Air Intake

R2026b

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

$\frac{d}{d t} P_{i m} = \frac{R_{a i r} T_{a m b}}{V_{i m}} ({\dot{m}}_{t h r} - {\dot{m}}_{c y l}),$

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

${\dot{m}}_{c y l} = \frac{ω V_{d} P_{i m}}{2 R_{a i r} T_{a m b}},$

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

${\dot{m}}_{t h r} = {\begin{cases} \frac{S_{t h r}}{\sqrt{T_{a m b}}} c_{1} (P_{a m b} - P_{i m}) Laminar \\ \frac{S_{t h r}}{\sqrt{T_{a m b}}} P_{a m b} \sqrt{c_{2} [{(\frac{P_{a m b}}{P_{i m}})}^{c_{b}} - {(\frac{P_{a m b}}{P_{i m}})}^{c_{a}}]} Subsonic \\ \frac{S_{t h r}}{\sqrt{T_{a m b}}} c_{3} P_{a m b} Choked \end{cases}$

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

$\begin{array}{l} c_{a} = \frac{κ + 1}{κ} \\ c_{b} = \frac{2}{κ} \\ c_{1} = \frac{\sqrt{c_{2} (Π_{l a m}^{c_{b}} - Π_{l a m}^{c_{a}})}}{1 - Π_{l a m}} \\ c_{2} = \frac{2 κ}{R_{a i r} (κ - 1)} \\ c_{3} = \sqrt{\frac{κ}{R_{a i r}} Π_{c r}^{c_{a}}} \end{array}$

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

$Π_{c r} = {(\frac{2}{κ + 1})}^{\frac{κ}{κ - 1}} .$

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

$S_{t h r} (θ) = k_{0} + k_{1} θ + k_{2} θ^{2} + k_{3} θ^{3},$

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:

$\begin{matrix} S_{t h r} (0) = S_{e n g} (0) \\ S_{t h r} (\frac{π}{2}) = S_{e n g} (A_{p e a k}) \\ \frac{d}{d θ} S_{t h r} (A_{r e s t}) = \frac{d}{d θ} S_{e n g} (A_{r e s t}) \\ {\frac{d}{d θ}}_{t h r} S_{t h r} (A_{p e a k}) = 0 \end{matrix}$

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

$S_{e n g} (θ) = π {(\frac{D_{p l a t e}}{2})}^{2} (1 - \frac{\cos (θ)}{\cos (A_{r e s t})}) + S_{l e a k} .$

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

Throttle open area with respect to throttle angle. The polynomial approximation has a different shape than the engineering equation, but they trend close to one another.

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

expand all

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.

Programmatic Use

Port: thr_cmd

EngSpd — Rotational engine speed, rad/s
physical signal

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

Programmatic Use

Port: w

Output

expand all

Pim — Intake manifold pressure input, kPa
physical signal

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

Programmatic Use

Port: Pim_out

Parameters

expand all

Dry air specific gas constant — Dry air specific gas constant
`287.058` `J/(K*kg)` (default) | positive scalar

Specific gas constant of dry air.

Programmatic Use

Parameter: R_air

Dry air specific heat ratio — Dry air specific heat ratio
`1.4` (default) | positive scalar

Specific heat ratio of dry air.

Programmatic Use

Parameter: kappa

Ambient pressure — Reference air pressure
`101.325` `kPa` (default) | positive scalar

Pressure of the air entering the intake.

Programmatic Use

Parameter: P_amb

Ambient temperature — Reference temperature
`298.15` `K` (default) | positive scalar

Temperature of the air entering the intake.

Programmatic Use

Parameter: T_amb

Throttle rest angle — Released throttle position
`3` `deg` (default) | positive scalar

Radial distance from the resting throttle position to 0 degrees.

Programmatic Use

Parameter: thr_rest

Throttle plate diameter — Throttle plate diameter
`5` `cm` (default) | positive scalar

Diameter of the butterfly valve disc in the throttle body.

Programmatic Use

Parameter: D_plate

Throttle leakage area — Throttle leakage area
`1` `cm^2` (default) | nonnegative scalar

Cumulative area of throttle leakage.

Programmatic Use

Parameter: S_leak

Intake manifold volume — Intake manifold volume
`1000` `cm^3` (default) | positive scalar

Volumetric capacity of the intake manifold.

Programmatic Use

Parameter: V_im

Engine displacement volume — Engine displacement volume
`1500` `cm^3` (default) | positive scalar

Combined displacement of all engine pistons.

Programmatic Use

Parameter: V_displ

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.

Programmatic Use

Parameter: c_thr

Version History

Introduced in R2022a

Air Intake

Description

Equations

Examples

Single Cylinder Spark Ignition Engine

Ports

Input

Thr — Throttle command input, unitless physical signal

Programmatic Use

EngSpd — Rotational engine speed, rad/s physical signal

Programmatic Use

Output

Pim — Intake manifold pressure input, kPa physical signal

Programmatic Use

Parameters

Dry air specific gas constant — Dry air specific gas constant 287.058 J/(K*kg) (default) | positive scalar

Programmatic Use

Dry air specific heat ratio — Dry air specific heat ratio 1.4 (default) | positive scalar

Programmatic Use

Ambient pressure — Reference air pressure 101.325 kPa (default) | positive scalar

Programmatic Use

Ambient temperature — Reference temperature 298.15 K (default) | positive scalar

Programmatic Use

Throttle rest angle — Released throttle position 3 deg (default) | positive scalar

Programmatic Use

Throttle plate diameter — Throttle plate diameter 5 cm (default) | positive scalar

Programmatic Use

Throttle leakage area — Throttle leakage area 1 cm^2 (default) | nonnegative scalar

Programmatic Use

Intake manifold volume — Intake manifold volume 1000 cm^3 (default) | positive scalar

Programmatic Use

Engine displacement volume — Engine displacement volume 1500 cm^3 (default) | positive scalar

Programmatic Use

Throttle response time constant — Throttle response time constant 0.1 s (default) | positive scalar

Programmatic Use

Version History

See Also

Thr — Throttle command input, unitless
physical signal

EngSpd — Rotational engine speed, rad/s
physical signal

Pim — Intake manifold pressure input, kPa
physical signal

Dry air specific gas constant — Dry air specific gas constant
`287.058` `J/(K*kg)` (default) | positive scalar

Dry air specific heat ratio — Dry air specific heat ratio
`1.4` (default) | positive scalar

Ambient pressure — Reference air pressure
`101.325` `kPa` (default) | positive scalar

Ambient temperature — Reference temperature
`298.15` `K` (default) | positive scalar

Throttle rest angle — Released throttle position
`3` `deg` (default) | positive scalar

Throttle plate diameter — Throttle plate diameter
`5` `cm` (default) | positive scalar

Throttle leakage area — Throttle leakage area
`1` `cm^2` (default) | nonnegative scalar

Intake manifold volume — Intake manifold volume
`1000` `cm^3` (default) | positive scalar

Engine displacement volume — Engine displacement volume
`1500` `cm^3` (default) | positive scalar

Throttle response time constant — Throttle response time constant
`0.1` `s` (default) | positive scalar