Aerodynamics for engineering students - part 8

hoặc, trong số Reynolds Re, điều này trở thành (7,81) (Re) 115 Sự phát triển của lớp và lớp hỗn loạn cho một vận tốc dòng nhất định được hiển thị vẽ trong hình. 7,23. Để ước tính số lượng độ dày khác cho lớp hỗn loạn, các tích phân sau đây phải được đánh giá: | Viscous flow and boundary layers 419 Therefore i s5 4 v 7 uc 5 X 4 5 V y s 4 s k 4 uj or in terms of Reynolds number Rex this becomes 5 .Rex 1 7 The developments of laminar and turbulent layers for a given stream velocity are shown plotted in Fig. . In order to estimate the other thickness quantities for the turbulent layer the following integrals must be evaluated fS l-ũ2 d í ỹ 1 - J V dỹ Jo Jo L8 Jo 7 7 i-ĩỉ c Using the value for I in Eqn a above I 2 and substituting appropriately for Ỗ from Eqn and for the integral values from Eqns b and c in Eqns and leads to c rZ 5 e x 1 5 s 5 yyy Rexf5 X metres Fig. Boundary layer growths on flat plate at free stream speed of 60 m s 1 420 Aerodynamics for Engineering Students Fig. Turbulent velocity profile The seventh-root profile with the above thickness quantities indicated is plotted in Fig. . Example A wind-tunnel working section is to be designed to work with no streamwise pressure gradient when running empty at an airspeed of 60ms-1. The working section is m long and has a rectangular cross-section which is m wide by m high. An approximate allowance for boundary-layer growth is to be made by allowing the side walls of the working section to diverge slightly. It is to be assumed that at the upstream end of the working section the turbulent boundary layer is equivalent to one that has grown from zero thickness over a length of m the wall divergence is to be determined on the assumption that the net area of flow is correct at the entry and exit sections of the working section. What must be the width between the walls at the exit section if the width at the entry section is exactly m For the seventh-root profile 6t 7 Eqn 7-82 At entry m. Therefore Rex X 105 V X IO-6 ReỊ 5 Viscous flow and boundary layers 421 . 5 x ------------ m At exit X m. .