Potential Flow Model Research Articles

Experimental investigation of three-dimensional Rayleigh–Taylor instability of a gaseous interface

Validating the theoretical work on Rayleigh–Taylor instability (RTI) through experiments with an exceptionally clean and well-characterized initial condition has been a long-standing challenge. Experiments were conducted to study the three-dimensional RTI of an SF $_6$ –air interface at moderate Atwood numbers. A novel soap film technique was developed to create a discontinuous gaseous interface with controllable initial conditions. Spectrum analysis revealed that the initial perturbation of the soap film interface is half the size of an entire single-mode perturbation. The correlation between the initial interface perturbation and Atwood numbers was determined. Due to the steep and highly curved feature of the initial soap film interface, the early-time evolution of RTI exhibits significant nonlinearity. In the quasi-steady regime, various potential flow models accurately predict the late-time bubble velocities by considering the channel width as the perturbation wavelength. Differently, the late-time spike velocities are described by these potential flow models using the wavelength of the entire single-mode perturbation. These findings indicate that the bubble evolution is influenced primarily by the spatial constraint imposed by walls, while the spike evolution is influenced mainly by the initial curvature of the spike tip. Consequently, a recent potential flow model was adopted to describe the time-varying amplitude growth induced by RTI. Furthermore, the self-similar growth factors for bubbles and spikes were determined from experiments and compared with existing studies, revealing that a large amplitude in the initial soap film interface promotes the spike development.

The past, present and future of multi-scale modelling applied to wave-structure interaction in ocean engineering.

Concepts and evolution of multi-scale modelling from the perspective of wave-structure interaction have been discussed. In this regard, both domain and functional decomposition approaches have come into being. In domain decomposition, the computational domain is spatially segregated to handle the far-field using potential flow models and the near field using Navier-Stokes equations. In functional decomposition, the velocity field is separated into irrotational and rotational parts to facilitate identification of the free surface. These two approaches have been implemented alongside partitioned or monolithic schemes for modelling the structure. The applicability of multi-scale modelling approaches has been established using both mesh-based and meshless schemes. Owing to said diversity in numerical techniques, massively collaborative research has emerged, wherein comparative numerical studies are being carried out to identify shortcomings of developed codes and establish best-practices in numerical modelling. Machine learning is also being applied to handle large-scale ocean engineering problems. This paper reports on the past, present and future research consolidating the contributions made over the past 20 years. Some of these past as well as future research contributions have and shall be actualized through funding from the Newton International Fellowship as the next generation of researchers inherits the present-day expertise in multi-scale modelling. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Pressure and Velocity Profiles over a Weir Using Potential Flow Model

Pressure and Velocity Profiles over a Weir Using Potential Flow Model

A hybrid potential flow model for shedding flow around a circular cylinder

A Hybrid Potential Flow (HPF) model for flow around a circular cylinder in the subcritical Reynolds number range (300≤Re≤3×105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$300 \\le Re \\le 3\ imes 10^5$$\\end{document}) is developed using a combination of elementary flow solutions and empirical data. By joining this developed near-body solution with von Karman’s model for the vortex wake, a complete solution for flow around a circular cylinder is calculated. Results for oscillatory forces, including the transverse lift force, due to vortex shedding as well as shedding frequencies are then calculated and presented. With the complete solution for flow around a cylinder calculated, the HPF model can be used as a step to calculate the flow around other bluff bodies using conformal mapping, an approach that has been developed and presented by the authors in a related paper.

Simulation of Depth-Limited Breaking Waves in a 3D Fully Nonlinear Potential Flow Model

Simulation of Depth-Limited Breaking Waves in a 3D Fully Nonlinear Potential Flow Model

Wave–structure interaction by a two–way coupling between a fully nonlinear potential flow model and a Navier–Stokes solver

A two-way domain decomposition coupling procedure between a fully nonlinear potential flow model and a Navier–Stokes solver capturing the free surface with a Volume of Fluid method is used to study wave–structure interaction applied to offshore wind turbines. Away from the structure, the large-scale inviscid wave field is modeled by the potential code. Wave generation and absorption in this 3D hybrid model take place in the outer potential domain. The codes exchange data in the region around their common boundaries. Through the two-way coupling, waves propagate in and out of the viscous subdomain, making the hybrid algorithm suitable to study wave diffraction on marine structures, while keeping the viscous subdomain small. Each code uses its own mesh and time step. Subdomains are overlapping, therefore continuity conditions on velocity and free surface have to be verified on two distinct coupling surfaces at any time. Parallel implementation with communications between the models relying on the Message Passing Interface library allows calculations on large spatial and temporal scales. The coupling algorithm is first tested for regular nonlinear waves and then applied to simulate wave loads exerted on a vertical monopile in 3D. Attention is paid to the high-order components of the horizontal force.

Clogging of toe drain drastically affects phreatic seepage in earth dams

In aged levees, toe (blanket) drains get clogged with time due to seepage-induced suffusion and translocation of fine soil fractions from the upstream to the downstream part of the embankment. These particles deposit on the top of the drain (usually, Terzhagi's graded gravel) as a cake. Also, high hydraulic gradients in the vicinity of the drain move the fine particles into the body of the coarse filter material such that “internal colmation” takes place. In this paper 2-D seepage to a clogged drain is studied experimentally, analytically and numerically. In a sandbox, we illustrate the difference in the position of a phreatic surface and the seepage flow rate between an equipotential toe drain and a clogged one. In the analytical solution, a potential flow model is used and the Neumann (Kirkham-Brock) boundary condition on the clogged drain surface (horizontal segment) is imposed. A circular triangle is mapped conformally onto a reference half-plane, where Hilbert's boundary value problem for a holomorphic function is solved. For a given size of the levee, clogging causes a significant rise of the phreatic surface, although the seepage flow rate drops. In HYDRUS2-D simulations, a FEM-meshed Richards’ equation for a saturated-unsaturated 2-D flow is used for solving in a composite polygon, which mimics a vertical cross-section of a rectangular levee and a clogged-colmated blanket drain. Numerical results are in rough agreement with the analytical model.

Estimating the performance of wind turbines misaligned with respect to the wind direction using a simplified CFD based approach

Wind direction in atmospheric boundary layer changes constantly. As such, the power extracted from the wind turbines in a wind farm is subjected to change. This change in wind direction impacts the wake pattern which in turn affects the power output of the downstream wind turbines. Empirical wind farm models are useful in such cases to assess the overall performance of the wind farms. However, the results provided by these models can be made more useful if fluid-structure interaction (FSI) effects are also considered. In the present work, we begin by looking at the potential flow model and the issues associated with it and used a modified model with constant vorticity to analyze the wind power available to the downstream wind turbines in a wind farm misaligned with respect to wind direction for irrotational flow. A simplified FSI based approach is used to carry out the simulations without the need of modelling the complicated wind turbine geometry.

A new parametrization of the Global Blockage Effect

An existing potential flow model for describing the interaction of complex structures and flow currents is adapted for the modeling of a wind farm. The aim is to investigate if such a simple formulation could improve the representation of the global blockage effect (GBE) in engineering models. The model is then coupled with a parametrization of GBE from LES in order to describe the power extraction redistribution GBE is normally associated with. Despite the original model formulation being found to not apply particularly well to the description of a wind farm, the further development introduces dependency on the atmospheric stratification above the wind farm, a feature of GBE observed in LES. Furthermore, it agrees with the trend of power extraction redistribution in a wind farm. However, more research is necessary to promote a better quantitative match between LES and the proposed model.

Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

We frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz–Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier–Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier–Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.

Vortex shedding from bluff bodies: a conformal mapping approach

A model to calculate flow around bluff bodies of various geometries is presented. A conformal map between the plane of the bluff body and the plane of a unit circular cylinder is established by using a combination of Karman–Trefftz transformations and Fornberg’s method. Flow in the circle plane is calculated using the authors’ Hybrid Potential Flow (HPF) model and mapped back to the shape plane. By joining this calculated near-body flow with von Karman’s model for a vortex wake, forces due to vortex shedding and shedding frequencies are calculated. In this manner, a complete solution for the flow around bluff bodies of various geometries is established. Results for two shapes are presented, along with recommendations for further work.

Modelling the far-field effect of drag-induced dissipation in wave–structure interaction: a numerical and experimental study

In the interaction of water waves with marine structures, the interplay between wave diffraction and drag-induced dissipation is seldom, if ever, considered. In particular, linear hydrodynamic models, and extensions thereof through the addition of a quadratic force term, do not represent the change in amplitude of the waves diffracted and radiated to the far field, which should result from local energy dissipation in the vicinity of the structure. In this work, a series of wave flume experiments is carried out, whereby waves of increasing amplitude impinge upon a vertical barrier, extending partway through the flume width. As the wave amplitude increases, the effect of drag – which is known to increase quadratically with the flow velocity – is enhanced, thus allowing the examination of the far-field effect of drag-induced dissipation, in terms of wave reflection and transmission. A potential flow model is proposed, with a simple quadratic pressure drop condition through a virtual porous surface, located on the sides of the barrier (where dissipation occurs). Experimental results confirm that drag-induced dissipation has a marked effect on the diffracted flow, i.e. on wave reflection and transmission, which is appropriately captured in the proposed model. Conversely, when diffraction becomes dominant as the barrier width becomes comparable to the incoming wavelength, the diffracted flow must be accounted for in predicting drag-induced forces and dissipation.

A multiscale hydro-elastoplastic model for large floating structures in two-dimension

A novel fluid–structural model was presented considering hydro-elastoplastic behavior, which coupled multiple hydro-structural-material scales. A large floating sandwich structure (LFSS) comprising upper and lower high-strength panels and a low-weight core was considered as an illustration. The mesoscale characteristics of materials and elastoplastic parameters of the low-weight perforated components were coupled by utilizing the representative volume element (RVE) method. Through the parameterized relations from RVE analysis, the flexure dynamics model for the floating sandwich structure with an equivalent homogenized core was deduced. With the flexure dynamic equation, yield criterion, and potential flow model, a multiscale hydro-elastoplasticity theoretical model was established, which combined the wave action, hierarchical component, material configuration, and structural behavior. The dynamic responses of the large floating structure under fluid–structure interaction were calculated, and the internal deformation (i.e., core strain) was set as the determining variable for the plastic region. The initially intact floating structure became hinged multi-modules after plastic cracking, and the high-strength layers at the cracking positions behaved as flexible hinges, which was defined as a hydro-elastoplastic process. The elastoplastic state evolutions of the LFSSs with different structural parameters and material configurations were solved for practical optimization. The results indicated that the multiscale coupled calculation model can provide great scientific guidance for designing large floating structures.

Dissipative potential flow models and energy evolution characteristics for curtain-wall caisson breakwaters under wave action

Curtain-wall caisson breakwaters are a kind of coastal protection structure, which is composed of semi-submersible vertical thin curtain walls, a rear vertical caisson, and wave chambers formed by the curtain walls and rear caisson. When water waves interact with the curtain-wall caisson breakwater, the wave energy may be partially dissipated owing to the flow separation and vortex formation near the edges of curtain walls. The conventional potential flow solution without considering wave energy dissipation gives unreasonable results of full wave reflection by the curtain-wall caisson breakwater. To address this issue, this study develops a dissipative potential flow model for predicting the hydrodynamic performance of the curtain-wall caisson breakwaters. The wave energy dissipation near the breakwater is considered by introducing a quadratic pressure loss condition at the entrances of wave chambers. By adopting appropriate dimensionless dissipation coefficients, the analytical predictions of the reflection coefficient and the wave amplitude inside chambers are in good agreement with published experimental results. The differences in the hydrodynamic quantities predicted by the dissipative and conventional potential flow solutions are examined, and further discussion based on the dissipative analytical solution is performed. Moreover, viscous numerical simulations based on a meshless particle method are carried out to clarify the characteristics of wave energy evolution, wave energy dissipation, and local fluid motion near the curtain-wall caisson breakwaters. The results show that the front curtain wall plays the leading role in the wave energy dissipation process of the whole double-chamber curtain-wall breakwater.

On the nonlinear moonpool responses in a drillship under regular heading waves

In this study, the nonlinear and viscous damping effects on the free-surface elevations of the recess-type moonpool inside a drillship are investigated. Based on a three-dimensional nonlinear potential flow (NPF3D) model, the nonlinear moonpool responses excited by regular heading waves are simulated in the time domain. To consider the vortex-shedding damping effects, induced by nonlinear moonpool responses, the pressure drop model of Chu et al. [Chu et al., “Effects of nonlinearity and viscous damping on the resonant responses in two-dimensional moonpools with a recess,” Appl. Ocean Res. 127, 103295 (2022)] is extended to three-dimensional and combined with NPF3D to form a viscous modified nonlinear potential flow model (referred to as NPF3D_V). The pressure drop model is composed of two parts in order to account for the energy loss from the first harmonic (piston-mode motions) and higher harmonics (sloshing-mode motions), respectively. The investigation focuses on the piston-mode resonance and secondary resonances of the first and second longitudinal sloshing modes. The response amplitude operators of the higher harmonics, by which the nonlinear effects are evaluated, are computed by the NPF3D_V model. It is found that the higher harmonics are noticeable at the excitation frequencies ωn0/m, where secondary resonances of the nth longitudinal sloshing mode are triggered. In addition, it is found that increasing the length of the recess can promote the nonlinear response of the moonpool significantly. For the moonpool with a long recess, the higher harmonics at secondary resonance are comparable to the first harmonics.

Magnus Force Estimation Using Gauss’s Principle of Least Constraint

The flow around a rotating cylinder is one of the fundamental problems that have piqued the interests of many venerable fluid mechanicians since the time of Rayleigh. The force caused by the rotation of the cylinder has always been considered as an immediate consequence of viscosity, since the potential flow model failed entirely to predict the value of the circulation due to the lack of a Kutta-like condition. On the other hand, Glauert modeled the flow outside the boundary layer of a rotating cylinder as a potential flow with an unknown circulation. He then obtained an approximate solution of Prandtl’s boundary-layer equations and applied the no-slip condition to estimate the circulation in the outer flow. Interestingly, for rapidly rotating cylinders (α=(ωR/U)≫1), up to fourth-order in the small parameter ϵ=(1/α), the obtained circulation is independent of viscosity. In this work, we use Glauert’s model of the outer flow (i.e., a potential flow with an unknown circulation). However, instead of the tedious boundary-layer calculations, we rely on Gauss’s principle of least constraint to obtain the unknown circulation. A perfect match with Glauert’s solution is found. Moreover, our solution, in contrast to Glauert’s, points to the existence of different physics at small rotational speeds. The obtained results, given their perfect matching with Glauert’s solution (relying on the no-slip condition), point to a potential equivalence between the no-slip condition and fluid body forces.

MODIFICATION OF TI-6AL-4V TITANIUM ALLOY SURFACE RELIEF BY COMPRESSION PLASMA FLOWS IMPACT

Investigation of compression plasma flows impact on surface relief of Ti-6Al-4V titanium alloy was carried out in this work. Profilometry, x-ray diffraction, scanning electron microscopy, and sample weight measurements were used as investigation techniques. The findings showed that plasma impact led to the formation of developed surface relief (R<sub>a</sub> parameter was changed in the range of 0.7-2.7 μm) due to the action of hydrodynamic instabilities at the melt-plasma border. Increase in the number of pulses resulted in the growth of R<sub>a</sub> value. Numerical simulation of surface evolution under plasma impact was carried out on the basis of the model of incompressible fluid potential flow. Simulation data correlated with experimental data set. The hydrodynamic flow of the melt during plasma impact led to another process: surface erosion. Increase in both the absorbed energy density and the number of pulses resulted in erosion intensity increase. Formation of titanium nitride on the surface was observed as a result of the interaction of nitrogen (as a plasma generating gas) with the surface heated under plasma impact. Titanium nitride film prevented the development of the surface relief formed by the action of hydrodynamic instabilities.

Linear hydrodynamic model of rotating lift-based wave energy converters

A linear potential flow model of a rotating lift-based wave energy converter is developed by assuming that the lift is generated by a pair of equal and opposite circulations and that the amplitude of motion is small. The linearisation of the hydrodynamics means that the forces can decomposed and expressions for the wave excitation force and radiation damping force are derived independently and shown to be related to each other through the Haskind Relations. The expressions for the forces are used to show that there is an optimum phase and product of circulation and radius of rotation to maximise the wave power extracted, which is equivalent to the optimum phase and amplitude of motion from ‘conventional’ wave energy converter theory. It is also shown that at this optimum condition 100% of the incident wave energy can be extracted. It is shown that the forces are directly proportional to the velocities due to the motion of the vortices, the water particle velocities due to the incident wave, and the water particle velocities induced by the vortices. The effect of the vortex-induced water particle velocities is considered and the importance of including these velocities on the passive generation of circulation, e.g. by hydrofoils, is highlighted. The impact of a sub-optimum product of circulation and radius of rotation is also investigated and shown that the power capture is not highly sensitive to the optimal conditions in the same way as ‘conventional’ wave energy converters

Wave environment analysis at Norwegian harbours for land-based aquaculture facilities using a combined phase-averaging and phase-resolving numerical modelling approach

Numerical wave modelling of Norwegian coastal areas is challenging due to the drastically varying bathymetry, irregular coastline, and large domains of interest. The widely used phase-averaging models are limited by such bathymetric and topographic conditions. Phase-resolving models provide higher accuracy regarding strong nonlinear wave transformations with the trade-off of a higher computational cost. This study provides a combined phase-averaging and phase-resolving modelling approach to analyse the wave conditions for on-shore aquaculture facilities at the site candidates Fiskenes and Breivik, Andøya, Norway. The phase-averaging spectral model SWAN is used for the offshore sea state analysis based on the offshore hind-cast data. The analysis is performed on cascade nested grids, with increasing accuracy closer to the proposed harbour locations. A novel interpolation algorithm is proposed to provide comprehensive sea state information with every offshore wave directions without requiring additional simulations. The critical wave conditions are identified from SWAN and used as input to the open-source phase-resolving fully nonlinear potential flow model REEF3D::FNPF. Four scenarios are investigated and densely spaced wave gauges in the entire computational domain provide the distribution of significant wave height. The combined and cascade simulation approach helps to achieve a balance between computational efficiency and accuracy for large-scale marine environment assessment. The results show detailed wave statistics in the entire area of relevance near both harbours and provide a quantitative reference for both the site choice and the harbour design.

On the behavior of higher harmonics in the evolution of nonlinear water waves in the presence of abrupt depth transitions

The presence of abrupt depth transitions might trigger strong nonlinear effects on propagating water waves near coastal regions. In this study, the dynamics of nonlinear monochromatic waves over a submerged step representing the abrupt depth transitions are investigated both experimentally and numerically. Within the framework of the free-surface Euler equations, a fully nonlinear potential flow model based on a conformal mapping method is established to investigate the higher harmonics. The numerical method has been well validated with experimental measurements. To analyze the wave nonlinearity at the transitions, the higher harmonics are extracted both in the spatial and time domains. It is shown that abrupt depth transitions enhance the higher harmonic amplitudes in the shallower regions on the step. The effects of the incident wave frequency and height are studied. It is found that the higher harmonics induced by the abrupt depth transitions become more significant with increasing wave steepness. An analysis of the evolution of the skewness and kurtosis demonstrates the high asymmetry of the surface elevation on the upstream junction. The asymmetry shows clear nonlinear effect from the higher harmonics.