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A quasi-coupled wind wave experimental framework for testing offshore wind turbine floating systems
C. Feist, F. Sotiropoulos, M. Guala
Accepted Manuscript
[Abstract] (0) [FullText HTML] (0) [PDF 0KB] (0)
Abstract:
Two sets of experiments in the St. Anthony Falls Laboratory (SAFL) wave tank facility and atmospheric wind tunnel are integrated to provide a scaled representation of a floating wind turbine under heave and pitch motions due to ocean waves. The quasi-coupling is established by controlling the turbine rotor speed to generate a thrust force mimicking steady or fluctuating wind gusts in the wave tank, and by using two actuators to oscillate a miniature turbine in the wind tunnel. Measured pitch and heave motions under varying waves are scaled down using rotor geometry and the wake meandering frequency to study the effect of the floating platform kinematics on the evolution and characteristics of the oscillating turbine wake. For a limited case of experimental conditions results provide a phenomenological and quantitative description of the floating-turbine system under variable waves and simulated wind gusts. Specifically, we demonstrate that wind gusts contribute to increase the platform pitch range, and that periodic large scale flow patches of high and low momentum flow are generated by the oscillating rotor in the turbulent boundary layer and are coherently convected through the wake. Both mechanisms could amplify the pitch response of downwind floating turbine units within the offshore power plant, in particular if the wave and/or wind forcing frequencies happen to approach the pitch natural frequency of the floating system.
Coherent vorticity dynamics and dissipation in a utility-scale wind turbine wake with uniform inflow
Daniel Foti
Corrected proof
[Abstract] (37) [FullText HTML] (31) [PDF 0KB] (0)
Abstract:
The vorticity dynamics and its relationship to dissipation in the wake of a utility-scale wind turbine are investigated through large-eddy simulation. The vorticity dynamics is assessed through the enstrophy, which is related to the turbulent dissipation. The averaged enstrophy and turbulent dissipation are shown to be quantitatively similar in the wake. Using temporal phase averaging, the vorticity fluctuations are decomposed into coherent and random fluctuations with respect to the frequency of the tip vortices. The enstrophy in the tip vortices is dominated by coherent fluctuations, while the coherent fluctuations of root vortices are immediately saturated by the random vorticity fluctuations of the unstable hub vortex. The coherent strain rate has significant differences compared to the coherent enstrophy within one diameter downwind of blade tip, but the random enstrophy and strain rate are relatively similar. Differences in coherent enstrophy and strain rate decrease further from the rotor.
Alternating minimization for data-driven computational elasticity from experimental data: kernel method for learning constitutive manifold
Yoshihiro Kanno
Corrected proof
[Abstract] (35) [FullText HTML] (32) [PDF 0KB] (0)
Abstract:
Data-driven computing in elasticity attempts to directly use experimental data on material, without constructing an empirical model of the constitutive relation, to predict an equilibrium state of a structure subjected to a specified external load. Provided that a data set comprising stress–strain pairs of material is available, a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie (Kanno 2021, Jpn. J. Ind. Appl. Math.). From the perspective of physical experiments, stress field cannot be directly measured, while displacement and force fields are measurable. In this study, we extend the previous kernel method to the situation that pairs of displacement and force, instead of pairs of stress and strain, are available as an input data set. A new regularized least-squares problem is formulated in this problem setting, and an alternating minimization algorithm is proposed to solve the problem.
Closed-Form Solution for Shock Wave Propagation in Density-Graded Cellular Material Under Impact
Vijendra Gupta, Addis Kidane, Michael Sutton
Corrected proof
[Abstract] (47) [FullText HTML] (32) [PDF 0KB] (4)
Abstract:
Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required. Cellular materials subjected to high impact loading result in a compaction type deformation, usually modeled using continuum-based shock theory. The resulting governing differential equation of the shock model is nonlinear, and density gradation further complicates the problem. Earlier studies have employed numerical methods to obtain the solution. In this study, an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact. Solutions for the velocity of the impinging rigid body mass, the energy absorption capacity of the cellular material, and the incident stress are obtained for a single shock propagation. The results obtained are in excellent agreement with the existing numerical solutions found in the literature. The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.
Optimization of the forearm angle for arm wrestling using multi-camera stereo digital image correlation: a preliminary study
Zixiang Tong, Xinxing Shao, Zhenning Chen, Xiaoyuan He
Corrected proof , doi: 10.1016/j.taml.2021.100287
[Abstract] (51) [FullText HTML] (45) [PDF 0KB] (0)
Abstract:
This study analyzes the function of different muscles during arm wrestling and proposes a method to analyze the optimal forearm angle for professional arm wrestlers. We built a professional arm-wrestling platform to measure the shape and deformation of the skin at the biceps brachii of a volunteer in vivo during arm wrestling. We observed the banding phenomenon of arm skin strain during muscle contraction and developed a model to evaluate the moment provided by the biceps brachii. According to this model, the strain field of the area of interest on the skin was measured, and the forearm angles most favorable and unfavorable to the work of the biceps brachii were analyzed. This study demonstrates the considerable potential of applying DIC and its extension method to the in vivo measurement of human skin and facilitates the use of the in vivo measurement of skin deformation in various sports in the future.
Mei's symmetry theorem for time scales nonshifted mechanical systems
Yi Zhang
Accepted Manuscript
[Abstract] (73) [FullText HTML] (51) [PDF 0KB] (3)
Abstract:
We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities. Firstly, the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton's principle. Secondly, the definitions of Mei symmetry on time scales are given and its criterions are deduced. Finally, Mei's symmetry theorems for time scales nonshifted holonomic conservative systems, time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved, and new conserved quantities of above systems are obtained. Results are illustrated with two examples.
Displacement reconstruction and strain refinement of clustering-based homogenization
Lei Zhang, Shaoqiang Tang
Corrected proof
[Abstract] (81) [FullText HTML] (63) [PDF 0KB] (4)
Abstract:
Recently proposed clustering-based methods provide an efficient way for homogenizing heterogeneous materials, yet without concerning the detailed distribution of the mechanical responses. With coarse fields of the clustering-based methods as an initial guess, we develop an iteration strategy to fastly and accurately resolve the displacement, strain and stress based on the Lippmann-Schwinger equation, thereby benefiting the local mechanical analysis such as the detection of the stress concentration. From a simple elastic case, we explore the convergence of the method and give an instruction for the selection of the reference material. Numerical tests show the efficiency and fast convergence of the reconstruction method in both elastic and hyper-elastic materials.

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Letter
Error of large-eddy simulation in the wall pressure fluctuation of a turbulent channel flow
Rong Li, Bowen Yang, Zixuan Yang, Shizao Wang, Guowei He
Theoretical and Applied Mechanics Letters  11 (2021) 100248.   doi: 10.1016/j.taml.2021.100248
[Abstract] (362) [FullText HTML] (156) [PDF 1226KB] (26)
Abstract:
We analyze the error of large-eddy simulation (LES) in wall pressure fluctuation of a turbulent channel flow. To separate different sources of the error, we conduct both direct numerical simulations (DNS) and LES, and apply an explicit filter on DNS data to obtain filtered DNS (FDNS) data. The error of LES is consequently decomposed into two parts: The first part is the error of FDNS with respect to DNS, which quantifies the influence of the filter operation. The second part is the difference between LES and FDNS induced by the error of LES in velocity field. By comparing the root-mean-square value and the wavenumber-frequency spectrum of the wall pressure fluctuation, it is found that the inaccuracy of the velocity fluctuations is the dominant source that induces the error of LES in the wall pressure fluctuation. The present study provides a basis on future LES studies of the wall pressure fluctuation.
Electrothermal analysis of radiofrequency tissue ablation with injectable flexible electrodes considering bio-heat transfer
Min Hu, Zhixiong Feng, Yuguang Chu, Yuhang Li
Theoretical and Applied Mechanics Letters  11 (2021) 100258.   doi: 10.1016/j.taml.2021.100258
[Abstract] (148) [FullText HTML] (105) [PDF 1776KB] (4)
Abstract:
Flexible electrodes have been widely focused on in recent years due to their special mechanical properties, which can be directly integrated onto human soft tissues to actively take effects on human body or passively monitor human vital signs. These flexible electrodes provide a new routine to realize clinical treatment of accurate thermal ablation in the biological tissues via radiofrequency ablation (RFA). Meanwhile, accurately controlling of thermal field is very significant for the thermal ablation in the clinical therapeutics to prevent the healthy tissue from excessive burning. In this paper, both one-dimensional and two-dimensional axisymmetric analytical models for the electrothermal analysis of radiofrequency ablation considering bio-heat transfer are established, which are verified by finite element analysis (FEA) and in vitro experiments on pig skins. In the model, the electrical field and thermal field are both derived analytically to accurately predict the temperature rise in the biological tissues. Furthermore, parameters, such as the blood flow convection in living tissues and thickness of tissue, have obvious effects on the thermal field in the tissues. They may pave the theoretical foundation and provide guidance of RFA with flexible electrodes in the future.
Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals
Zhiteng Zhou, Hongping Wang, Shizhao Wang
Theoretical and Applied Mechanics Letters  11 (2021) 100259.   doi: 10.1016/j.taml.2021.100259
[Abstract] (256) [FullText HTML] (147) [PDF 788KB] (3)
Abstract:
A simplified surface correction formulation is proposed to diminish the far-field spurious sound generated by the quadrupole source term in Ffowcs Williams and Hawkings (FW-H) integrals. The proposed formulation utilizes the far-field asymptotics of the Green's function to simplify the computation of its high-order derivatives, which circumvents the difficulties reported in the original frequency-domain surface correction formulation. The proposed formulation has been validated by investigating the benchmark case of sound generated by a convecting vortex. The results show that the proposed formulation successfully eliminates the spurious sound. The applications of the proposed formulation to flows with some special parameters are also discussed.
On the capability of the curvilinear immersed boundary method in predicting near-wall turbulence of turbulent channel flows
Fei Liao, Xiaolei Yang
Theoretical and Applied Mechanics Letters  11 (2021) 100279.   doi: 10.1016/j.taml.2021.100279
[Abstract] (110) [FullText HTML] (83) [PDF 1574KB] (3)
Abstract:
The immersed boundary method has been widely used for simulating flows over complex geometries. However, its accuracy in predicting the statistics of near-wall turbulence has not been fully tested. In this work, we evaluate the capability of the curvilinear immersed boundary (CURVIB) method in predicting near-wall velocity and pressure fluctuations in turbulent channel flows. Simulation results show that quantities including the time-averaged streamwise velocity, the rms (root-mean-square) of velocity fluctuations, the rms of vorticity fluctuations, the shear stresses, and the correlation coefficients of \begin{document}$ u'$\end{document} and \begin{document}$ v'$\end{document} computed from the CURVIB simulations are in good agreement with those from the body-fitted simulations. More importantly, it is found that the time-averaged pressure, the rms and wavenumber-frequency spectra of pressure fluctuations computed using the CURVIB method agree well with the body-fitted results.
End-to-end differentiable learning of turbulence models from indirect observations
Carlos A. Michelén Ströfer, Heng Xiao
Theoretical and Applied Mechanics Letters  11 (2021) 100280.   doi: 10.1016/j.taml.2021.100280
[Abstract] (113) [FullText HTML] (87) [PDF 1176KB] (2)
Abstract:
The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields. The framework consists of a Reynolds-averaged Navier--Stokes (RANS) solver and a neural-network-represented turbulence model, each accompanied by its derivative computations. For computing the sensitivities of the indirect observations to the Reynolds stress field, we use the continuous adjoint equations for the RANS equations, while the gradient of the neural network is obtained via its built-in automatic differentiation capability. We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures. We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier--Stokes equations for which no true underlying linear closure exists. The trained deep-neural-network turbulence model showed predictive capability on similar flows.
Theory of adaptive mechanical drive
K.S. Ivanov
Theoretical and Applied Mechanics Letters  11 (2021) 100281.   doi: 10.1016/j.taml.2021.100281
[Abstract] (119) [FullText HTML] (89) [PDF 537KB] (3)
Abstract:
A kinematic chain with two degrees of freedom and one input can have definability of motion only if there is an additional constraint of forces and velocities. Such a chain is a mechanism that has the brand new property of force adaptation.The article presents a kinematic and force analysis of two-mobile adaptive mechanisms and describes the principle of definability of motion.
A 2D numerical ocean model on the Coriolis and wind stress effects using stochastics
Sudhakar Matle
Theoretical and Applied Mechanics Letters  11 (2021) 100282.   doi: 10.1016/j.taml.2021.100282
[Abstract] (164) [FullText HTML] (90) [PDF 724KB] (19)
Abstract:
Ocean basin is modeled as a two-dimensional closed, bounded domain in which the fluid flow is governed by the complex partial differential equations in the flow function. Keeping in view that the ocean currents are non-viscous, no normal flow conditions are used at the basin boundaries. The parameters investigated here are; Coriolis parameter, wind stress coefficient, and latitude. Stochastic differential equations in time scales are solved by deterministic and stochastic methods. Deterministic results concluded that streamlines are symmetric about stagnation point (no flow) for \begin{document}$0<R_{p}<6.57$\end{document}. Stochastic controls are introduced to account for variability in time scales. Euler-Maruyama (direct) and Fokker-Planck equation schemes (indirect) are proposed. It is concluded that stream functions in both direct and indirect methods are of the same qualitatively and quantitatively when \begin{document}$0<R_{p}<79$\end{document}.
Tunnel effects on ring road traffic flow based on an urgent-gentle class traffic model
Yongliang Zhang, M.N. Smirnova, Jian Ma, N.N. Smirnov, Zuojin Zhu
Theoretical and Applied Mechanics Letters  11 (2021) 100283.   doi: 10.1016/j.taml.2021.100283
[Abstract] (96) [FullText HTML] (79) [PDF 2353KB] (1)
Abstract:
To explore tunnel effects on ring road traffic flow, a macroscopic urgent-gentle class traffic model is put forward. The model identifies vehicles with urgent and gentle classes, chooses the tunnel speed limit as free flow speed to express the fundamental diagram in the tunnel, and adopts algebraic expressions to describe traffic pressure and sound speed. With two speed trajectories at the Kobotoke tunnel in Japan, the model is validated, with good agreement with observed data. Numerical results indicate that in the case of having no ramp effects, tunnel mean travel time is almost constant dependent on tunnel length. When initial density normalized by jam density is above a threshold of about 0.21, a traffic shock wave originates at the tunnel entrance and propagates backward. Such a threshold drops slightly as a result of on-ramp merging effect, the mean travel time drops as off-ramp diversion effect intensifies gradually. These findings deepen the understanding of tunnel effects on traffic flow in reality.
A general model for trailing edge serrations simulation on wind turbine airfoils
Huijing Cao, Mingming Zhang, Yinan Zhang, Teng Zhou
Theoretical and Applied Mechanics Letters  11 (2021) 100284.   doi: 10.1016/j.taml.2021.100284
[Abstract] (78) [FullText HTML] (63) [PDF 2639KB] (5)
Abstract:
Trailing edge serrations (TESs) are capable of noticeably suppressing the turbulent trailing edge noise induced by rotating wind turbine blades and become an integral part of a blade. However, the challenges involved in the dimensional design of serration height 2\begin{document}$ h $\end{document}, wavelength \begin{document}$ \lambda $\end{document} and flap angle \begin{document}$ \varphi $\end{document} are yet to be dealt with in a satisfactory manner. To address the problem, a general model for simulating the effects of serrations on the hydrodynamic and aeroacoustic performance is proposed due to its ease of use and relatively low requirements for user input. The solid serrations are replicated by momentum sources calculated by its aerodynamic forces. Then, a case relevant to wind turbine airfoil is examined, a hybrid IDDES method coupled with FW-H integration is deployed to obtain the flow features and far-field sound pressure level. It is found that the modeling method could reproduce the flow field and noise as serrated airfoil.
Crack propagation simulation in brittle elastic materials by a phase field method
Xingxue Lu, Cheng Li, Ying Tie, Yuliang Hou, Chuanzeng Zhang
2019, 9(6): 339-352   doi: 10.1016/j.taml.2019.06.001
[Abstract](1073) [FullText HTML](602) [PDF 3845KB](81)
On the Weissenberg effect of turbulence
Yu-Ning Huang, Wei-Dong Su, Cun-Biao Lee
2019, 9(4): 236-245   doi: 10.1016/j.taml.2019.03.004
[Abstract](618) [FullText HTML](334) [PDF 2579KB](71)
Mechanistic Machine Learning: Theory, Methods, and Applications
2020, 10(3): 141-142   doi: 10.1016/j.taml.2020.01.041
[Abstract](5792) [FullText HTML](484) [PDF 3081KB](70)
Frame-indifference of cross products, rotations, and the permutation tensor
Maolin Du
2020, 10(2): 116-119   doi: 10.1016/j.taml.2020.01.015
[Abstract](688) [FullText HTML](369) [PDF 2494KB](60)
Dynamic mode decomposition and reconstruction of transient cavitating flows around a Clark-Y hydrofoil
Rundi Qiu, Renfang Huang, Yiwei Wang, Chenguang Huang
2020, 10(5): 327-332   doi: 10.1016/j.taml.2020.01.051
[Abstract](637) [FullText HTML](445) [PDF 2862KB](57)
A modified Lin equation for the energy balance in isotropic turbulence
W.D. McComb
2020, 10(6): 377-381   doi: 10.1016/j.taml.2020.01.055
[Abstract](431) [FullText HTML](255) [PDF 2541KB](56)
On the interaction between bubbles and the free surface with high density ratio 3D lattice Boltzmann method
Guo-Qing Chen, A-Man Zhang, Xiao Huang
2018, 8(4): 252-256   doi: 10.1016/j.taml.2018.04.006
[Abstract](1124) [FullText HTML](695) [PDF 2725KB](55)
Effects of tide-surge interaction and wave set-up/set-down on surge: case studies of tropical cyclones landing China's Zhe-Min coast
Qingyong Wuxi, Jiachun Li, Bingchuan Nie
2018, 8(3): 153-159   doi: 10.1016/j.taml.2018.03.002
[Abstract](1606) [FullText HTML](741) [PDF 4354KB](50)
Continuum percolation of porous media via random packing of overlapping cube-like particles
Jianjun Lin, Huisu Chen
2018, 8(5): 299-303   doi: 10.1016/j.taml.2018.05.007
[Abstract](1262) [FullText HTML](742) [PDF 3697KB](49)
Multiscale mechanics
G.W. He, G.D. Jin
11 (2021) 100238   doi: 10.1016/j.taml.2021.100238
[Abstract](279) [FullText HTML](240) [PDF 2196KB](48)