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