_Applied_  
_sciences_  
_Article_  
Hydrodynamic Forces of a Semi-Submerged Cylinder  
in an Oscillatory Flow  
[PERSON] **1,2**, [PERSON] **1,2,*, [PERSON] **3**, [PERSON] **1,2**, [PERSON] **1,2** and [PERSON] **4**  
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; [EMAIL_ADDRESS] (H.R.); [PERSON]SS] (M.Z.); [EMAIL_ADDRESS] (Y.X.)  
Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China  
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA; [EMAIL_ADDRESS]  
Department of Marine Technology, Norwegian University of Science and Technology,  
7052 Trondheim, Norway; [EMAIL_ADDRESS]  
Correspondence: [EMAIL_ADDRESS]  
Received: 26 August 2020; Accepted: 10 September 2020; Published: 14 September 2020  
**Featured Application: The present work highlights a novel empirical formula to estimate both mean and fluctuating lift force on a semi-submerged cylinder under oscillatory flow. It greatly avoids the complicated and time-consuming hydrodynamic calculation problem and will be helpful to calculate the hydrodynamic force in the design of relevant marine structures, such as floating collar of fish farming.**  
This work experimentally investigated the performance of hydrodynamic forces on a semi-submerged cylinder under an oscillatory flow. To generate the equivalent oscillatory flow, the semi-submerged cylinder is forced to oscillate in several combinations of different periods and amplitudes. The mean downward lift force was observed to be significant and the fluctuating lift forces show dominant frequency is twice that of oscillatory flow and amplitude that is the same as the mean lift force. Based on this main hydrodynamic feature, a novel empirical prediction formula for the lift forces on semi-submerged cylinder under oscillatory flow is proposed where the lift forces expression is proportional to the square of oscillatory flow velocity. This novel empirical formula directly assigns the fluctuating lift force with frequency twice of oscillatory flow and the amplitude that is the same as the mean lift force. This assignment of empirical lift force formula reduces parameters required to determine a dynamic lift force but is demonstrated to well predict the fluctuating lift force. The lift coefficient can reach 1.5, which is larger than the typical value 1.2 of the drag coefficient for a fully submerged cylinder with infinite depth. Moreover, relationships among hydrodynamic coefficients, Keulegan-Carpenter (KC) number, Stokes number and Froude number are studied. With the increase of KC number, the Froude number has a more significant influence on the distribution of hydrodynamic coefficients. As Froude number is increasing, the drag coefficient shows a nonlinear decay (KC \(<\) 20) but a linear increase (KC \(>\) 20), while the added mass coefficients show a nonlinear (KC \(<\) 20) and a linear (KC \(>\) 20) increase trend. The present work can provide useful references for design of the relevant marine structures and serve as the useful guideline for future research.  
semi-submerged cylinder; oscillatory flow; hydrodynamic force; free surface; empirical prediction