Cav03-GS-9-003 Fifth International Symposium on Cavitation (Cav2003) Osaka, Japan, November 1-4, 2003
A Near Field Study of a Non-Cavitating and Cavitating Hydrofoil Qiao Qin St. Anthony Falls Laboratory, University of Minnesota
[email protected]
Charles C.S. Song St. Anthony Falls Laboratory, University of Minnesota
[email protected]
Abstract The near field study of a non-cavitating hydrofoil has received much attention recently. In the mean while, there are few references in the literature describing the near field of a cavitating hydrofoil. To better understand the complex physics of cavitation, a virtual single-phase natural cavitation model with barotropic flow assumption, which has been proved to be able to capture the main dynamics of complex cavitating flows, is used to study the near field physics around a cavitating hydrofoil. In addition, the weakly compressible flow model is used to study the near field physics around a non-cavitating hydrofoil. Velocity and pressure distributions immediately upstream of the nose will be analyzed in detail in this work. By comparing numerical pressure and vorticity flow visualization video with computed lift time series, a link between near field flow pattern and lift fluctuation is established for sheet/cloud cavity regime. Introduction Increasing effort has been put on the flow near the leading edge and trailing edge of lifting surfaces such as hydrofoils under non-cavitating condition, especially when the flow is highly turbulent (Bourgoyne et al, 2000, 2001a, 2001b; Kornilov et al, 2002). In the meanwhile, few references describing flow near the leading edge and trailing edge of lifting surfaces under cavitating condition can be found. A popular 2D NACA 0015 hydrofoil is again selected in this study. Theoretical basis of the virtual single phase natural cavitation model used in this study can be found in Qin et al (2003a). Time averaged velocity distributions, including stream wise velocity component, vertical velocity component and total velocity and time averaged pressure distribution on a vertical line located 1% chord length upstream of the nose are studied in detail. Time averaged stream wise velocity distribution at slightly different locations upstream of the hydrofoil is also computed. The relationship between large lift oscillation and the shedding of cloud cavity has been noted recently. This paper describes in more detail the relationships between lift peaks and the cavity and vortex patterns for the hydrofoil at 8 degree attack angle with cavitation number equal to 0.5.
Roger E.A. Arndt St. Anthony Falls Laboratory, University of Minnesota
[email protected]
Following the idea in Bourgoyne et al (2000), time averaged velocity and pressure distribution on a vertical line located 1% chord length upstream of the nose has been computed (see figure 1), for 6 and 8 degrees angle of attack, respectively. It should be mentioned here that the y-coordinate increases in the up ward direction and y=0 is set at mid-chord. In addition, all velocities presented here are normalized by the upstream specified velocity U0 and the pressure is normalized by the dynamic pressure, 1 2 ρU 02 . The time averaged pressure distribution on the line parallel with y axis at two attack angles for three different flow conditions are shown in figure 2. For non-cavitating flow, Fig. 2(a) shows very sharp pressure gradient varying from nearly stagnation pressure on the pressure side to the minimum pressure on the suction side within very short distance. It also shows that the stagnation point is nearly independent of the attack angle while the magnitude of the minimum pressure peak increases significantly with attack angle. Thus, the greater the attack angle the greater the pressure gradient. It is instructive to compare Fig. 2 (a) with Figs. 2 (b) and (c). The positive pressure peak is little affected by cavitation while the negative pressure peak is greatly affected. This is because the negative pressure peak occurs very close to the cavity surface, and its magnitude roughly reflects the cavity pressure and the cavitation number. At smaller cavitation number, i.e. σ = 0.5, the pressure distribution on the suction side is flat and nearly independent of attack angle, a sharp contrast to the noncavitating case.
1% chord length
o
x
Fig. 1 Coordinates and grid system
Computational Results Pressure and velocity distributions near the nose
1
Figures 3 (a), 3 (b) and 3 (c) show the total velocity (speed) distribution on the same vertical line for the two attack angles and the three flow conditions. Other than the fact that velocity and pressure are inversely related, the trend described for pressure distribution is roughly applicable to the velocity distribution.
(a) Non-cavitating flow
(a) Non-cavitating flow
(b) Cavitating flow,
σ
=1.0
(b) Cavitating flow,
(c) Cavitating flow,
σ
σ
= 1.0
= 0.5
Fig. 2 Time-averaged pressure distribution at 1% of the chord length ahead of the hydrofoil leading edge at 6 and 8 degrees angle of attack, respectively
2
(c) Cavitating flow,
σ
= 0.5
(b) Cavitating flow,
σ
=1.0
(c) Cavitating flow,
σ
=0.5
Fig. 3 Time-averaged total velocity distribution at 1% chord length ahead of the hydrofoil leading edge at 6 and 8 degrees angle of attack, respectively Figure 4 shows time averaged stream wise velocity distribution for non-cavitating and cavitating conditions. The stream wise velocity one chord length below is nearly undisturbed (point A of Fig. 4a) but, the stream wise velocity one chord length above is significantly greater than the free stream velocity (point B of Fig. 4b). The stream wise velocity changes sharply near the nose where pressure also changes sharply. Fig. 4 (a) shows that the flow is disturbed more on the suction side of the hydrofoil than the flow on the pressure side. It is interesting to point out that the stream wise velocity ahead of the stagnation point is smaller when the attack angle is smaller. It is also interesting to note that the streamwise velocity becomes more symmetrical as the cavity size increases. It indicates that the cavity increases the blockage effect on the cavity side and pushes the flow toward the pressure side.
B
A
Fig. 4 Time-averaged streamwise velocity distribution at 1% of the chord length ahead of the hydrofoil leading edge at 6 and 8 degrees angle of attack, respectively Figure 5 shows the time averaged vertical velocity distribution on the same vertical line that is 1% chord upstream of the nose. The results shown in Fig. 5 (a) for non-cavitating case are somewhat surprising. The maximum vertical velocity located near the nose is even greater than the free stream velocity indicating very large gradient. The vertical velocity is positive for the whole region of y>0. Only in a small region of 0.5
