Modelling of Super Cavitation on Wing using Partial nonlinear model of Boundary Element Methods

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-76395 mme.modares.ac.ir 3 * - - -3 fard_m@um.ac.ir 9775- *.. -.... 66.

Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran 3- Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Iran * P.O.B.

1 mme.modares.ac.ir 3 * fard_m@um.ac.ir * : 395 : : Modelling of Super Cavitation on Wing using Partial nonlinear model of Boundary Element Methods Javad Jafari, Mahmood Pasandide Fard *, Maziar Changizian 3,- Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran 3- Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Iran * P.O.B , Mashhad, Iran, fard_m@um.ac.ir ARTICLEINFORMATION ABSTRACT OriginalResearchPaper ReceivedMarch6 Accepted3May6 AvailableOnline3July6 Keywords: Super cavity Kutta condition Boundary Element Method (BEM) Wing.. In this paper simulation of steady super cavitation phenomenon has been considered by using partial non-linear model of Boundary Element Method(BEM).The grid mesh used is fixed and the strength of dipole and source are constant on each element. With the assumption of a partial non-linear model the cavity condition is applied on the body with the assumption that cavity height is low. Thus there is not any calculation on the cavity surface, but it is restricted to only the panels on the body surface. Cavitation number is known at first and the cavity length is determined in every iteration. When the lengths obtained in two successive iterations are very close to each other it is assumed to be the answer. Based on this method two Kutta conditions including Morino condition and Iterative Pressure Kutta Condition(IPKC) are studied to satisfy the wake surface condition. The application is a wing with NACA66 section. IPKC condition compared to Morino one needs higher computational costs, but on the other hand leads to more accurate results. It has been shown that simulation of the flows with super cavitation over wing leads to a pressure difference at the trailing edge of each strip if Morino s Kutta condition is used. While if Iterative Pressure Kutta Condition is used the results are satisfactory. Comparison of the results shows that this method leads to very accurate predictions for the behavior of flows with cavitation, while significantly lower computational cost is required if the simple cavity closure condition is used. -. Pleasecitethisarticleusing: : J. Jafari, M. Pasandide Fard, M. Changizian, Modelling of Super Cavitation on Wing using Partial nonlinear model of Boundary Element Methods, Modares Mechanical Engineering, Vol. 6, No. 7, pp. -, 6 (in Persian)

2 .. [8] [7]..[9]...[9] -.[] [] []. [3]. -.[4].[5] [6] Re-entrantjet 3 Partialynon-linear 4 Pressurerecovery []. ().. []. [6,5] [4] [3].. (987) Fullynon-linear

3 lim = (7).. = (7) (8). ()... (3) = +.[3] (9) cos + sin + in 3 ( =). (6).(. =).[] () () cos + cos = sin. (9) () - - (). ± ± = [] () ±..[] = () () ( ) ) (, ) = () = () ) () (, ) = + (, ) () = + - (3) (3). = = (5) (6) (3) (6) + + = (). (4). Fig. Boundary of the flow domain and reference surface. D view

4 ( ) 4, () = BC B ( + + ) W CW (9) : ( ) (, ) = () (, ) (, ) = = (8) () () () (() ) (8). - ( ) (). - [3] (8). ()(, ) = () (, ) (, ) (,) (, ) (, ) (, ) + (, ) (, ) () () ) =,..., : =,..., : =,..., : =,..., : :. =.[7] (3) = = C =.[7] (4) (5) (6) C (4)..(5 ) (4) (6) (4) (4).[7] = ( ) (7) - Error! Reference source not found...[7] Fig. Discretization parameters of three-dimensional wetted flow around the geometry model [] [] - 3 x :[] (, ) (, ) ()(, ) = (, ) (, ) B C (, ) (, ) + (, ) (, ) (8)

5 = ) ).5 Fig. 3 Pressure distribution for mid span section of 3D wing with NACA66 section at. = 5 for different number of elements a)all over b) Optional point 66 3 (a) (b) ( ( N= 4x N= 4x N= 5x N= 5x N= 8x N= 4x N= 4x N= 5x N= 5x N= 8x = 5 (, ) (, ). () ()(, ) = (,) + (, ) () () (, ) (, ) (, ) (, ) (, ) (, ) () (, ) () = = (3) (3) (4) () = (, ) = (4) ) (4) (3) (. (3). (4) () ()(, ) + (, ) (, ) + (, ) (, ) (5) ( (),, ) = ( (), ) ( (6) =.[] (6)

. 7 =5 -C p NACA66 Fig. 5 Pressure distribution for mid span section compared with experimental data [8]. 3D wing with NACA66 section at = 5 66 5 -C p Current Study Experimental [8] Fluent Software.

6 . 7 =5 -C p NACA66 Fig. 5 Pressure distribution for mid span section compared with experimental data [8]. 3D wing with NACA66 section at = C p Current Study Experimental [8] Fluent Software = 5 [8] Current Study Experimental [8] Fluent software Fig. 6 Pressure distribution for tip span section, compared with experimental data [8]. 3D wing with NACA66 section at = = 5 [8] 3 = 5 = 5.. = [8] ) (a) Wake Length=C(m) Wake Length=4C(m) Wake Length=6C(m) Wake Length=8C(m) Wake Length=C(m) Wake Length=C(m) Wake Length=4C(m) Wake Length=6C(m) Wake Length=8C(m) Wake Length=C(m) Fig. 7 Pressure distribution. 3D NACA66 hydrofoil = 5 = ) Fig. 4 Pressure distribution for mid span section. 3D NACA66 hydrofoil. = 5 for different number of elements a)all over b) Optional point 66 4 (b) ( ( =

7 = 5 Table Comparison of two Kutta conditions for = 5 without cavitation NACA66 =.6 =4. [6] =.68 = ) (a) Fig. 9 Cavity lengths along the span for 3D wing with NACA66 section at = 4, =.6 for different chord-wise elements 66 9 ( =.6 = 4 ) ) (b) Fig. 8 Pressure distribution.at mid-span on 3D wing with NACA66 section at = 5, with and without IPKC conditions a)all over b)t.e region 8 ( ( ( = 5 66 )

. 3 9 =4 - =.6 4 Fig. 3 Pressure distribution over the 3D wing with NACA66 section at = 6, =.68 = 6 )66 3 3 ( =.68 L C /C.35 N =x N =x4.3 N =x6 N =x...5..4.6.8 Y/C Fig.

Cavity length ( ) on 3D rectangular wing at = 4 and =.6 ( =.6 = 4 ).9.8.7.6 L C /C - ) Without IPKC With IPKC..4.6.8 (a).4.3.. Experiment [6] Current Study without IPKC -.

8 . 3 9 =4 - =.6 4 Fig. 3 Pressure distribution over the 3D wing with NACA66 section at = 6, =.68 = 6 ) ( =.68 L C /C.35 N =x N =x4.3 N =x6 N =x Y/C Fig. Cavity length along the span on 3D wing with NACA66 section at = 4, =.6 for different spanwise elements 66 ( =.6 = 4 ) Fig. Cavity length ( ) on 3D rectangular wing at = 4 and =.6 ( =.6 = 4 ) L C /C - ) Without IPKC With IPKC (a) Experiment [6] Current Study without IPKC Y/C Fig. Cavity lengths along the span for 3D wing with NACA66 section at = 6 and =.68. compared with experiments [6] [6] =.68 =

9 L C /C.5 Fig. 5 Cavity length ( ) on half of the rectangular wing at = 4 and =.6 for with and without IPKC. 5 L C /C.. ( =.6 = 4 ) Fig. 6 Super cavity length ( ) on half of rectangular wing.at = 8 and = for with and without using IPKC 6 ( = = Y/C Dang[9] Current Study Without IPKC Current Study With IPKC Vaz[] Current Study Without IPKC Current Study With IPKC Y/C ) 6 8 ) (b) Fig. 4 Pressure distribution.at mid-span on rectangular wing at = 4, =.6 with and without using IPKC a)all over b)t.e region =4 ) 4 ( ( ( =.6 =.6 = 4 Table Comparison of two Kutta conditions in modeling of partial cavitation at = 4 = (b ). 5 [9] 5. - [] = Without IPKC With IPKC =8. 6 [] 76395

=8 8. =...5. 6 ). ( - 5 66.. Fig. 7 Super cavity length ( ) on the rectangular wing at = 8 and = for with and without IPKC.

10 =8 8. = ). ( Fig. 7 Super cavity length ( ) on the rectangular wing at = 8 and = for with and without IPKC. 7 ( = = 8 ) ) (a) 3 = = 8 Table 3 Comparison of Kutta conditions in current study. = 8 = ) Fig. 8 Pressure distribution.at mid-span of rectangular wing at = 8, = for with and without IPKC. a)all over b)t.e region 8 =8 (b) ) ( ( ( = 76395

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