Đang chuẩn bị liên kết để tải về tài liệu:
Aerodynamics for engineering students - part 4

Không đóng trình duyệt đến khi xuất hiện nút TẢI XUỐNG Tải xuống

Để lấy được các phương trình quản lý một trong những cần phải nhận ra rằng, với điều kiện là chất gây ô nhiễm không phải là được tạo ra trong lĩnh vực dòng chảy, sau đó khối lượng của chất gây ô nhiễm được bảo toàn. Các vấn đề chất gây ô nhiễm có thể được vận chuyển bằng hai cơ chế vật lý riêng biệt, cụ thể là đối lưu và khuếch tán phân tử. | 164 Aerodynamics for Engineering Students Fig. 4.4 Consider this by the reverse argument. Look again at Fig. 4.3b. By definition the velocity potential of c relative to A ộcÀ must be equal to the velocity potential of c relative to B cb in a potential flow. The integration continued around ACB gives r ỘCA ỘCB 0 This is for a potential flow only. Thus if r is finite the definition of the velocity potential breaks down and the curve ACB must contain a region of rotational flow. If the flow is not potential then Eqn ii in Section 3.2 must give a non-zero value for vorticity. An alternative equation for r is found by considering the circuit of integration to consist of a large number of rectangular elements of side 6x ôy e.g. see Section 2.7.7 and Example 2.2 . Applying the integral r J u dx V dy round abed say which is the element at P x y where the velocity is u and V gives Fig. 4.5 . dv 6x f du 6y dv 6x dx 2 dy 2 J dx 2 J du by a - V 5x oy 2 J A 0V dù Ar 53 0X dy J The sum of the circulations of all the areas is clearly the circulation of the circuit as a whole because as the AT of each element is added to the AT of the neighbouring element the contributions of the common sides disappear. Applying this argument from element to neighbouring element throughout the area the only sides contributing to the circulation when the ATs of all areas are summed together are those sides which actually form the cữcuit itself. This means that for the circuit as a whole r y d W over the area round the circuit and ỠV du _ dx d Q This shows explicitly that the circulation is given by the integral of the vorticity contained in the region enclosed by the circuit. Two-dimensional wing theoiY 165 Fig. 4.5 If the strength of the circulation r remains constant whilst the circuit shrinks to encompass an ever smaller area i.e. until it shrinks to an area the size of a rectangular element then r c X Ếxểy X area of element Therefore . r vorticity lim - - . . 4.3 area 0 area of circuit Here the