Aerodynamics for engineering students - part 6

Tuy nhiên, đi từ khu vực cánh-tip, eqn (5,23) làm giảm khoảng eqn (4,103), một xấp xỉ tốt, C, phân phối thu được cho aerofoils đối xứng có thể được sử dụng cho các phần cánh. Đối với đầy đủ kết quả này được thể hiện chính thức ngay lập tức dưới đây. Tuy nhiên, nếu điều này là không quan tâm trực tiếp đến phần tiếp theo. | Compressible flow 297 If a disturbance of large amplitude . a rapid pressure rise is set up there are almost immediate physical limitations to its continuous propagation. The accelerations of individual particles required for continuous propagation cannot be sustained and a pressure front or discontinuity is built up. This pressure front is known as a shock wave which travels through the gas at a speed always in excess of the acoustic speed and together with the pressure jump the density temperature and entropy of the gas increases suddenly while the normal velocity drops. Useful and quite adequate expressions for the change of these flow properties across the shock can be obtained by assuming that the shock front is of zero thickness. In fact the shock wave is of finite thickness being a few molecular mean free path lengths in magnitude the number depending on the initial gas conditions and the intensity of the shock. One-dimensional properties of normal shock waves Consider the flow model shown in Fig. in which a plane shock advances from right to left with velocity Ml into a region of still gas. Behind the shock the velocity is suddenly increased to some value M in the direction of the wave. It is convenient to superimpose on the system a velocity of Ml from left to right to bring the shock stationary relative to the walls of the tube through which gas is flowing undisturbed at Ml Fig. . The shock becomes a stationary discontinuity into which gas flows with uniform conditions Pl pl Ml etc. and from which it flows with uniform conditions P2 P2 M2 etc. It is assumed that the gas is inviscid and non-heat conducting so that the flow is adiabatic up to and beyond the discontinuity. The equations of state and conservation for unit area of shock wave are State P _ P2 p T P2T2 Mass flow m Pl Ml P2U2 Pi P Pi pi a Pzpz Stationary shock b Fig. 298 Aerodynamics for Engineering Students Momentum in the absence of external and dissipative .

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