Air Intake

Combustion cylinder air supply intake

Since R2022a

• 

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

Description

The Air Intake block represents an abstract air intake system that computes lumped-parameter air flow dynamics. This block is suitable for internal combustion engines. The block computes the intake manifold pressure from the throttle and engine speed.

Equations

The Air Intake block computes the intake manifold pressure as

$$\frac{d}{dt}{P}_{im}=\frac{R_{air}{T}_{amb}}{V_{im}}\left({\dot{m}}_{thr}-{\dot{m}}_{cyl}\right),$$

where

• R_air is the Dry air specific gas constant parameter.

• T_amb is the Ambient temperature parameter.

• V_im is the Intake manifold volume parameter.

The block calculates the combustion cylinder mass flow rate, ṁ_cyl, as

$${\dot{m}}_{cyl}=\frac{\omega V_d{P}_{im}}{2R_{air}{T}_{amb}},$$

which is a time derivative formulation of the ideal gas law. ω is the engine speed the block receives from port EngSpd, and V_d is the Engine displacement volume parameter.

The block calculates the throttle mass flow rate, ṁ_thr as

$${\dot{m}}_{thr}=\{\begin{array}{l}\frac{S_{thr}}{\sqrt{T_{amb}}}{c}_1\left(P_{amb}-P_{im}\right)\text{ Laminar}\\ \frac{S_{thr}}{\sqrt{T_{amb}}}{P}_{amb}\sqrt{c_2\left[{\left(\frac{P_{amb}}{P_{im}}\right)}^{c_b}-{\left(\frac{P_{amb}}{P_{im}}\right)}^{c_a}\right]}\text{ Subsonic}\\ \frac{S_{thr}}{\sqrt{T_{amb}}}{c}_3{P}_{amb}\text{ Choked}\end{array}$$

depending on the flow conditions. In this equation, S_thr is the area of the throttle opening, and P_amb is the ambient pressure. The block defines the equation constants as

$$\begin{array}{l}{c}_a=\frac{\kappa +1}{\kappa }\\ c_b=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\kappa $}\right.\\ c_1=\frac{\sqrt{c_2\left({\Pi }_{lam}^{c_b}-{\Pi }_{lam}^{c_a}\right)}}{1-{\Pi }_{lam}}\\ c_2=\frac{2\kappa }{R_{air}\left(\kappa -1\right)}\\ c_3=\sqrt{\frac{\kappa }{R_{air}}{\Pi }_{cr}^{c_a}}\end{array}$$

where

• κ is the Dry air specific heat ratio parameter.

• Π_lam is the laminar flow threshold constant.

• Π_cr is the critical pressure ratio.

The block finds Π_cr as

$${\Pi }_{cr}={\left(\frac{2}{\kappa +1}\right)}^{\frac{\kappa }{\kappa -1}}.$$

Throttle Open Area

The block treats the throttle open area, S_thr, as a third-order polynomial that functions with respect to the throttle angle, θ. This method simplifies the block computation to improve performance. The block computes the throttle open area as

$$S_{thr}\left(\theta \right)=k_0+k_1\theta +k_2{\theta }^2+k_3{\theta }^3,$$

where the block derives the coefficients, k_i, using these quantities:

• D_plate — Throttle plate diameter parameter

• A_rest — Throttle rest angle parameter

• A_peak — 85°

• S_leak — Throttle leakage area parameter

The throttle open area uses these constraints:

$$\begin{array}{c}{S}_{thr}\left(0\right)=S_{eng}\left(0\right)\\ S_{thr}\left(\frac{\pi }{2}\right)=S_{eng}\left(A_{peak}\right)\\ \frac{d}{d\theta }{S}_{thr}\left(A_{rest}\right)=\frac{d}{d\theta }{S}_{eng}\left(A_{rest}\right)\\ {\frac{d}{d\theta }}_{thr}{S}_{thr}\left(A_{peak}\right)=0\end{array}$$

where S_eng is the engineering formula for the throttle open area, such that

$$S_{eng}\left(\theta \right)=\pi {\left(\frac{D_{plate}}{2}\right)}^2\left(1-\frac{\cos \left(\theta \right)}{\cos \left(A_{rest}\right)}\right)+S_{leak}.$$

This figure shows a comparison of the polynomial result and the engineering result.

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.

• Open Model

Ports

Input

Thr — Throttle command input, unitless

physical signal

Physical signal input associated with the normalized throttle command, where 0 represents a fully closed throttle, and 1 represents a fully open throttle. The block maps this input to a throttle-open angle between 0 and 90 degrees.

EngSpd — Rotational engine speed, rad/s

physical signal

Physical signal input associated with the rotational speed, in rad/s.

Output

Pim — Intake manifold pressure input, kPa

physical signal

Physical signal input associated with the intake manifold, in kPa.

Parameters

Dry air specific gas constant — Dry air specific gas constant

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

Specific gas constant of dry air.

Dry air specific heat ratio — Dry air specific heat ratio

1.4 (default) | positive scalar

Specific heat ratio of dry air.

Ambient pressure — Reference air pressure

101.325 kPa (default) | positive scalar

Pressure of the air entering the intake.

Ambient temperature — Reference temperature

298.15 K (default) | positive scalar

Temperature of the air entering the intake.

Throttle rest angle — Released throttle position

3 deg (default) | positive scalar

Radial distance from the resting throttle position to 0 degrees.

Throttle plate diameter — Throttle plate diameter

5 cm (default) | positive scalar

Diameter of the butterfly valve disc in the throttle body.

Throttle leakage area — Throttle leakage area

1 cm^2 (default) | nonnegative scalar

Cumulative area of throttle leakage.

Intake manifold volume — Intake manifold volume

1000 cm^3 (default) | positive scalar

Volumetric capacity of the intake manifold.

Engine displacement volume — Engine displacement volume

1500 cm^3 (default) | positive scalar

Combined displacement of all engine pistons.

Throttle response time constant — Throttle response time constant

0.1 s (default) | positive scalar

Time constant associated with the response rate of the engine to the throttle command.

Version History

Introduced in R2022a