Exhaust Manifold Thermal

R2026b

Thermodynamics of combustion engine exhaust manifold

Since R2022a

• 

Exhaust Manifold Thermal block

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Libraries:
Simscape / Driveline / Engines & Motors / Engine Subcomponents

Description

The Exhaust Manifold Thermal block represents the abstracted thermodynamics of a combustion engine exhaust manifold. The block integrates with the SI Combustion Cylinder block.

Equations

The block takes exhaust gas flow from the SI Combustion Cylinder blocks and computes the exhaust manifold temperature, T_exh, which the block outputs at port Texh. The block calculates the output using a lumped-parameter model, such that

$$C_{exh}{M}_{exh}\frac{d}{dt}{T}_{exh}=h_{exh}-h_{x,}$$

where

• C_exh is the Heat capacity of exhaust wall parameter.

• M_exh is the Mass of exhaust wall parameter.

• h_exh is the heat flow at the exhaust manifold.

• h_x is the heat exchange between the exhaust gas and the environment.

The block calculates h_x as

$$h_x=S_{exh}\left(h_{convec}\left(T_{exh}-T_{amb}\right)-k_{ra}\sigma \left(T_{exh}^4-T_{amb}^4\right)\right),$$

where

• S_exh is the Surface area of exhaust wall parameter.

• h_convec is the Convective heat transfer coefficient for the outer side of exhaust parameter.

• k_ra is the Radiation constant parameter.

• σ is the Stefan-Boltzmann constant parameter.

• T_amb is the Ambient temperature parameter.

The block finds h_exh as

$$k_{gas}\frac{d}{dt}{h}_{exh}=h_{in}-h_{exh},$$

where k_gas is the Time constant of exhaust heat flow parameter, and h_in is the instantaneous heat flow from the engine exhaust outlets to the exhaust manifold. The instantaneous heat flow is the sum of the individual instantaneous heat flows at the exhaust outlets, h_i, such that

$$h_{in}={\displaystyle \sum _{i=1}^{N_{ports}}{h}_i},$$

where N_ports is the Number of exhaust ports parameter.

Examples

Single Cylinder Spark Ignition Engine

A crank-angle-resolved, naturally aspirated spark ignition engine. Control inputs such as throttle, intake VVT, air-to-fuel ratio, and spark advance vary during the simulation. You can simulate results from either an Otto cycle engine or an Atkinson cycle engine.

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Ports

Input

Qeng — Gas energy flow, W

physical signal

Physical signal input port associated with the gas energy flow, in W. Attach this port to the Weo physical signal output port on the SI Combustion Cylinder block.

Programmatic Use

Port: heatflow_eng

Output

Texh — Exhaust manifold temperature, K

physical signal

Physical signal output port associated with the lumped-parameter exhaust manifold temperature, in K.

Programmatic Use

Port: T_out

Parameters

Number of exhaust ports — Number of exhaust ports

1 (default) | positive scalar

Number of SI Combustion Cylinder blocks.

Programmatic Use

Parameter: numPorts

Ambient temperature — Reference temperature

298.15 K (default) | positive scalar

Temperature of the air entering the intake.

Programmatic Use

Parameter: T_amb

Surface area of exhaust wall — Exhaust wall surface area

pi * ((1.5 / 2) ^ 2) m^2 (default) | positive scalar

Surface area of the exhaust wall. This is only the surface area of the internal wall that makes contact with the exhaust.

Programmatic Use

Parameter: S_exh

Mass of exhaust wall — Exhaust wall total mass

5 kg (default) | positive scalar

Mass of the exhaust wall.

Programmatic Use

Parameter: M_exh

Heat capacity of exhaust wall — Exhaust wall heat capacity

100 J/(K*kg) (default) | positive scalar

Heat capacity of the exhaust wall.

Programmatic Use

Parameter: C_exh

Time constant of exhaust heat flow — Exhaust heat flow time constant

10 s (default) | positive scalar

Time constant for the rate of exhaust heat flow.

Programmatic Use

Parameter: k_gas

Convective heat transfer coefficient for the outer side of exhaust — Exhaust external convective heat transfer coefficient

100 W/(K*m^2) (default) | positive scalar

Convective heat transfer coefficient for the outer side of the exhaust.

Programmatic Use

Parameter: h_convection

Radiation constant — Exhaust radiation constant

0.3 (default) | positive scalar

Radiation constant of the exhaust.

Programmatic Use

Parameter: k_radiation

Stefan-Boltzmann constant — Stefan-Boltzmann constant of exhaust

5.7e-8 W/(K^4*m^2) (default) | positive scalar

Stefan-Boltzmann constant for the total exhaust.

Programmatic Use

Parameter: sigma

Version History

Introduced in R2022a