Refine the mesh and improve the mesh quality

Open AccessArticleA Simple Approach to Estimate the Drag Coefficients of a Submerged Floater *📷byYuval Hoffman,Liav Nagar,Ilan ShacharandRoee DiamantHatter Department of Marine Technologies, University of Haifa, Haifa 3498838, Israel*Author to whom correspondence should be addressed.Sensors 2023, 23(3), 1394; https://doi.org/10.3390/s23031394Submission received: 3 January 2023/ Revised: 19 January 2023/ Accepted: 23 January 2023/ Published: 26 January 2023(This article belongs to the Special Issue Advanced Sensing Technology for Ocean Abstract The calculation of the drag force is a fundamental requirement in the design of any submerged system intended for marine exploration. The calculation can be performed by analytic analysis, numerical modeling, or by a direct calculation performed in a designated testing facility. However, for complex structures and especially those with a non-rigid design, the analytic and numerical analyses are not sufficiently accurate, while the direct calculation is a costly operation. In this paper, we propose a simple approach for how to calculate the drag coefficient in-situ. Aimed specifically at the complex case of elastic objects whose modeling via Computer-Aided Design (CAD) is challenging, our approach evaluates the relation between the object’s speed at steady-state and its mass to extract the drag coefficient in any desired direction, the hydro-static force, and, when relevant, also the thruster’s force. We demonstrate our approach for the special case of a highly complex elastic-shaped floater that profiles the water column. The analysis of two such floaters in two different sea environments shows accurate evaluation results and supports our claim for robustness. In particular, the simplicity of the approach makes it appealing for any arbitrary shaped object.drag force; hydrostatic force; thruster force; submerged floatersKeywords:

1. Introduction Floaters are a valuable tool for probing the water column. They can provide water current estimation [1] by tracking their drift motion over time, characterize internal waves [2] by observing spatial changes in the depth of the bathymetrical layer, or monitor changes in the marine environment by measuring temperature profiles over time with fine resolution [3]. Examples of floaters include profiling floats such as the Argo floats [4], which traverse the water column from the seabed to the sea surface for conductivity–temperature–depth (CTD) measurements, and Lagrangian floats, which are designed to drift with the water current [5]. For both types, calculating the drag coefficient is important information for improving the system design. Floaters are also used to evaluate the water current’s properties [6]. Here, the analysis of the floater’s drag is essential to filter out friction forces from the measurements. The drag is an attribute of how well the float drifts in the water current and is a function of the float’s shape and size. A perfect, rounded, neutrally buoyant float with a narrow edge on its endfire will sense little resistance as it traverses through the water, while a square float with a large surface facing the drifting direction will sense high friction-like resistance.The calculation of the drag coefficient of a submerged object is performed either by analytical modeling, using numerical finite-elements simulations, or directly in designated testbeds. The first analytical expression to calculate the drag coefficient is the seminal work by Jean le Rond d’Alembert in 1752, who calculated the drag force of a flow acting on a cylinder shape object using the potential flow theory (incompressible and inviscid, for a Reynolds number Re >>1

). The analysis yielded a zero drag force, which was in contrast to the experiments made. This mismatch is referred to as the D’Alembert’s paradox and is due to neglecting the water boundary layers. The later theoretical work of Munk and Glauert in the 1920s [7] presented the base for thin airfoil theory, which uses potential flow theory to calculate the drag and lift force on a thin wind. For Re