Investigation of Scaling Effects in Submarine Flows

Abstract

The simulation of the flow past a ship poses a particular challenge because of the size of the ship and the resulting large values of dimensionless parameters such as Reynolds number. Computational fluid dynamics (CFD) can simulate these flows, but validation data at large Reynolds number are lacking. Experimental measurements were made on a smallscale model of length 0.286 m and a large-scale model of length 7.03 m. Drag coefficients of both models were measured. Thrust coefficients for a propeller on the large-scale model were measured over a range of advance ratio. Computational simulations of the flows at both of these length scales were obtained to see how well the solutions agreed with the experimental results over the large change in length scale. This was done to see if the predictions over this change in length scale would provide insight into how well the CFD results would track the flow over a similar-order change in length scale from the LCC model to a full-scale prototype. The experimental and CFD drag coefficients were in reasonable agreement for the small-scale model. For the large-scale model, the computational simulations showed a continuous decrease in the drag coefficient with Reynolds number, which is typical behavior for a flow in which the drag is dominated by skin friction. The large-scale model experiments showed that the drag coefficient leveled off at large Reynolds number, indicating the likely presence of a separated region that would cause the drag to be dominated by pressure forces rather than by skin friction. LDV measurements of the flow at the stern of the large-scale model indicated a small separated region with reversed flow, a region not obvious in the computational results. The computed and measured propeller thrust coefficients were in excellent agreement. It was concluded that a higher resolution grid and solution was probably necessary to capture fully the separated region behind the submarine and accurately predict the drag behavior. This is a not uncommon problem in CFD, where large scale geometries at large Reynolds number require large grids with high resolution to simulate the flow accurately.