3 Swept and Displaced Volumes Inlet PortSwept Volume/cylinder:s x ApVs = swept volume dB = bore diameter s = strokeNote: In valve design the Volume which flows into the cylinder must equal the volume which flows through the inlet port. The velocity past the valve must then be considerably greater than the velocity in the cylinder.s
4 Port Sizing and Mach Index (Z) Mach Index is the ratio of the velocity of the gases flow area to the speed of soundDb = cylinder bore dia.Dp = port dia.n = number of portsFor mean values:
5 Port Sizing and Mach Index (Z) For instantaneous relationships:s = length of stroke L = length of connecting rodθ = crank position Cd = flow coefficient
6 Port Sizing and Mach Index (Z) Speed of Sound:Temperature and F/A ratio dependantAt Standard Temperature and Pressurec = 1100 ft/secc = 340 m/sec
7 Port Sizing and Mach Index (Z) Modern performance engines will use multiple inlet and exhaust valves per cylinder.Many are using multiple intake runners per cylinder to improve cylinder filling over a broader range of RPM.A single runner is used at lower RPM while a second runner will be opened at higher RPM.The second and the combined each have their own tuning peak.
9 Inlet air density Law of Partial Pressures: If each is considered as a perfect gas
10 Inlet air density Inlet Pressures and Densities: ma = 29 mw = 18 mgas = 113Fc = chemically correct mixFi = % vaporized (Fc)
11 Inlet air density Inlet Pressures and Densities: From Ideal Gas Law R = 1545 ft-lb/(lbm-mole-oR)
12 Inlet air densityInlet Densities:for P in psia and T in oR
13 Inlet air density Example Problem: Find the change in indicated power when changing from Gasoline to Natural Gas fuelsAssume: Pi = 14.0 psia Ti = 100oF = 1.2 => 20 % Richh = 0.02 lbm/lbm airGASOLINE:F/A = 1.2 x 1/14.8 = lbfuel/lbairAssume fuel is 40% vaporized(Use fuel distilation curves)
14 Inlet air density Gasoline: F/A = 1.2 x 1/17.2 = 0.0697 lbfuel/lbair Natural gas:F/A = 1.2 x 1/17.2 = lbfuel/lbairFuel is a gaseous fuel and is 100% vaporized
26 Multiple Stack with pressure box Courtesy: Dan Butts, Derek Harris, Chris Brockman, Tiffany Dickinson
27 Acoustic Modeling For a single degree of freedom system A1 = Average Area of Runner and Port L1 = LPort + LrunnerK1 = 77 (English) K1 = 642 (Metric)C = Speed of Sound
28 Individual Throttle Body with Plenum Courtesy: Dan Butts, Derek Harris, Chris Brockman, Tiffany Dickinson
29 Helmholtz TuningWriting Clearance Volume in Terms of Compression Ratio:The Primary Volume is considered to be the Cylinder Volume with the Piston at mid-stroke (effective volume).
30 Helmholtz TuningThe tuning peak will occur when the natural Helmholtz resonance of the cylinder and runner is about twice the piston frequency.Volume (V1) = Cylinder VolumeVolume (V2) = Volume in the path from V1 to the PlenumUsing Engelman's electrical analogy we can define the system as a system defined by capacitances and inductances.
31 Helmholtz TuningThe EFFECTIVE INDUCTANCE for a pipe with different cross-sections may be defined as the sum of inductances of each section.The INDUCTANCE RATIO (a) is defined as the ratio of the secondary inductance to the primary inductance.
32 Helmholtz Tuning 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)
33 Helmholtz Tuning Calculate the Separate Inductances: Determine the Inductance Ratio (a)
34 Helmholtz Tuning Determine the Capacitance Ratio (b) Determine the Induction system Resonances(IND)1 = Inductance of the primary length(IND)1 = Iport + Irunner
35 Helmholtz Tuning Determine the Primary Resonance: Determine the Frequency Ratios:Determine the Tuning Peak:A1 = Average Area of Runner and Port L1 = LPort + LrunnerK1 = 77 (English) K1 = 642 (Metric)C = Speed of Sound
37 Helmholtz TuningA combined equation is possible indicating it’s 2nd order
38 David Visard’s “Rule of thumb” Equations Using Visard's Equation for Runner Length1. Starting point of 7 inches for 10,000 RPM2. Add length of 1.7 inches for each 1000 RPM lessUsing Visard's Equation for Runner Diameter