Wake of an accelerating foil in stratified environment
M.Sc. thesis seminar of Hadar Ben Gida, supervised by Alex Liberzon (Tel Aviv University) and Roi Gurka (Ben Gurion University) , performed at the Turbulence Structure Laboratory
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 3/27 Introduc.on Ø Flows with a background density gradient (increase in density with depth) Ø For example, flows in the ocean thermocline layer Ø Underwater vehicles operate most efficiently in the thermocline Atlantic ocean characterization Flow types in the ocean
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 4/27 Introduc.on Ø Studied behind towed spheres and cylinders (Lin and Pao 1979; Boyer 1989; Chomaz 1993; Spedding 1996) ) 10 ( Re 3 O D U = = ∞ ∞ ν ) 1 ( O ND U Fr = = ∞ ∞ dz d g N ρ ρ − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ sec rad Ø Stratification effect ‘pancakes’ Wake evolution of a sphere in a stratified medium shown from above (Spedding et al. 1996) Stratified wake evolution behind a body
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 5/27 Introduc.on Ø Two perspectives: • Body is held fixed and the flow accelerates • Body accelerates in stagnant fluid Ø For accelerating wings: (Freymuth 1985) (Sarpkaya 1991) ν 5 . 1 5 . 0 Re c a a = ∞ ∞ = t U c A p U∞ - Final steady velocity of the wing at the end of the acceleration period t∞ - Time at the end of the acceleration period
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 6/27 Research Goals Engineering Perspective: Underwater vehicles Ø Commercial - make detailed maps of the seafloor for oil gas industry Ø Military - surveillance and monitoring missions Ø Research - measuring the ocean thermocline layer properties Tend to accelerate/decelerate during their missions! Fluid Mechanics Perspective: How buoyancy forces affect the initial growth of von Kármán vortices behind a hydrofoil accelerated from rest?
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 11/27 Experimental Setup Late trigger case t = 5.1 sec Early trigger case t = 3.2 sec An example of the PIV images that were taken during the experiments of fresh water with two different triggers; late trigger/wake and early trigger/wake
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 12/27 Experimental Setup 32X32 pixels2 interrogation window with 50% overlap 20cm 50cm 35cm 6cm 2.9 cm 14cm 10cm Camera Field of View PIV Analysis Area 5cm 7.5cm 7.5cm 8cm 18cm Fluid level Hydrofoil location at t=0sec Hydrofoil location when PIV images were taken Aquarium
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 14/27 Experimental Setup ρ(y) x Aquarium Tank 1 Tank 2 Fresh Water C1 = 0 M V = 15 L C(t) V(t) NaCl Solution C(t=0) = 0.5 M V(t=0) = 11 L q1 q2 = 2q1 V-1 V-3 V-2 H = 20 cm L = 50 cm W = 20 cm ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⋅ ⋅ + = ) 0 ( 2 ) 0 ( ) 0 ( 1 V C C y A C C y W L A ⋅ = Ø Modified Oster method min / 0 . 1 1 L q = min / 5 . 0 2 L q =
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 17/27 Results ∑ = ∞ ∞ = n i avg i U n U 1 , 1 300 , 5 Re = ∞ 0 . 2 = ∞ Fr sec / 0 . 10 , cm U avg = ∞ 07 . 0 = p A 400 , 1 Re = a 1 sec 1 . 1 − = N 2 sec / 5 . 1 cm aavg = ∑ = = n i i avg a n a 1 1
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 18/27 Results ωz c/U∞ x/c=0 x/c=7.5 Hydrofoil at rest Hydrofoil at U∞ Laminar wake (Re=9,000) behind a NACA 0012 airfoil at 0o angle of attack as being visualized by a dye (Neuhart and Pendergraft 1988) Water - late
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 19/27 Results ωz c/U∞ x/c=0 x/c=7.5 Hydrofoil at rest Hydrofoil at U∞ Water - late ωz c/U∞ x/c=0 x/c=7.5 Hydrofoil at rest Hydrofoil at U∞ Stratification - late
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 20/27 Results Ωz c/U∞ x/c=0 x/c=7.5 Hydrofoil at rest Hydrofoil at U∞ Ωz c/U∞ x/c=0 x/c=7.5 Hydrofoil at rest Hydrofoil at U∞ ∑ = = Ω N i i z z y x N y x 1 ) , ( 1 ) , ( ω N - No. of PIV images Water - late Stratification - late
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 21/27 Results Local normalized streamwise velocity profiles (u’/U) of the ensemble wakes behind a hydrofoil accelerating through water and stratified layer (Re∞ =5,300). Squares - water; Asterisks - stratification x/c=0 Hydrofoil at U∞ Hydrofoil at rest ) ( ) , ( ) , ( ' x U y x u y x u + =
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 22/27 Results dy U u U u c x c y y ∫ = = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = 2 0 ' 1 ' 1 ) ( θ Hydrofoil at U∞ Water (late) Stratification (late) Water (early) Stratification (early) Normalized momentum thickness with error bars along the ensemble wakes behind a hydrofoil accelerating through water and stratified layer (Re∞ =5,300)
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 22/27 Results dy dv dx du dx dv dy du y x Swirl ci − = = ) , ( λ ⇒ ∇ ) det( u 0.60 0.70 0.80 0.90 1.00 1.10 1.20 4.00 4.50 5.00 5.50 6.00 6.50 7.00 y/c x/c Water Stratification Vortices positions in the wake behind a hydrofoil at Re=5,300 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 (b/Re∞ )·104 [cm] x/c Water Stratification Vertical distance between vortex cores, b, normalized to the steady state Reynolds number (5,300) in the wake behind a hydrofoil
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 23/27 Results Hydrofoil rest position for late wakes Hydrofoil at U∞ Hydrofoil rest position for early wakes 2D-NW NEQ 2D-FW Stratification (late) Stratification (early) Phase I Phase II Phase III Normalized momentum thickness with error bars along the ensemble wakes behind a hydrofoil accelerating through a stratified layer (Re∞ =5,300; Fr∞ =2.0)
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 24/27 Conclusions Ø Stratification effects on the wake (compared to water): • Vortices being stretch • Lower spanwise vorticity values • Less deficit and vertical extent of the wake • Relatively short stratified wake life cycle DRAG reduction! Higher efficiency for accelerating underwater vehicles Smaller “finger tips”
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 25/27 Future Work Ø Change angle of attack (AoA) – how lift is being manifested by stratification? Ø Repeat the experiments at higher accelerations Ø Characterize the wake of a hydrofoil connected to a self-propelled body
Experimental Setup Results Conclusions Future Work Seminar -‐ Stra.fied Wake Behind an Accelera.ng Hydrofoil -‐ Hadar Ben-‐Gida 07/11/12 27/27 Faculty of Engineering Department of Mechanical Engineering Faculty of Engineering School of Mechanical Engineering
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