Hydrodynamic behaviour of parallel submarine pipelines near a sloping boundary
P.L.Vijayakumari, K.Murali and V.Sundar
Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600 036
The hydrodynamic interference effect of submerged parallel pipelines near a rigid sloping bed was carried out experimentally by keeping two identical parallel pipelines at different clear horizontal spacing (w) between them. Both the pipelines were subjected to the action of regular waves with its crest parallel to pipeline. The circumferential distribution of dynamic pressure on the test pipe in the presence of another pipe on the seaward side was measured using pressure transducers. The forces were calculated by integration of the measured pressures. The pressures and forces were normalized and plotted as a function of relative water depth. The effect of the bottom boundary and the proximity of the free surface were determined by keeping both pipes at different vertical clear gap (h) from the free surface. The details of the experimental set up, collection of data, analysis and discussion of results have been presented in this paper.
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Correlation coefficient incorporated joint distribution model for wave heights and periods and estimation of design wave height parameters
V.K. Praveen¹, S.P. Satheesh², G. Muraleedharan³ and P.G. Kurup4
¹CAOS, Indian Institute of Science, Bangalore-560 012
²National Institute of Oceanography-Regional Centre, Kochi-682 016
³Centre for Atmospheric Sciences, IIT Delhi, Hauz Khas, New Delhi-110 016
4Amrita Institutions, Ashram Lane, Kochi-682017
Instrumentally recorded wave data (CESS, 1984) are used in this study for understanding the seasonal behaviour of wave heights and periods off the southwest coast of India. Distribution of digitised zero-up crossing wave heights from wave recorder charts for the month of January 1981 off Valiathura are simulated by the depth factor accommodated Weibull model. Significant wave heights are predicted using the parametric relations derived fromWeibull model and validated using relative and mean RMS error values. The predicted conventional significant wave heights are comparable with computed values with maximum deviation of only 0.21 m. A shoaling coefficient in addition to a depth factor is also included in the prediction formulae for estimating the significant wave heights, stems from the fact that since it is the average of the one third highest waves, the higher side of the wave height distribution is influenced by both depth factor and shoaling coefficient. The maximum wave height distribution off Alleppey, southwest coast of India during southwest monsoon season (June-October) found to follow the Modified Weibull distribution model derived for maximum wave heights. A depth factor is included in the model to accommodate the shallow water attenuation effects. Certain wave height parameters such as mean maximum wave height, most frequent maximum wave height, extreme wave height, return period of an extreme wave and probability of realising an extreme wave in a time less than the designated return period are estimated by the prediction formulae derived and compared with computed values giving reliable results. The observed surface plots of wave heights and periods are fitted to Bretschneider and Gluhovskii (with zero correlation) and Weibull-Gamma (with non-zero correlation) joint distributions and it was found that the joint distribution with marginal density functions - Weibull for wave heights and Gamma (or Erlang) for wave periods simulate more effectively the real 3D plot.
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Application of Gamma and Erlang statistical models for zero up-crossing and significant wave period distributions
V. Jagadish Kumar¹, G. Muraleedharan² and P.G. Kurup³
¹Elcome Surveys Pvt. Ltd., Elcome House, M.I.D.C., Nerul, Navi Mumbai-400 706
²Centre for Atmospheric Sciences, IIT Delhi, Hauz Khas, New Delhi-110 016
³Amrita Institutions, Ashram Lane, Kochi - 682 017
The available competing theoretical models Gamma, Rayleigh, exponential and Bretschneider were considered to simulate the zero up-crossing wave period distribution of the active southwest monsoon season (May-October) off southwest coast of India recorded by Center for Earth Science Studies, Thiruvananthapuram from 1980-84 (5 years). There is an empirical support in all cases for the simulations by Gamma at 0.05 level of significance. A theoretical explanation is provided for the distribution of wave periods to follow Gamma Law. The distribution function of Gamma is an infinite power series and hence any further mathematical treatment will result in complexity. When the shape parameter of Gamma is approximated to the nearest integer, then it will be an Erlang model. Hence, an expression is derived for various significant wave period estimations from Erlang as the model for wave periods for simplicity as
where t - zero up-crossing period, a and l are the shape and scale parameter of the Erlang model. The simulation capability of the expression is tested using relative and mean RMS error values affirming its validity. An Erlang distribution model is suggested theoretically for the conventional significant wave period distribution from the mathematical logic
where m'(x) is the derivative of m(x). F(x) is the distribution function of Erlang model. Its empirical validity is established using 10 years visually estimated wave period data compiled by NPOL (1978).
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Wave loads on a perforated circular caisson and suction pipe of a seawater intake well
K. Vijayalakshmi, S. Neelamani¹, K. Murali and R. Sundaravadivelu
Ocean Engineering Department, Indian Institute of Technology Madras, Chennai–600036.
¹Coastal Engg. and Air Pollution Dept, Environmental and Urban Development Division, Kuwait Institute for Scientific Research, P.O. Box : 24885, 13109 SAFAT, Kuwait.
The wave force on a seawater intake structure model consisting of a perforated circular caisson (0.50 m diameter) encircling a vertical suction pipe (0.05 m dia) is measured experimentally. The effect of porosity of the caisson wall, incident wave height and wave period on the in-line forces on the caisson and suction pipe is investigated. The porosity of the caisson was varied from 4.54% to 19.15%. Waves of wide ranges of heights and periods were used. The wave forces on the outer caisson and inner cylinder, water surface fluctuations in the interior & exterior of the caisson and wave run-up on the outer caisson and inner cylinder were studied for both regular and random waves. Numerical study was carried out using Green's identity method in order to compute the force on the perforated caisson. The present paper includes the wave forces on the outer perforated circular caisson and inner circular cylinder due to random waves and a few numerical results.
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Application of interface tracking methods in ocean engineering
M.R. Behera and K. Murali
Department of Ocean Engineering, Indian Institute of Technology, Madras, 600036.
Numerical simulations of multiphase flows, using a front-tracking method, are presented. The method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties. Interfacial terms are accounted for by adding the appropriate sources as d functions at the boundary separating the phases. The unsteady Navier–Stokes equations are solved by a conventional finite difference method on a fixed, structured grid and the interface, or front, is tracked explicitly by connected marker points. Interfacial source terms are computed on the front and transferred to the fixed grid. Advection of fluid properties such as density is done by following the motion of the front. The method has been implemented for two-dimensional and axisymmetric flows. The representation of the moving interface and its dynamic restructuring, as well as the transfer of information between the moving front and the fixed grid, is discussed. Applications and extensions of the method to homogeneous bubbly flows, and free surface flows are then presented.
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A polar method for obtaining resonating quadruplets in computation of nonlinear wave-wave interactions
V. Prabhakar and J. Pandurangan
Department of Mathematics, MIT Campus, Anna University, Chromepet, Chennai – 600 044
A polar method for obtaining resonating wave quadruplets in the computation of nonlinear wave-wave interaction source term for deep waters is presented with results. It is shown that when , the number of points on the locus varies when the orientations of the input wave vectors are changed and reduces when the difference in the magnitude of the input wave vectors increases. A significant advantage in this method is that the angular spacing on the locus is kept constant.
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Comparative study of natural frequencies of offshore structure - automated approach
A. Vittal Hegde and Satish Jadhav
Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka. Srinivasnagar – 575025, Karnataka
Fixed offshore structures are constructed in open ocean, where rough sea conditions often exist. Dynamic behavior of ocean waves develop high dynamic forces in the structure, which in turn result in resonant state, if the natural frequency of the structure is close to that of frequency of loading. Hence, it is important to predict the natural frequencies of the structures realistically. For such predictions, the complete structural system must be modeled accurately, and reliable numerical procedure must be used. Here is an attempt made to compare two methods which are frequently used. The study was carried out by developing software, which computes the natural frequencies and modes of vibration of a fixed offshore structure accurately.
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Comparison of physical model test with
numerical 3D-simulations at a movable gate of a large storm surge barrier
Jens Scheffermann, Andreas Matheja and Claus Zimmermann
Franzius-Institut for Hydraulic, Waterways and Coastal Engineering, University of Hannover, Nienburger Str. 4, 30167 Hannover; Germany
An approach of transient free surface flow computations for a moving gate of a storm surge barrier using moving mesh is presented. For validation results from the numerical model are compared with physical model measurements with Acoustic Doppler Velocimeter (ADV) and Particle Image Velocimeter (PIV). There is a good agreement between flow simulations and measurements. Deviation may be from insufficient grid resolution and/or selected turbulence model.
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Wave past flexible porous breakwater in a two-layer fluid
P. Suresh Kumar and T. Sahoo
Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology, Kharagpur – 721302
An analysis has been carried out to study the performance of a flexible porous plate breakwater in a two-layer fluid having a free surface. The breakwater is extended over the entire water depth in a two-layer fluid, each fluid being of finite depth. The porous breakwater is fixed at the seabed and is free at the free surface. The problem is analyzed in the linearised theory of water waves with the assumption of small amplitude plate response. The breakwater is idealized as a one-dimensional beam of uniform flexural rigidity and uniform mass per unit length. The velocity potentials of the wave motion in a two-layer fluid are coupled with the equation of motion of the breakwater. The associated mixed boundary value problem is reduced to a linear system of equations by utilizing a more general orthogonal relation along with least-squares approximation method. The reflection coefficients for the surface and internal modes, the non-dimensional breakwater deflection, the free surface and interface elevations are computed for various physical parameters like the non-dimen-sional porous-effect parameter, fluid density ratio, ratio of water depths of the two fluids, and plate flexural rigidity to analyze the efficiency of porous plate as a breakwater in the two-layer fluid.
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Two-Dimensional hydrodynamic modeling of Cochin estuary using finite element method
T.I. Eldho and Naveen Chandra
Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai – 400 076
Estuaries, coastal water bodies and its adjacent environment are generally characterized by complex interactions between physical, chemical and biological processes. The engineering works in such region positively need to be designed for data supplied from the hydrodynamics simulation. The solution to estuary problems can be obtained through physical models, analytical solutions or numerical models. The physical models are difficult to make and expensive and very few analytical solutions are available for simplified problems. In the numerical modeling, the hydrodynamic information is obtained by solution of shallow water equations. Very complex geometry and boundary conditions that are peculiar to estuary problems can be handled in numerical modeling. In this paper, a two-dimensional implicit finite element model is used for the simulation of the hydrodynamics of estuaries. The model has been used for the simulation of the complex hydrodynamics of Cochin estuary and the results were compared with the observed values and other model results.
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Performance of triple pontoon floating breakwater - a numerical approach
S.S. Amar and J.S. Mani
Department of Ocean Engineering, IIT Madras, Chennai-600036
The performance of a three pontoons rigidly interconnected, as a wave attenuator is evaluated numerically, considering two dimensional linear diffraction effects. The potentials havebeen evaluated by the application of Green's identity method. The effect of gap between the pontoons on the performance of the breakwater is evaluated and an optimum gap ratio (Ratio of interconnectivity gap to width of pontoon) of 0.5 to achieve a transmission ratio of less than 20 percent has been obtained. The transmission and reflection coefficients are obtained for various drafts of the breakwater with a fixed optimum gap and the results are presented as the function of width of float to wavelength ratio.
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Performance of perforated seawater intake and outfall systems
N. Sudharsan, S. Ramkumar, K. Prasanna Venkatesan and J.S. Mani
Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600 036.
Seawater intake and outfall systems are often employed by coastal industries to meet the demand of either seawater intake or effluent discharge into the marine environment. As the dimension of the intake and outfall structure is controlled by the quantum of either seawater intake or effluent discharge, the dimension of the structure becomes so large that they are subjected to abnormal wave loads leading to complexity in the design of the structure.
This paper explores the possibility of reducing the wave load on the structure without compromising on its dimension. The paper discusses on the performance of a conventional seawater intake and outfall systems and compares with those of the perforated intake and outfall systems through numerical and experimental studies. The studies indicate that the force on the perforated intake and outfall systems would reduce by about 40% when compared with the non-perforated intake and outfall systems. Further, the variations in water surface elevation around the perforated and non-perforated systems suggest that the former would minimise the variation in water surface elevation by 28% when compared with the later.
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Hydrodynamic characteristics and stability of rubble mound breakwater with geobags as core
T. Nasar, R. Balaji and V. Sundar
Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai - 600036
A detailed experimental model study was carried out to investigate the performance of GEOBAGS, as a substitute for core layers in the case of rubble mound breakwaters. The breakwater sections were tested for the different fractions of the significant wave heights and their stability was assessed in terms of damage levels. In addition, the reflection and transmission characteristics of the breakwater models were studied. The details of the breakwater models, instrumentation, testing procedure and results are discussed in this paper. Back
Uncertainties in predicted maneuverability of surface ships on hydrodynamic derivatives
Debabrata Sen and Amit Tyagi
Dept. of Ocean Engineering & Naval Architecture, Indian Institute of Technology, Kharagpur-721302
The influence of hydrodynamic derivatives on the predicted turning and zig-zag maneuvers for surface vessels are presented. These two are the most important definitive maneuvers, results from which need to comply to the IMO maneuverability standard for any vessel over 100 m in length. As during design stage these are assessed based on suitable dynamic models along-with empirically or otherwise estimated coefficients, the values of these coefficients become important. While inertia forces or equivalently the acceleration derivatives can be more confidently estimated, it is the damping or velocity-derivatives (,,,) on which the simulated trajectories depend more significantly. Of these, the yaw-velocity derivatives are found to be most important.
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Breaking wave modeling and estimation of energy dissipation
L. Bhaskar Mulagaleti¹, G. Muraleedharan², P.G. Kurup³ and N. Unnikrishnan Nair4
¹Dept. of Physical Oceanography, Cochin University of Science and Technology, Kochi-682 016
²IIT Delhi, Hauz Khas, New Delhi-110 016
³Amrita Institutions, Ashram Lane, Azad Road, Kochi-682 017
4Dept. of Statistics, Cochin University of Science and Technology, Kochi-682 022
The dissipated wave energy due to breaking in shallow waters is the input energy source for alongshore currents, littoral drift, wave induced sediment transport etc. which affect the coastal stability. An accurate estimation of the dissipated wave energy in coastal waters will provide to implement appropriate measures for the dynamic balance of the coastline with changing wave conditions due to monsoon and non-monsoon seasons. The Modified Weibull Model simulates the observed breaking wave height distribution better than the other two probabilistic models by chi-square test at 0.05 level of significance. The concept of a Weibull probability density function for wave heights and the modified Weibull model for breaking wave heights is more realistic than considering different probability models. The distribution of the estimated dissipated wave energy seems to be having the same trend of the computed except for lower wave heights. The data considered are the daily maximum significant wave height data obtained by the Coastal Engineering Research Center at Duck, North Carolina (depth of wave recording=8.5 m), daily maximum significant wave height recorded by National Institute of Ocean Technology, Chennai and the maximum wave heights off Valiathura recorded by Center for Earth Science Studies, Thiruvananthapuram.
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Hydrodynamic analysis of a space capsule impacting water
Ravi Challa, V.G. Idichandy and C.P. Vendhan
Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600036.
The space capsule recovery experiment (SRE) helps to demonstrate the recovery technology of space modules from arbitrary space vehicles. Future Indian Space Missions will involve the acquisition, storage and return of sample materials collected during space flight or planetary exploration. During reentry, the module will be decelerated by aerobraking andthen by a parachute deceleration system. The final phase of any Sample Return mission requires an earth entry, descent, and landing capsule (water recovery). This paper presents the results obtained by a series of drop tests conducted on the model of a space capsule to assess the hydrodynamic forces acting on the capsule. The determination of hydrodynamic forces experienced by a body entering the water surface is an extremely difficult task since the sea surface is not planar and is constantly changing, thus making the impact parameters statistical in nature.
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Wave environment in the vicinity of an isolated structure of arbitrary shape - a numerical approach
K. Praveen Reddy and J.S. Mani
Department of Ocean Engineering, IITM, Chennai- 600 036.
A numerical model study conducted to determine wave field transformation and wave force on a single structure of arbitrary shape (circular, oblong) is presented in this paper. In the formulation of the scheme, the boundary-value problem is restricted to two-dimensions and the solution is written in terms of velocity potential ( f (x, y)) of the waves, which satisfies Laplace equation. The scattered portion of velocity potential of the wave is solved numerically through source distribution method. The results indicate that force ratio (Fr= Fmax/ r gD 3 ) increases with increase in Hi/L. The increase is in order of 70% for the range of Hi/L (0.02 < Hi/L < 0.08). The force ratio decreases by around 30% from circular shape to oblong shape (b = 1D, h = 1.1D). Wave field studies in the vicinity of circular and oblong shape intake structures, experimental and numerical validation has also been carried out. The paper emphasizes the need for considering wave environment around the structure for conservative design.
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Experiments on ringing response of vertical cylinder in waves
G.N.V. Prasad, R. Sundaravadivelu and V. Sundar
Ocean Engineering Department, Indian Institute of Technology, Madras, Chennai–600 036
Recent model tests on tension leg platforms (TLP) and gravity-based platforms (GBS) have revealed strong transient resonant responses during extreme wave-frequency responses. These responses, termed ringing, are associated with large-crested, steep wave events. Such wave conditions and the responses are very important for the safety of the structures in offshore engineering practice. The frequency transient type response has been observed in offshore system, particularly in TLP and GBS, constructed with vertical cylinders, which may have a resonance periods 3 to 5 s. These platforms may in high sea-states experience responses of considerable amplitude suddenly that are generated at this resonance period, which is a concern with respect to extreme loading. The generation of the higher harmonic loads leading to ‘ringing' of offshore structures is not completely understood yet. Therefore, a need exists for clear identification of the system characteristics and environmental conditions, which lead to its onset. A laboratory measurement program on the wave loads acting on a fixed vertical cylinder has been considered. The aim is to study wave loads, which may generate high frequency resonant responses of vertical cylinders. This paper reviews model-test measured responses of a monotower GBS to draw conclusions on the nature of loads causing ringing. The details of model, instrumentation, analysis of the data and the results are presented and discussed in this paper.
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Numerical model of wave forces on semi submerged obstacle
M.R. Abbasi¹, V. Sundar² and A Schlenkhoff¹
¹Hydraulic Engineering Section, Dept. of Civil Engineering, Bergische University of Wuppertal, Germany
²Department of Ocean Engineering, I.I.T. Madras, Chennai, India
Due to the rapid increase in the computational capability, there has been a steady progress in numerical modeling of wave structure interaction problems. Several investigators have developed formulations and mathematical tools to understand the behaviour of fixed and floating structures in waves. In the present work, a numerical model based on the Boundary Element Method (BEM) using the Green's Function has been developed. With this numerical model, the hydrodynamic wave forces and the transmission characteristics of semi submerged obstacles near the free surface have been evaluated and presented as a function of the scattering parameter. Further, a parametric study has been carried out, in which the effect of the relative depth of submergence and the geometrical shape of the obstacle is examined. For this purpose, three different shapes (circular and rectangular cylinder and a thin impermeable barrier) and five different relative depths of submergence of the obstacle were considered.
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