Scaling the Roughness of Submarine Non-Skid Coatings

A portion of the upper deck surface of a submarine can be coated with roughness for crew safety when walking on the hull. The roughness factor for the non-skid coating on a full scale submarine is very large, on the order of 400 under typical ship operation conditions. Boundary layer development, flow separation, cross flow drag, hull surface pressure, and ship motion may be modified by the presence of this coating during turning maneuvers. Free-running model submarines (FRM) are routinely employed by the Naval Surface Warfare Center to characterize submarine maneuvering behavior, and the application of an appropriately sized non-skid coating to the model is required for fidelity of model maneuvering experiments. Three methods to scale the coating have been investigated, and conventional geometric scaling and wall shear velocity scaling methods were found to be inadequate. A new scaling method termed the momentum boundary layer thickness (MBLT) method has been developed. This method relates the cross flow drag on the FRM with that on the full scale vehicle. Boundary layer velocity profiles on an axisymmetric body at model and full scale Reynolds numbers have been computed by a RANS code. Velocity profiles encountered by the full scale non-skid coating are found to match well with those developed on the FRM with roughness sized using the MBLT method. The scaled roughness size compares favorably with two empirically determined roughness sizes that have been previously used on FRM models that have shown good correlation with full scale maneuvering data.