Lifting Surfaces
Characteristics of Sheet/Cloud Cavitation
Figure 1.Cavity length as a function of a composite variable
Visual observation have been made of the cavity pocket length as a function of both cavitation number and angle of attack. These observations have been made for both a 2D and a 3D hydrofoils. Based on the results, shown in Figure 1, we're able to estimate the cavity length as a function of a composite variable.
In Figure 1 the cavity length, l, is devided by chord length, c, and plotted as a function of combined variable containing both the angle of attack, in radians, and the cavitation number. If a linear fit is made we end up with the following approximate expression.
Rearranging the equation such that the cavitation number is a function of angle of attack we can plot the result for constant l/c's in the general map of cavitation regimes (Figure 2). Figure 2 is also based on visual observations as well as dynamics measured using different transducers. NOTE: Supercavitation is defined as the condition when the foil is embedded in the cavity pocket at any phase of a shedding cycle (if any).
Figure 2. Cavitation regimese
Dynamic Regions
For small angles of attack and relatively high cavitation number pressure side cavitation was observed on the pressure side of the foil. Using a static theory this cavitation was not supposed to occur, thus, a dynamic feature needed be involved. The same observation also suggested that the pressure side cavitation was in-phase with the regular cavity cycle on the suction side. Figure 3 shows measured lift (with a lift/drag balance) and the instantaneous pressure drop over the foil as measured with two pressure transducers at the base of the test section. The two pressure transducers are at 0.5c, are rotating with the foil and spaced approx. 60 mm apart. Maximum thickness of the foil is 15 mm. The amplitudes of the pressure fluctuations on both the suction and the pressure side were of the same order of magnitude.
Figure 3. Lift and instantaneous pressure drop over the foil
In order to distinguish between the different shedding regimes so-called ramping experiments were performed. Basically the flow reference velocity was kept cosntant while pressure was allowed to increase or decrease linearily. For the providing the results a Joint Time Frequency Analysis method was made.
The equation can be considered a windowed FFT analysis. Where gamma is the window function centered in t. In Figure 4 a typical result is shown. In Figure 4 color intensity indicates amplitude of the signal as found in the time-frequency plane. Please note shift in frequency content at a cavitation number close to 0.9
