1. Wave Action Theory for Turning of Intake & Exhaust Manifold
P M V Subbarao
Professor
Mechanical Engineering Department
Matching of Set of CVs for effective breathing….

2. Integrated Description of Wave Action

3. Dynamic Behaviour of A CV
The behavior of a CV that exhibits linear behavior is mathematically represented in the general form of expression given as
Here, the coefficients a2, a1, and a0 are constants dependent on the particular part of a intake/exhaust system.
The left hand side of the equation is known as the characteristic equation.
It is specific to the internal properties of the CV and is not altered by the way the engine is used.

4. Forcing Functions
The specific combination of forcing function input and CV characteristic equation collectively decides the combined output response.
Solution of the combined behavior is generally obtained using Laplace transform methods to obtain the output responses in the time or the complex frequency domain.

5. Behaviour of A CV
Zero order
First order
Second order
nth order

6. Behaviour of A CV
Note that specific names have been given to each order.
The zero-order situation is not usually dealt because it has no time-dependent term and is thus seen to be trivial.
It is an amplifier (or attenuator) of the forcing function with gain of a0.
It has infinite bandwidth without change in the amplification constant.
The highest order usually necessary to consider in first-cut CV analysis is the second-order class.
Higher-order systems do occur in.
Computer-aided tools for systems analysis are used to study the responses of higher order systems.

7. Generalized Model for ith Second Order Cv

8. Acoustic Theory for Development of Manifold
The intake manifold to an internal combustion (IC) engine will consist of a network of interconnecting CVs.
The lengths of these CVs, and to a certain extent their diameters, must be chosen carefully as they will determine the resonant frequencies of the manifold.
When the engine is run at a speed where one or more of these resonances is excited, then both the volumetric efficiency and the intake noise level maybe affected.

9. General Rule for Acoustic Design
The tuning peak will occur when the natural Helmholtz resonance of the cylinder and runner is about twice the piston frequency.
The Engine can generate highest Torque at turning peak conditions.
The aim of acoustic design is to achieve tuning peak at highest speed or highest power conditions.
Tuned port simply means that the intake runners are tuned to have highest volumetric efficiency at specific rpm range.

10. Acoustic Modeling of Manifold
Induction System Model

11. Primary & Secondary Induction Systems
The system responsible for flow of air is called as primary system.
The remaining part of the system, which is not actively feed the cylinder is called as secondary system.

12. Build Considerations for Resonating manifold
Variable Length Runners for RPM matching
Materials Selection Criteria:
Weight, Fabrication, Surface Finish, Heat Isolation
Intake placement
Isolate from heat sources (Engine, Exhaust, Radiator, Pavement)
Fuel Injector Placement

13. Experimental Methods to Understand Resonant Frequencies of Induction System

14. Modulation of Acoustic Waves

15. Pipe with Throttle

16. Junctions
The most complex cause of pressure waves is when the intake valve closes.
Any velocity left in the intake port column of air will make high pressure at the back of the valve.
This high pressure wave travels toward the open end of the intake tract and is reflected and inverted as a low pressure wave.

17. Acoustic Characterization of Components
Using Engelman's electrical analogy we can define the system as a system defined by capacitances and inductances.
For a Helmholtz Resonator : n=fH

18. Acoustic Modeling of Runner
Ideal Helmholtz Resonator:
The theory behind what happens in the intake (and exhaust systems) is called A Helmholtz Resonator.
Induction pressure waves can have an effect on how well the cylinders are filled.
It can help (or hurt) power in a narrow rpm Range.
V : Capacitance of Primary Volume

19. Primary Volume/Capacitance

20. Determination of Primary Capacitance
The Primary Volume is considered to be the Cylinder Volume with the Piston at mid-stroke (effective volume).
Writing Clearance Volume in Terms of Compression Ratio:

21. Acoustic Modeling of Runner with Port
For a single degree of freedom system
A1 = Average Area of Runner and Port
L1 = LPort + Lrunner
K1 = 642
C = Speed of Sound

22. Effective Inductance
The EFFECTIVE INDUCTANCE for a pipe with different cross-sections may be defined as the sum of inductances of each section.

23. Relative Dynamic Responses of Primary & Secondary Systems
The INDUCTANCE RATIO (a) is defined as the ratio of the secondary inductance to the primary inductance.
INDUCTANCE RATIO (a)
The CAPACITANCE RATIO (b) is defined as the ratio of the Secondary Volume to the Primary Volume.
V2 = Secondary Volume
= Volume of Intake Runners that are ineffective (n-1)

24. Inductance ratio for Intake System
Calculate the Separate Inductances:
Determine the Inductance Ratio (a)

25. Determine the Capacitance Ratio (b)
Determine the Induction system Resonances
(IND)1 = Inductance of the primary length
(IND)1 = Iport + Irunner

26. Helmholtz Tuning of Complete System
Determine the Primary Resonance:
Determine the Frequency Ratios:
Determine the Tuning Peak:

27. Intake Tuning Peaks become:

28. A combined equation is possible indicating it’s 2nd order

29. David Visard’s “Rule of thumb” Equations
Using Visard's Equation for Runner Length
1. Starting point of 7 inches for 10,000 RPM
2. Add length of 1.7 inches for each 1000 RPM less
Using Visard's Equation for Runner Diameter