CHAPTER 11 SUBSONIC COMPRESSIBLE FLOW OVER AIRFOILS: LINEAR THEORY11.4 PRANDTL-GLAUERT COMPRESSIBILITYCORRECTIONThe methods that approximately take into account ofthe effects of compressibility by correct the incompressible flow results is called compressible corrections.We will derive the most widely known correction of Prandtl-Glauertcompressibility correction in this section. Since the Prandtl-Glauert method is based on the linearized perturbation velocity potential equation: So it has restrictions: thin airfoil at small angle of attack;purely subsonic;give inappropriate results at Boundary Condition :In (x,y) space:In transformed space:SoThis Equation implies that the shape of the airfoil in the transformedspace is the same as the physical space. Hence, the above tranforma-tion relates the compressible flow over an airfoil in (x,y) space to the in space over the same airfoil.(11.51)11.5 IMPROVED COMPRESSIBILITYCORRECTIONS(11.54)(11.55)11.6 CRITICAL MACH NUMBERIn this section we deal with several aspects of transonic flow from a qualitative point of view.What is the definition of Critical Mach Number?The critical Mach numberis that free stream Mach number at which sonic flowis first achieved on theairfoil surface. Derivation of critical pressure coefficient:(11.6)Estimation of : Eq.(11.51),(11.54),or(11.55)11.7 DRAG-DIVERGENCE MACH NUMBE:THE SOUND BARRER The definition of drag divergence Mach number:The value of at which the sudden increase in drag starts is defined the as drag divergence Mach number.11.8 The Area Rule The Area Rule is a design concept which has effectively reducedthe drag rise near Mach 1 for complete airplane.FIGURE 11.10 FIGURE 11.11 The area rule for transonic flow:The cross-sectional area distribution of an airplane, including fuselage, wing, and tail, should have a smooth distribution along the axis of the airplane.11.9 THE SUPERCRITICAL AIRFOIL The purpose of a supercritical airfoil is increase the value of drag-divergence Mach number. Supercritical airfoils are specially designed profiles to increase the drag-divergence Mach number.