Drag of a rectangular planform cavity in a flat plate with a turbulent boundary layer for Mach numbers up to 3. Part II: Open and transitional flows.
ESDU 00007 develops an empirical method for predicting the drag where the cavity length is small compared to its depth and the shear flow bridges the gap between the front and rear walls, with the dividing streamline ending in a stagnation point at or near the top of the rear wall, trapping one or more vortices in the cavity (i.e. open flow). A single trapped vortex is typical for depth-to-length ratios between 0.5 and 1. For lower depth-to-length values a tandem pair of vortices can arise, while for higher depth-to-length values vertically stacked double or even triple vortices may occur. Families of curves are given to suggest a lower limit of cavity depth-to-length ratio for open flow in terms of freestream Mach number and cavity width-to-length ratio. If the cavity length is long compared to its depth, the shear flow enters the cavity and attaches to the floor before separating to exit over the rear wall with a stagnation point near the top of the wall (i.e. closed flow); the closed flow case is treated in the companion document, ESDU 00006. A family of curves repeated from that document is given to suggest an upper limit of cavity depth-to-length ratio for closed flow in terms of freestream Mach number and cavity width-to-length ratio. For a given cavity width and depth, at given flow conditions, as the cavity length is progressively increased from zero there is a range of values over which, for subsonic freestream speeds, the flow type gradually changes from open to closed flow, with the flow entering the cavity over the front wall but not attaching to the floor before passing over the rear wall (i.e. transitional flow). For supersonic speeds a similar range exists but the change from open to closed flow is more complex and abrupt, passing through two intermediate stages (i.e. transitional-open and transitional-closed). ESDU 00007 continues the open flow prediction method with a smooth progression into the transitional region. The interface region between transitional and closed flows, which is not precise and may need the construction of a short fairing, is discussed and illustrated by means of an example. Tables give the ranges of parameters covered by the method. The prediction of the ratio of the drag coefficient, based on floor area, to the local skin friction coefficient at the cavity mid-length station (in the absence of the cavity) is assessed to be within 2. However, that accuracy requires certain data to be excluded from the analysis, and for freestream Mach numbers greater than 0.5 their inclusion would lower the agreement to within 5. The concerns with the data are discussed and all the details of the analysis are explained. Worked examples illustrate the use of the method. The third item in the series, ESDU 10016, deals with the effect on cavity drag of a pair of doors open at 90°, including the effects of three different treatments of the door leading and trailing edges.
Software for the method is provided as ESDUpac A1607 and also with an interface as Toolbox 16007.
|Data Item ESDU 00007
|Toolbox 16007 Run
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|Boundaries for closed flow (closed flow likely below each curve)
|Boundaries for open flow, M1 ≤ 1 (open flow likely above each curve)
|Boundaries for open flow, 1 ≤ M1 ≤ 3 (open flow likely above each curve)
|Value of d
|Local skin friction coefficient on a flat plate
|Boundary-layer thickness on a flat plate