Nonlinear Drag Research Articles

CFD-assisted linearized frequency-domain analysis of motion and structural loads for floating structures with damping plates

Damping plates are widely used on floating offshore structures to reduce the dynamic responses in waves. Linearization of the nonlinear drag loads are needed to solve the floater motions by frequency-domain methods, which, to date, still dominate the analysis of wave-frequency responses of floating structures in engineering practice. While existing studies focus on damping effects on heave motions, there is a lack of understanding on how the drag loads on damping plates should be modeled to predict the angular motions and structural loads of the floaters. Two different configurations of Morison elements are investigated in this paper. The first considers the entire damping plate as a whole, while the second locates Morison elements at the estimated ‘points of acting’ of drag loads for different parts of the damping plate. Computational Fluid Dynamics (CFD) analysis is utilized to obtain the required drag coefficients and the ‘points of acting’ as function of Keulegan–Carpenter number. In comparison to full CFD analysis of the same floater in regular waves, a hybrid approach is shown to give satisfactory wave-frequency results, not only for motion responses, but also bending moments and shear forces on the damping plate. However, non-negligible second-harmonic structural loads that cannot be properly accounted for by the existing Morison-drag formulation are also identified in CFD analysis, calling for special attention to structural assessment under extreme wave conditions. This study also demonstrates that locating the Morison elements at ‘points of acting’ improves the prediction of motion responses and structural loads at resonance.

Ratchet universality in the directed motion of spheres by unbiased driving forces in viscous fluids

Directed motion of a sphere immersed in a viscous fluid and subjected solely to a nonlinear drag force and zero-average biharmonic forces is studied in the absence of any periodic substrate potential. We consider the case of two mutually perpendicular sinusoidal forces of periods T and T/2, respectively, which cannot yield any ratchet effect when acting separately, while inducing directed motion by acting simultaneously. Remarkably and unexpectedly, the dependence on the relative amplitude of the two sinusoidal forces of the average terminal velocity is theoretically explained from the theory of ratchet universality, while extensive numerical simulations confirmed its predictions in the adiabatic limit. Additionally, the dependence on the dimensionless driving frequency of the dimensionless average terminal velocity far from the adiabatic limit is qualitatively explained with the aid of the vibrational mechanics approach.

Turbulent Drag at the Ice‐Ocean Interface of Europa in Simulations of Rotating Convection: Implications for Nonsynchronous Rotation of the Ice Shell

AbstractEuropa's geologically scarred surface shows significant evidence that the ice shell may have rotated nonsynchronously in the past. The long‐term spin state of the ice shell is controlled by the time‐mean torques acting upon it. A torque that has not been previously considered is exerted due to drag from oceanic currents beneath the ice. We estimate this torque for the first time by performing global, nonhydrostatic, three‐dimensional simulations of Europa's ocean, including nonlinear turbulent boundary layer drag at the seafloor and ice‐ocean interface. Our simulations show that ocean dynamics, which manifest in alternating east‐west jets, result in a net torque on the ice shell. The torque can act to either spin up or spin down the ice shell depending on the strength of convection, suggesting that a torque reversal can occur as Europa's interior thermally evolves. Scaling analysis indicates that an average jet speed of at least ∼1 cm s−1 is required for the ice‐ocean torque to be comparable to the tidal torque acting to spin up the ice shell. Our results suggest that ocean currents may contribute to any nonsynchronous rotation of the ice shell. Consequently, Europa's present‐day spin state may hold information about the dynamics of its subsurface ocean.

Virtual holonomic constraints based super twisting sliding mode control for motion control of planar snake robot in the uncertain underwater environment

In this article, the snake robot having nine links with eight joints is considered for serpentine motion in the underwater environment. The movement of a snake robot occurs due to nonlinear drag forces and fluidic torque in underwater conditions. The uncertainties in drag forces and fluidic torque are considered to track the head angle and tangential velocity in this work. The virtual holonomic constraints are formulated to track all the joints by designing a controller for single joint. The parameters of gait pattern are obtained using the sliding surface. The sliding surface is formulated for head link angle and velocity tracking. Super twisting sliding mode control approach is proposed to deal with uncertainties, and results are compared with sliding mode control and adaptive sliding mode control. The robustness of controller is verified by inputting measurement noise. The significant improvement has been observed in chattering indicator and control effort by using the proposed super twisting sliding mode control. The investigation of this research article focuses on how to get almost chattering free operation in underwater uncertain environmental conditions with minimum control effort.

Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

In this paper, the multiphase lattice Boltzmann flux solver (MLBFS), where the phase field model and the apparent liquid permeability model are built-in, is developed to simulate incompressible multiphase flows in fractal pore structure at the representative elementary volume scale. MLBFS takes advantage of the traditional Navier–Stokes solver (e.g., geometric flexibility and direct handling of complex boundary conditions) and lattice Boltzmann method (e.g., intrinsically kinetic nature, simplicity, and parallelism). It is easily applied to simulate multiphase flows transport in the porous medium with large density ratios and high Reynolds numbers. This study focuses on the fluid flow in fractal pore structures and provides an in-depth discussion of the effects of non-Newtonian index, fractal parameters, and density ratios on multiphase flow. The proposed model is validated with benchmark problems to test the applicability and reliability of the MLBFS in describing fluid flow in fractal pore structures with large density ratios and viscosity ratios. Simulation results show that the fractal parameters (i.e., fractal dimension, tortuous fractal dimension, porosity, and capillary radius ratio) can accurately characterize fractal pore structure and significantly affect the apparent liquid permeability. In addition, the flow rate increases with the fractal dimension and decreases with the tortuous fractal dimension, while both flow rate and apparent liquid permeability decrease as the capillary radius ratio. It is also noteworthy that the effect of nonlinear drag forces cannot be neglected for shear-thickened flows.

A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge

Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED), which integrates scientific discipline wisdom in a scientist-in-the-loop approach, with state-of-the-art symbolic regression (SR) methods. SciMED combines a wrapper selection method, that is based on a genetic algorithm, with automatic machine learning and two levels of SR methods. We test SciMED on five configurations of a settling sphere, with and without aerodynamic non-linear drag force, and with excessive noise in the measurements. We show that SciMED is sufficiently robust to discover the correct physically meaningful symbolic expressions from the data, and demonstrate how the integration of domain knowledge enhances its performance. Our results indicate better performance on these tasks than the state-of-the-art SR software packages , even in cases where no knowledge is integrated. Moreover, we demonstrate how SciMED can alert the user about possible missing features, unlike the majority of current SR systems.

Nonlocal transport of heat in equilibrium drift-diffusion systems

The amount of heat an integer quantum Hall edge state can carry in equilibrium is quantized in universal units of the heat flux quantum ${J}_{q}=\frac{\ensuremath{\pi}{k}_{B}^{2}}{12\ensuremath{\hbar}}{T}^{2}$ per edge state. We address the question of how heat transport in realistic one-dimensional devices can differ from the usual chiral Luttinger liquid theory. We show that a local measurement can reveal a nonquantized amount of heat carried by the edge states, despite a globally equilibrium situation. More specifically, we report a heat enhancement effect in edge states interacting with Ohmic reservoirs in the presence of nonlocal interactions or chirality-breaking diffusive currents. In contrast to a nonequilibrium, nonlinear drag effect, we report an equilibrium, linear phenomenon. The chirality of the edge states creates additional correlations between the reservoirs, reflected in a higher-than-quantum heat flux in the chiral channel. We show that for different types of coupling the enhancement can be understood as static or dynamical back action of the reservoirs on the chiral channel. We show that our results qualitatively hold by replacing the dissipative Ohmic reservoirs by an energy-conserving mesoscopic capacitor and consider the respective transmission lines for different types of interaction.

Mixture of Experts for Unmanned Aerial Vehicle Motor Thrust Models

AbstractThis study aims to analyze three unmanned aerial vehicles’ static and dynamic motor thrust models and to compare them with flight test telemetry motor angular velocity data as ground truth. This comparison determines which model is the most accurate based on the root mean square of the difference between the motor models and the telemetry data values. The Burgers and Staples models are dynamic thrust models with nonlinear drag, while the Gibiansky model is a static thrust model with linear drag. The mixture of experts (MoE) architecture assigns weights to each thrust model through a gating network such that higher weights map to the more accurate models. Flight tests include two maneuvers: triangle and shoelace loop. The triangle maneuver uses the cornering option to stop and turn at each waypoint. In contrast, the shoelace loop maneuver uses the curved option to fly smooth curves at waypoints instead of stopping and turning at each waypoint. Simulation results of the motor thrust models use the telemetry data to compute the motor angular velocities with tuned model parameters tailored to the type of maneuver. Regarding motor angular velocity estimation, the Gibiansky and Burgers models tend to overestimate, while the Staples model tends to underestimate. The combination of the simulation results of the models with the mixture of experts allows us to achieve higher accuracy than any of the individual models.

An effective approach for VARANS-VOF modelling interactions of wave and perforated breakwater using gradient boosting decision tree algorithm

In this paper, we propose a systematic and time-efficient approach to calibrate 2D VARANS-VOF models for simulation of wave interaction with porous plate in numerical wave tank. To reach this goal, we develop a data-driven approach in combination with numerical and experimental data to figure out the optimal empirical coefficient associated with linear and non-linear drag force coefficients (α, β). Advanced gradient boosting decision trees algorithms (GBDT) are adopted to capture the accuracy of the prediction model. Although only limited samples, for instance 72 samples are generated and chosen to train and test the prediction model, the GBDT model is able to identify the trend in non-linear influence of model parameters. The advantage of GBDT algorithm can obviously be seen through the regression analysis with very high regression coefficient (R2 > 0.99). The developed model is subsequently employed for a large range of considered parameters as input features of the models to predict the possible hydrodynamics characteristics. The smallest mean squared error between predicted and experimental results, which is 0.00204, is found and used to determine the best performing combination of these model parameters. The numerical model together with selected values of empirical coefficients is then validated using available experimental data in literature. The free surface elevations in front of and behind the structure from the numerical model are nearly identical with the experimental data.

Submerged marine towed instrument array: A theoretical investigation using Lagrange mechanics

Towed instrument arrays (TIA) measure physical data in the ocean surface boundary layer (OSBL). The TIA consists of n probes mounted on a cable and towed behind a vessel. The comparably low interpolation errors of the two-dimensional results vastly enrich research on ocean energy dissipation.Here, we develop a new theoretical framework considering the mounted probes and their effects on the dynamics of the TIA in analogy to multiple pendulums on a moving suspension point. The dynamics are induced by external velocity-dependent drag- and coordinate-dependent depressor forces.We show that our method of including nonlinear drag forces is consistent and that our discrete approach is capable of computing continuous solutions in the limit n≫1. Hence, the proposed method unifies earlier approaches and is tested against several analytical and known numerical solutions. The phase space for the case n=1 is similar to that of a damped harmonic oscillator. A typical timescale estimates the equilibrium state of the dynamical system. We provide evidence of our method by comparing the results with real measurement data.Based on the theoretical investigations, test cases, and the comparison with real data, our method is a powerful tool, suitable for campaign planning, instrument design, and post-processing purposes.

Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag.

We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog–Fokker–Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.

Drift simulation of a floating offshore wind turbine with broken mooring lines in a dynamic sea condition

This study investigates the aero-hydro-mooring coupled dynamics of the National Renewable Energy Laboratory (NREL) offshore 5-MW baseline wind turbine supported by the Offshore Code Comparison Collaboration Continuation (OC4) DeepCwind semisubmersible floating platform by considering the effects of suddenly broken mooring behaviour. The wind and wave loads can be selected as the Cummins time-domain equation inputs based on the Norwegian Petroleum Directorate wind and Joint North Sea Wave Project wave spectrums. The nonlinear viscous drag was estimated using the quadratic damping matrix rather than Morison's element. Additionally, the quadratic transfer function matrix was used to calculate the slow-drift force. Compared to the multi-segmented quasi-static mooring model, the lump-mass method is a dynamic mooring model that can solve real-time motion on the platform. Once a single or a pair of mooring lines is intentionally disconnected from the floating platform at a certain time, the transient responses of mooring line tensions and turbine performance will be evaluated. The novelty of this study is that the drift trajectories and power performances of OC4 DeepCwind semisubmersible floating offshore wind turbine under different conditions of environmental loads and broken mooring lines can be approximately estimated in the offshore wind farm. The analysis can be used for the environmental impact assessment in harsh sea conditions.

Statistical linearisation of a nonlinear floating offshore wind turbine under random waves and winds

This paper investigates the stochastic nonlinear dynamics of a floating offshore wind turbine (FOWT) in the frequency-domain under irregular waves and turbulent winds. The main sources of nonlinearities are estimated using statistical linearisation, which are calculated based on probability density functions (PDFs) between the degrees-of-freedom and the environment. The nonlinear mooring model captures the coupling between degrees-of-freedom when the platform has a mean displacement caused by the wind thrust, changing the natural frequency especially in surge. In addition, the nonlinear viscous drag loads offer an hydrodynamic damping that lead to better estimates of the responses. The nonlinear aerodynamic loads uses the relative motion experienced by the wind turbine under turbulent wind, and the concept of aerodynamic admittance function, which has not been applied yet to FOWTs, is included to capture the spatial effects of the wind turbulence. The results are benchmarked against nonlinear time-domain simulations using OpenFAST, and good agreement is obtained in terms of power spectral densities, PDFs and standard deviations. Several environmental conditions are used to explore some of the platform characteristics and salient features from the model. The main advantage of the following approach is the low computational cost, while providing reliable estimates of the response.

Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag.

Loosely speaking, the Mpemba effect appears when hotter systems cool sooner or, in a more abstract way, when systems further from equilibrium relax faster. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically (by employing the tools of kinetic theory) and numerically (direct simulation Monte Carlo of the kinetic equationand event-driven molecular dynamics). The analysis is carried out via two alternative routes, recently considered in the literature: first, the kinetic or thermal route, in which the Mpemba effect is characterized by the crossing of the evolution curves of the kinetic temperature (average kinetic energy), and, second, the stochastic thermodynamics or entropic route, in which the Mpemba effect is characterized by the crossing of the distance to equilibrium in probability space. In general, a nonmutual correspondence between the thermal and entropic Mpemba effects is found, i.e., there may appear the thermal effect without its entropic counterpart or vice versa. Furthermore, a nontrivial overshoot with respect to equilibrium of the thermal relaxation makes it necessary to revise the usual definition of the thermal Mpemba effect, which is shown to be better described in terms of the relaxation of the local equilibrium distribution. Our theoretical framework, which involves an extended Sonine approximation in which not only the excess kurtosis but also the sixth cumulant is retained, gives an excellent account of the behavior observed in simulations.

A review of the analysis of wind-influenced projectile motion in the presence of linear and nonlinear drag force

A review of the analysis of wind-influenced projectile motion in the presence of linear and nonlinear drag force

Nonlinear hydrodynamic analysis and optimization of oscillating wave surge converters under irregular waves

To evaluate the mean annual capture width ratio (CWR) of the oscillating wave surge converters (OWSCs) under irregular waves, the time-domain dynamic equation was derived by considering the nonlinear hydrostatic stiffness, drag, and nonlinear power take-off (PTO) system. A Python code was developed to solve the response and capture performance with 4th-order Runge–Kutta integration. The wave spectrum was corrected according to the water depth in shallow water. Unlike the inflexible drag coefficients in steady flow, the drag coefficients in irregular waves (calibrated with OpenFOAM) are strongly affected by OWSC thickness. Multi-objective genetic algorithm (MOGA) optimization of OWSC geometric sizes, internal water filling, and PTO parameters was conducted for two objective functions: maximizing the mean annual CWR and minimizing the structural mass per unit width. The optimized result presents a slender OWSC that neutrally balances these two objectives. The effects and local sensitivities of the width, thickness, axis depth, water filling, PTO stiffness, damping, and friction were comprehensively discussed. The results show that the axis depth has the greatest positive influence on the CWR, and the increase of thickness creates significant economical disadvantage due to a heavier structure. However, inertia adjustment by filling water does not benefit the mean annual CWR.

Similarity between the turbulent transports of heat and momentum in viscoelastic channel flows

This study examined the heat transfer reduction in drag-reduced turbulent flows of dilute polymer solutions. To this end, direct numerical simulations of fully developed viscoelastic turbulent channel flows (Reτ = 125 and Pr = 5) were conducted under a constant heat flux boundary condition. The polymer stress was modeled using the finitely extensible nonlinear elastic-Peterlin constitutive model, and low (15%), intermediate (34%), and high drag reduction (52%) cases were examined. In drag-reduced flows, the turbulent transport of momentum and heat were still analogous, similar to the case of Newtonian flow; however, the Colburn analogy cannot be applied. Further, the two-point correlations between the temperature fluctuations and velocity components were almost identical to those of the streamwise velocity fluctuations. In addition, the spectral density distribution of the turbulent heat flux was found to be similar to that of the Reynolds shear stress in both Newtonian and drag-reduced flows. The conditionally averaged fields for the events that considerably contributed to the wall-normal turbulent heat flux were quite similar to those for the second quadrant events most contributing the Reynolds shear stress in both Newtonian and viscoelastic flows. The results of the study indicated that the turbulent transport of momentum and heat are associated with approximately identical flow structures in drag-reduced and Newtonian flows. Furthermore, an analysis of the three-dimensional joint probability density function clearly confirmed that the turbulent motions contributing to the Reynolds shear stress contributed equivalently to the turbulent heat flux in both Newtonian and drag-reduced flows.

Enhanced settling and dispersion of inertial particles in surface waves

Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.

Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

Effect of nonlinear drag on the onset and the growth of the miscible viscous fingering in a porous medium

Strong nonexponential relaxation and memory effects in a fluid with nonlinear drag.

We analyze the dynamical evolution of a fluid with nonlinear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, algebraic, relaxation, and strong memory effects, presents scaling properties: the time evolution of the temperature-for both relaxation and memory effects-falls onto a master curve, regardless of the details of the experiment. To account for the observed behavior in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation-which considers not only the fourth cumulant but also the sixth one.