CFD Approach to Steady State Analysis of an Underwater Glider Yogang Singh, S.K. Bhattacharyya and V.G. Idichandy Department of Ocean Engineering IIT Madras, Chennai India Abstract Underwater glider moves vertically by change in buoyancy and moves horizontally due to wings. In this paper, we validate the experimental lift and drag characteristics of a glider from the literature using Computational Fluid Dynamics (CFD approach. This approach is then used for the assessment of the steady state characteristics of a glider under development. Flow behavior and lift and drag force distribution at different angles of attack are studied for Reynolds numbers varying from 10 5 to 10 6. The state variables of the glider are the velocity, gliding angle and angle of attack which are simulated by making use of the hydrodynamic drag and lift coefficients obtained from CFD. The effect of net change in buoyancy is examined in terms of the gliding angle, glider velocity, angle of attack and glider saw-tooth trajectory. Keywords CFD; Glider; Trajectory; Underwater II. PRINCIPE OF STEADY STATE GIDING I. INTRODUCTION Underwater gliders are silent, high endurance underwater vehicles that help oceanographers in long term ocean observations with minimum maintenance and low cost. In this paper, experimental lift and drag characteristics of a well studied glider called AEX have been validated against the results obtained from computational fluid dynamics (CFD [1]. This approach is then used for CFD analysis of a laboratory glider under development for Reynolds numbers varying from 10 5 to 10 6. ift and drag force distributions on different parts of the glider at several angles of attack are studied. The steady state gliding motion of an underwater glider is defined as: For a change in buoyancy and the position of moving mass, the state variables of glider remain unchanged and angular velocity remains zero for its sawtooth gliding motion []. In this study, we simulate the state variables which are velocity, gliding angle and angle of attack of the laboratory glider under using the drag and lift coefficients obtained from CFD. Motion performance of the laboratory glider is also studied by simulating the sawtooth motion for a few chosen values of net change in buoyancy ( B for fixed gliding angle and angle of attack. It was found that the glider with larger B covers a larger horizontal distance and takes less time to reach the operational depth as a result of higher gliding velocity at same gliding angle and angle of attack. This suggests that a glider with larger change in buoyancy is more efficient in operation and can achieve a longer range. Fig. 1. Force balance relationship in underwater glider The force balance relationship of a underwater glider is shown in Fig. 1 where the origin of body-fixed coordinate is set in the center of buoyancy. In this figure, θ is the gliding angle, α is the angle of attack, γ is the pitch angle, U is the gliding speed, and D are vehicle lift and drag, respectively. When gliding down, γ and θ are defined as positive and α is defined as negative. When gliding up, γ and θ are defined as negative and α is defined as positive. The kinematic and equilibrium relations follow from Fig. 1 as [3]: θ = γ α; Δ B = G B; B = ρv Δ B cos γ = ; Δ Bsin γ = D where, G is the net mass of the glider, B is the buoyancy of the glider, ρ is the density of water, V is the glider volume and B is the net change in buoyancy. The hydrodynamic drag and lift can be defined as: 1 D = ( KD0 + KDα U = CDρSU 1 = ( K0 + Kα U = CρSU ( where, K D0 and K D are the zero-lift drag coefficient and liftinduced drag coefficient respectively,k 0 and K are the zero lift coefficient and induced lift coefficient, C D is the non (1
dimensional drag coefficient, C is the non dimensional lift coefficient and S is the wetted surface area. Equations (1-( are used to define the relation between α and γ as: K tan γ 4KDcot γ ( KD0cot γ + K0 α = 1± 1 K D K (3 Gliding speed refers to maximum speed obtained by glider using specific driving buoyancy. The gliding speed can be expressed as a function of gliding angle using equations (1-(3 as follows: KD ΔB U = K K cosγ + K sin γ( K ± K 4K K cot γ 4K K cot γ D 0 D D0 D 0 (4 Equation (4 shows that for an underwater glider, its horizontal speed will be uniquely determined by the gliding angle for given specific driving buoyancy. Once we obtain γ, Equation ( and (3 can be solved to obtain U and the corresponding α, then horizontal (U H and vertical (U V velocity vectors are as follows: X = UH = Ucos( θ + α Z = U = Usin( θ + α V III. CFD VAIDATION OF GIDER AEX Fig.. 3-D CAD model of AEX (5 TABE I. DESIGN PARTICUARS OF AEX AND ABORATORY GIDER Design particulars AEX aboratory glider ength 0.83 m 1.6 m Breadth (Wing Span 0.83 m 1.1 m Breadth (Hull 5 m 0.140 m Wing profile NACA 0009 NACA 0001 Wing chord 0.1 m 0.134 m (Mean 0.169 m (Root 0.1 m (Tip Operation depth 5 m 4 m Wetted surface area 114 m 0.7076 m Wetted surface area (Bare Hull 0.385 m 46 m The CFD analysis software SHIPFOW was used to determine the lift and drag forces acting on glider AEX under steady flow. The design particulars of this glider are given in Table 1. Fig. 3 shows the 3D computational domain and structured grid around the body. Continuity equation and Navier-Stokes equations are the governing equations. The finite volume method was adopted wherein the convective terms are discretized with a Roe scheme and a second order explicit defect correction is used to achieve second order accuracy. The rest of the terms were discretized using central difference scheme. A local artificial time-step is added to the equations and the discrete coupled equations were solved using an ADI solver [4]. The domain around the body is discretized with H-type structured grid. For computational efficiency and stability of the solution, the mesh should be such that it is dense in areas where the flow velocities are sensitive to grid spacing and coarse in other areas. The grid will be stretched towards NO SIP boundary conditions to get a y + value of approximately 1. The SST (Shear-Stress-Transport k-ω model is chosen for turbulence model, which is widely used for considering flow separations. The total number of points and cells in the model were 19050 and 134603 respectively. There were 101 grid nodes over the length of the body and 60 grid nodes in its circumferential direction For four glider velocities (0.5,, 0.7 and 0.8 m/s and nine angles of attack ( 8 to +8 in steps of, the lift and drag forces were calculated. The results are presented in Figs. 4 and 5 where the comparison with experimental as well as CFD values presented in [1] are also shown. Fig. 3. Computational domain and structured grid around glider AEX
9 7 6 5 3 1 9 7 6 5 3 CFD (Present CFD (Present (a (c 1 0.1 0.10 6 0.1 0.10 6 CFD (Present (b CFD (Present (d 0 Fig. 4. Experimental drag coefficient as a function of angle of attack for the glider AEX with CFD comparisons for (a U = 0.5 m/s (b U = m/s (c U = 0.7 m/s (d U = 0.8 m/s 0. -0. 0. -0. CFD (Present CFD (Present (a (c 0. -0. 0.8 0. -0. CFD (Present (b CFD (Present (d -0.8 Fig. 5. Experimental lift coefficient as a function of angle of attack for the glider AEX with CFD comparisons for (a U = 0.5 m/s (b U = m/s (c U = 0.7 m/s (d U = 0.8 m/s It is clear that whereas the lift coefficient matches well with CFD results of [1] as well as the present work, the drag coefficient shows significant differences with both CFD results of [1] as well as the present work. However, the CFD of [1] always over-predicted the drag by a large margin. On the other hand CFD of the present work mostly underpredicts drag but its match with experiment is reasonably good and is much superior to the CFD of [1]. Clearly, the CFD approach can be adopted with confidence in predicting the steady motion of the laboratory glider. CFD grid around this glider is shown in Fig. 7. Fig. 6. 3-D schematic CAD model of laboratory glider The drag and lift coefficients, as calculated by CFD, are presented in Fig. 8 for five glider velocities (0.1, 0., 0.3, and 0.5 m/s and eleven angles of attack ( 10 to 10 in steps of. The lift to drag ratios, presented in Fig. 9 as a function of α for all five glider velocities show that its maximum value of about 8, which is sufficiently high, occurs at α = ±6. Fig. 7. Structured grid for CFD of laboratory glider Fig. 8. ift and drag coefficients of the laboratory glider using CFD Table shows the contributions of the hull, NACA 001 wings and the tail to the total drag and lift forces for U = 0.1 m/s. The contribution of the tail is insignificant. The contribution of the wings to both drag and lift is significantly more than the bare hull. IV. CFD ANAYSIS OF ABORATORY GIDER The design particulars of the laboratory glider are given in Table 1 and its schematic drawing is shown in Fig. 6. The
B. Simulation of state variables TABE II. Fig. 9. ift to drag ratio of the laboratory glider DRAG AND IFT FORCE DISTRIBUTION ON ABORATORY GIDER Fig. 11. Gliding velocity vs. gliding angle The gliding velocity (U as a function of gliding angle (θ for three values of ΔB are shown in Fig. 11. The maximum U occurs at θ = 37 for downward gliding and at θ = 37 for upward gliding for all values of ΔB. The maximum values of U for ΔB = 0.3 kg, kg and 0.9 kg are 0.198 m/s,0.81 m/s and 0.345 m/s respectively. α Drag (in terms of % ift (in terms of % Hull Wings Tail Hull Wings Tail 0 35 65 0 35 57 8 4 30 69 1 19 81 0 8 7 7 1 0 80 0 4 30 69 1 19 81 0 8 8 70 0 0 0 0 V. STEADY STATE MOTION STUDY Equation (, which implies C = K + K α CD = KD0 + KDα and 0, can be used to obtain the coefficients K D0, K D, K 0 and K from the CFD generated data of C D and C in Fig. 8 by polynomial fitting. Typical examples of this fitting are given in Fig. 10. The values obtained are K D0 =.8304, K D = 76, K 0 = 3538 and K = 3.538. A. Identification of drag and lift cofficients 3 0.1 Fig. 1. Angle of attack vs. gliding angle The angle of attack (α as a function of θ are shown in Fig. 1. In this figure, for θ = (37, 37, α = ( 1.016, 1.106 and γ = (38.016, 35.984. Non-Dimensional Drag 1 Non-Dimesionsional ift 5 0-10 -5 0 5 10-5 0-10 -5 0 5 10-0.1 Fig. 10. Curve fitting of drag and lift for the laboratory glider
Fig. 13. Trajectories of the laboratory glider Fig. 13 presents 100 s simulation results of the glider trajectory with operational depth set to 4 m. The times the glider takes to reach this depth is 33 s, 3.5 s and 19 s for B = 0.3 kg, kg and 0.9 kg respectively covering a horizontal distance of 15.4 m, 1.9 m and 6.9 m respectively. CONCUSIONS The performance of a laboratory glider with NACA001 wing profile is studied using a CFD methodology. This profile gives sufficiently high lift to drag ratio. The state variables of the glider are obtained from steady state simulation for three values of B and the glider trajectories obtained for a chosen operational depth. REFERENCES [1] M.Arima, N. Ichihashi, and T. Ikebuchi,"Motion characteristics of an underwater glider with independently controllable main wings,"oceans 008-MTS/IEEE Kobe Techno-Ocean. IEEE, 008. [] J.G Graver,R.Bachmayer, N.E eonard, and D.M.Fratantoni, Underwater Glider Model Parameter Identification, Proceedings 13 th Int. Symp. on Unmanned Untethered Submersible Technology (UUST, August 003. [3] N.E eonard, and J.G Graver, Model-based feedback control of autonomous underwater gliders, IEEE J. Ocean. Eng., vol. 6(4,pp. 633-645, 001. [4] XCHAP Manual, SHIP FOW User Guide, 014.