realized in initial outlay, maintenance, and reduced operating cost.

The use of air entrainment to control hydrofoil boats has been attempted with some degree of success by the German design company Supramar in the 1960’s (Gunston, 1970). The highly successful Supramar PT.50 hydrofoil boat used air entrainment to control the lift of both the forward and aft lifting foils. Supramar also used this concept effectively for a number of other hydrofoil boats, from the smaller PT.20 to the larger PT.150. Through venting air over the suction side of the foils, the lift on the hydrofoils was adjusted to control the motions of the vessel. A fully submerged rear foil fitted with separate air-stabilization systems on the port and starboard sides showed that the stabilization reduced the roll response of the ship by 75% in roll (Gunston 1970). This same concept can conceivably be adapted to high speed catamaran ferries.

Previous investigations into ventilated foils dates back to the 1960s and earlier, where the concept was explored by model tests (Lang 1959; Lang et al. 1959). These tests conducted at the US Naval Ordinance Test Station’s (NAVORD) water tunnel on a NACA 0010 (10% thickness) foil indicated significant reduction in lift by varying vent location and air flow rate at a given Reynolds number. The air cavity development was found to be unstable initially, and cavity length varied until the air flow was increased to a critical value. At this critical ventilation number, the cavity closure point shifted to two chord lengths downstream, and the foil was fully vented. Increasing the air flow rate beyond this point was found to produce marginal changes to the foil performance. Reducing the airflow after reaching the critical point also did not appreciably change the lift force, pointing to a hysteresis effect The slope of the lift coefficient—angle of attack curve for an infinite span hydrofoil was found to change from the unvented theoretical value of 2π, to a value close to π, when the vents were successively moved from the trailing edge to about 3% of chord from the leading edge. It was noted that the drag coefficient in a fully vented flow increased to about 150% of the fully wetted value. While a portion of the increase was attributed to tunnel interference effect, it was found that the drag force decreased once the critical ventilation number was reached.

The topic of foil cavitation has been studied extensively in the past, and is not reviewed in this paper. While the mechanisms of occurrence are different for cavitation and ventilation, some flow similarities may be expected, particularly when a long cavity exists behind the foil. Based on this flow similarity, theoretical treatment of cavitating flows may be extended for ventilated foil flows. A linear theory for cambered foils with long trailing cavity at zero incidence and zero cavitation number was developed by Tulin and Burkart (1955). The solution strategy was based on reducing the flow characteristics of the foil and the trailing cavity to an equivalent problem of the classical thin airfoil. Observation of cavitating flows showed that the slenderness ratio of the cavity (ratio of diameter to length of cavity) approached a value of σ/2 (σ −cavitation number) as σ→0 and the trailing cavity shape was elliptic (Tulin, and Burkart, 1955). Comparison with experiments showed that linear theory predicted the length of the cavity to within 5% of the measured value. Tulin and Hsu (1980) developed a theory for foils with short cavity, and were able to include effects of foil thickness in the formulation. Kinnas (1991) extended the linear cavity theory further to incorporate leading edge correction, for foils with cavity initiating close to the leading edge. Results from this theory were found to correlate well with linear theory for cases where cavity starts further from the leading edge.

A theory for potential flow past thin airfoils with ventilation was developed by Fabula (1962), using the open and closed cavity termination models of Tulin (1956). A conformal mapping technique was employed to transform the foil surface to a semi-circle, and the problem solved as a function of cavity inception point and cavity length. Results of this theory applied to vented flat plates are used in this paper. As will be shown later, these results show remarkably close correlation with the experimental results of Lang et al. (1959) and those of FLUENT.

2. Aspects of flow past a ventilated foil

If a foil is ventilated on its suction (low pressure) side, the overall pressure distribution is altered.

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