CFD ANALYSIS OF DROGUE ASSEMBLY FOR UNDERWATER APPLICATION

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1 2th Annual CFD Symposium, August 9-1, 218, Bangalore CFD ANALYSIS OF DROGUE ASSEMBLY FOR UNDERWATER APPLICATION KUNJUNNI M*, RONI FRANCIS, DIWAKAR V M, P. VINOD Naval Physical & Oceanographic Laboratory, Kochi ABSTRACT Drogue assemblies are integrated at the tail end of underwater towed systems to generate drag force and necessary back tension. They are widely used in industrial as well as military underwater towed systems. This paper deals with numerical analysis of turbulent flow over a drogue assembly inside a tube using RANS k-ω SST model. The effect of drogue geometry and spacing on drag force is studied by varying drogue diameter, length, spacing and shape. It is found that diameter and shape of the drogues have high effect on the drag force whereas length and spacing have negligible effect on drag. It is also found that cylindrical drogues have highest drag coefficient. Keywords: Drogue assembly, RANS k-ω SST model, Drag force, Towed systems, ANSYS Fluent 1. INTRODUCTION Drogue assemblies are systems in which objects called drogues are integrated on a rope inside a tube at certain spacing. They are used in under water applications for generating high drag force thus providing motion for the rope and associated system along the flow direction. Applications of drogue assemblies are mainly in towed systems such as seismic arrays used in oil exploration systems and towed systems in military applications. Similar application can be observed in hydraulic capsule pipelines and coal log pipelines where capsules (cylindrical containers) or coal logs are transported through pipes using a liquid (usually water) to suspend and propel them. Present study focuses on the drogue assembly consisting of drogues integrated on a polypropylene rope and passing through a tube. One end of the rope is connected to the towed system and other end is kept free. One end of the tube, is connected to the discharge of a centrifugal pump and other end is open, as shown below in Figure 1. Figure 1. Graphical representation of drogue assembly inside the tube. 1

2 Even though there are numerous literatures available on drag developed by flow over different objects of various configurations, there are only a few available literatures on the flow over objects inside a tube. Liu H et al. [1] measured the pressure distribution around a stationary cylindrical capsule in a pipe due to water passing over the capsule. That result was used to determine the lift and drag on the capsule. M.F. Khalil et al. [2] numerically analysed turbulent flow around single concentric long capsule in a pipe and estimated velocity and pressure distributions around a moving capsule. Wenjuan Li et al. [3] done an experimental study on the hydraulic characteristics of a coal log train in a pipe. Drag and lift coefficients of coal logs are calculated from the pressure distribution for different fluid velocities. Govier and Aziz [4] presented an overview for laminar and turbulent capsule flows in concentric and eccentric pipelines. They studied both cylindrical and spherical shapes of capsule. Garg [5] studied the effect of a nonuniform clearance over the capsule length taking into account the friction between the capsule and the pipe surfaces. Garner and Raithby [6] estimated the capsule velocity and velocity profiles for laminar eccentric capsule flow in the annulus. Tomita and Fujiwara [7] analyzed the laminar flow capsule velocity and pressure drop across the capsule in hydraulic and pneumatic pipelines. Fujiwara et al. [8] and Tomita et al. [9] used the method of characteristics to study hydraulic capsule transport parameters such as the pressure drop, capsule velocity, capsule specific gravity, and the type of flow. Laminar turbulent transition was numerically modeled by Ogawa et al. [1] to predict the velocity profile and pressure gradient in concentric annuli. The wake of capsule and the effect of interaction between two capsules on the drag were studied experimentally by Tsuji et al. [11]. Sud and Chaddock [12] presented a numerical model for developing and fully developed flow in annulus. They reports drag calculations for vehicles in very long tubes. The objective of the present study is to numerically analyze the effect of configurations of the drogue assembly such as diameter, length, spacing and shape of drogues on the drag force developed. 2. PROBLEM DEFINITION In this paper drag force developed on a drogue assembly is analysed. Drogue assembly consists of drogues attached on a rope and the entire system is placed inside a tube. For the brevity of the analysis only two drogues are considered. The geometrical configuration of the drogues are varied keeping the Reynolds number based on the hydraulic diameter at the inlet constant (Re Dh =1 5 ) such that the flow is fully turbulent. The variables in the study are drogue diameter (D), drogue length (L), spacing (S) and shape of the drogue. Drogue diameter is changed from 5mm to 7mm, drogue length is varied from 5mm to 15mm, spacing varied from 2mm to 1mm and shape varied as cylindrical, spherical and fish. The geometry of the assembly is shown in Figure 2. Dimensions in mm Figure 2. Geometry of drogue assembly (Not to scale) 2

3 3. METHODOLOGY The problem is simplified as 2D axisymmetric flow in steady state. Drogues and rope are modelled stationary and fluid is allowed to flow over the assembly with uniform flow at the inlet. The flow over drogues consist of sudden contraction, expansion, flow separation and flow through narrow gaps, hence RANS k-ω SST model [13,14] with wall y+ insensitive function is used for numerical simulation. Figure 3 shows mesh around a single drogue. Figure 3. Computational domain of drogue assembly (magnified section) At inlet constant velocity corresponding to Re Dh =1 5 (Dh =21mm Hydraulic diameter of pipe at inlet) with a turbulent Intensity =.16 x (Re D ) -1/8 % was given. Outflow boundary condition was applied at the outlet. No-slip wall condition was given at rope, tube and drogue surfaces. Coupled Scheme was used for Velocity coupling. Second order discretization schemes were used for pressure, momentum and turbulent quantities for higher accuracy. Convergence of the solution was set as Residuals at Mesh Independence Study For the above numerical method, a mesh independence study is done. Two cylindrical drogues with 5mm diameter and 1 spacing on a rope of length 6m is used for mesh independency study Mesh Count Figure 4. Coefficient of pressure (Cp) v/s Dimensionless distance along the length of capsule The above Figure 4 shows the result of grid independence study. of both drogues and rope is plotted against the corresponding number of mesh element. From the results it can be seen that the mesh corresponding to 8 elements gives results with reasonable accuracy. 3.2 Validation of the Method Validation of the numerical model and the axisymmetric flow assumption is carried out. The results obtained for both models after simulation is found to be similar with some minor differences which are expected in 2D and 3D cases. Velocity profile obtained for both cases (Figure. 5) are found to be similar except increased flow turbulence in 3D. 3

4 Cp Figure 5 Axial Velocity contours of 2D axisymmetric case, 3D case. The drag force experienced by drogue and rope calculated by 3D simulation and 2D simulation are N and N respectively. Hence the assumption of 2D axisymmetric flow is found valid for the current study. For the validation of present numerical method, a study by Liu and Graze [1] on experimental estimation of drag force on a capsule inside a pipe is analyzed using the proposed numerical model. The pressure distribution on the capsule versus the dimensionless distance and the drag coefficient measured found to be in good agreement with that obtained using numerical analysis. Figure 6 shows the result of the validation study Measured Data by Liu & Grace Data through analysis Dimension less Distance Figure 6. Pressure coefficient (Cp) v/s Dimensionless distance along the length of capsule 4. RESULTS & DISCUSSION The results of the numerical simulation were represented in terms of axial velocity contours and coefficient of drag ( ) based on the combined frontal areas of both drogues. The first case studied was effect of drogue diameter on drag force. It was found that up to 65 mm drogue diameter drag force generation was gradual but after 65mm drag coefficient increased rapidly from 17.5 to 68.5 corresponding to diameter variation from 65mm to 7mm. This 4

5 shows the strong dependence of drogue diameter on drag force. Increase in diameter causes increase in flow blockage and flow recirculation at the rear end of drogues which in turn develops pressure drag. This is can be observed from axial velocity contours given in Fig. 7. (c) (d) Figure 7. Contours of axial velocity D=5mm, D=55mm (c) D=6mm (d) D=7mm Subsequent case study was carried out by varying the length of drogues between 5, 1 and 15mm. From the results (shown in Fig. 8) it is seen that as length increases edge effects at the entry becomes negligible. As length increases more of the flow gets aligned in stream-wise direction thus pressure drag developed on the subsequent drogue reduces. The viscous drag force generated on the drogue surface is negligible compared to the pressure drag generated on the front and back faces of drogue. Hence even though the viscous force the increase in length of the drogue doesn t cause increase in total drag force. Figure 8. Contours of axial velocity L=5mm, L=15mm 5

6 The effect of spacing on the drag coefficient was found to be negligible except for less than 2mm spacing. This occurs due to the bypassing of fluid from one drogue-tube gap to another without impacting on the subsequent drogue front-surface. This can be understood from axial velocity contours given in Fig.9 Figure 9. Contours of axial velocity S=2mm, S=1mm Shape of the drogues were varied between cylindrical, spherical and fish shapes and studies were carried out. It was observed that due to the higher blockage and blunt shape, cylindrical drogue produces higher drag whereas the spherical drogue produces least drag due to streamlined flow. Drag force produced on the fish drogue is inbetween that of cylindrical and spherical since, fish drogue has blunt face only at the rear side. The axial velocity contours for different shapes are given in Fig.1. (c) Figure 1: Axial velocity contour for cylindrical, spherical and fish shaped (c) drogues Figure. 11 shows the variation of drag coefficient with change in diameter, length, spacing and shape of drogues respectively. The results clearly shows that drogue diameter and shape of drogues has higher influence on drag force than that of drogue length and spacing. 6

7 8 2 6 Cylindrical 15 Cylindrical Drogue diameter(mm) Drogue Length(mm) Cylindrical 6 Cylindrical Spacing (mm) 4 2 Shape Spherical Fish (c) (d) Figure 11: Effect of drogue geometry and spacing on drag force 5. CONCLUSION The present study utilized RANS k-ω SST model for predicting flow properties for flow over drogue assembly inside a tube. Various parameters such as diameter, length, spacing and shape of drogues were varied to find their respective effects on drag force generated. It can be concluded that the drogue diameter and shape have higher influence on drag force. Length and spacing of drogues showed low or negligible effect on the drag force. This is due to the fact that pressure force is dominant than viscous force and pressure force depends mainly on the flow blockage and recirculation at the rear end of drogues. Hence cylindrical drogues with 7mm diameter is found to be the best configuration among the studied cases. Analysis based on diameter, length and spacing were done only for the cylindrical drogues and these results may vary for spherical or fish drogues. This variation is mainly because of the varying flow characteristics for different drogue shapes, which can be further studied in detail. ACKNOWLEDGEMENTS The authors wish to thank Shri. S Kedarnath Shenoy, Director NPOL and Dr. Sabu Sebastian, Group Director Engineering for the encouragement, direction and permission to publish this report. 7

8 REFERENCES [1] Liu, H., and Graze, H. R. (1983). Lift and Drag on Stationary Capsule, Journal of Hydraulic Engineering, Transactions of the ASCE, Vol. 19, pp [2] Khalil, M.F., Kassab, S.Z., Adam, I.G. and Samaha, M.A. (21). Turbulent Flow around Single Concentric Long Capsule in a Pipe, Applied Mathematical Modelling, Vol. 34, pp [3] Wenjuan Li, Shengyong Lu, Yong Liu, Jianhua Yan and Alfons G. Buekens. (216). Experimental Study of the Hydraulic Characteristics of a Coal Log Train in a Pipe, the Canadian Journal of Chemical Engineering. Vol. 94, pp [4] Govier, G. W., and Aziz, K. (1972). "The Flow of Capsules in Pipes." The flow complex mixtures in pipes. Van Nostrand-Reinhold, New York, N.Y. [5] V.K. Garg (1977), Capsule pipelining-an improved theoretical analysis, J. Fluids Eng., Trans. ASME [6] R.G. Garner, G.D. Raithby (1978), Laminar flow between a circular tube and a cylindrical eccentric capsule, Canadian J. Chem. Eng. 56, [7] Y. Tomita, Y. Fujiwara (1992), Capsule velocity in pipelines, JSME Int. J. 35, [8] Y. Fujiwara, Y. Tomita, H. Satou, K. Funatsu (1994), Characteristic of Hydraulic Capsule Transport, JSME Int. J. 37, [9] Y. Tomita, K. ABE, T. Jotaki (1981), Analysis of capsule pipeline system by the method of characteristics, Bull. JSME 24, [1] K. Ogawa, S. Ito, C. Kuroda (198), Laminar-turbulent velocity profile transition for flows in concentric annuli, parallel plates and pipes, J. Chem. Eng. Jpn. 13, [11] Y. Tsuji, Y. Morikawa, S. Chono, T. Hasegawa (1984), Wake of capsule and the effect of interaction between two capsules on the drag, Bull. JSME 27, [12] I. Sud, J.B. Chaddock (1981), Drag calculations for vehicles in very long tubes from turbulent flow theory, J. Fluids Eng., Trans. ASME 13, [13] Menter FR. Performance of popular turbulence models for attached and separated adverse pressure gradient flow. AIAA J 1992; 3(8): [14] Menter FR. Two-equation k omega turbulence model for aerodynamic flows. AIAA J 1994; 32(8):