FEDSM SIMULATIONS OF AN AIR-VENTILATED STRUT CROSSING WATER SURFACE AT VARIABLE YAW ANGLES

Transcription

1 Proceedings of the ASME th Joint US-European Fluids Engineering Summer Conference FEDSM2018 July 15-20, 2018, Montreal, Quebec, Canada FEDSM SIMULATIONS OF AN AIR-VENTILATED STRUT CROSSING WATER SURFACE AT VARIABLE YAW ANGLES Konstantin I. Matveev Washington State University Pullman, WA, USA Miles P. Wheeler Washington State University Pullman, WA, USA Tao Xing University of Idaho Moscow, ID, USA ABSTRACT Hydrodynamic devices intended to produce lift, control actions, or propulsion can be prone to air ventilation when operating near the free water surface. The atmospheric air may propagate to the low-pressure zones around these devices located under the nominal water level. This often leads to performance degradation of hydrodynamic systems. Modeling of air-ventilated flows is challenging due to complex flow nature and many factors in play. In this study, the computational fluid dynamics simulations are carried out for a surface-piercing strut at different yaw angles. At small yaw angles, the strut underwater surfaces remain wetted, whereas at large yaw and sufficiently high Froude numbers the suction side becomes air ventilated. At the intermediate yaw angles, both wetted and ventilated flow regimes are possible, and the existence of a specific state depends on the history of the process. The present computational results demonstrate good agreement with available experimental data. INTRODUCTION Hydrofoils, struts, rudders, and propellers crossing the free water surface or operating in its proximity are often subject to the air ventilation phenomena. In the presence of disturbed water surface and unsteady flow, the atmospheric air may propagate to and accumulate on the suction (low-pressure) sides of these devices. This process often leads to reduction of lift or other desirable forces produced by hydrodynamic elements and hence to degradation of their performance. Moreover, the air ventilation may have unsteady nature resulting in unstable characteristics of lifting and propulsive devices. Extensive experimental studies of ventilation phenomena have been conducted since the 1950 s upon the introduction of hydrofoil boats. Air ventilation was found to be one of the performance limiting factors for these craft, since the penetration of the atmospheric air to low-pressure zones on struts and hydrofoils led to reduced lift capabilities and unstable or history-dependent hydrodynamic characteristics. Straub and Wetzel [1] experimentally investigated ventilation on cylinders and streamlined bodies crossing the water surface. Fridsma [2] tested a ventilation-prone V-shaped hydrofoil with a wedge section at different attack angles and Froude numbers. Breslin and Skalak [3] and Swales et al. [4] described experimental observations of different types of the ventilation inception on vertical surface-piercing struts. These types included the water rupture at the leading edge of the strut, at the tail part, through the tip vortex, via vaporous cavitation, and as combinations of these kinds of the ventilation inception. Well-defined experiments with air-ventilated struts were recently reported by Harwood et al. [5], and their results are used in this paper for validation purposes. Young et al. [6] provided an extensive review of ventilation phenomena on lifting bodies. Modeling of air-ventilation processes is challenging due to complex nature of the associated multi-phase and surface flows, which are often unsteady and exhibit nonlinear dynamics phenomena, such as hysteresis. While the two-dimensional potential-flow solutions and their adaptations to threedimensional cases can be used as approximations for simple geometries [5], designs of more complex practical systems and real-life conditions require higher-fidelity computational fluid dynamics (CFD) simulations. Some CFD studies for specific configurations of hydrofoils and struts prone to ventilation were recently reported [7,8]. Harwood et al. [9] described a CFD study with NFA code for a single test condition with a very large number of numerical cells in the domain, about 50 million in the coarse mesh and about 400 million in the fine mesh. However, more validation studies are certainly needed to gain confidence in the ability of CFD tools, especially with moderate cell counts, to adequately simulate the air-ventilated flows. In this study, we employed CFD program STAR-CCM+, which is often used for simulations in marine hydrodynamics. 1 Copyright 2018 by ASME

2 As benchmark experiments, we selected well-defined data reported by Harwood et al. [5] for a vertical surface-piercing strut tested at different yaw angles in the steady incident flow. Due to limited computational resources, we focused on several steady-state conditions that exhibited drastically different flow regimes. In the experiments, it was observed that the strut s suction side is ventilated at large yaw angles and sufficiently high Froude numbers, while the side walls remain wetted at small yaw angles. For some intermediate yaw angles, both wetted and ventilated flow states are possible, implying the hysteresis effect. These conditions are simulated with CFD and compared below to the test data. The goal of this study is to evaluate the accuracy of using relatively coarse (economical) grid resolutions to predict the force and moment coefficients for the surface-piercing strut and the flow regimes (ventilated vs wetted). SOLVER AND MESHER SETTINGS The finite-volume CFD program employed in this work was STAR-CCM+, version The segregated flow solver with SIMPLE solution algorithm and the second order upwind convection scheme was used [10]. The first-order implicit unsteady stepping was utilized, but only the statistically steady state results are reported here, corresponding to solution times when the time-averaged flow characteristics stopped evolving. The Eulerian multiphase approach involved constantdensity water and air with the fluid properties evaluated at 15⁰C. The volume-of-fluid (VOF) method served as the interface capturing technique. A surface tension model was included. The unsteady RANS approach with the realizable two-layer K-Epsilon model was employed. A number of other turbulence models available in STAR-CCM+ were tried as well, but the K-Epsilon model was found to be the best when modeling the ventilated flow in conditions near the ventilation inception. Because of our goal to use a moderate cell count, we relied on the wall functions with average Y+ values for the nearwall cells being around 50. The time step of about was used, where is the strut chord and is the velocity of the incident flow. Ten inner iterations on each time step were performed during simulations. The strut section geometry was the same as in the experimental study by Harwood et al. [5]. The top and side views of the strut can be seen in Figs. 1 and 2. The strut chord is = m. The numerical domain boundaries are located (with respect to the strut leading edge at the bottom tip) at upstream, downstream, to the port and starboard sides, and to the bottom and top planes. Two plane sections spreading over the numerical domain are shown in Fig. 3. The strut extended up to the top of the domain. The incident flow is aligned with the positive X axis, whereas the Z axis is directed upward perpendicular to the undisturbed free surface. Fig. 1 Top view of the yawed strut with the surrounding mesh shown on the plane corresponding to the undisturbed water level. The incident flow direction is from left to right. Fig. 2 Side view of the strut with the surface mesh. The horizontal line indicates the undisturbed water level. The trimmed mesh, containing predominantly hexahedral mesh, was generated in the numerical domain. It involves refinement based on the user-assigned surface and volumetric controls and increased cell dimensions away from these regions. Some features of the mesh are visible in Figs In the vicinity of the strut surface a numerical prism layer was formed to capture a boundary layer. Several blocks around the submerged part of the strut and in the proximity the nominal water surface level had finer mesh resolution. It was found that in order to adequately capture the air ventilation, a sufficiently fine mesh region is required near the strut leading edge crossing the water surface. 2 Copyright 2018 by ASME

3 Fig. 3 Strut with two plane sections showing the mesh. The horizontal section corresponds to the undisturbed water level and the vertical section passes through mid-chord of the strut. The boundary conditions assigned on all sides of the domain (except for the downstream boundary) corresponded to the velocity inlets with the constant horizontal velocity, whereas the downstream boundary was treated as the pressure outlet. The no-slip condition was enforced on the strut surface. The VOF-wave damping zones of one chord long were used near the side and downstream boundaries. In most simulations, the initial conditions comprised the undisturbed water and air flows with the constant velocity reported in the experiments. However, one studied configuration with the yaw angle of 15⁰ can have two stable but different flow regimes (wetted and ventilated). In this situation, the initial condition with the undisturbed flow produced the wetted steady-state solution. In order to achieve a ventilated regime in the steady state, the flow with an existing air-ventilated cavity was utilized as the initial disturbed condition. This condition was interpolated from the flow around strut yawed at 30⁰ as if the strut yaw angle was suddenly changed to 15⁰. SOLUTION VERIFICATION The solution verification was carried out for the most challenging case in the present simulations, when the strut yaw angle is 15⁰ and the strut suction side is air-ventilated. Three mesh resolutions (coarse, medium and fine) were generated with the approximate growth factor for the cell linear dimension (between the mesh types) of 1.6. For the convergence metrics, we used the strut lift, drag and moment coefficients. The lift force was defined in the transverse direction perpendicular to the flow (along the negative Y axis), the drag force is aligned with the flow (along the positive X axis), and the moment is calculated about the vertical axis (parallel to the positive Z axis) that passes through the strut mid-chord. The characteristic area is defined as the product of the chord,, and the strut depth,, which the distance between the strut submerged tip and the undisturbed water level. For all simulated cases, the strut depthchord ratio was chosen as one,. The flow velocity corresponded to the depth Froude number of three,, where is the gravitational acceleration, while the chord-based Reynolds number for water was about 1.2 million. The dependence of the force and moment coefficients on the number of cells is shown in Fig. 4. One can notice the monotonic convergence for all parameters. Using Richardson extrapolation and estimates for the numerical uncertainty employing factors of safety [11], we determined that the grid uncertainty for the lift coefficient on the fine mesh is less than 6%, and for the drag and moment coefficients it is less than 14% of the hydrodynamic characteristics corresponding to the converged (mesh independent) solution. For all subsequent simulations, the fine mesh with about 1.3 million cells was employed. C L C D C M Number of cells x Number of cells x Number of cells x 10 5 Fig. 4 Force and moment coefficients obtained with coarse, medium and fine meshes. 3 Copyright 2018 by ASME

4 VALIDATION Simulations using the fine mesh were carried out for the strut at yaw angles of 0⁰, 15⁰, and 30⁰ and Froude number of 3. At 0⁰ and 30⁰ yaw, the initial conditions were the undisturbed uniform flow. The solutions eventually settled in steady-state regimes. At 0⁰ yaw, the strut underwater sides remained wet. At 30⁰ yaw, the strut suction side became ventilated with air. In case of 15⁰ yaw, two initial conditions were used. The first corresponded to the undisturbed water flow, and the second had an air-ventilated cavity extrapolated from the 30⁰-yaw solution. Both cases with 15⁰ yaw eventually settled in steady states corresponding to different flow regimes, with the wetted and ventilated zones on the suction side of the strut. Results obtained in steady states for the force and moment coefficients are compared in Fig. 5 with experimental data reported by Harwood et al. (2016) for the same flow conditions. Similar to test observations, the simulations showed the wetted state for 0⁰ yaw, ventilated for 30⁰ yaw, and both wetted and ventilated states for 15⁰ yaw. The reported experimental uncertainty values are depicted in Fig. 5 with error bars. A good agreement between numerical and test data is observed, indicating the ability of the CFD tool to predict the macroscopic characteristics (force and moment coefficients and flow regimes) of complex air-ventilated flow, even in conditions when non-unique flow states are possible. The results in Fig. 5 for the strut at 15⁰ yaw demonstrate why the air ventilation can be detrimental. The lift coefficient decreases about 50% and drag stays nearly the same) when the flow regime changes from the wetted to ventilated state. If the strut were a rudder or operated as a hydrofoil in an inclined position, the air ventilation would drastically reduce effectiveness of this control or lifting device. Moreover, the ventilated strut at 30⁰ yaw has only slightly higher lift coefficient than the wetted strut at 15⁰ yaw, whereas its drag becomes about three times larger. To provide additional insight on the flow patterns, the water surface elevations and the volume fractions of water on the strut suction side are shown in Figs The air-water interfaces (isosurfaces) in these figures are obtained using the threshold for the water fraction of 0.5. In case of multi-phase flows, these isosurfaces are not necessarily the same as the real flow patterns, since the air can be present under and the water can appear above the isosurfaces; more discussion on that is given below. However, the isosurfaces can be used as approximate boundaries between air and water. In Figure 6, one can see a significant air cavity formed near the strut suction side at 30⁰ yaw, as well as pronounced spray regions at the strut and downstream. In contrast, the flow is only weakly disturbed when the strut has zero yaw (Fig. 7), with only a small ventilated region present behind the strut base. The wetted and ventilated cases with yaw of 15⁰ are shown in Figs The water rise behind the pressure side looks similar, but the flow near the suction side is drastically different. In case of the wetted flow, almost all of suction side is in contact with water, and a modest drop of the water level is noticeable toward the strut tail. In case of the ventilated flow, there is little water contact with the suction side: at the leading edge, near the bottom and above the nominal water level (in form of spray). C L C D C M [deg] [deg] [deg] Fig. 5 Force and moment coefficients at three yaw angles. Circles, experimental data; squares, computational results. Error bars indicate experimental uncertainties. Two different flow states can exist at 15⁰ yaw. To elucidate why the isosurfaces can only roughly approximate the air-water boundaries in case of violent multiphase flows, illustrations of the isosurfaces for the same flow but with different water fraction thresholds of 0.05 and 0.95 are 4 Copyright 2018 by ASME

5 Fig. 6 Top, air-water interface (suction side-aft view); bottom, water fraction on the strut suction side. Yaw angle of 30⁰. Fig. 8 Top, air-water interface (suction side-aft view); bottom, water fraction on the strut suction side. Wetted flow at yaw 15⁰. Fig. 7 Top, air-water interface (suction side-aft view); bottom, water fraction on the strut suction side. Yaw angle of 0⁰. Fig. 9 Top, air-water interface (suction side-aft view); bottom, water fraction on the suction side. Ventilated flow at yaw 15⁰. 5 Copyright 2018 by ASME

6 shown in Fig. 10. The lower threshold emphasizes the water spray above the nominal water level, while the higher threshold indicates some air presence in the vortex originating from the strut submerged tip. This underwater air can be visible in real flows in form of foam and bubbles. With numerical mesh significantly finer than used in this study, one may try to obtain better resolution of small-scale flow features. However, the basic flow patterns and main forces are sufficiently accurately resolved with the current mesh. Fig. 10 Pressure-side (starboard) views on air-water interfaces of the same ventilated flow around the strut at 15⁰ yaw obtained with the water fraction threshold of 0.05 (top) and 0.95 (bottom). Incident flow is from right to left. CONCLUDING REMARKS Modeling of air-ventilated flows around control, lifting and propulsion devices can take advantage of modern CFD tools. However, due to complex flow patterns and dynamics, validation studies are required to gain confidence in such simulations. In this study, we have shown that with relatively coarse mesh settings and the wall function treatment it is possible to adequately predict the force and moment coefficients of the surface-piercing strut. A good agreement was obtained between numerical results and experimental data with meshes of a modest overall cell count (around 1 million). The non-unique flow regimes that can exist at the same external conditions were successfully demonstrated in simulations as well. Thus, the goal of this study has been achieved. The authors recommend using the realizable K-Epsilon turbulence model and a fine mesh region near the strut leading edge in the vicinity of the water surface for numerical modeling of this type of air-ventilated flows. ACKNOWLEDGMENTS This work was supported by ONR through Grant No. N REFERENCES [1] Straub, L.G. and Wetzel, J.M., 1957, Experimental Studies of Air Ventilation of Vertical, Semi-Submerged Bodies, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Project Report No. 57. [2] Fridsma, G., 1963, Ventilation Inception on a Surface Piercing Dihedral Hydrofoil with Plane Surface Wedge Section, Davidson Laboratory, Stevens Institute of Technology, Hoboken, NJ, Technical Report No [3] Breslin, J.P. and Skalak, R., 1959, Exploratory Study of Ventilated Flows about Yawed Surface-Piercing Struts, NASA Technical Memorandum, Washington, DC, Technical Report No W. [4] Swales, P.D., Wright, A.J., McGregor, R.C., and Rothblum, R., 1974, The Mechanism of Ventilation Inception on Surface Piercing Foils, J. Mech. Eng. Sci., 16(1), pp [5] Harwood, C.M., Young, Y.L., and Ceccio, S.L., 2016, Ventilated Cavities on a Surface-Piercing Hydrofoil at Moderate Froude Numbers: Cavity Formation, Elimination and Stability, J. Fluid Mech., 800, pp [6] Young, Y. L., Harwood, C. M., Montero, F. M., Ward, J. C., and S. L. Ceccio, 2017, Ventilation of lifting surfaces: review of the physics and scaling relations, Applied Mechanics Reviews, vol. 69, [7] Keller, T., Henrichs, J., Hochkirch, K., and Hochbaum, A.C., 2016, Numerical Simulations of a Surface Piercing A-Class Catamaran Hydrofoil and Comparison against Model Tests, 22 nd Chesapeake Sailing Yacht Symposium, Annapolis, MD. [8] Brizzolara, S. and Villa, D., 2012, Three Phases RANSE Calculations for Surface-Piercing Super-Cavitating Hydrofoils, Proceedings of the 8th International Symposium on Cavitation CAV2012, Singapore, Paper No. 90. [9] Harwood, C.M., Brucker, K.A., Montero, F.M., Young, Y.L., and Ceccio, S.L., 2014, Experimental and Numerical Investigation of Ventilation Inception and Washout Mechanisms of a Surface-Piercing Hydrofoil, 30th Symposium on Naval Hydrodynamics, Hobart, Tasmania, Australia. [10] Ferziger, J.H. and Peric, M., 1999, Computational Methods for Fluid Dynamics, Springer, Berlin. [11] Xing, T. and Stern, F., 2010, "Factors of Safety for Richardson Extrapolation," ASME Journal of Fluids Engineering, 132(6), Copyright 2018 by ASME