of species i in the exhaust (constant)
• Y3,i = [Xi]MWi∑
[Xi]MWi- mass fraction of species i in the cylinder
Stanford University Modeling for Control of HCCI Engines - 13 Dynamic Design Lab
Exhaust Manifold Modeling (Mass Flow)
� Exhaust Manifold Mass Flow Diagram:
(a) (b) (c)
(d) (e) (f)
mce .
mec.
me,maxme,residual
me,EVC-me,residual
EVO-EVCωme,EVC
� (a) residual mass from previous exhaust cycle, θ = EV O
� (b) increase in mass due to cylinder exhaust, EV O < θ < 720
� (c) maximum amount of exhaust manifold mass, θ = 720
� (d) decrease in mass due to reinduction, 0 < θ < EV C
� (e) post-reinduction mass, θ = EV C
� (f) decrease in mass to residual value, EV C < θ < EV O
Stanford University Modeling for Control of HCCI Engines - 14 Dynamic Design Lab
Exhaust Manifold Modeling (Internal Energy)
� An internal energy rate equation can be formulated from the first law, as:
ue =1
meγ
[
mce (hc − he) + hA (Tambient − Te)]
where:
Qe = −heAe (Te − Tambient)
� So the condition of the product gases in the exhaust manifold is characterized w/ twostates:
• the mass: me
• the internal energy: ue
Stanford University Modeling for Control of HCCI Engines - 15 Dynamic Design Lab
Combustion Chemistry Modeling: Temperature Threshold Approach
� The rate of reaction of propane is approximated as a function of crank angle andvolume following the crossing of a temperature threshold:
wC3H8=
[C3H8]iViθexp[
−((θ−θinit)−θ)
2σ2
]
V σ√
2πT ≥ Tth
0 T < Tth
where:
• θinit - crank angle when T = Tth
• Vi - crank angle when T = Tth
• [C3H8]i - propane concentration when T = Tth
• σ - crank angle standard deviation
• θ - mean crank angle
Stanford University Modeling for Control of HCCI Engines - 16 Dynamic Design Lab
Combustion Chemistry Modeling: Temperature Threshold Approach (cont.)
� The complete combustion of a stoichiometric propane/air mixture to major productsis assumed, such that the global reaction equations is:
C3H8 + 5O2 + 18.8N2 → 3CO2 + 4H2O + 18.8N2
� By inspection of the global reaction equation:
wO2= 5wC3H8
wN2= 0
wCO2= −3wC3H8
wH2O = −4wC3H8
Stanford University Modeling for Control of HCCI Engines - 17 Dynamic Design Lab
Combustion Chemistry Modeling: Temperature Threshold Approach (cont. 2)
� Model Results:
−50 0 500
10
20
30
40
50
60
70
Crankshaft °ATC
Pre
ssur
e (b
ar)
experimenttemp. threshold
IVO @ 25deg., EVC @ 165
−50 0 500
10
20
30
40
50
60
70
Crankshaft °ATCP
ress
ure
(bar
)
experimenttemp. threshold
IVO @ 45deg., EVC @ 185
� Combustion phasing not captured
� REASON: Combustion phasing depends on temperature AND concentrations
Stanford University Modeling for Control of HCCI Engines - 18 Dynamic Design Lab
Combustion Chemistry Modeling: Integrated Arrhenius Rate Approach
� The rate of reaction of propane is approximated as being a function of crank angleand volume following the crossing of an integrated Arrhenius rate:
wC3H8=
[C3H8]iViθexp
[
−((θ−θinit)−θ)
2σ2
]
V σ√
2π
∫
RR ≥∫
RRth
0∫
RR <∫
RRth
where:∫
RR =
∫ θ
IV OAexp(Ea/(RT ))[C3H8]
a[O2]bdθ
� This equation gives insight into combustion phasing with VVA
• IVO: residence time for mixing (start of integration)
• IVO + EVC: initial reactant concentrations, [C3H8]init[O2]init, and mixture temperature, Tinit.
Stanford University Modeling for Control of HCCI Engines - 19 Dynamic Design Lab
Combustion Chemistry Modeling: Integrated Arrhenius Rate Approach (cont.)
� The complete combustion of a stoichiometric propane/air mixture to major productsis assumed, such that the global reaction equations is:
C3H8 + 5O2 + 18.8N2 → 3CO2 + 4H2O + 18.8N2
� By inspection of the global reaction equation:
wO2= 5wC3H8
wN2= 0
wCO2= −3wC3H8
wH2O = −4wC3H8
Stanford University Modeling for Control of HCCI Engines - 20 Dynamic Design Lab
Combustion Chemistry Modeling: Integrated Arrhenius Rate Approach (cont. 2)
� Model Results:
−50 0 500
10
20
30
40
50
60
70
Crankshaft °ATC
Pre
ssur
e (b
ar)
experimentIntegrated Arrhenius rate threshold
IVO @ 25deg., EVC @ 165
−50 0 500
10
20
30
40
50
60
70
Crankshaft °ATC
Pre
ssur
e (b
ar)
experimentIntegrated Arrhenius rate threshold
IVO @ 45deg., EVC @ 185
� Combustion phasing captured
� Pressures well predicted
Stanford University Modeling for Control of HCCI Engines - 21 Dynamic Design Lab
Cycle-to-Cycle Coupling
� Cycle-to-Cycle coupling through the re-inducted exhaust gas is clearly evident:
300 350 400 450 5
15
25
35
45
55
65
Simulated HCCI Combustion Over a Valve Profile Transition
Crank Angle Degrees
Cyl
inde
r P
ress
ure
[kP
a]
Cycle 1
Cycle 2
Cycle 3 Cycle 4
IVO 40 EVC 165
IVO 70 EVC 185
Steady State (A) Valve Profiles A B
� Model allows prediction of these dynamics
Stanford University Modeling for Control of HCCI Engines - 22 Dynamic Design Lab
Conclusion
� Combustion Model
• Uniform complete combustion to major products
• Simplified chemistry models developed
� Temperature threshold approach
• propane reaction evolves as fcn. of crank angle following temp. threshold crossing
• Does not capture combustion phasing
� Integrated Arrhenius Rate threshold approach
• propane reaction evolves as fcn. of crank angle following int. threshold crossing
• Captures combustion phasing
• Discrepancy along pressure peak
� Independent control of phasing and load seem feasible:
• with variation of IVO/EVC, should be able to vary inducted reactant charge (relatedto load) and phasing (Int. Arr. Model suggests this)
Stanford University Modeling for Control of HCCI Engines - 23 Dynamic Design Lab