空气动力学 chap 11..ppt

PART 3 Inviscid, Compressible Flow 无粘可压缩流 RESULT HOW DO WE SOLVE EQUATION Note behavior of sign of leading term for subsonic and supersonic flows Equation is almost Laplace’s equation, if we could get rid of b coefficient Strategy Coordinate transformation Transform into new space governed by ξ and η In transformed space, new velocity potential may be written TRANSFORMED VARIABLES (1/2) Definition of new variables (determining a useful transformation is done) Perform chain rule to express in terms of transformed variables TRANSFORMED VARIABLES (2/2) Differentiate with respect to x a second time Differentiate with respect to y a second time Substitute in results and arrive at a Laplace equation for transformed variables Recall that Laplace’s equation governs behavior of incompressible flows FINAL RESULTS Insert transformation results into linearized CP Prandtl-Glauert rule: If we know the incompressible pressure distribution over an airfoil, the compressible pressure distribution over the same airfoil may be obtained Lift and moment coefficients are integrals of pressure distribution (inviscid flows only) SWEPT WINGS: SUPERSONIC FLIGHT WING SWEEP COMPARISON SWEPT WINGS: SUPERSONIC FLIGHT 例11.3 (b)用解析法 求NACA0012 翼型的临界马赫数。 -0.6363 -0.6363 0.7371 -0.6367 -0.6362 0.737 -0.6331 -0.6372 0.738 -0.6260 -0.6393 0.74 -0.6621 -0.6292 0.73 -0.6996 -0.6196 0.72 讨论：本例结果的精度 11.6.1 对最小压力点（速度最大点）的讨论 结论： （1）速度最大点出现在最大厚度之前，其出现的位置取决于整个翼型的形状而不是当地局部区域的形状。 （2）对于不同马赫数，最大速度点位置基本不变。 11.7 DRAG-DIVERGENCE MACH NUMBER: THE SOUND BARRIER （阻力发散马赫数：音障） a b c d e f g h MCR drag divergence Mach number(阻力发散马赫数）: The value of at which the sudden increase in drag starts is defined the as drag divergence Mach number. （阻力开始急剧增大时所对应的自由来流马赫数，称为阻力发散马赫数）。 道格拉斯定义(常用): 波音定义(较少使用): 注：1）阻力发散马赫数与迎角相关； 2）工程上经常使用零升力或者指定设计升力下的阻力发散马赫数。 IMPACT ON AIRFOIL / WING DRAG 波阻 Only at transonic and supersonic speeds Dwave= 0 for subsonic speedsbelow Mdrag-divergence Profile Drag (型阻)