Body Force Distribution Research Articles

Optimizing electrode arrangement in plasma actuators: a study on induced velocity and efficiency

This study investigates the performance of two types of multi-encapsulated electrode (MEE) plasma actuators, compared to typical dielectric barrier discharge (DBD) plasma actuators, in quiescent air. The objective is to determine whether the multiple encapsulated structure can enhance the performance of the plasma actuator. In the present paper, flow characteristics are investigated by using particle image velocimetry (PIV) and Schlieren visualisation. In addition, the distribution of body force over the gas volume based on the Navier–Stokes equations is calculated from velocity measurements. The obtained results demonstrate that the starting vortex behavior is influenced by electrode arrangement. Specifically, it can be observed that when the first encapsulated electrode is positioned closer to the exposed electrode, then a significantly higher induced velocity can be obtained compared to the baseline condition. In fact, the induced velocity can be increased by up to 1.5 times under this optimize configuration. These results highlight the importance of electrode arrangement in the plasma actuator design. Based on body force estimation, MEE plasma actuators exhibit a significantly higher momentum transfer, particularly in the wall normal direction. The investigation on the mechanical efficiency also reveals that the optimized configuration proposed in the present study can significantly enhance the efficiency. In fact, a four-fold increase in maximum efficiency compared to the typical configuration is observed. These results suggest that the proposed configuration could be considered a promising solution for improving the mechanical efficiency of plasma actuators.

Disagreements in Geodetically Inferred Strain Rates in the Western US With Stress Orientations and Geologic Moment Rates

AbstractI employ an elasticity‐based method to invert a geodetically derived surface velocity field in the western US using for present‐day surface strain rate fields with uncertainties. The method uses distributed body forces in a thin elastic sheet and allows for discontinuities in velocity across creeping faults using the solution for dislocations in a thin elastic plate. I compare the strain rate fields with previously published stress orientations and moment rates from geological slip rate data and previous geodetic studies. Geologic and geodetic moment rates are calculated using slip rate and off‐fault strain rates from the 2023 US National Seismic Hazard Model (NSHM) deformation models. I find that computed total geodetic moment rates are higher than NSHM summed moment rates on faults for all regions of the western US except the highest deforming rate regions including the Western Transverse Ranges and the northern and southern San Andreas Fault (SAF) system in California. Computed geodetic moment rates are comparable to the moment rates derived from the geodetically based NSHM deformation models in all regions. I find systematic differences in orientations of maximum horizontal shortening rate and maximum horizontal compressive stress in the Pacific Northwest region and along much of the SAF system. In the Pacific Northwest, the maximum horizontal stress orientations are rotated counterclockwise 40–90° relative to the maximum horizontal strain rate directions. Along the SAF system, the maximum horizontal stresses are rotated systematically 25–40° clockwise (closer to fault normal) relative to the strain rates.

Fracture behavior of superconductor REBCO tapes with multiple edge cracks under electromagnetic force

It is often necessary to narrow wide tapes through a slitting process in applications of the second-generation high-temperature superconductor REBa2Cu3O7-x (REBCO, RE = rare earth) tapes. However, this results in some random length edge cracks appearing on the slit edge and extending at certain angles towards the center of the tape. In this paper, we proposed a randomly distributed multiple-edge crack model to investigate the fracture mechanism of the superconducting tape under electromagnetic force due to high magnetic fields and current density (∼10 T and ∼ 1010A/m2). The electromagnetic body force distributions within the superconducting tape, incorporating multiple edge cracks, are simulated based on the H-formulation. Then a fracture analysis is conducted under the combined loading of tensile and electromagnetic forces, with the numerical calculation of stress intensity factors (SIFs) using the J-integral method. To validate the model's accuracy, we compare the body force distribution caused by an edge crack and the SIFs of edge cracks under uniform tension with existing results. Detailed analyses are undertaken to explore the impacts of electromagnetic body force non-uniformity, interactions between neighboring cracks, and the stochastic nature of geometrical parameters (length, angle, and spacing) on the fracture behavior under an alternating magnetic field. Numerical results indicate that non-uniform electromagnetic body forces arising from defects are a critical factor in crack propagation. Furthermore, the randomness of the geometrical parameters amplifies the interactions between some of the neighboring cracks, causing the tendency of the tape containing random edge cracks to fracture. Therefore, it is advisable to avoid random cracks with substantial length, angle, and spacing during the mechanical slitting process.

On the interplay of body-force distributions and flow speed for dielectric-barrier discharge plasma actuators

The dielectric-barrier discharge plasma actuator is a well-established device commonly operated in boundary-layer airflows for active flow control. In the present experimental investigation, their ability to cause momentum transfer to the surrounding fluid is analyzed by means of spatio-temporal body-force distributions in both quiescent air and external airflow conditions. The work is motivated by the limitation to quiescent-air operating conditions of frequent previous efforts. Available analytical velocity-information-based force derivation approaches are contrasted to investigate the actuator performance under conditions of their area of application. Results of body force in quiescent air, in agreement with literature, confirm the major taken assumption for Navier–Stokes-based body-force formulations—a negligible pressure gradient. However, the previous circumstance turns out as an invalid assumption for plasma actuation encountering an external airflow. These outcomes coincide with the findings in the numerical work of (2015 Numerical investigation of plasma-actuator force-term estimations from flow experiments J. Phys. D: Appl. Phys. 48 395203), following the recommendation to apply a vorticity-equation-based approach under such conditions. Furthermore, the shape of the spatio-temporal body-force distribution is observed to undergo changes when the airflow speed increases. On the other hand, the integral force magnitude is found to remain approximately constant. Moreover, the choice of phase resolution of the discharge cycle has an implication on the accuracy of the temporal force evolution, therefore, clarifying the importance of a priori defining the type of body-force analysis in an experiment; i.e. integral force magnitude, time-averaged or time-resolved evaluation. As a promising finding of utmost importance for the actuator performance, the actuator remains as effective as in quiescent air under presence of the external airflow, which immediately renders the actuator fluid-mechanic efficiency to increase for increasing airflow speed.

Data-driven modeling on anisotropic mechanical behavior of brain tissue with internal pressure

Brain tissue is one of the softest parts of the human body, composed of white matter and grey matter. The mechanical behavior of the brain tissue plays an essential role in regulating brain morphology and brain function. Besides, traumatic brain injury (TBI) and various brain diseases are also greatly influenced by the brain's mechanical properties. Whether white matter or grey matter, brain tissue contains multiscale structures composed of neurons, glial cells, fibers, blood vessels, etc., each with different mechanical properties. As such, brain tissue exhibits complex mechanical behavior, usually with strong nonlinearity, heterogeneity, and directional dependence. Building a constitutive law for multiscale brain tissue using traditional function-based approaches can be very challenging. Instead, this paper proposes a data-driven approach to establish the desired mechanical model of brain tissue. We focus on blood vessels with internal pressure embedded in a white or grey matter matrix material to demonstrate our approach. The matrix is described by an isotropic or anisotropic nonlinear elastic model. A representative unit cell (RUC) with blood vessels is built, which is used to generate the stress-strain data under different internal blood pressure and various proportional displacement loading paths. The generated stress-strain data is then used to train a mechanical law using artificial neural networks to predict the macroscopic mechanical response of brain tissue under different internal pressures. Finally, the trained material model is implemented into finite element software to predict the mechanical behavior of a whole brain under intracranial pressure and distributed body forces. Compared with a direct numerical simulation that employs a reference material model, our proposed approach greatly reduces the computational cost and improves modeling efficiency. The predictions made by our trained model demonstrate sufficient accuracy. Specifically, we find that the level of internal blood pressure can greatly influence stress distribution and determine the possible related damage behaviors.

Numerical prediction of ducted propeller performance based on a BEM–RANS coupling method

This paper presents a coupling method that combines the boundary element method (BEM) and the Reynolds-averaged Navier–Stokes (RANS) method to calculate the ducted propeller performance. The software ANSYS CFX is primarily used to calculate the viscous flow around the duct considering the action of the propeller through the distribution of body forces, and the performance of the propeller is evaluated using the BEM in the effective inflow field. A conservative interpolation scheme that converts the pressure obtained from the BEM into the body force of the RANS solver is described. Then, a Kriging interpolation method is used to determine the effective wake by combining the total viscous field and induced velocities from the BEM. Compared with a full RANS approach, this coupling method allows for investigation of the interaction between the duct and propeller with a significantly reduced computational effort and ensures accuracy with a smaller number of meshes. In addition, the coupling method provides a significant effective wake field for propeller design. The proposed coupling method is first applied to the case of an open propeller and is then assessed for the case of a ducted propeller under uniform flow. The results show that the proposed coupling method provides similar prediction results as those obtained using the full RANS approach, with a 79.6% reduction in computational time.

PIV Analysis Of Skin Friction And Coherent Structures In Turbulent Drag Reduction Regimes

In the present work, planar and tomographic PIV are used to investigate how the organisation of wall turbulence is altered when actuators are operated with the objective of reducing the skin friction drag. When the wall is mechanically oscillated in the spanwise direction, high-resolution planar PIV enable the direct measurement of wall shear and a 15% reduction of skin friction is observed. The use of tomographic PIV enables access to the threedimensional organisation of low- and high-speed streaks, along with ejection events and associated hairpin vortices. These observations help forming a conceptual model of the salient drag reduction mechanism, whereby hairpin autogeneration is inhibited through a tilting action at the tail of low-speed streaks. The second part of the study documents an effort to surrogate the mechanical oscillation by means of a densely distributed array of AC-DBD plasma actuators. The latter are first characterised in quiescent flow, where the induced velocity distribution is obtained and compared to the solution of the classical second Stokes problem that models the mechanical oscillation. The induced peak of spanwise velocity is found to surpass the velocity of the oscillating wall. However, the wall jet height develops further away from the wall. More importantly, the spatially inhomogeneous distribution of the unsteady body force produces an unwanted lattice of starting streamwise vortices. The latter are deemed to be detrimental for the purpose of drag reduction, compared to the orderly and homogeneous sideways motion induced by mechanical wall motion. The application of the AC-DBD actuator currently leads to a pronounced momentum deficit in the logarithmic region and increases skin friction. Finally, further research directions are anticipated, that potentially circumvent the formation of streamwise vortices by means of AC-DBD actuators operating in steady regime.

A 2D warping theory for shear deformable elastic beams of axisymmetric cross section in flexure

Shear deformable elastic beam models in flexure are considered in the hypothesis of cross section symmetric with respect to the flexure axis, whereby the external transverse forces act as distributed body forces. A 2D warping theory is presented where the shear-warping process is driven by a shear-warping parameter, say τ, 0≤τ≤1, in such a way that equilibrium between zero external (t(n)i=0) and internal (σ(n)i=0) tractions upon the lateral surface of the beam is complied with no matters the value of τ∈(0,1). On letting τ vary within (0,1), a continuous beam family, say B≔{Bτ:0≤τ≤1}, is generated, which spans from the Euler–Bernoulli (EB) beam model B0 at τ=0 (no shear strain, nor warping effects), to a series of shear deformable beam models Bτ up to τ=1. For intermediate values of τ, 0<τ<1, every beam model is featured by transversally nonuniform shear stresses accompanied by suitable 2D warping effects, while the boundary equilibrium condition with zero applied tractions is satisfied. The warping theory herein presented is an original generalization of a previous 1D type warping theory devised for rectangular cross sections. Applications are reported in which a circular cross section is considered and a beam problem in static conditions is worked out.

Deformation induced by distributions of single forces in a layered half-space: [formula omitted

In the present paper we introduce a numerical model for the representation of displacement, strain and stress due to single forces embedded in a layered elastic half-space. The code EFGRN/EFCMP (Elastic Forces GReeN functions/Elastic Forces CoMPutation) is able to represent the mechanical effects due to pre-assigned distributions of single forces. Even if internal deformation sources can be described by distributions of equivalent body forces with vanishing resultant and moment, single forces are employed in geophysics to represent hydraulic and/or lithostatic loads, effects of internal density anomalies, and even some kind of seismic events. A distribution of single forces is also used to describe the effects of an inelastic inclusion located inside an elastic medium. In fact, the recent literature shows that poro-elastic and thermo-elastic inclusions can be represented using single forces distributed on their boundaries. EFGRN/EFCMP shares the benefits of rapid and semi-analytical calculation offered by the parent code, EDGRN/EDCMP, which is instead suitable for the representation of extended dislocation sources, as seismic faults. The present code also provides an option for computing the effects of a distribution of single forces embedded in a homogeneous half-space, by using the analytical solutions of Mindlin. Accordingly, EFGRN/EFCMP can be a valid support both for the representation of forward models of deformation sources and for the procedures of inversion of geodetic data in a layered medium. We show some applications of the code and we provide several scripts in MATLAB language which help the user to quickly start using EFGRN/EFCMP.

Development of a Micro Plasma Actuator Array for Near-Wall Body-Force Generation

In order to apply plasma actuator to boundary layer transition control, it is necessary to introduce a body force into the appropriate part of the boundary layer, especially near the wall surface. To develop a device that can introduce body force only near the wall surface, we fabricated micro plasma actuators arrays using photolithography, and investigated the generated body force and jet characteristics. Velocity distribution measurements using a hot-wire anemometer were used to analyze the jet characteristics, and the body force distribution of the conventional and micro plasma actuators was clarified.

A device for reducing the resistance of transom stern hulls

A novel idea to reduce the resistance of a transom stern hull in displacement and semi-planing modes is investigated. By placing a spoon-shaped device in the recirculating zone behind the transom, the momentum of the forward-moving water will be absorbed, and a pushing force generated on the device. Numerical and experimental techniques are applied on a transom stern hull to optimize the shape and position of the device and to explore in detail the physics behind the gain. For the towed hull at a Froude number of 0.4, the maximum measured resistance reduction is 11%, while the computed maximum reduction is 17%. In self-propulsion with one propeller, the measured power reduction is 15%. The power cannot be computed with the applied propeller model, which is an axial body-force distribution in the propeller disk, but the reduction in thrust using the device is 11%. More significant gains are possible at smaller Froude numbers, while the effect is reduced at higher Froude numbers. Larger gains are achieved by splitting the thrust on two propellers.

Study on vehicle drag reduction simulation based on Suzen–Huang model

In the past numerical simulation of plasma and fluid coupling, the usually used Suzen numerical simulation model has the defect that the error increases with the increase in excitation voltage. The static test of the ionic wind is used to modify the parameters of the Suzen simulation model, and it applied the modified Suzen model to the flow control of the automobile external flow field, which shows good consistency with the wind tunnel test results. Results show that the Suzen model modified by the static test results of the ionic wind is suitable for different excitation voltage conditions. The corrected body force and charge density distribution conform to the change trend of plasma discharge, and the error between the maximum ionic wind velocity obtained by simulation and the test result is within 4%; the modified Suzen model is successfully applied to the plasma flow control of automobile aerodynamic drag reduction. The results show that the exciter suppresses the generation of periodic separation vortices in the tail of the model, which makes the vorticity in the wake significantly decrease, thereby reducing the energy dissipation and the aerodynamic drag of the model. Through the research in this paper, the modified Suzen model reduces the simulation error. Plasma flow control technology is applied to the field of automobile aerodynamic drag reduction, which has accumulated important experience methods and data foundation for the engineering application of this technology. It also provides new methods for improving vehicle aerodynamic performance and fuel economy.

Modeling and Wind Flow Analysis of an Eiffel (Open) Type Sub-Sonic Wind Tunnel

Wind tunnel (WT) is a device that artificially produces airflow relative to a stationary body and measures aerodynamic force and pressure distribution, simulating the actual conditions with an important aspect of accurately feigning¬ the full complexity of fluid flow. The aim of the present study is to design the three dimensional geometry of a small, open-circuit (also known as Eiffel Type), and subsonic (low speed) wind tunnel (WT) capable of demonstrating or acting as a vital tool in aero-mechanics research. The project and fabrication itself, poses as an onerous task with the cynosure/central theme being the delineation/depiction of wind tunnel components such as Test Section, contraction cone, diffuser, drive system and settling chamber.

Paddling motion of a free-swimming jellyfish and Lagrangian coherent structure analysis

Swimming and prey capture by prolate and oblate jellyfishes are numerically examined in two-dimensions using multi-relaxation-time lattice Boltzmann (MRT-LB) and immersed boundary (IB) methods. The near-field fluid structure interaction (FSI) and predator-prey interaction mechanisms are revealed via the simulated Eulerian flow characteristics, finite-time Lyapunov exponent (FTLE) field, and Lagrangian coherent structures (LCS). We implement appropriate periodic body force (Fb) distribution at nodal points of the elastic bell in radial direction to model the paddled swimming as well as complex feeding behavior. For a paddling jellyfish the evolved starting and stopping vortices, as move close to each other in near-wake, create the necessary vortex induced thrust that facilitate the forward body motion. The forced bell contraction in power stroke assists quicker propulsive swimming, whereas passive bell expansion in resting phase facilitates the continued vortex induced forward movement for larger duration, via the refilled fluid momentum. For feeding the detailed prey interception and precise capture areas for various jellyfish models are identified hereby via the computed prey tracks, forward and backward time FTLE fields, and LCS. Swimming performances are analyzed based on interactive thrust and drag forces, input power (energy rate required for bell contraction), output power (thrust multiplied by centroid velocity), and cost of transport (COT). At low Reynolds number (Re) the COT becomes higher for an oblate jellyfish than that of a prolate one; while with increased Re the oblate species appears more economical. However, for enhanced paddling force (Fb) or reduced flapping frequency of bell, the COT for an oblate jellyfish steadily decreases. Hereby impacts of the varied force duration, flapping amplitude, flapping frequency, and bell-elasticity on the swimming are analyzed in greater detail. Notably, the propulsion efficiency increased for higher flapping frequency. The present numerical model efficiently unfolds prey capture mechanisms that are adopted by prolate and oblate medusae and quantifies their success rate (clearance rate, CR) in prey capture. Unlike in past studies, the FTLE fields and LCS that are computed here by tracking the transient motion of a large number of suspended Lagrangian prey particles exhibit the realistic predator-prey interaction and precise prey capture surface, which are difficult to measure or analyze empirically.

Stability of the solitary wave boundary layer subject to finite-amplitude disturbances

The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output analysis, in which the environment noise is modelled as distributed body forces. The most dangerous perturbations in a time frame until flow reversal are found to be arranged as counter-rotating streamwise-constant rollers. One of these roller configurations is then selected and deployed to nonlinear equations, and streaks of various amplitudes are generated via lift-up mechanism. By means of secondary stability analysis and direct numerical simulations, the dual role of streaks in the boundary-layer transition is shown. When the amplitude of streaks remains moderate, these elongated features remain stable until the adverse-pressure-gradient stage and have a dampening effect on the instabilities developing thereafter. In contrast, when the low-speed streaks reach high amplitudes exceeding 15% of free-stream velocity at the respective phase, they become highly unstable to secondary sinuous modes in the outer shear layers. Consequently, a subcritical transition to turbulence, i.e., bypass transition, can be already initiated in the favourable-pressure-gradient region ahead of the wave crest.

On the fractional deformation of a linearly elastic bar

Abstract Fractional derivatives have non-local character, although they are not mathematical derivatives, according to differential topology. New fractional derivatives satisfying the requirements of differential topology are proposed, that have non-local character. A new space, the Λ-space corresponding to the initial space is proposed, where the derivatives are local. Transferring the results to the initial space through Riemann-Liouville fractional derivatives, the non-local character of the analysis is shown up. Since fractional derivatives have been established, having the mathematical properties of the derivatives, the linearly elastic fractional deformation of an elastic bar is presented. The fractional axial stress along the distributed body force is discussed. Fractional analysis with horizon is also introduced and the deformation of an elastic bar is also presented.

Separated Flow Control of Small Horizontal-Axis Wind Turbine Blades Using Dielectric Barrier Discharge Plasma Actuators

The flow control over the blades of a small horizontal-axis wind turbine (HAWT) model using a dielectric barrier discharge plasma actuator (DBD-PA) was studied based on large-eddy simulations. The numerical simulations were performed with a high-resolution computational method, and the effects of the DBD-PA on the flow fields around the blades were modeled as a spatial body force distribution. The DBD-PA was installed at the leading edge of the blades, and its impacts on the flow fields and axial torque generation were discussed. The increase in the ratios of the computed, cycle-averaged axial torque reasonably agreed with that of the available experimental data. In addition, the computed results presented a maximum of 19% increase in the cycle-averaged axial torque generation by modulating the operating parameters of the DBD-PA because of the suppression of the leading edge separation when the blade’s effective angles of attack were relatively high. Thus, the suppression of the leading edge separation by flow control can lead to a delay in the breakdown of the tip vortex as a secondary effect.

Experimental validation and improvement of actuator line model in the large-eddy simulation of wind-turbine wakes

Wind-turbine wakes significantly affect the power output of downstream wind turbines. In order to improve the calculation accuracy of wind-turbine wakes in the atmospheric boundary layer, a new improved actuator line - large-eddy simulation (AL-LES) method is proposed and verified by experiments. The traditional AL-LES method is improved in three aspects. Firstly, the atmospheric turbulence is generated by a dynamic k-equation LES with a wall shear stress model and a buoyancy effect model. Secondly, the nacelle and tower are modelled based on the static actuator line method. Finally, the distribution of blade body force is improved by using an anisotropic 3D Gaussian function. Based on the results of three wind tunnel experiments conducted by Norwegian University of Science and Technology (NTNU), China Aerodynamics Research and Development Centre (CARDC) and Von Karman Institute for Fluid Dynamics (VKI), the improved AL-LES method is validated from the aspects of wind-turbine power performance, the generation of tip vortex, and the distribution of wake velocity under typical offshore and onshore conditions. In addition, a full-scale wind turbine installed in Gansu is used for the experimental and numerical research. The main conclusion is that compared with the traditional method, the new AL-LES method improves the numerical accuracy by nearly 22%, and can more accurately simulate the interaction between atmospheric turbulence and wind-turbine wakes. The results can help the research of wind-turbine wakes and the micro-location selection of wind farm.

Numerical simulation of air flow in needle-to-cylinder electrohydrodynamic device

The paper presents the methodology and results of numerical simulation of the flow induced by corona discharge obtained with open-source environment Multiphysics Object-Oriented Simulation Environment (MOOSE) framework released by Idaho National Laboratory. Coupled system of governing partial differential equations is solved for the values of electric potential φ and space charge density ρq. The solution is used to calculate the spatial distribution of body force acting on the fluid as FEHD = ρq∇φ. The body force is subsequently introduced as a source term in Navier-Stokes equations solved in MOOSE for the value of fluid velocity. The results are presented as velocity profiles at the outlet of the flow generator and integrated to yield volumetric flow rate and the efficiency of the device. Comparison of the results with data available in literature reference for similar configuration shows satisfactory agreement.

A methodology for modeling and simulating frictional translational clearance joint in multibody systems including a flexible slider part

The objective of this paper is to present a simple and effective methodology for modeling and simulating frictional translational clearance joint in planar multibody systems including a flexible slider part. By using the finite element method (FEM), the slider is divided into finite elements, and the distributed body forces and boundary stresses (contact forces) on the slider are equivalent to the nodal forces. The normal contact forces are described by a nonlinear viscoelastic contact force model, while the frictional forces are evaluated by the Coulomb dry friction model. By lumping the mass matrix and presenting it in diagonal form, the equations of motion are then inertially decoupled, and the frictional forces are solved independently via trial-and-error algorithm. A penalty method for the revolute joint connecting the slider and other bodies is applied, and equations of motion are integrated numerically. Finally, two numerical examples are given to test the feasibility and effectiveness of the methodology in this paper.