Numerical prediction of the flow past a 2-D planing plate at low Froude number

• Flow past a 2D planing plate solved using CFD for varying speed and angle of attack.
• Results compared to linearized potential flow to determine when assumptions are invalid.
• At low Froude number and high angle of attack nonlinear effects are important.
• Potential-flow method accurate for angle of attack <10°<10° and Froude number >0.8>0.8.
• Wave breaking limit found at constant immersion-based Froude number of 2.75.

The problem of a two-dimensional planing flat plate is studied using a nonlinear CFD solver for varying Froude number and angle of attack. This work extends several classical works, which typically use potential-flow assumptions and either assume linear free-surface and body boundary conditions or ignore gravitational effects. In the current study, the effects of viscosity and free-surface nonlinearity are studied via quasi-steady CFD calculations. The objective is to determine the regimes in which the linearized potential-flow assumptions become invalid and nonlinear methods must be used. The results show that nonlinear and viscous effects are important when the angle of attack is greater than approximately 10° and when the Froude number based on the initial immersed length is lower than 0.8. In addition, the unsteadiness limit due to wave breaking is found to occur for a nearly constant immersion-based Froude number of approximately 2.75.