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Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction Xiaosong Zhang State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University CMHL Symposium, Shanghai, Dec. 13, 2019

OUTLINE Background and Motivation Bubble Drag Reduction • Development of the bubble flow solver • Bubble drag reduction in turbulent boundary layer Air-Layer Drag Reduction • Steramwise characteristics • Air layer in a cavity Conclusion and Future works Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

OUTLINE Background and Motivation Bubble Drag Reduction • Development of the bubble flow solver • Bubble drag reduction in turbulent boundary layer Air-Layer Drag Reduction • Steramwise characteristics • Air layer in a cavity Conclusion and Future works Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Background and Motivation Reducing the fuel consumption of ships has always been an important goal in ship design and management, especially against the background of the shipping industry recession in recent years. Total orders of ship all over the world Number of ships Number of ships Years Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Background and Motivation Year of ship Energy saving Phases built to the baseline 0 2013-2015 0 1 2015-2020 10% 2 2021-2025 20% Most of the Oil tankers, Gas carries and Bulk carriers are far away from the requirement of phase-3. 2025- 3 30% (Maybe 2022) Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Background and Motivation Propulsion Wake optimization in front of propeller Wake Equalizing Duct Energy Saving Device Energy recovery behind propeller Rudder Ball Vortex elimination Propeller Boss Cap Fins Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Background and Motivation Hull form optimization Ship Hull Drag Reduction Super-hydrophobic coating Techniques Air lubrication Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Background and Motivation Bubble Drag Reduction Porous plate Bottom plate of ship  Submillimeter microbubbles are produced through porous plates  Microbubbles should enter the turbulent boundary layer Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Background and Motivation Air-Layer Drag Reduction  A complete layer of air is formed to adhere to the bottom of the ship with relatively large air injection flow rate.  Separate most of the bottom plate directly from water, reducing the wetted surface area Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

OUTLINE Background and Motivation Bubble Drag Reduction • Development of the bubble flow solver • Bubble drag reduction in turbulent boundary layer Air-Layer Drag Reduction • Steramwise characteristics • Air layer in a cavity Conclusion and Future works Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Basic numerical method Euler-Lagrange method is used to model the flow mixed with a large number of discrete bubbles.  The liquid flow is solved on the grid based on Euler Euler 网格 framework.  The motion of each bubble is tracked individually by 气泡 solving the kinematic equation based on Lagrange framework. Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Main modules in the solver Bubble Flow Solver Fluid Solving Two-way Coupled Bubble Solving Module Module Module Hydrodynamic Coupled Source Forces Term Tracking Coalescence Collision Breakup Module Module Module Module Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Governing equation for bubble motion: dv      m f f f f f D L P G C dt      3 mC m m Du                  D l l  l  u v u v C u v u mg 1 f    L C   4 d Dt b b b Pressure Drag Lift Gradient Buoyancy Collision force Drag coefficient C D and lift coefficient C L are obtained by models Drag coefficient: Tomiyama drag model:       16 48 8 Eo   0.687     C max min 1 0.15Re , ,  D     Re Re 3 Eo 4 Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Governing equation for bubble motion: dv      m f f f f f D L P G C dt      3 mC m m Du                  D l l  l  u v u v C u v u mg 1 f    L C   4 d Dt b b b Pressure Drag Lift Gradient Buoyancy Collision force Drag coefficient C D and lift coefficient C L are obtained by models Lift coefficient:          min 0.288tanh 0.121Re , f Eo Eo 4   Tomiyama lift model: d d  C =   L     f Eo 4 Eo 10.7 d d       3 2 f Eo 0.00105 Eo 0.0159 Eo 0.0204 Eo 0.474 d d d d Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Collision modeling: Bubble collision is modeled by a elastic soft sphere model. A non-linear collide force model is adopted. Elastic force 2           F 18.5 2.0   elastic  R  eq Viscous force Heitkam S , et al. A    simple collision model 0.5     3 R R 12 for small bubbles[J].         eq eq l F uC 0.34 0.0002 4.0 3.0 R Journal of Physics:      viscous bc a 2 R h h Condensed Matter,     eq 0 0 2017, 29(12):124005. Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Model Validation —— Microbubble Rise Up The rising velocity of single microbubble is in good agreement with the experimental results, which proves the accuracy of the computational hydrodynamic forces on the microbubble. Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Model validation —— Collision with wall The accuracy of collision force calculation is validated by deformation and trajectory of microbubble colliding with a plate obliquely. The numerical results are in good agreement with the experimental data. Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Coalescence & Breakup Critical We number criteria: Film drainage model: 𝑿𝒇 𝒅𝒔𝒋𝒖 = 𝝇 𝒎 𝜺𝒗(𝒆) 𝟑 𝒆 𝝉 Daughter bubble size distribution: 1 𝑔 𝛿 = If two bubbles contact long enough to drain the 𝜌 𝛿 1 − 𝛿 liquid film between them, then coalescence happen Conservation: Position: 𝑄𝑝𝑡𝑗𝑢𝑗𝑝𝑜 𝑑 = 𝑒 𝑏 𝑄𝑝𝑡𝑗𝑢𝑗𝑝𝑜 𝑏 + 𝑒 𝑐 𝑄𝑝𝑡𝑗𝑢𝑗𝑝𝑜 𝑐 Δ𝑦 = 𝑠𝑑𝑝𝑡𝛽𝑑𝑝𝑡𝛾 𝑒 𝑏 + 𝑒 𝑐 Δ𝑧 = 𝑠𝑑𝑝𝑡𝛽𝑡𝑗𝑜𝛾 Δ𝑨 = 𝑠𝑡𝑗𝑜𝛽 3 1/3 3 + 𝑒 𝑐 𝑒 𝑑 = 𝑒 𝑏 𝑠 = 0.6 𝑒 1 + 𝑒 2 𝛽 = 𝑠𝑏𝑜𝑒𝑝𝑛(−𝜌, 𝜌) 3 𝑉 𝑏 + 𝑒 𝑐 3 𝑉 𝑐 𝑉 𝑑 = 𝑒 𝑏 𝛾 = 𝑠𝑏𝑜𝑒𝑝𝑛(0, 2𝜌) 3 + 𝑒 𝑐 3 𝑒 𝑏 Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Bubble breakup: Case design ： Numerical result ： Fluid impact Fluid impact Bubble rise up Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Bubble coalescence: Case design ： Numerical result ： Flow push Flow push the bubbles the bubbles Bubble rise up Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction

Development of the bubble flow solver  Two-way coupling: Governing equations for the liquid phase solving ： 𝜖𝛽 𝑔 𝜖𝑢 + 𝛼 ⋅ 𝛽 𝑔 𝑣 = 0 𝜖𝜍 𝑔 𝛽 𝑔 𝑣 + 𝛼 ⋅ 𝜍 𝑔 𝛽 𝑔 𝑣𝑣 = −𝛼𝑞 + 𝜉Δ𝑣 + 𝜍 𝑔 𝛽 𝑔 𝑕 − 𝐺 𝑞𝑔 𝜖𝑢 where 𝐺 𝑞𝑔 is the coupled force from bubble to liquid, 𝛽 𝑔 is liquid volume fraction in cell. The calculation of these two variable is the key problem in two-way coupled algorithm. Traditionally, the void fraction was defined in each computational cell as the ratio of the total volume of bubbles in the cell by the cell volume: N   16 3 d     i 1 1  f V However, this algorithm is correct only when the bubble diameter is smaller than the grid size. Numerical Simulation of Bubble Drag Reduction and Air Layer Drag Reduction