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Application of data assimilation for parameter correction in super cavity modelling

The super cavity model describes the very fast motion of body in water. In the super cavity model the drag coefficient plays important role in body's motion. In some references this drag coefficient is simply chosen by different values in the interval 0.8-1.0. | Tạp chí Khoa học và Công nghệ 54 (3) (2016) 430-447 DOI: 10.15625/0866-708X/54/3/6566 APPLICATION OF DATA ASSIMILATION FOR PARAMETER CORRECTION IN SUPER CAVITY MODELLING Tran Thu Ha1, 2, 4, *, Nguyen Anh Son3, Duong Ngoc Hai1, 2, 4, Nguyen Hong Phong1, 2 1 Institute of Mechanics -VAST – 264 Doi Can and 18 Hoang Quoc Viet Hanoi, Vietnam 2 University of Engineering and Technology -VNU,144 Xuan Thuy, Hanoi, Vietnam 3 National University of Civil Engineering, 55 Giaiphong Str., Hai Ba Trung Hanoi 4 Institute of Science and Technology -VAST 18 Hoang Quoc Viet Hanoi, Vietnam * Email: tran_thuha1@yahoo.com Received: 27 July 2015; Accepted for Publication: 2 May 2016 ABSTRACT On the imperfect water entry, a high speed slender body moving in the forward direction rotates inside the cavity. The super cavity model describes the very fast motion of body in water. In the super cavity model the drag coefficient plays important role in body's motion. In some references this drag coefficient is simply chosen by different values in the interval 0.8-1.0. In some other references this drag coefficient is written by the formula k = CD 0 (1 + σ ) cos2 α with σ is the cavity number, α is the angle of body axis and flow direction, CD 0 is a parameter chosen from the interval 0.6-0.85. In this paper the drag coefficient k = k1CD 0 (1 + σ ) cos 2 α is written with fixed CD 0 = 0.82 and the parameter k1 is corrected so that the simulation body velocities are closer to observation data. To find the convenient drag coefficient the data assimilation method by differential variation is applied. In this method the observing data is used in the cost function. The data assimilation is one of the effected methods to solve the optimal problems by solving the adjoin problems and then finding the gradient of cost function. Keywords: data assimilation, optimal, Runge-Kutta methods. 1. INTRODUCTION When slender body running very fast under water (velocity is higher than 50 m/s) the cavity .