Jl. Kusumanegara 157 Yogyakarta 55165, Indonesia. PETRONAS, Bandar Seri Iskandar, Tronoh, Perak Darul Ridzuan, Malaysia

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1 On the Numerical Simulations of Drag Forces Exerted by Subaqueous Mudflow on Pipeline: A Laboratory Experiment Assessment Zainul Faizien Haza 1,a and Indra Sati Hamonangan Harahap 2,b 1 Department of Civil Engineering, Faculty of Engineering, Universitas Sarjanawiyata Tamansiswa, Jl. Kusumanegara 157 Yogyakarta 55165, Indonesia 2 Department of Civil & Environmental Engineering, Faculty of Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Tronoh, Perak Darul Ridzuan, Malaysia a zainulfaiz@gmail.com, b indrasati@petronas.com.my Keywords: Submarine slide; Mudflow; Kaolin clay; Lock-exchange; Gravity flow; Drag force coefficient Abstract. The collision between submarine slide and sub-sea pipelines was numerically simulated using commercial software of CFD. The work was also conducted in order to investigate drag force generated during collision, which has been observed in the related laboratory experiment. Rheological data of laboratory experiment was also used as input data of the current CFD simulation. Slurries of kaolin clay-water mixtures were used as model of submarine sediment. The simulation model produced the collision event (between mudflow and pipeline), which has similar with laboratory work in term of sequential views images of head flow impaction and the propagation trend line of the drag force coefficient values. Introduction One of serious and complex geo-hazards is well known as submarine slide. It has potential detrimental consequences against offshore installations such as fixed platforms, submarine pipelines, cables and other seafloor installations [1-2]. Development of oil and gas industry is now rapidly moving to depth over 1000 m along or in propinquity of the continental slope [3]. The Society of Underwater Technology estimates the cost to repair pipelines damaged by submarine slides to reach US$ 400 million per year [4]. Consequently, geologically hazardous condition is becoming the threat of the current development especially on main facilities of pipelines. Submarine slide involved two main materials; those were sediment deposit (normally as muddy material) and seawater. Accordingly, sub-aqueous mudflow is appropriate to be considered as analogy of that condition. In sub-aqueous mudflow analysis, there is no time for excess pore water dissipation because the rate of movement is fast enough. The mechanic of this movement cannot be adequately explained by soil mechanics principles alone, therefore, applying fluid mechanics principles is necessary [5]. In reference to these situations, Computational Fluid Dynamic (CFD) is become the most suitable tool to be utilized as a numerical solution for sub-aqueous mudflow experiments, which represent the submarine slide event. Therefore, commercial software of ANSYS Fluent 14.0 is utilized to conduct the numerical simulation. Related Laboratory Experiment An experimental program of submarine slide model has been conducted at Hydraulics Laboratory of Universiti Teknologi PETRONAS, Malaysia. It was implemented by development of the equipment of a rectangular channel of 8.53 m length, 0.25 width, and heights of 0.7 m and 1.30 m at the beginning and the end, respectively (as seen in Fig. 1). The details of experimental work described above could be found in [6]. Page 181

2 Fig. 1. Scheme of laboratory experiment setup (not to scale) According to data of field observation conducted by Hance [7], the highest frequency density distribution of the average angle of the slope at failure for the seafloor slope failures was in the range of 3 to 4, therefore the laboratory experiment was implementing 3 of the sloping base. The gravity flow principles and lock-exchange system were combined to build the simulation model. The mud was made from a mixture of kaolin and water with percentage variation of kaolin clay content (KCC) in range 10% to 35%, with 5% increment. In accordance to ASTM D2196 [8] rheological test using Brookfield Digital Viscometer DV-I+ equipment addressed results as listed in Table 1 [6]. The rheological model of the mud was expressed as Herschel Bulkley model (H-B model), which has general form as follow. n τ c )= K γ (1) (τ where τ c is the yield strength, K is equivalent to the dynamic viscosity, γ is the shear rate, and n is positive parameters of model factor [9]. Furthermore, density measurement using Fann Mud Balance results values of mud densities (ρ f ) in the range of 1054 kg/m 3 to 1266 kg/m 3 [6]. KCC (%) Table 1. Rheological test results of mud model and H-B model Density, ρ f (kg/m 3 ) Specific Gravity (GS) H-B model τ c K n A pipe model with outside diameter (OD) 2.13 cm was placed at the path of mudflow as shown in Fig. 1. The drag force was observed upon the collision event between mudflow and pipe model. Calculation and analysis of drag force of mudflow on pipe model in the current work was elaborated using fluid dynamics approach in order to accommodate the additional effect of flow plasticity on the drag force related to the dynamic pressure, which is proportional to mud density and the squared flow velocity as described by Bruschi et al. [3]. Therefore, drag force generated by mudflow on pipe stem is expressed by traditional fluid dynamic force and rheology properties of non-newtonian fluid flow as the following equation [10]. C d = F d 1 2 ρ A u 2 f (2) Page 182

3 where C d is the drag coefficient, F d is the drag force components perpendicular to pipe axis, ρ f is the mud density, A is area of pipe stem which is facing opposite to mudflow direction, and u is flow-front velocity of mudflow. CFD Approach and Formulation Multiphase model is adopted in the current CFD simulation. The problem formulation is referring to the constitutive equations of mass and momentum conservation for incompressible and viscous fluid, which in perspective of 2D; it is expressed as Eq. 2 and Eq. 4, respectively. Equations of mass conservation is based on principles that rate of inflow is equal to outflow rate [11]. ρ + ( ρu) = S m (3) t where ρ is mud density, u is velocity, and S m is the mass added to continuous phase from the dispersed second phase (specified mass sources). While, the momentum conservation is formulated as follow. Pre-processing of CFD Simulation The area on simulation domain was m 2 consisting of mud and water area. The meshing process was implemented by using the ANSYS Meshing (ANSYS ICEM CFD) with 2D behaviour of plane stress and Lagrangian reference frame. The 18,871 nodes and 18,425 elements were created by using size function of on proximity and curvature with proximity minimum size of E-003 m and maximum face size of 2E-002 m. Boundary conditions were applied into the domain. The left side edge, bed surfaces, and the right side edge of channel were modelled as wall (glass wall, as actual condition in laboratory) with rough no slip boundary condition. The pressure outlet boundary condition was applied for the top line of the domain (i.e. the mud and water surface in contact with air). CFD Simulation Setup The use of ANSYS Fluent solver in this work was consisted of figuring the drag force coefficient of the mudflow. As seen in Eq. (2) that the flow-front velocity (u) was the main factor of drag force (F d ) beside the density (ρ f ). Therefore, the solver was set as the type pressure-based Navier-Stokes (pbns) with absolute velocity formulation. In accordance with two types of fluid (mud and water), the mixture-model was selected for multiphase model with two phases of Eulerian phases and slip velocity of mixture parameters. Result and Discussion Collision event between mudflow and pipe model. Investigation of the collision event was conducted within time range, at when the leading edge of the mudflow reached the pipe until the head of the flow impacted the pipe. According to time recording, it was a very short duration, which was about 0.8 s. For instance, the collision event between mudflow of 15% KCC and pipe model for both laboratory experiment and CFD simulation are shown in Fig. 2. Page 183

4 Fig. 2. Collision event of 15% KCC between mudflow and pipe: (a) laboratory experiment; (b) CFD simulation Fig. 2 shows that CFD simulation produced the representative collision images as indicated by the shape of head flow and the short duration of the collision. In the laboratory experiment work, measurement data of drag force (F d ) magnitude were obtained from signal responses provided by load cell, which was converted by data logger into force unit of Newton (N). While, in CFD simulation, drag force coefficient (C d ) based on simulation time duration was obtained directly from the simulation. Flow-front velocity of mudflow. The fourth level of contour line (i.e. about 5.000E-001 of volume fraction) was used as reference to assign the leading edge for the purpose of run-out determination. CFD simulation addressed result of velocity in the range of 0.28 m/s to 0.38 m/s. Based on these 2 ρ f u velocities data, the Reynolds number was calculated using Re =, where τ was obtained from τ H-B model as in Table 1. The range values of Reynolds number were in the range Drag force exerted by mudflow. CFD simulation provided the result of drag force coefficient (C d ) directly upon running the simulation based on the boundary conditions zone of pipe. In such condition, CFD simulation addressed the C d propagation values as shown in Table 2. Table 2. Summary of data obtained from laboratory experiment and CFD simulation Mud Laboratory CFD model ρ u Re Fd max Cd u Re Fd max Cd (%KCC) (kg/m 3 ) (m/s) (N) (m/s) (N) In order to observe the similarity result of both non-dimensional C d and R e, equation is then developed by based on Table 2 to express the C d as relative to Reynolds number (R e ), which is representing the C d values propagation of the two types of experiment, laboratory and CFD. The formulation of C d - R e relationship is expressed as follow. Page 184

5 ( 1.15) d = Re C (4) Concluding Remark The application of commercial software of ANSYS Fluent to create the back calculation of laboratory experiment was presented. The numerical simulation results provide the model, which has similar collision event (between mudflow and pipeline) to laboratory work in term of sequential views images of head flow impaction and the propagation trend line of the drag force coefficient values. Furthermore, the Eq. 7 represents the C d values propagation data, which has a high similarity trend line of fitted curve between current works and the previous research by Zakeri et al. [12]. References [1] F. Nadim, "Challenges to geo-scientists in risk assessment for sub-marine slides," Norwegian Journal of Geology, vol. 86, pp , [2] S.-K. Hsu, J. Kuo, C.-L. Lo, C.-H. Tsai, W.-B. Doo, C.-Y. Ku, and J.-C. Sibuet, "Turbidity Currents, Submarine Landslides and the 2006 Pingtung Earthquake off SWTaiwan," Terr. Atmos. Ocean. Sci., vol. 19, pp , [3] R. Bruschi, S. Bughi, M. Spinazze, E. Torselletti, and L. Vitali, "Impact of debris flows and turbidity currents on seafloor structures," Norwegian Journal of Geology, vol. 86, pp , [4] D. C. Mosher, L. Moscardelli, R. C. Shipp, J. D. Chaytor, C. D. P. Baxter, H. J. Lee, and R. Urgeles, "Submarine Mass Movements and Their Consequences," in Submarine Mass Movements and Their Consequences, Advances in Natural and Technological Hazards Research. vol. 28, D. C. Mosher, et al., Eds., New York: Springer, 2010, pp [5] J. Locat and H. J. Lee, "Submarine Landslides: Advances and Challenges," presented at the The 8th International Symposium on Landslides, Cardiff, U.K, [6] Z. F. Haza, I. S. H. Harahap, and L. M. Dakssa, "Experimental studies of the flow-front and drag forces exerted by subaqueous mudflow on inclined base," Natural Hazards, vol. 68, pp , [7] J. J. Hance, "Development of a Database and Assessment of Seafloor Slope Stability based on Published Literature," Master of Science in Engineering, Faculty of the Graduate School, The University of Texas, Austin, [8] Standards, "ASTM D Standard Test Methods for Rheological Properties of Non- Newtonian Materials by Rotational (Brookfield type) Viscometer", ASTM International, United States, [9] P. Coussot, Mudflow Rheology and Dynamics. Rotterdam: AA Balkema, [10] H. Pazwash and M. Robertson, "Forces on Bodies in Bingham fluids," Journal of Hydraulic Research vol. 13, pp , [11] P. A. Sleigh and I. M. Goodwill, The St Venant Equations: School of Civil Engineering, University of Leeds, England, [12] A. Zakeri, K. Høeg, and F. Nadim, "Submarine debris flow impact on pipelines Part II: Numerical analysis," Coastal Engineering, vol. 56, pp. 1-10, Page 185