Research and application of 2-D water entry simulation (constant velocity)

Transcription

1 Research and application of 2-D water entry simulation (constant velocity) College of Shipbuilding and Engineering Harbin Engineering University Zhu Xin Supervisor: Prof. Duan Wen-yang 1

2 Background of Research Fig.1 2D+t theory When the planing craft passes through an Earth-fixed plane, the problem is similar to 2D water entry of a body with changing form and constant downward velocity Usin(τ).. U=ship speed, τ=trim angle (rad) 2

3 Background of Research 2D+t theory: Analogy of 3-D problem to 2-D water entry problem. Restricted by two conditions: 1. Slender hull 2. High speed Tradition: The concept of the 2D+t approximation was proposed by Munk (1924) in his slender body theory for airships The idea was applied to slender planing surfaces by Tulin (1957). The effect of gravity was neglected in his study.... (3) Faltinsen(2005) <hydrodynamics of high-speed marine vehicles > 3

4 Simulation of 2-D Water entry Fig. 2 The coordinate system and definitions The water is assumed inviscid, incompressible, irrotational,, the gravity is neglected 4

5 Simulation of 2-D Water entry 1. The earliest analytical methods was presented by Von Karman and Wagner in 1930ies. 2. Dobrovol skaya derived an analytic solution of wedges entry problem by taking advantage of the simplicity of the body geometry. 3. Zhao et al.(1993) solved the problem numerically using BEM.Ignored the near-field flow at the water intersection. And applied to arbitrary hull section shapes including the case of hard chine. 4. CFD et al. The simulation model we used is based on the MLM, (Alexander Korobkin, 2004 ). The MLM improved the classical Wagner theory by taking account the higher orders in the Bernoulli equation. We applied the MLM to wedge with hard chine, and the flow separation from the chine was taken into account. 5

6 MLM (Modified Logvinovich Model) No flow separation!! Fig. 3 6

7 MLM (Modified Logvinovich Model) 1. Wedge section 2. Constant velocity V f(x)= x *tan tanβ h(t) = Vt 7

8 Finite width wedge-section entry force with constant velocity Fig. 4 8

9 Stage 1: before the chine immersion No flow separation, follow the (4)~(7) 9 Fig. 5 the integration region of positive pressure before the flow separation and the value of ξ

10 Stage 1: before the chine immersion Table 1 the total vertical force F/ρV3t Deadrise angle (deg) MLM BEM (Zhao&Faltinsen) Similarity solution (Xu Guodong) _

11 Stage 2: after the chine immersion Introduce fiction body surface after flow separation 11

12 Comparison with fully nonlinear solution results 12

13 Comparison with experiments (a) β=5, v=0.24m/s, (b) β=10, v=0.48m/s, (c) β=15, v=0.48m/s (d) β=15, v=0.72m/s, (e) β=30, v=0.72m/s, (f) β=45, v=1.19m/s. : T.Tveitnes et al.(2008)experimental data : Simulations 13

14 Advantage of the simulation model 1. Less time-costing 2. The influence of flow separation is taken into account 14

15 Application (prismatic hull) the influence of transom to the lift contribution the dynamic free surface boundary condition states that the pressure is continuous through the water surface. So the pressure should be atmospheric at the transom. The 2D model is overestimate the pressure near the transom. 15

16 Hydrodynamic lift force of prismatic planing hull 16

17 Running attitude in calm water Prismatic planing hull in which all forces pass through COG. N is the force due to hydrodynamic pressures acting on the wetted hull. This has a vertical component F Lβ Mg= vessel weight, and a longitudinal component T = thrust from propulsion unit, R V = viscous frictional force on the hull (Savitsky 1964). Table 2 The parameters of simulation models Model C Δ =Δ/ρB3 LCG (%L) (L/B) deadriseang le (deg)

18 Running attitude in calm water 18

19 Time domain simulation of palning vessel in regular head waves Definition of the motion degrees of freedom heave, η 3, and pitch, η 5, (positive bow down). The XZ-system is a local inertial system and the x 1 x 3- system is body fixed. 19

20 Time domain simulation of palning vessel in regular head waves (14) the hydrodynamic force of section is formally expressed as the time rate of change of momentum. The vector of relative velocity between hull and water is defined by where Φ w is the undisturbed incident wave potential, V is forward peed, η and its time derivative are hull position and velocity respectively. The subscripts refer to the cause of velocity: to wave, forward speed and hull motion. (15) (16) In 3 direction still need to add buoyoncy and Froude-Kriloff forces 20

21 Time simulation of palning vessel in regular head waves In the x 3 direction the time rate of change of momentum can written as (17) where the first term is modelled as where T is the section draught whose variation with time, the terms in the bracket indicates the relative velocity The second term is developed as 21

22 Time simulation of palning vessel in regular head waves In consistence with the 2-dimensional approach the section forces are expressed in hull-fixed coordinates. Equations of motions, implicit in time, is set up as n+1 n+1 n+1 ( M A) η = F( η, η...) + (18) (18) 22

23 Captive model test in regular head waves Principal captive test set-up. Ta is the draught at transom, τ the trim angle and a is the amplitude of the incident wave Table 3 the conditions of captive model test β(deg) 30 B(m) 0.2 τ(deg) 5 L(m) 1.2 T a (m) 0.065; 0.05 U m/s 3.2; 3.7 Wave amplitude 2.6~2.8cm Wave frequency 1hz 23

24 Captive model test in regular head waves : experiments : simulations 3.7m/s, Ta=0.065m, a=0.028m 3.7m/s, Ta=0.05m, a=0.028m 3.2m/s, Ta=0.065m, a=0.026m 3.2m/s, Ta=0.065m, a=0.027m 24

25 Motion response in regular head waves Wave condition: Table 4 Fridsma s Model A (1969) Deadrise angle B L/B C Speed ratio LCG(L) 20 9 inch

26 Motion response in regular head waves Wave condition: Fridsma s Model A (1969) 26

27 Motion response in regular head waves Heave phase of A Pitch phase of A 27

28 Motion response in regular head waves Table 5 The parameters of model B Deadrise angle B L/B C Speed ratio LCG(L) 20 9 inch Heave phase of B Pitch phase of B 28

29 Conclusions 1. The constant velocity of wedge section with hard chine is investigated. And the flow separation was taken into account. The agreement between the simulations and experiments is generally good. 2. The running attitude in calm waters and motion response in head waves of planing vessel is investigated. Benefit from the accurate and effective 2-D water entry simulation, the results are satisfactory. Next work in the future: 1. apply to arbitrary hull section water entry problem with flow separation 2. More accurate treatment of the near transom pressure 29

30 Thank you! 30