Pitch Excitation Research Articles

Experimental study of sloshing flows in a rectangular tank under coupled pitch and heave excitations

Sloshing in partially filled containers under external forces has significant implications across industries like aerospace and oil and gas transportation. The present study aims to explore the influence of the first and second order Faraday waves on both resonant and non-resonant pitch sloshing, as well as the effects of coupled resonance. Laboratory experiments were conducted to analyze sloshing impact pressures and record wave elevations, delving into how Faraday waves alter wave shapes and impact pressure dynamics, especially in shallow water conditions. Key findings reveal significant effects of Faraday waves on both resonant and off-resonant pitch excitation. In shallow water, the presence of the first mode Faraday wave leads to reduced pressure through upward-deflected breaking impact waves, while the second mode Faraday wave intensifies impact pressure by generating flip-through waves carrying substantial energy before impacting the sidewall. Furthermore, the study explores the interaction between pitch and heave excitations, revealing how combined resonance affects sloshing behavior. Coupled-resonant sloshing waves induce periodic pressure behavior due to energy dissipations, providing insights into the complex dynamics of sloshing flows under various excitations, crucial for optimizing design and ensuring safety in engineering applications.

Experimental Study on the Sloshing of a Rectangular Tank under Pitch Excitations

Fluid sloshing within containers subjected to external motion is a crucial yet intricate phenomenon with implications across various industries. This study investigates sloshing in a rectangular liquid tank through a series of experiments examining pitch excitations with diverse excitation frequencies and amplitudes across different liquid carrying rates. By analyzing pressure data and imagery of the free liquid surface, statistical trends in peak pressure at measurement points within the tank are identified, revealing the nonlinear behavior of the fluid. Spectral analysis generates power spectrum curves that delineate frequency components and energy distribution within the sloshing dynamics. Key findings include the identification of resonance-induced violent sloshing at a 20% liquid-carrying rate and a resonant frequency shift at a 70% liquid-carrying rate due to nonlinearity, displaying a “soft spring” characteristic in the frequency response. The free liquid surface exhibits four distinct waveforms depending on frequency. Notably, at a 70% liquid-carrying rate and resonant frequency excitation, three-dimensional vortex waves emerge, highlighting a complex three-dimensional effect within the tank. The power spectrum shows that the dominant response frequency aligns with the excitation frequency and its multiples. This investigation enhances our understanding of the intricate nature of sloshing in various liquid-carrying conditions, offering insights valuable for diverse industrial applications.

A numerical study of wave baffles on sloshing reduction of rectangular containers under combined excitation

The effect of horizontal wave baffles on slosh reduction of rectangular tanks under combined surge and pitch excitation is investigated in this work. Two-dimensional numerical modeling of a rectangular tank is performed using the Volume of Fluid (VoF) technique. The validation studies are performed, and the results agree with the data available in the literature. This study also considers the influence of baffle characteristics on sloshing reduction, such as wave baffle amplitude and the number of wave baffle cycles. The cosine baffles with negative amplitude and increased baffle amplitude performed better than others.

Physics-informed data-driven reduced-order models for Dynamic Induction Control

In this work, we find a reduced-order model for the wake of a wind turbine controlled with dynamic induction control. We use a physics-informed dynamic mode decomposition algorithm to reduce the model complexity in a way such that the physics of the wake mixing can be investigated and that the model itself can be easily embedded into control-oriented frameworks.After discussing the advantage of forcing the linear system resulting from the algorithm to be conservative (as a consequence of the periodicity of the pitch excitation) and the choice of observables, we describe a procedure for calculating the energy associated with individual modes. The considered data-set is composed of large eddy simulation (LES) results for a single DTU 10 MW wind turbine in uniform flow. Simulations were performed first with baseline control (for reference) and then with the Pulse and the Helix approaches with constant excitation amplitude and different excitation frequencies. The frequencies and energies associated with the resulting modes are discussed.

Slosh Damping in Rectangular Liquid Tank With Additional Blockage Effects Under Pitch Excitation

Abstract The quantification and damping of slosh responses are significant due to the increasing demand for safety of the liquid-based applications under severe external excitation. Recently, the solid or perforated baffle plates have been used to damp the slosh response of the liquid. However, there is uncertainty in the selection of an effective configuration of the baffle plates. In addition, most of the studies reported the slosh response under surge excitation. Therefore, this study focuses on the slosh response of the rectangular tank fitted with perforated baffle plates of different configurations under pitch excitation. For this, the liquid sloshing is simulated using the concepts of computational fluid dynamics (CFD) using pressure-based solver in the time domain. A detailed parametric study is carried out to develop an effective configuration of the perforated baffle plates considering the area of perforations, interperforation distance, size of perforations, distance between the perforated baffle plates, alignment of perforations, and the vertical position of perforated baffle plate as the parameters. The slosh responses are observed in terms of free surface elevation, hydrodynamic pressure, turbulence kinetic energy, velocity streamlines, power spectral density corresponding to the free surface elevation and the free surface deformation. The study developed a “zig-zag blocking alignment” of perforations for effective slosh damping, with the solid area between the perforations being 50%–60% of the area of perforations. In addition, “single-acting range” and “damping range” are identified to pilot the positioning of the multiple baffle plates in a rectangular tank under pitch excitation.

A Semi-Analytical Solution of Liquid Response in a Two-Dimensional Rectangular Tank with a Vertical Rigid Baffle Under Pitching Excitation

The present work uses a semi-analytic mathematical model to study the dynamic response of the partially liquid-filled rectangular tank equipped with a vertical rigid baffle at the bottom subjected to pitching excitation. The velocity potential consists of the rigid container velocity potential and the disturbance potential, which contains a Stokes–Joukowski potential. The liquid domain is divided into four simple sub-domains. The formal solution of the Stokes–Joukowski potential in each sub-domain is solved using the superposition principle and the separation of variables method. The dynamic response equation is established by using the free liquid surface equation. The ADINA solution is compared with the present method solution, which verifies the correctness of the proposed method. Finally, the effect of baffle parameters on liquid sloshing for a baffled tank subjected to harmonic and seismic pitching excitations is discussed in detail.

An experimental study of two-layer liquid sloshing under pitch excitations

The non-resonant and resonant responses of a two-layer liquid system in a tank under pitch excitation were investigated experimentally in this study. The movement of both the free surface and the interface was automatically identified simultaneously by an image processing method, which can rectify the visually tilted frames in a moving system. When the frequency of external excitation was near the natural frequency related to upper layer liquid, free surface resonance can be triggered. On the other hand, when the frequency of the external excitation was close to the natural frequency related to lower layer, resonant response of the interface between two liquids occurred. It is also found that Kelvin-Helmholtz instabilities with different length scales can be generated due to the reverse direction of velocities near the interface under different conditions. Such length scale of the Kelvin–Helmholtz instability can be estimated by using the critical Richardson number. In addition, the bottom of the tank may restrict the development of wave trough on the interface when the depth of lower layer was relatively shallow, while the free surface may limit the wave crest of interface when the thickness of the upper layer was small. Further investigations of the interface displacements for both non-resonant and resonant responses were also conducted in frequency domain.

Physics informed DMD for periodic Dynamic Induction Control of Wind Farms

Dynamic Induction Control (DIC) is a novel, exciting branch of Wind Farm Control. It makes use of time-varying control inputs to increase wake mixing, and consequently improve the velocity recovery rate of the flow and the power production of downstream turbines. The Pulse and the Helix are two promising DIC strategies that rely on sinusoidal excitations of the collective pitch and individual pitch of the blades, respectively. While their beneficial effects are evident in simulations and wind tunnel tests, we do not yet fully understand the physics behind them. We perform a systematic analysis of the dynamics of pulsed and helicoidal wakes by applying a data-driven approach to the analysis of data coming from Large Eddy Simulations (LES). Specifically, Dynamic Mode Decomposition (DMD) is used to extract coherent patterns from high-dimensional flow data. The periodicity of the excitation is exploited by adding a novel physics informed step to the algorithm. We then analyze the power spectral density of the resulting DMD modes as a function of the Strouhal number for different pitch excitation frequencies and amplitudes. Finally, we show the evolution in time and space of the dominant modes and comment on the recognizable patterns. By focusing on the modes that contribute the most to the flow dynamics, we gather insight on what causes the increased wake recovery rate in DIC techniques. This knowledge can then be used for the optimization of the signal parameters in complex layouts and conditions.

Airfoil buffet aerodynamics at plunge and pitch excitation based on long short-term memory neural network prediction

In the present study, a nonlinear system identification approach based on a long short-term memory (LSTM) neural network is applied for the prediction of transonic buffet aerodynamics. The identification approach is applied as a reduced-order modeling (ROM) technique for an efficient computation of time-varying integral quantities such as aerodynamic force and moment coefficients. Therefore, the nonlinear identification procedure as well as the generalization of the ROM are presented. The training data set for the LSTM–ROM is provided by performing forced-motion unsteady Reynolds-averaged Navier–Stokes simulations. Subsequent to the training process, the ROM is applied for the computation of the aerodynamic integral quantities associated with transonic buffet. The performance of the trained ROM is demonstrated by computing the aerodynamic loads of the NACA0012 airfoil investigated at transonic freestream conditions. In contrast to previous studies considering only a pitching excitation, both the pitch and plunge degrees of freedom of the airfoil are individually and simultaneously excited by means of an user-defined training signal. Therefore, strong nonlinear effects are considered for the training of the ROM. By comparing the results with a full-order computational fluid dynamics solution, a good prediction capability of the presented ROM method is indicated. However, compared to the results of previous studies including only the airfoil pitching excitation, a slightly reduced prediction performance is shown.

Dynamic investigation of a seven-tier container stack with different lashing arrangements subject to rolling and pitching excitation

ABSTRACT The current safety assessments of lashing systems and container stacks in various classification societies are based on static conditions, while dynamic behaviours are neglected. In this paper, the dynamic mechanical behaviour of a seven-tier 20-ft ISO freight container single stack and lashing devices under the combined rolling and pitching excitation is studied respectively. Through experiments and numerical simulations, five typical lashing arrangements are compared. The results show that a reasonable configuration of lashing stiffness, twist lock gap and lashing arrangement can decrease the dynamic response of the system. The external lashing arrangement is more suitable for the heavy stowage situation. The twist lock structure is more prone to failure in the horizontal direction than in the vertical direction, and a reasonable horizontal gap can effectively prevent the shear force from exceeding the allowable value. Finally, the benefits and drawbacks of each lashing arrangement for shipping companies are discussed.

Effect of Double-Side Curved Baffle on Reducing Sloshing in Tanks under Surge and Pitch Excitations

Sloshing is associated with the structural safety of liquid storage vessel. Installing the baffles inside the containers would be beneficial for the mitigating the damage due to the severe sloshing. In this study, an innovative type of double-side curved baffle was proposed to evaluate its effect on reducing sloshing in a rectangular tank under surge and pitch excitation. For comparison with conventional baffles, effects of the vertical baffle and the T-type baffle on mitigating sloshing were also studied experimentally and numerically by analyzing the free surface wave elevation as well as the hydrodynamic pressure on the tank wall. The effective stress at the double-side curved baffle along the height direction of the baffle is much smaller than that at the T-type baffle although they have the same mitigation effect on sloshing wave heights. The sloshing-induced effective stress on the double-side curved baffles was analyzed by varying their radian. Findings show that the effective stress on the baffle tends to decrease with the increase in the radian. The velocity field was presented to observe effect of the baffles on sloshing with the aid of ADINA and laboratory experiments conducted on a hexapod motion platform.

Experimental and numerical investigation on dynamic response of a four-tier container stack and lashing system subject to rolling and pitching excitation

This research aims to investigate the dynamic responses of the lashing force, twist lock force, and container stack displacement under conditions close to real, providing a better understanding of the mechanism behind container damage and loss. Based on Froude scaling laws, a four-tier 20-ft ISO freight container stack and lashing assembly scaled model was built. The rolling and pitching driving excitation is provided by a shaking table. Input variables for the experimental and numerical simulation include driving excitation (amplitude and frequency), lashing methods (internal and external), twist lock gap (horizontal and vertical), contact and friction between adjacent corner castings. Output variables of the system contain the lashing force, twist lock's tensile and shear force as well as displacement of the container stack. The results of the present study are compared via numerical simulation, experiments, and theoretical calculations, suggesting that the external lashing is superior to the internal lashing when encountering high stack and heavy stowage. There are mutual coupling effects between the lashing methods, lashing force, twist lock force and twist lock gap. Moreover, decreasing the gap can minimize the stack displacement and lashing force, while it is not a viable solution to reduce the twist lock force.

Application of autoregressive dynamic adaptive (ARDA) model in real-time wind power forecasting

Wind prediction technology has been the focus on the national research with the basis of the power system planning, a reference for power dispatch, and the optimal power flow distribution. Prediction technology is moving into the direction of controlling refinement with the development of the information technology, the artificial intelligence technology, and the improvement of edge computing devices. The wind farms can use real-time wind power prediction to improve their overall efficiency through advanced planning of the wind turbine adjustment and the pre-setting of the yaw, pitch, and generation excitation control systems. This paper proposes an innovative autoregressive dynamic adaptive (ARDA) model based on the improvement of the autoregressive (AR) model. The fixed parameter estimation method of the AR model is improved in the proposed model to a dynamically adaptive stepwise parameter estimation method. Meanwhile, the coefficients of the model are updated adaptively based on the characteristics of wind power data, which improves the accuracy of the proposed model. The prediction accuracy of the proposed model is further improved by the residual function. It was observed that the model adapts well to wind power data with different degrees of volatility. The ARDA model and two other models were tested by using stationary and fluctuating wind power data (unit: seconds), and the wind power prediction results at different forecasting step lengths were compared. It was observed that the ARDA model is more accurate, with faster calculation rate, and better dynamic adaptability to data fluctuations than the ARIMA and LSTM models. This paper proposes an important method for real-time power prediction that can be employed for the advanced control and improved the power generation of wind farms.

Aerodynamic damping investigations of light dynamic stall on a pitching airfoil via modal analysis

This study presents an investigation of the aerodynamic damping of light dynamic stall phenomena on a pitching NACA 0012 airfoil via Dynamic Modal Decomposition (DMD) and Proper Orthogonal Decomposition (POD) techniques. DMD analysis predicts a dominant mode having the same frequency of the pitching excitation and contributing all of the aerodynamic damping of the system. The temporal orthogonality of the DMD technique renders all other DMD modes orthogonal to both the dominant DMD mode as well as the pitching motion, resulting in zero aerodynamic work due to these DMD modes. However, the lack of temporal orthogonality of POD modes implies several modes contributing to the aerodynamic damping of the system. The leading-edge suction and the trailing-edge vortex were considered the most energetic features by the two most dominant POD modes and was also observed as the most significant spatial feature in the dominant DMD mode shape. A recently developed Hilbert transform-based methodology was extended here for computing chord-wise intra-cycle aerodynamic damping distribution. This method shows large variations of the intra-cycle aerodynamic damping distribution obtained from DDES surface pressure data over the cycle, which poses a challenge to extract meaningful information for possible flow control applications. However, the dominant DMD modal aerodynamic damping distribution shows no intra-cycle variations and predicts negative damping hot-spots near the leading and trailing edges of the chord. Such conclusions are significantly different than observed for an attached flow case or observed in a related study considering a deep dynamic stall regime at lower Reynolds number.

Three-dimensional sloshing in a scaled membrane LNG tank under combined roll and pitch excitations

This paper experimentally investigates the three-dimensional sloshing in a membrane-type LNG (liquefied natural gas) tank under combined roll and pitch excitations. Seven groups of roll and pitch amplitudes are studied. For each group, the roll and pitch have the same frequency, and around ten frequencies are tested in a frequency band that ranges from 0.5 times of the resonance frequency in the length direction of the tank to 1.4 times of the resonance frequency in the tank breadth. The characteristics of the sloshing waves and impact pressures are analysed in detail. It is found that the steady-state sloshing waves can be classified into four patterns: the length-dominant wave, swirling wave, diagonal wave, and breadth-dominant wave. Highlighted is the swirling wave that is observed in most of the cases where the roll and pitch amplitudes are significant and the excitation frequency locates between the resonant frequencies in the two directions. It is hypothesized that the rotational motion of the tank imposes necessary initial conditions to trigger the swirling wave. The swirling wave is always associated with wave impingements at tank corners and induce violent impact pressures. The practical implementation is that reinforcements of the membrane layer should be added or the sloshing wave should be suppressed near the tank corner to mitigate the damages to the interior layer of the membrane-type LNG tank.

Optimized perforated bulkhead for sloshing mitigation and control

The phenomenon of sloshing consists in the violent liquid motion inside partially filled containers and it is a major concern for the design of a number of structures in naval and offshore industry. The use of perforated swash bulkheads is an effective technique to mitigate the sloshing. In the present work, a comprehensive investigation of the sloshing within box-shaped tanks equipped with perforated bulkheads is carried out. The investigation considered a broad range of parameters, which includes several open-area ratios and different filling levels under pitching excitations encompassing the first three sloshing resonant modes of a non-compartmented tank. As a result, a relation of optimized open-area ratio as function of the filling ratio is achieved for overall sloshing mitigation. The effectiveness of the obtained relation is confirmed by numerical simulations using proposed swash bulkhead geometries that follow the optimized open-area distribution. As the perforated bulkheads introduces additional complexity to the already challenging sloshing phenomenon, the numerical simulations of the present work were performed by adopting a fully-Lagrangian particle-based method, which easily deals with phenomena involving nonlinear free surface conditions, such as large free surfaces deformation and fragmentation, and complex geometries.

Coupled Responses in a Partially Liquid-Filled Container with the Multi-Elastic Baffles Subjected to Pitching Excitation

The coupled responses in the partially liquid filled container with multi-elastic annular baffles are investigated by the semi-analytical method subjected to the pitching excitations. The trial solutions of the dynamic deflections of the multi-elastic baffles, the surface wave height and the velocity potential can be obtained by introducing the time-dependent generalized coordinates. The Stokes-Joukowski potentials, which are relevant to the kinematical boundary condition of the container, can be obtained analytically. Based on the coupled vibration equations of the multi-elastic baffles and the boundary conditions on the free surface, the coupled dynamic response equations can be established. Parameter studies are carried out to investigate the effects of the parameters of the multi-elastic baffles on the coupled responses of the system.

Vibration characteristics simulation and comparison of traditional cab system model and seat–cab coupled model for trucks

To define the application fields of the traditional cab system model and the seat–cab coupled model, this paper mainly aims to investigate the differences of the vibration characteristics of the two models. First, the two models and their motion equations were introduced. Then, based on the mechanical parameters of the seat and cab system for a truck, the transmissibility characteristics of the two models were analyzed. The results show that the traditional model can relatively accurately predict the pitch and roll vibration characteristics of the real seat–cab system. However, it overvalues the vertical vibration transmitted from the front suspensions of the cab. Third, the typical excitation conditions and the measuring points were selected. Finally, under the typical excitation conditions, the dynamic responses of the measuring points were calculated. The results show that under the vertical excitation condition, the dynamic responses of the two models have obvious differences. Under the roll excitation condition and the pitch excitation condition, the roll responses and the pitch responses of the cab between the two models show almost no obvious difference. Under the random excitation condition, the vertical acceleration responses have relatively larger deviations between the two models, however, the angular acceleration responses are almost the same. For the preliminary design of the cab system, the traditional cab system model can be used. However, for the accurate design and the optimization of the seat–cab system, the seat–cab coupled model is recommended.

Analytical solution of capsizing moments in ship chamber under pitching excitation

As the core structure of the shiplift, the ship chamber is a typical rectangular container with filling water depth less than 0.1. Even small pitching excitation could produce large liquid sloshing and significant capsizing moment, and lead to a catastrophic overturning accident. As a basis of dynamical modeling and simulation of the shiplift, a fluid dynamic model is presented to predict the capsizing moments based on the Housner theory. Assuming a time-harmonic pitching excitation, the potential solution reflecting dynamic characteristics between pitching excitation and the fluid free surface oscillation angle is expanded analytically. A series of engineering formulas for the capsizing moments, including impulsive and convective parts, are then imposed. Comprehensive numerical analysis further extends the applicability of formulations to the cases for most of ship chambers or other rectangular tanks with similar filling water depth. The validation of proposed scheme is extensively demonstrated through comparison with other theoretical method and experimental results, and the interaction between the forcing frequency, the capsizing moments and fluid natural frequency has been qualitatively descripted. The results exhibited that the present model has accurate description under the conditions of small pitching angles and only considering the capsizing moments coming from the convective pressures can ensure high accuracy in engineering design.

Coupled Responses in a Partially Liquid‐Filled Cylindrical Tank with the Single Flexible Baffle under Pitching Excitations

Antisloshing baffles are widely used in many engineering fields, including aerospace, ocean engineering, and nuclear engineering. The semianalytical scheme is proposed to explore the effect of the single flexible baffle on the coupled responses in the rigid cylindrical tank partially filled with ideal liquid undergoing the pitching excitation. The function series for the velocity potential, the dynamic deflection of the flexible baffle, and the surface wave height are given by introducing the time‐dependent generalized coordinates. The Stokes–Joukowski potentials which are contained in the liquid velocity potential can be solved analytically. According to the dynamic and kinematic equations for the free surface and the coupled vibration equation for the flexible baffle, the coupled dynamic response equations are obtained. The additional damping terms are introduced to account for the sloshing damping. The semianalytical method is validated by the comparison study with the numerical results. Parameter studies are conducted to investigate the effects of the parameters of the flexible baffle on the coupled responses of the system.