Calculation Of Potential Flow Research Articles

Experimental decomposition of nonlinear hydrodynamic loads and hydroelastic responses in wave–structure interactions of monopile wind turbines

This study explores the nonlinear effects of hydrodynamic loads and hydroelastic responses in monopile-supported offshore wind turbines, with a focus on their harmonic structures. High-quality experimental data were collected in a shallow water basin across various irregular waves. Their harmonic components up to the fourth order were successfully isolated using a novel four-phase decomposition technique, which effectively extracts harmonics from random time series. The results highlight significant contributions of higher-order harmonics across various sea states. Specifically, two physical models were employed: a flexible monopile to capture structural hydroelastic deformations during large wave events and a rigid monopile to accurately estimate hydrodynamic loads without hydroelastic effects. Additionally, numerical results from fully nonlinear potential-flow calculations were compared, revealing that while the potential-flow solver underestimates total wave loading, especially for higher harmonics. In terms of the free-surface elevations and hydrodynamic forces, this study confirms that their higher-order harmonics align well with the scaling of their corresponding linear components in both amplitude and phase. This enables the prediction of higher-order profiles based solely on their linear components. However, this efficient model is inadequate for accurately estimating the higher-order harmonics of monopile's hydroelastic responses during these extreme wave events, highlighting the need for further refinement.

Computation of potential flow in multiply connected domains using conformal mapping

Computation of potential flow in multiply connected domains using conformal mapping

Potential-flow computations in infinite or zero gravity limits via a weakly singular boundary integral equation

Potential flow computations, based on a weakly singular integral equation, are considered in the infinite-gravity limit g=∞ and the zero-gravity limit g=0. The weakly singular integral equation, obtained via a straightforward and rigorous application of Green’s basic identity, involves a distribution of weak dipoles that is continuous across the body surface. The integral equation is solved via a low-order panel method, which is validated for a half sphere and applied to the S60 ship model in translation along the x, y or z-axis. A systematic numerical analysis of the convergence of numerical predictions shows that the number of panels that is required to obtain a 0.1% accuracy is significantly different for the infinite-gravity or zero-gravity flows, and for translation of the S60 hull along the x, y or z-axis. In particular, a very large number of panels is required for translation of the S60 ship model along the horizontal x or y-axis in the zero-gravity limit.

Potential and real spatial models: Differences and response characteristics from the perspective of flow

Exploring the coupled relationship between the potential laws of a region and the actual spatial model and identifying regional development trends and the rationality of the model structure are important for realizing integrated development and regional coordination. In this study, we first expounded the basic connotation of regional spatial structure and flow, reviewed the relevant research, and discussed the potential interaction and flow calculation. Supported by the theory of “space of places” and “complex network”; we then proposed a quantitative research framework to identify the regional structural characteristics, differences and responses in structure under the regional potential model and the real model. Second, we selected Guangdong-Hong Kong-Macao Greater Bay Area as a representative study object. Our results showed that the potential model and the real model is relatively similar in network structure and is mismatched in space. We further defined this response characteristics through the three states of “overloaded, balanced and surplus”. Specifically, the Great Bay Area is characterized by overloaded of the inner ring, balanced of the outer ring and local surplus. We designed different network robustness simulation experiments to study their overall network difference, hoping to help improve the rationality of decision-making in urban spatial planning and governance.

Computation of plane potential flow around multi-element airfoils using the Schottky–Klein prime function

Potential flow is computed around multi-element airfoils in two dimensions using numerical conformal mapping combined with the calculus of the Schottky–Klein prime function. The corners at the trailing edges of the airfoils are successively removed by Kármán–Trefftz maps. The map from the domain exterior to disks to the domain exterior to the smooth images of the airfoils is computed using an extension of a Fourier series method for the disk due to Fornberg. The velocity potential for flow in the circle domain, with circulation calculated to satisfy the Kutta condition in the airfoil domain, is computed using the Schottky–Klein prime function. The computations are compared to examples from the aerospace engineering literature.

The wave interference and the wave drag of a leader–follower ship fleet

The wave interference and the corresponding effects on the wave drag of the leader–follower ship fleet are researched here, via a 4-point model and the Neumann-Michell potential flow computation. A simple analytical relation of the dominant wake angle is given, which considers both the wave interferences between the ship bow and the stern, and the wave interferences between the leader ship and the follower ship. Moreover, a simple relation of the destructive interference region (where the wave drag of the follower ship decreases) for the wave drag is given based on the research on the effects of the ship distance ℓ2 and the Froude number F on the wave drag of the leader ship or the follower ship. An interesting finding is that the destructive interference relation is invalid at low Froude numbers or very high Froude numbers, since the constructive interference of the divergent waves is apparent at low Froude numbers and the transverse waves is relatively small at high Froude numbers. These findings can be used to decrease the wave drag of ship fleets or ship formations.

Fog Harvesting with Highly Wetting and Nonwetting Vertical Strips.

Highly wetting and nonwetting substrates have been widely used in fogwater collection systems for enhanced water harvesting. In this work, fog harvesting substrates comprising PVC strips of different wetting properties and widths ranging from 1-5 mm were vertically aligned and spaced apart at regular intervals to give the same solid area fraction of 0.8. Evaluation of the water collection efficiencies of the tested configurations revealed that 1 mm wide superhydrophilic strips was the most efficient, achieving double the amount of water harvested compared with 2.8 mm wide strips. This finding was attributed to the low Stokes numbers of the aerosol particle distribution of the fog which tended to result in them being brought by the flow streamlines toward the air gaps between the strips. Stagnant flow regions at the edges of each strip, revealed through potential flow calculations, then caused higher liquid imbibition and impaction there for water harvesting. It was also found that the Cassie nonwetting substrates that originally exhibited contact angles of 161° transformed to Wenzel wetting with zero contact angle within 60 min of fog interception. Optical profilometry revealed no obvious difference in surface roughness between the central region and edges of the strips, indicating that surface morphology was unlikely to be a contributing factor for enhanced water collection at the edges. The findings here indicated that highly wetting vertical strip architectures with narrow widths (1 mm) were favorable over wider strips for water harvesting provided that clogging and re-entrainment were not significant factors.

Gap resonance from linear to quartic wave excitation and the structure of nonlinear transfer functions

Resonant response of water waves in a narrow gap, with the interaction of multiple highly resonant modes, is an interesting hydrodynamic phenomenon with practical applications. Gap resonances between two identical fixed rectangular boxes are experimentally investigated for unidirectional waves with broadside incidence. We show that gap resonances can be driven through both linear wave excitation and nonlinear processes, i.e. frequency doubling, tripling and quadrupling – apparently new observations. It is striking that the time histories of the gap resonances excited through different nonlinear interactions are remarkably similar to each other. It seems likely that the nonlinear sum-frequency transfer functions for gap resonances depend strongly on the output frequency sum of the interacting linear components, but only weakly on the frequency difference. In terms of their structure in multiple frequency space (at second order the bi-frequency plane for two components), these transfer functions must then have a near-flat form in the direction(s) perpendicular to the leading diagonal. This is supported by our potential flow calculations of the quadratic transfer functions (QTFs). It is therefore convenient to approximate the QTF matrix as ‘flat’ in the direction perpendicular to the leading diagonal. This approximation is justified through experimental data that includes viscous damping. It is too complex, if not impossible, to calculate the full cubic or quartic transfer functions as direct evidence. However, the experimental analysis does provide some support for the near-flat structure being applicable to transfer functions above second order. The flat form approximation greatly reduces lengthy calculations of the high-order transfer functions.

Design waves and statistics of linear gap resonances in random seas

Water wave resonance between two side-by-side vessels is a multimode resonant hydrodynamic phenomenon with low damping. The potential flow damping and viscous damping inside the gap play a significant role, influencing the amplitudes of the gap resonances. The frequencies of the gap modes can be well predicted by linear potential flow theory, while much effort has been made to explore the nature of the viscous damping. A series of experiments is conducted to explore the temporal (Zhao et al., Journal of Fluid Mechanics, vol. 812, 2017, 905–939) and spatial structure (Zhao et al., Journal of Fluid Mechanics, vol. 883, 2020, A22) of the resonant responses along the gap. Ultimately, it is of practical interest to understand the response statistics along the gap in random seas, to facilitate decision making for safe offshore operations. Following our previous studies which focused on new physics, here we identify the design waves that produce the most probable maximum responses under unidirectional random linear wave excitation. This is achieved through an efficient prediction model within linear theory. Combining the experimental data and linear potential flow calculations, we provide the lower and upper bounds of gap responses, bracketing possible responses at field scale. The statistical model is expected to be of practical importance for offshore operations.

Impeller design and CFD analysis of fluid flow in rotodynamic pumps

The intricate internal flows in the rotodynamic water pump impellers can be well predicted by using computational fluid dynamics and mathematical modeling. An impeller is a radial type rotor that increases the acceleration of the fluid due to the centrifugal action and the fluid is pumped through the casing to a higher potential head. The efficiency and performance of the centrifugal pump can be enhanced by optimizing certain design parameters of the impeller. In this work, the impeller design and development of potential flow calculations for the liquid flow using the MATLAB software was performed. NX-CAD was used to model the impeller and pump. CFD analysis in ANSYS CFX showed the flow of liquid through the variable cross-section of the volute casing of the pump. Modification in impeller design showed that the overall performance of the pump can be improved. The program developed in the MATLAB also served as a type of calculator for determining the type of pump that can be used for various industrial purposes based on the velocity of the liquid, head and discharge rate.

On the velocity at wind turbine and propeller actuator discs

Abstract. The first version of the actuator disc momentum theory is more than 100 years old. The extension towards very low rotational speeds with high torque for discs with a constant circulation became available only recently. This theory gives the performance data like the power coefficient and average velocity at the disc. Potential flow calculations have added flow properties like the distribution of this velocity. The present paper addresses the comparison of actuator discs representing propellers and wind turbines, with emphasis on the velocity at the disc. At a low rotational speed, propeller discs have an expanding wake while still energy is put into the wake. The high angular momentum of the wake, due to the high torque, creates a pressure deficit which is supplemented by the pressure added by the disc thrust. This results in a positive energy balance while the wake axial velocity has lowered. In the propeller and wind turbine flow regime the velocity at the disc is 0 for a certain minimum but non-zero rotational speed. At the disc, the distribution of the axial velocity component is non-uniform in all actuator disc flows. However, the distribution of the velocity in the plane containing the axis, the meridian plane, is practically uniform (deviation <0.2 %) for wind turbine disc flows with tip speed ratio λ>5, almost uniform (deviation ≈2 %) for wind turbine disc flows with λ=1 and propeller flows with advance ratio J=π, and non-uniform (deviation 5 %) for the propeller disc flow with wake expansion at J=2π. These differences in uniformity are caused by the different strengths of the singularity in the wake boundary vorticity strength at its leading edge.

Unsteady response of airfoils due to small-scale pitching motion with considerations for foil thickness and wake motion

Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow and unsteady Reynolds-Averaged Navier–Stokes calculations are performed on various Joukowski foils undergoing sinusoidal, variable amplitude, small-scale pitching motion at a chord-based Reynolds number of 106 over a range of reduced frequencies between 0.01–100. These calculated results from both approaches are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin, flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict conditions are explored, and the particular terms which control the unsteady responses are identified and discussed. For increasing pitch amplitudes and reduced frequencies the shed wake is seen to become quite non-planar and to form coherent vortex structures. Despite this wake behavior, the normalized airfoil responses at the disturbance reduced frequency are seen to be largely unaffected. However, non-negligible responses are generated across a wide range of other frequencies. Potential flow calculations for symmetric Joukowski foils show that there is marginal effect of foil thickness at reduced frequencies less than one. For higher reduced frequency conditions however, the unsteady lift response is seen to experience both an amplification of level and a phase shift relative to the Theodorsen model. A specific augmenting expression is developed for this behavior through analysis within the potential flow framework.

Analysis of Numerical Errors of the Hess Smith Panel Method With Asymmetric Meshes

AbstractAlthough less accurate in comparison with most of the existing high-order panel methods, the Class Hess Smith panel method is still popular for potential flow calculations due to its simplicity, robustness, and especially efficiency. In the application where the method is adopted for the problems of concern, the method is usually first validated and analyzed for numerical accuracy prior to the application. This is a common practice as also seen in almost all the literature. However, the objects chosen for validation and accuracy analysis are often geometrically symmetric (most typically, spheres) and discretized into symmetric meshes. However, such analysis with symmetric meshes does not actually reveal the numerical errors as the body involved in the problem in concern or the flow around the body may not be symmetrical. In this paper, the numerical errors of the Hess Smith method are systematically analyzed with asymmetrical meshes. The values of various quantities associated with isolated panels and also the entire body are obtained and compared with the Hess Smith panel method does exhibit a very different error pattern.

Investigation of the unsteady responses of airfoils due to small-scale motion

Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow calculations are performed on Joukowski foils of varying thickness undergoing variable amplitude, small-scale, heaving or pitching motion over a range of reduced frequencies between 0.01 and 100. These calculated results are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict assumptions of the Theodorsen model are explored, and focus is placed on results which show deviations from the Theodorsen model. These include altered unsteady responses for finitely thick foils and non-zero mean angle of attack conditions, non-linearity of the wake of shed vorticity, and analysis of the unsteady streamwise force. Further, within the potential flow framework the particular terms which control the unsteady responses are identified.

Validation of potential flow method for ship resistance prediction

Considering the extensive use of numerical methods in naval design, a question about the accuracy numerical tools that could estimate the flow around the ship and which are the limitations of these tools for practical design applications. In this context, experimental test on scaled models play an important role in validation of numerical simulations. This work is dedicated to validation of the method used to calculate the non-linear potential free-surface flow around the ship. Global quantities, as total resistance, wave resistance coefficient, residual resistance coefficient are flow characteristics concentrated in a single value, and their validation provides a criterion for choosing the optimum hull. Validation of physical phenomena is done using the wave profile, the pressure distribution on the body or the free surface topology. Validations were developed by comparing experimental data published for benchmark test cases, results of the resistance test performed in ICEPRONAV towing tank, against the results of numerical calculation performed by the author. Numerical simulations were performed using the XPAN module of the SHIPFLOW program, dedicated to the calculation of non-linear potential free-surface flow. Therefore, in order that the validation to be consistent and not influenced by scale effects, all calculations have been performed for the model scale. For this purpose, numerical studies have been considered for three ship models with different complex geometries. Two of the three hulls, the 60 Series and the DTMB 5415, are benchmark tests, chosen due to a wide range of detailed experimental and numerical results. The other one is case study for which experimental measurements were carried out in the frame of research projects.

Dynamic Aeroelasticity of Wings with Tip Propeller by Using Navier–Stokes Equations

Aeroelastic computations are made for a flexible wing with a tip-propeller system designed for electric aircraft. Flow is modeled using the Navier–Stokes equations, and wing structures are modeled using plate finite elements. A time-accurate procedure is developed to embed the flexible wing in an overset grid topology along with rotating blades. Results are validated with existing data from wind-tunnel and potential flow computations. Aeroelastic responses are compared for the wing with and without a tip-propeller system. The present work extends the capabilities of current Navier–Stokes solvers to simulate the aeroelasticity of complex configurations and impacts the design of electric aircraft for urban transportation.

Comparison of actuator disc flows representing wind turbines and propellers

Actuator disc theory is the basis for rotor design and analysis, valid for discs representing wind turbine rotors as well as propellers. In Froude’s momentum theory swirl is absent, in Joukowsky’s momentum theory this is included. The momentum theory including swirl, developed in WES, 2:307-316,2017, as well as potential flow calculations have been expanded to propeller discs. For the rotational speed Ω → ∞ the classical Froude results are recovered. For low values of Ω the propeller discs show an expanding instead of contracting wake, like wind turbine discs. Both flow regimes show a complete blockage of the flow for a low but non-zero Ωmin. For all wind turbine discs, so irrespective of Ω, the velocity in the meridian plane, is constant at the disc, for all propeller discs this is not.

Bank effects for KVLCC2

A study is presented on ship–bank interaction effects in which viscous-flow solvers are used to predict the hydrodynamic forces and moments on the ship. The ship under consideration is the KRISO Very Large Crude Carrier (KVLCC2). For this hull form, Flanders Hydraulics Research (FHR) has conducted shallow water model tests in their towing tank equipped with surface-piercing banks and a vertical quay wall. The forces and moments on the KVLCC2 model were obtained for various water depths and lateral distances to the banks. Additionally, the wave elevation was measured between the quay wall and the ship model. In this study, two different CFD codes are used to predict the loads on the KVLCC2 as a function of the water depth and lateral position in the channel. The effect of propeller suction and free surface modelling on the results is quantified. Furthermore, comparisons will be made with CFD results from literature and potential flow computations to highlight the benefits of each approach. It will be shown that with careful setup of the computations, reliable predictions of the ship–bank interaction effects can be obtained.

URANS predictions on the hydrodynamic interaction of a conceptual FLNG-LNG offloading system in regular waves

Using an unsteady Reynolds-Averaged Navier-Stokes solver, numerical investigations of hydrodynamic interactions of a conceptual FLNG-LNG offloading system in regular head sea waves are presented. Initially, a verification study is performed on estimating the numerical uncertainties within the URANS model. Based on the validated computational setup, the gap wave responses and wave loads on the FLNG and LNG vessels are studied for different wave frequencies and varying lateral separations. URANS predictions on the gap wave responses are compared with that from the experiments and demonstrate better accuracy over potential flow calculations especially at relatively high wave frequency conditions where gap wave resonance occurs. From the data gathered, it is seen that the gap wave resonance appears when the incident wave frequency approaches the natural frequency of the gap fluid, resulting in significant variation of wave loads in the directions of sway, heave, pitch and yaw. Meanwhile, reduction in the lateral separation shifts the occurrence of gap wave resonance to a higher wave frequency and brings more significant exaggerations on the gap waves and wave loads. Furthermore, when comparing model and full scale wave loads and gap wave responses, the two series of data correlate well implying insignificant influence of scale effects.

URANS predictions of wave induced loads and motions on ships in regular head and oblique waves at zero forward speed

The paper presents predictions on the hydrodynamics of a conceptual floating liquefied natural gas (FLNG) and a liquefied natural gas (LNG) carrier in regular head and oblique sea waves using an unsteady Reynolds-Averaged Navier–Stokes (URANS) solver. Initially, a verification and validation study is performed on estimating the numerical uncertainties in the presented URANS simulations. Using the verified numerical setup, ship hydrodynamic properties including wave induced loads as well as ship motion responses are investigated for different wave conditions. The computed time history results are decomposed by Fourier Series to estimate the wave load and ship motion transfer functions. These results show good correlation with predictions from model tests and potential flow calculations. From the computations, it is observed when increasing the wave length, wave diffraction around the ship becomes less profound and the water depth starts to influence the transfer functions. Full scale computations in head and oblique sea waves are also presented and compared with model scale predictions for investigating possible scale effects. The differences are found to be close to the numerical uncertainties, indicating minor influences of scale effects on the prediction of wave loads and ship motion responses for the tested cases.