CI Engine Torque Structure Model
The CI core engine torque structure model determines the engine torque by reducing the maximum engine torque potential as these engine conditions vary from nominal:
Start of injection (SOI) timing
Exhaust backpressure
Burned fuel mass
Intake manifold gas pressure, temperature, and oxygen percentage
Fuel rail pressure
To account for the effect of postinject fuel on torque, the model uses a calibrated torque offset table.
To determine the engine torque, the CI core engine torque structure model implements the equations specified in these steps.
Step  Description 

Step 1: Determine nominal engine inputs and states  Model uses lookup tables to determine these nominal engine inputs and states as a function of compression stroke injected fuel mass, F, and engine speed, N:

Step 2: Calculate relative engine states  To determine these relative engine states, the model calculates deviations from their nominal values.
For the intake manifold gas pressure, the block uses a pressure ratio to determine the relative state. The pressure ratio is the intake manifold gas pressure to the steadystate operating point gas pressure. $MA{P}_{ratio}=\frac{MAP}{{f}_{MAP}\left(F,N\right)}$ 
Step 3: Determine efficiency multipliers  Model uses gross indicated mean effective pressure (IMEPG)^{[1]} efficiency multipliers to reduce the maximum average pressure potential of combustion. The efficiency multipliers are lookup tables that are functions of the relative engine states.

Step 4: Determine indicated mean effective cylinder pressure (IMEP) available for torque production  To determine the IMEP available for torque production, the model implements these equations. $\begin{array}{l}IMEP=SO{I}_{eff}MA{P}_{eff}MA{T}_{eff}O2{p}_{eff}FUEL{P}_{eff}IMEPG\\ \\ IMEPG={f}_{IME{P}_{g}}(F,N)\end{array}$ The model multiplies the efficiency multipliers from step 3 by the IMEPG. The model implements IMEPG as lookup table that is a function of the compression stroke injected fuel mass, F, and engine speed, N. 
Step 5: Account for losses due to friction  To account for friction effects, the model uses the nominal friction mean effective pressure (FMEP)^{[1]} to implement this equation. $$FMEP={f}_{FMEP}(F,N){f}_{fmod}({T}_{oil},N)$$ The model implements FMEP as lookup table that is a function of the compression stroke injected fuel mass, F, and engine speed, N. To account for the temperature effect on friction, the model use a lookup table that is a function of oil temperature, T_{oil}, and N. 
Step 6: Account for pressure loss due to pumping  To account for pressure losses due to pumping, the model uses the nominal pumping mean effective pressure (PMEP)^{[1]} to implement these equations. $$\begin{array}{l}\Delta MAP={f}_{MAP}\left(F,N\right)MAP\\ \Delta EMAP={f}_{EMAP}\left(F,N\right)EMAP\\ \\ PMEP={f}_{PMEP}\left(F,N\right)\Delta MAP+\Delta EMAP\end{array}$$ The model implements MAP and EMAP as lookup tables that are functions of the compression stroke injected fuel mass, F, and engine speed, N. Under normal operating conditions, PMEP is negative, indicating a loss of cylinder pressure. 
Step 7: Account for late fuel injection SOI timing on IMEP  To account for late fuel injection SOI timing on IMEP, ΔIMEP_{post}, the model uses a lookup table that is a function of the effective pressure post inject SOI timing centroid, SOI_{post}, and the post inject mass sum, F_{post}. $\Delta IME{P}_{post}={f}_{\Delta IME{P}_{post}}\left(SO{I}_{post},{F}_{post}\right)$ 
Step 8: Calculate engine brake torque  To calculate the engine brake torque, T_{brake}, the model converts the brake mean effective pressure (BMEP)^{[1]} to engine brake torque using these equations. The BMEP calculation accounts for all gross mean effective pressure losses. V_{d} is displaced cylinder volume. Cps is the number of power strokes per revolution. $\begin{array}{l}BMEP=IMEPG+\Delta IME{P}_{post}FMEP+PMEP\\ \\ {T}_{brake}=\frac{{V}_{d}}{2\pi Cps}BMEP\end{array}$ 
Fuel Injection
In the CI Core Engine and CI Controller blocks, you can represent multiple injections with the start of injection (SOI) and fuel mass inputs to the model. To specify the type of injection, use the Fuel mass injection type identifier parameter.
Type of Injection  Parameter Value 

Pilot 

Main 

Post 

Passed 

The model considers Passed
fuel injections and fuel injected
later than a threshold to be unburned fuel. Use the Maximum start of injection angle
for burned fuel, f_tqs_f_burned_soi_limit parameter to specify the
threshold.
Percent Oxygen
The model uses this equation to calculate the oxygen percent, O2p. y_{in,air} is the unburned air mass fraction.
$O2p=23.13{y}_{in,air}$
Exhaust Temperature
The exhaust temperature calculation depends on the torque model. For both torque models, the block implements lookup tables.
Torque Model  Description  Equations 

 Exhaust temperature lookup table is a function of the injected fuel mass and engine speed. 
${T}_{exh}={f}_{Texh}(F,N)$ 
Torque Structure 
The nominal exhaust temperature, Texh_{nom}, is a product of these exhaust temperature efficiencies:
The exhaust temperature, Texh_{nom}, is offset by a post temperature effect, ΔT_{post}, that accounts for post and late injections during the expansion and exhaust strokes. 
$\begin{array}{l}{T}_{exhnom}=SO{I}_{exhteff}MA{P}_{exhteff}MA{T}_{exhteff}O2{p}_{exhteff}FUEL{P}_{exhteff}Tex{h}_{opt}\\ {T}_{exh}={T}_{exhnom}+\Delta {T}_{post}\\ \\ SO{I}_{exhteff}={f}_{SO{I}_{exhteff}}\left(\Delta SOI,N\right)\\ MA{P}_{exhteff}={f}_{MA{P}_{exhteff}}\left(MA{P}_{ratio},\lambda \right)\\ MA{T}_{exhteff}={f}_{MA{T}_{exhteff}}\left(\Delta MAT,N\right)\\ O2{p}_{exhteff}={f}_{O2{p}_{exhteff}}\left(\Delta O2p,N\right)\\ Tex{h}_{opt}={f}_{Texh}(F,N)\end{array}$ 
The equations use these variables.
F  Compression stroke injected fuel mass 
N  Engine speed 
Texh  Exhaust manifold gas temperature 
Texh_{opt}  Optimal exhaust manifold gas temperature 
ΔT_{post}  Post injection temperature effect 
Texh_{nom}  Nominal exhaust temperature 
SOI_{exhteff}  Main SOI exhaust temperature efficiency multiplier 
ΔSOI  Main SOI timing relative to optimal timing 
MAP_{exheff}  Intake manifold gas pressure exhaust temperature efficiency multiplier 
MAP_{ratio}  Intake manifold gas pressure ratio relative to optimal pressure ratio 
λ  Intake manifold gas lambda 
MAT_{exheff}  Intake manifold gas temperature exhaust temperature efficiency multiplier 
ΔMAT  Intake manifold gas temperature relative to optimal temperature 
O2P_{exheff}  Intake manifold gas oxygen exhaust temperature efficiency multiplier 
ΔO2P  Intake gas oxygen percent relative to optimal 
FUELP_{exheff}  Fuel rail pressure exhaust temperature efficiency multiplier 
ΔFUELP  Fuel rail pressure relative to optimal 
References
[1] Heywood, John B. Internal Engine Combustion Fundamentals. New York: McGrawHill, 1988.
See Also
CI Controller  CI Core Engine