Analyses of Current and Wave Forces on Velocity Caps

The primary environmental impact caused by seawater intake operation is marine life impingement resulting from the intake velocity. Environmental Protection Agency (EPA) of United State has regulated the use of velocity cap fitted at intake structures to reduce the marine life impingement. The engineering design parameters of velocity cap has not been well explored to date. This study has been set to determine the fundamental relationships between intake velocity and design parameters of velocity cap, using computational fluid dynamic (CFD) model. A set of engineering design criteria for velocity cap design are derived. The numerical evidence yielded in this study show that the velocity cap should be designed with vertical opening (Hvc) and horizontal shelf (ℓvc). The recommended intake opening ratio (Or) shall be 0.36 Vr−0.31, where Or = Hvc/ℓvc and Vr =V0/Vpipe. Vo is the velocity at the intake window and Vpipe is the suction velocity at the intake pipe. The volume ratio (ωr) between the velocity cap (ωvc) and intake tower (ωIT) is recommended at 0.11 Vr−1.23. The positive outlooks that yielded from this study can be served as a design reference for velocity cap to mitigate the detrimental impacts from the existing intake structure.

The cooling water system for the Seabrook Nuclear Power Station represents a unique venture in the utilization of the Ocean as a source for the plant's cooling water. An extensive tunnel system, bored out in bedrock, well under the waters surface will be used to connect the land based plant to the ocean by means of large diameter shafts located over a mile at sea in water depths exceeding 50 feet. The main thrust of this paper covers the design and installation techniques involved with the eleven 4 '-11" diameter discharge and the three 9'-5" diameter intake ocean shafts. The approach chosen permits the use of pre-fabricated shaft linings and incorporates a safe dry-tap method for connecting the offshore shafts to the tunnels. INTRODUCTION The Seabrook Power Station is located approximately 40 miles north of Boston, Massachusetts and two miles inland off the Atlantic Ocean at Seabrook, New Hampshire (Figure 1). The Plant, presently under construction, is a two unit, nuclear powered, electric generating station, with a capacity of 1150 megawatts (electric) per unit. The plants "once through" cooling water system requires 850,000 gallons/minute of water with temperatures less than 70°F to operate at its peak efficiency. The limitless source of water provided by the Atlantic Ocean, which in the Seabrook area will seldom exceed 65° F, provides an ideal location to satisfy the plants cooling water requirements. Although desirable to locate the plant immediately adjacent to the cooling water source, available land suitable for founding of the Nuclear plant limited its location to within two miles of the shore line. One of the basic objectives in selecting the cooling water system was to minimize environmental impact, particularly with respect to protection of the saltmarsh, clam flats and waterfront facilities. Among the alternate concepts evaluated, a deep tunnel system provided minimal environmental impact, although it does not represent the least cost approach. Many plants have similar water requirements, but it is unlikely that any other plant has purposely maintained the source of water at such a remote distance from the plant in order to assure minimal environmental impacts. The once through cooling system is comprised of two independent aquifers, one for the cool water intake and the other for the heated water discharge. Starting 260 feet below the plant level (240 feet below mean sea level), at the bottom of 19'-0" finished diameter land shafts, 19'-0" diameter tunnels extend out under the ocean at an ascending grade of about 0.5% until they reach their respective offshore terminus locations about 160 feet below the ocean's surface (MSL). (See Plan and Profile Figures 1 and 2). The intake tunnel is 17,140 feet long and connected to the ocean by means of three, 9'-5" finished diameter shafts, spaced 110 feet apart, located approximately 7000 feet off the Hampton Beach shoreline in 60 feet of water. A 30'-6" diameter concrete structure ("velocity cap") is mounted on the top of each shaft to reduce the intake velocity (See Figure 7).

Experimental study of interactions between multi-directional focused wave and vertical circular cylinder, part II: Wave force

Typical offshore structures are designed as tension-leg platforms or gravity based structures with cylindrical substructures. The interaction of waves with the vertical cylinders in high sea states can result in a resonant response called ringing. Here, the frequency of the structural response is close to the natural frequency of the structure itself and leads to large amplitude motions. This is a case of extreme wave loading in high sea states. This understanding of higher-order wave forces in extreme sea states is an essential parameter for obtaining a safe, reliable and economical design of an offshore structure. The study of such higher-order effects needs detailed near-field modelling of the wave-structure interaction and the associated flow phenomena. In such cases, a Computational Fluid Dynamics (CFD) model that can accurately represent the free surface and further the wave-structure interaction problem can provide important insights into the wave hydrodynamics and the structural response. In this paper, the open source CFD model REEF3D is used to simulate wave interaction with a vertical cylinder and the wave forces on the cylinder are calculated. The harmonic components of the wave force are analysed. The model employs higher-order discretisation schemes such as a fifth-order WENO scheme for convection discretisation and a third-order Runge-Kutta scheme for time advancement on a staggered Cartesian grid. The level set method is used to obtain the free surface, providing a sharp interface between air and water. The relaxation method is used to generate and absorb the waves at the two ends of the numerical wave tank. This method provides good quality wave generation and also the wave reflected from the cylinder are absorbed at the wave generation zone. In this way, the generated waves are not affected by the wave interaction process in the numerical wave tank. This is very essential in the studies of higher-order wave interaction problems which are very sensitive to the incident wave characteristics. The numerical results are compared to experimental results for higher-order forces on a vertical cylinder to validate the numerical model.

A mathematical model for the problem of wave diffraction by a floating fixed truncated vertical cylinder is formulated based on Boussinesq equations (BEs). Using Bessel functions in the velocity potentials, the mathematical problem is solved for second-order wave amplitudes by applying a perturbation technique and matching conditions. On the other hand, computational fluid dynamics (CFD) simulation results of normalized free surface elevations and wave heights are compared against experimental fluid data (EFD) and numerical data available in the literature. In order to check the fidelity and accuracy of the Boussinesq model (BM), the results of the second-order super-harmonic wave amplitude around the vertical cylinder are compared with CFD results. The comparison shows a good level of agreement between Boussinesq, CFD, EFD, and numerical data. In addition, wave forces and moments acting on the cylinder and the pressure distribution around the vertical cylinder are analyzed from CFD simulations. Based on analytical solutions, the effects of radius, wave number, water depth, and depth parameters at specific elevations on the second-order sub-harmonic wave amplitudes are analyzed.

Estimating hurricane-induced vertical surge and wave loads on elevated coastal buildings based on CFD simulations and ensemble learning

Wave forces on, and water-surface fluctuations around a vertical cylinder encircled by a perforated square caisson

The extreme shallow-water waves during a tropical cyclone are often simplified to solitary waves. Considering the lack of simulation tools to effectively and efficiently forecast wave forces on coastal box-girder bridges during tropical cyclones, this study investigates the impacts of solitary waves on box girders and accordingly develops a fast prediction model for solitary wave forces. Computational fluid dynamics (CFD) simulations are used to simulate the hydrodynamic forces on the bridge deck. A total of 368 cases are calculated for the parametric study by varying the submergence coefficients (Cs), relative wave heights (H/h) and deck aspect ratios (W/h). With the CFD simulation results as the training datasets, an artificial neural network (ANN) is trained utilizing the back-propagation algorithm. The maximum wave forces first increase and then decrease with the Cs, while they monotonically increase with H/h. For relatively large H/h and small Cs values, the relationship between the maximum wave forces and W/h presents strong nonlinearities. The observed correlation coefficients between the ANN predictions and the CFD results for the vertical and horizontal wave forces are 98.6% and 98.1%, respectively. The trained ANN-based model shows good prediction accuracy and could be used as an efficient model for the tropical cyclone risk analysis of coastal bridges.

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves. Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model, wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations. The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy. Then, the wave forces and characteristics around the cylinder are studied, including the velocity field, wave surface elevation and pressure. The effects of relative wave height, Keulegan-Carpenter (KC) number and cylinder locations on the wave forces are also discussed. The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number. Before the wave force peaks, the growth rate of the wave force shows an increasing trend as the cylinder moves onshore. The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region. As the cylinder moves onshore, the wave force on the cylinder initially increases and then decreases. For the cases considered here, the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline. Furthermore, the fluid velocity peaks when the maximum wave force appears at the same location.

Characteristics of higher-harmonic breaking wave forces and secondary load cycles on a single vertical circular cylinder at different Froude numbers

In this paper, the performance of different wave generation and absorption methods in computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) is analyzed. The open-source CFD code REEF3D is used, which solves the Reynolds-averaged Navier–Stokes (RANS) equations to simulate two-phase flow problems. The water surface is computed with the level set method (LSM), and turbulence is modeled with the k-ω model. The NWT includes different methods to generate and absorb waves: the relaxation method, the Dirichlet-type method and active wave absorption. A sensitivity analysis has been conducted in order to quantify and compare the differences in terms of absorption quality between these methods. A reflection analysis based on an arbitrary number of wave gauges has been adopted to conduct the study. Tests include reflection analysis of linear, second- and fifth-order Stokes waves, solitary waves, cnoidal waves and irregular waves generated in an NWT. Wave breaking over a sloping bed and wave forces on a vertical cylinder are calculated, and the influence of the reflections on the wave breaking location and the wave forces on the cylinder is investigated. In addition, a comparison with another open-source CFD code, OpenFOAM, has been carried out based on published results. Some differences in the calculated quantities depending on the wave generation and absorption method have been observed. The active wave absorption method is seen to be more efficient for long waves, whereas the relaxation method performs better for shorter waves. The relaxation method-based numerical beach generally results in lower reflected waves in the wave tank for most of the cases simulated in this study. The comparably better performance of the relaxation method comes at the cost of larger computational requirements due to the relaxation zones that have to be included in the domain. The reflections in the NWT in REEF3D are generally lower than the published results for reflections using the active wave absorption method in the NWT based on OpenFOAM.

Inline forces and bow wave height on a vertical cylinder moving in waves — Experimental study and CFD validation

The evaluation of the complex wave regime due to wave interaction with a large group of cylinders placed in proximity requires an efficient and accurate numerical model. This paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of wave forces and flow around vertical circular cylinders placed in groups of different configurations at low Keulegan-Carpenter (KC) numbers. The 3D numerical wave tank is validated by comparing the numerical results with experimental data. Further, the hydrodynamic effects associated with three cylinders placed in tandem, side by side and in a 3 × 3 square array of nine cylinders are investigated. Wave forces are seen to reduce along the row in a tandem array. In a side-by-side arrangement, the central cylinder experiences the highest force. A combination of these effects is seen in the 3 × 3 square array. The variation of the wave forces on the cylinders in the array for different center-to-center distances and incident wavelengths is evaluated and the results show that the wave forces are the highest on the cylinders when the center-to-center distance is slightly less than half the incident wavelength.

An experimental study of wave forces on the vertical cylinders in shallow waters was carried out in a wave channel. The wave parameters, wave forces and wave pressures are measured and studied in the paper. The study indicates that the distribution of wave pressures of the shallow water waves can be described by an exponential function with respect to water depth. The maximum surface elevation for shallow water waves can be estimated using the significant wave height. The wave pressure around circumference can be expressed as a simple form of cosine function. An experimental formula for the calculation of wave forces on vertical cylinders is proposed. As compared with test data, the predicted wave forces showed good agreement and high reliability. The calculated wave forces by different wave theories are less than those of the proposed method. Therefore, the wave force calculation method for shallow water waves should be modified for engneering applications.

The present investigation examines several simplifications and hydrodynamic approximations commonly employed in wave force analyses. Alternatives and modifications are sought which improve the resolution of a general Morison approach. This is accomplished by considering two basic arrangements; a vertical cylinder and a horizontal cylinder in progressive waves. The physical differences between the flows are explored and the results are compared to previous planar harmonic flow measurements. It was found that modifications to the usual Morison approach are required to adequately account for the orbital motions of the fluid and to account for the orientation of the orbits with respect to the cylinder axis. The consequences of this finding are discussed for inclined cylinders in waves and for cylinders in short-crested seas. The axial variations of the wave force on vertical cylinders are also examined in order to establish error bounds for the common practice of assuming constant values of Cm and CD over the entire span. Lastly, the methods of computing force transfer coefficients from a force record are examined and sources of error are identified and briefly discussed. INTRODUCTION In the face of rising construction costs, the increased importance of dynamic loadings, and in view of the more hostile sites under consideration, the accuracy of wave force computations becomes a critical question. The least well understood wave loading regime, hence the one with the least accurate descriptions, is the regime wherein both drag and inertia forces are important. The basis for most wave force computations in this regime is the usual Morison equation. In the past the Morison approach has been tailored with some success to particular applications. However attempts to generalize the approach have not been successful and consequently large uncertainties accompany each new application. The discrepancies between prediction and observation can be as large as 50 to 100 percent. For the most part these inaccuracies stem from a poor understanding of the unsteady vortex flows which occur in this regime and from several simplifications inherent in the usual Morison approach. In lieu of a complete hydrodynamic description of the various possible vortex flows, an unlikely accomplishment in the near future, an improved approach to wave force prediction appears to be one that can account for the major differences between vortex flows. This paper outlines such an approach and at the same time identifies uncertainties that can arise from differences in the methods of calculation. BACKGROUND The basis for many unsteady wave force calculations is the so-called Morison equation which may be written as (Available in full paper) for a unit length of the cylinder. Here CD and Cm are the usual force transfer coefficients, U is a characteristic maximum velocity, K = U T/D is the Keu1egan-Carpenter number, T is the wave period, and u is the velocity. A dot denotes a time derivative. The equation has its origins in the work of Stokes and, strictly speaking, pertains only to the component of force that is in line with a one dimensional unsteady flow.