Wave Action Theory for Turning of Intake

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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.
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Integrated Description of Wave Action
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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.
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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.

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

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Generalized Model for ith Second Order Cv
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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.

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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.

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Acoustic Modeling of Manifold
Induction System Model
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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.

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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

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Experimental Methods to Understand Resonant
Frequencies of Induction System
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Modulation of Acoustic Waves
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Pipe with Throttle
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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.
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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 ?nfH
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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
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Primary Volume/Capacitance
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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

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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
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Effective Inductance

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

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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)
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Inductance ratio for Intake System

• Calculate the Separate Inductances

• Determine the Inductance Ratio (a)

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• Determine the Capacitance Ratio (b)

• Determine the Induction system Resonances

(IND)1 Inductance of the primary length (IND)1
Iport Irunner
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Helmholtz Tuning of Complete System

• Determine the Primary Resonance
• Determine the Frequency Ratios
• Determine the Tuning Peak

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• Intake Tuning Peaks become

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• A combined equation is possible indicating its
  2nd order

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David Visards 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