Optimal Engine Design Using Nonlinear Programming and the ...

specifications are indicated by the Ki (i = 1,..., 12) and Li ( i = 1, 2) coefficients and summarizedin Table 3.3.1.2 Model B - Compound Valve Head Chamber GeometryThe geometry for the compound valve head design is shown in Figure 2. Accounting forthis new geometry will change Model A presented above with the addition of new design variablesand constraints. The new variables are the displacement volume v (considered a parameter inModel A), the deck height h, and the radius of curvature r. As displacement is now a variable,the objective function is selected to be brake power rather than specific brake power. Arelationship between clearance volume vc, displacement volume v, and compression ratio isimposed by the definition of the compression ratio:cr = (v/Nc + vc)/vc (35)dEHhead facerFigure 2. Schematic for compound valve designwhereThe clearance volume is the sum of deck volume and dome volume vd.vc = πhb 2 /4 + vd (36)vd = (1/3)π[(r 2 - b 2 /4) 1.5 - (r 2 - dI 2 /4) 1.5 - (r 2 - dE 2 /4) 1.5 ]- πr 2 [(r 2 - b 2 /4) 0.5 - (r 2 - dI 2 /4) 0.5 - (r 2 - dE 2 /4) 0.5 ] - (2/3)π r 3 (37)7