Body Force Distribution Research Articles

Inversion of displacement fields to quantify the magnetic particle distribution in homogeneous elastic media from magnetomotive ultrasound

Magnetomotive ultrasound (MMUS) contrasts superparamagnetic iron-oxide nanoparticles (SPIOs) that undergo submicrometer-scale displacements in response to a magnetic gradient force applied to an imaging sample. Typically, MMUS signals are defined in a way that is proportional to the medium displacement, rendering an indirect measure of the density distribution of SPIOs embedded within. Displacement-based MMUS, however, suffers from ‘halo effects’ that extend into regions without SPIOs due to their inherent mechanical coupling with the medium. To reduce such effects and to provide a more accurate representation of the SPIO density distribution, we propose a model-based inversion of MMUS displacement fields by reconstructing the body force distribution. Displacement fields are modelled using the static Navier-Cauchy equation for linear, homogeneous, and isotropic media, and the body force fields are, in turn, reconstructed by minimizing a regularized least-squares error functional between the modelled and the measured displacement fields. This reconstruction, when performed on displacement fields of two tissue-mimicking phantoms with cuboidal SPIO-laden inclusions, improved the range of errors in measured heights and widths of the inclusions from 54%–282% pre-inversion to-15%–20%. Likewise, the post-inversion contrast to noise ratios (CNRs) of the images were significantly larger than displacement-derived CNRs alone (p = 0.0078, Wilcoxon signed rank test). Qualitatively, it was found that inversion ameliorates halo effects and increases overall detectability of the inclusion. These findings highlight the utility of model-based inversion as a tool for both signal processing and accurate characterization of the number density distribution of SPIOs in magnetomotive imaging.

LoadDef: A Python-Based Toolkit to Model Elastic Deformation Caused by Surface Mass Loading on Spherically Symmetric Bodies.

Temporal variations of surface masses, such as the hydrosphere and atmosphere of the Earth, load the surfaces of planetary bodies causing temporal variations in deformation. Surface shear forces and gravitational fields also drive ongoing planetary deformation. Characterizing the spatiotemporal patterns of planetary deformation can constrain allowable models for the interior structure of a planetary body as well as for the distribution of surface and body forces. Pertinent applications include hydrology, glaciology, geodynamics, atmospheric science, and climatology. To address the diversity of emerging applications, we introduce a software suite called LoadDef that provides a collection of modular functions for modeling planetary deformation within a self‐consistent, Python‐based computational framework. Key features of LoadDef include computation of real‐valued potential, load, and shear Love numbers for self‐gravitating and spherically symmetric planetary models; computation of Love‐number partial derivatives with respect to planetary density and elastic structure; computation of displacement, gravity, tilt, and strain load Green's functions; and computation of three‐component surface displacements induced by surface mass loading. At a most basic level, only a planetary‐structure model and a mass‐load model must be supplied as input to LoadDef to utilize all the main features of the software. The end‐to‐end forward‐modeling capabilities for mass‐loading applications lay the foundation for sensitivity studies and geodetic tomography. LoadDef results have been validated with Global Navigation Satellite System observations and verified against independent software and published results. As a case study, we use LoadDef to predict the solid Earth's elastic response to ocean tidal loading across the western United States.

Filtered lifting line theory and application to the actuator line model

Lifting line theory describes the cumulative effect of shed vorticity from finite span lifting surfaces. In this work, the theory is reformulated to improve the accuracy of the actuator line model (ALM). This model is a computational tool used to represent lifting surfaces, such as wind-turbine blades in computational fluid dynamics. In ALM, blade segments are represented by means of a Gaussian body force distribution with a prescribed kernel size. Prior analysis has shown that a representation of the blade using an optimal kernel width$\unicode[STIX]{x1D716}^{opt}$of approximately one quarter of the chord size results in accurate predictions of the velocity field and loads along the blades. Also, simulations have shown that use of the optimal kernel size yields accurate representation of the tip-vortex size and the associated downwash resulting in accurate predictions of the tip losses. In this work, we address the issue of how to represent the effects of finite span wings and tip vortices when using Gaussian body forces with a kernel size larger than the optimal value. This question is relevant in the context of coarse-scale large-eddy simulations that cannot afford the fine resolutions required to resolve the optimal kernel size. For this purpose, we present a filtered lifting line theory for a Gaussian force distribution. Based on the streamwise component of the vorticity transport equation, we develop an analytical model for the induced velocity resulting from the spanwise changes in lift force for an arbitrary kernel scale. The results are used to derive a subfilter-scale velocity model that is used to correct the velocity along the blade when using kernel sizes larger than$\unicode[STIX]{x1D716}^{opt}$. Tests are performed in large-eddy simulation of flow over fixed wings with constant and elliptic chord distributions using various kernel sizes. Results show that by using the proposed subfilter velocity model, kernel-size independent predictions of lift coefficient and total lift forces agree with those obtained with the optimal kernel size.

Numerical prediction of the effective wake profiles of a high-speed underwater vehicle with contra-rotating propellers

A numerical method is proposed to predict the effective wake profiles of high speed underwater vehicles propelled by contra-rotating propellers (CRPs), in which the hydrodynamic effects of the CRPs are simulated by distributed body forces. First, Reynolds-averaged Navier-Stokes (RANS) simulations are conducted for identical body-force distributions in open-water and self-propulsion conditions. The effective wake profiles at the CRP disks are then obtained by subtracting the velocities induced by the body forces in the open water from those induced by the body forces in the self-propulsion condition. The effective wake profiles were then predicted for a generic underwater vehicle with an established CRP design. Next, the hydrodynamic performance of the CRPs in the effective wake was computed using an in-house vortex-lattice code. The potential-flow results agree well with those provided by the RANS simulation under the self-propulsion condition, indicating that the proposed method can predict the effective wake profiles for CRPs with reasonable accuracy. The influences of different wake components on the blade forces were investigated, determining that for CRPs, and especially for the aft propeller, the circumferential wake cannot be neglected in the design.

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.

Body Force Calculation of Steady-State Plasma Flow with Accurate Pressure Measurement

The pressure field of plasma flow induced by surface-dielectric-barrier-discharge plasma actuators in quiescent air is difficult to measure accurately due to the very slight variations in pressure of the induced flow. To solve this issue, a special pressure measurement system is designed. Several microtransient differential pressure sensors are placed on a plexiglass board that is arranged vertically to the plasma actuator to detect the inconspicuous changes of pressure gradient in the induced flow. The board is then moved in the horizontal direction, driven by the lead screw transmission. To verify the reliability of the experimental pressure field, the plasma computational model is applied to simulate the pressure distribution of plasma flow, and it is compared with the experimental results. To study how the pressure term contributes to the body force calculation of plasma flow, the measured pressure field from the experiment is regarded as the source term and substituted into Navier–Stokes equations to calculate the body force distribution. The body force neglecting the pressure term is compared with the body force that includes the pressure term. The experimental and computational results show that the pressure term is the critical factor of body force distribution, and therefore cannot be ignored.

Dominant parameters for maximum velocity induced by body-force models for plasma actuators

This study investigates the relationship between body-force fields and maximum velocity induced in quiescent air for development of a simple body-force model of a plasma actuator. Numerical simulations are conducted with the body force near a wall. The spatial distribution and temporal variation of the body force are a Gaussian distribution and steady actuation, respectively. The dimensional analysis is performed to derive a reference velocity and Reynolds number based on the body-force distribution. It is found that the derived Reynolds number correlates well with the nondimensional maximum velocity induced in quiescent conditions when the center of the Gaussian distribution is fixed at the wall. Additionally, two flow regimes are identified in terms of the Reynolds number. Considering the variation of the center of gravity of force fields, another Reynolds number is defined by introducing a new reference length. The nondimensional maximum velocity is found to be scaled with the latter Reynolds number, i.e., the maximum induced velocity in quiescent conditions is determined from three key parameters of the force field: the total induced momentum per unit time, the height of the center of gravity, and the standard deviation from it. This scaling turns out to be applicable to existing body-force models of the plasma actuator, despite the force distributions different from the Gaussian distribution. Comparisons of velocity profiles with experimental data validate the results and show that the flow induced by a plasma actuator can be simulated with simple force distributions by adjustment of the key body-force parameters.

Elastic models of dislocations based on atomistic Kanzaki forces

© 2018 authors. Published by the American Physical Society. This paper studies the relationship between the atomistic representation of crystalline dislocations as Kanzaki forces and the continuum representation of dislocations as Burridge-Knopoff (BK) force distributions. We first derive a complete theory of the BK force representation of dislocations in an anisotropic linear elastic continuum, showcasing a number of fundamental features found when dislocations are represented as distributions of body forces in defect-free continuum media. We then build, within the harmonic approximation, the Kanzaki force representation of dislocations in atomistic lattice models. We rigorously show that in the long-wave limit, the Kanzaki force representation converges to the continuum BK representation. We therefore justify employing the Kanzaki forces as source terms in continuum theories of dislocations. We do this by establishing a methodology to compute the Kanzaki forces of dislocations via the force constant matrix of the material's perfect lattice. We use it to study a model of a screw dislocation in bcc tungsten, where we show the existence of two distinct Kanzaki force terms: the slip Kanzaki forces, which we show directly correspond with the BK forces implied by a Volterra dislocation; and the core Kanzaki forces, which are computed from the relaxed dislocation structure, and serve to model all core effects not captured by the Volterra dislocation. We build a multipolar field expansion of both the core and the slip Kanzaki forces, showing that the dislocation core is agreeable to correction via the multipolar field expansion of the core Kanzaki forces.

Magnetic field advection in a rotating magnetic field driven flow induced by a non-ideal inductor

The limits of the axisymmetric ideal inductor approach and the low magnetic Reynolds number (Rem) approach are demonstrated for the case study of a flow driven by a rotating magnetic field induced by an explicit-pole non-ideal inductor. These effects are studied for an intermediate range of the magnetic Reynolds number 0.1 ≤ Rem ≤ 1. It is shown that phenomena that do not exist under the ideal inductor approach change the distribution of the electromagnetic body force (EMBF) from axial symmetry to rotational symmetry. However, it is found that the magnetic field advection (MFA), which is neglected under the low Rem approach, induces body force that changes the distribution of the EMBF so that it effectively becomes closer to being axisymmetric. Therefore, it is suggested that the ideal inductor approach should not be applied in low Rem applications; this approach can be applied in high Rem applications. It is also found that the effect of MFA on the averaged velocity field is negligible for higher values of Rem than traditionally assumed, but MFA has a significant effect in reducing the turbulent kinetic energy. The reduction is found to be a result of the MFA-induced EMBF reducing the turbulence production.

Numerical investigation of circle defining curve for two-dimensional problem with general boundaries using the scaled boundary finite element method

The scaled boundary finite element method (SBFEM) is applied to the static analysis of two dimensional elasticity problem, boundary value problems domain with the domain completely described by a circular defining curve. The scaled boundary finite element equations is formulated within a general framework integrating the influence of the distributed body force, general boundary conditions, and bounded and unbounded domain. This paper investigates the possibility of using exact geometry to form the exact description of the circular defining curve and the standard finite element shape function to approximate the defining curve. Three linear elasticity problems are presented to verify the proposed method with the analytical solution. Numerical examples show the accuracy and efficiency of the proposed method, and the performance is found to be better than using standard linear element for the approximation defining curve on the scaled boundary method.

Amplification of localized body forces in channel flows of viscoelastic fluids

The study of nonmodal amplification of distributed body forces in channel flows of viscoelastic fluids has provided useful insights into the mechanisms that may govern the initial stages of transition to elastic turbulence. However, distributed body forces are not easy to implement in experiments and so there is a need to examine amplification of localized body forces. In this work, we use the linearized governing equations to examine such amplification in Poiseuille flow of FENE-CR fluids. We first identify the wall-normal location at which the impulsive excitations experience the largest amplification and then analyze the kinetic energy of the fluctuations and the resulting flow structures. For both a Newtonian fluid at high Reynolds numbers and a viscoelastic fluid at low Reynolds numbers, the largest amplification occurs for disturbances that are located near the channel wall. Our analysis of the energy evolution shows that a localized body force in the spanwise direction has the largest impact and that the streamwise velocity component is most affected. For viscoelastic fluids we observe the development of vortical structures away from the source of impulsive excitation. This feature is less prominent in Newtonian fluids and it may provide a mechanism for triggering the initial stages of transition to elastic turbulence.

A pseudo-static method for seismic responses of underground frame structures subjected to increasing excitations

The determinant factor for the seismic response of underground structures is the deformation of surrounding soil, which is different from above-ground structures. Considering that the existing deformation-based seismic design methods for underground structures are based on elastic hypotheses, this study proposes an improved Finite Element method called New Pseudo-Static Analysis (NewPSA) to predict the nonlinear behavior of underground frame structures subjected to increasing horizontal seismic excitations. A new method for one-dimensional(1-D) seismic analysis of soil layers is proposed to calculate the distributions of displacements and shear stresses along the depth in the free-field with increasing bedrock motions. Pseudo-static Finite Element analysis is then carried out by imposing the distributions of body forces derived from the 1-D analysis. A series of comparisons were made to validate the applicability of the proposed method. Its prediction capacity was also compared with that of a well-known method. The proposed method is able to predict the nonlinear performances of underground structures under horizontal earthquake loadings. Particularly, similar to the push-over analysis of above-ground structures, the method has the potential to predict the seismic capacity of underground frame structures subjected to design seismic loadings.

Optimal smoothing length scale for actuator line models of wind turbine blades based on Gaussian body force distribution

AbstractThe actuator line model (ALM) is a commonly used method to represent lifting surfaces such as wind turbine blades within large‐eddy simulations (LES). In the ALM, the lift and drag forces are replaced by an imposed body force that is typically smoothed over several grid points using a Gaussian kernel with some prescribed smoothing width ε. To date, the choice of ε has most often been based on numerical considerations related to the grid spacing used in LES. However, especially for finely resolved LES with grid spacings on the order of or smaller than the chord length of the blade, the best choice of ε is not known. In this work, a theoretical approach is followed to determine the most suitable value of ε, based on an analytical solution to the linearized inviscid flow response to a Gaussian force. We find that the optimal smoothing width εopt is on the order of 14%‐25% of the chord length of the blade, and the center of force is located at about 13%‐26% downstream of the leading edge of the blade for the cases considered. These optimal values do not depend on angle of attack and depend only weakly on the type of lifting surface. It is then shown that an even more realistic velocity field can be induced by a 2‐D elliptical Gaussian lift‐force kernel. Some results are also provided regarding drag force representation. Copyright © 2017 John Wiley & Sons, Ltd.

The effect of cubic material nonlinearity on the propagation of torsional wave modes in a pipe.

The effect of cubic material nonlinearity on the propagation in a pipe of the lowest axially symmetric torsional wave mode has been investigated in this paper. Two cases, one that the material of the whole pipe is nonlinear, and the second that a small segment of the pipe is nonlinear, have been considered. For the first case, a first and a third harmonic have been obtained by the perturbation method. Analytical expressions for the two cumulative harmonics have been derived. The second case leads to a scattering problem. The segment produces nonlinear terms in the equation of motion, which can be regarded as a distribution of body forces. The problem is then reduced to a linear scattering problem. An analytical expression for the backscattered wave can be easily obtained by using the elastodynamic reciprocity theorem. Due to the low amplitude of the backscattered wave, the authors propose to add another higher frequency wave to the primary wave, to increase the total magnitude of the scattered wave. An example that the originally scattered wave is amplified 50 times by selecting proper frequencies is presented. Both cases considered here have a potential application to determine the material properties in a region of nonlinear material behavior.

Frequency-Dependent Capacitance-Based Plasma Model for Direct Simulation of Navier–Stokes Equation

The effects of single dielectric barrier discharge plasma actuators on flow control are studied using a new frequency and pressure-dependent capacitance-based model by calculating the spatiotemporal distribution of surface charge density in the present work. The proposed model is an improvement over earlier similar efforts, but it retains the superior features of previous macroscopic models. It can be used to accurately compute the spatiotemporal distribution of body force due to plasma actuation without computing the complex electrodynamics equations for charge density on microscopic scales. It has been shown that the proposed model estimates the time-averaged total body force more accurately than similar models developed earlier, as compared to experimental results. The effects of plasma excitation frequency and the voltage waveform were considered. The proposed model has been incorporated into a Navier–Stokes equation solver in a time-accurate manner to study single dielectric barrier discharge plasma actuation in a quiescent flow environment. The onset of plasma actuation causes the creation of a complex transient vortical flowfield: one of its actions is to create a wall jet. Computed instantaneous velocity profiles at downstream locations show this wall jet, and they are compared with the experimental results. The computed results of the evolution of a starting vortex in a quiescent air induced by initiation of single dielectric barrier discharge plasma actuation display an excellent match with the experimental results of Whalley and Choi (“The Starting Vortex in Quiescent Air Induced by Dielectric-Barrier-Discharge Plasma,” Journal of Fluid Mechanics, Vol. 55, July 2012, pp. 192–203).

Numerical Simulation of Flow Separation Control using Multiple DBD Plasma Actuators

A numerical simulation method is employed to investigate the effect of the steady multiple plasma body forces on the flow field of stalled NACA 0015 airfoil. The plasma body forces created by multiple Dielectric Barrier Discharge (DBD) actuators are modeled with a phenomenological plasma method coupled with 2-dimensional compressible turbulent flow equations. The body force distribution is assumed to vary linearly in the triangular region around the actuator. The equations are solved using adual-timeimplicit finite volume method on unstructured grids. In this paper, the responses of the separated flow field to the effects of single and multiple DBD actuators over the broad range of angles of attack ( 9^0-〖30〗^0) are studied. The effects of the actuators positions on the flow field are also investigated. It is shown that the DBD have a significant effect on flow separation control in low Reynolds number aerodynamics.

Field emission microplasma actuation for microchannel flows

Microplasmas offer attractive flow control methodology for gas transport in microsystems where large viscous losses make conventional pumping methods highly inefficient. We study microscale flow actuation by dielectric-barrier discharge (DBD) with field emission (FE) of electrons, which allows lowering the operational voltage from kV to a few hundred volts and below. A feasibility study of FE-DBD for flow actuation is performed using 2D particle-in-cell method with Monte Carlo collisions (PIC/MCC) at 10 MHz in nitrogen at atmospheric pressure. The free diffusion dominated, high velocity field emission electrons create a large positive space charge and a body force on the order of 106 N m−3. The body force and Joule heat decrease with increase in dielectric thickness and electrode thickness. The body force also decreases at lower pressures. The plasma body force distribution along with the Joule heating is then used in the Navier–Stokes simulations to quantify the flow actuation in a microchannel. Theoretical analysis and simulations for plasma actuated planar Poiseuille flow show that the gain in flow rate is inversely proportional to Reynolds number. This theoretical analysis is in good agreement with the simulations for a microchannel with closely placed actuators under incompressible conditions. Flow rate of FE-DBD driven 2D microchannel is around 100 ml min−1 mm−1 for an input power of 64 μW mm−1. The gas temperature rises by 1500 K due to the Joule heating, indicating FE-DBD’s potential for microcombustion, micropropulsion and chemical sensing in addition to microscale pumping and mixing applications.

印加電圧波形が DBD プラズマアクチュエータの性能に与える影響の数値解析

Dielectric barrier discharge (DBD) plasma actuator is widely researched as one of active flow control devices. To enhance the performance, a new voltage waveform made by the combination of gradual and steep voltage slope was suggested; it was shown the waveform can generate stronger body force by 60 % or more. In this research, we investigated the body force of DBD plasma actuator with suggested new waveform (Gradual-Steep Slope, GSS waveform) using the plasma simulation to clarify the performance improvement mechanism. For the first step of the research, we disucuss the characteristics of discharge and body force of the GSS voltage waveform by comparing with those of the sinusoidal (SN) waveform. First, we confirmed the simulation can reproduce many of time-historical discharge currents and body force characteristics. Second, we compared the GSS waveform with the SN waveform. We found the GSS voltage waveform generates dense discharge in the steep voltage slope period, and in the gradual slope period which follows after the steep slope period large body force is effectrively generated. From the viewpoint of the time-averaged body force distribtution, the GSS waveform make the body force distribution expands larger.

Plasma-actuated Manipulation of Secondary Flow Towards Pressure Recovery Enhancement in a 3D Diffuser Modelled by an Eddy-resolving Second-moment Closure

A computational study is presented of the enhancement of pressure recovery in a three-dimensional diffuser by using plasma actuators, as experimentally investigated by Grundmann et al., Exper. Fluids 50, (1), 217–231 (2011). The flow configuration utilizes a streamwise-oriented arrangement of dielectric barrier discharge (DBD) plasma actuators mounted on the top wall of the inflow duct. Spanwise motion directed towards the duct corners was generated, modifying the inflow with locally intensified turbulence. The most advantageous enhancement was achieved using an actuator pulsed with 40 % duty cycle. For comparison an actuator operating continuously (100 % duty cycle) was also considered. The present computational study examines both cases, comparing them to the baseline configuration with no actuation. Simulations were performed within the scale-adaptive version of the Unsteady RANS (Reynolds-Averaged Navier Stokes) framework by using an eddy-resolving second-moment closure as the turbulence model. The plasma actuator was represented using a spatial body-force distribution based on PIV (Particle Image Velocimetry) measurements of the flow induced by a plasma actuator, Kriegseis et al., J. Phys. D: Appl. Phys. 48, 329401 (2015). The results obtained for both pressure-recovery enhancement and suppression correlate well with the experimental findings.

Optimization of micro single dielectric barrier discharge plasma actuator models based on experimental velocity and body force fields

Recently, the Micro Single Dielectric Barrier Discharge Plasma Actuator has become attractive for application in aeronautics and micropopulsion thrusters. The present work carried out a preliminary characterization of such device, acting on initially quiescent air by experimental and numerical approaches. Sinusoidal voltage excitation with amplitude up to 7kV and frequency up to 2.5kHz was applied. The induced flow was investigated by particle image velocimetry and the measured velocity fields were used to estimate experimentally the time-averaged induced body force distributions by a differential method. Plasma induced forces were modeled by following three different approaches, later implemented as a source term in the Navier–Stokes equations for the fluid flow simulations. Potentialities, advantages and disadvantages of the considered force modeling methods were investigated. Quantitative comparison of the experimental and numerical induced force, as well as of the velocity fields, allowed establishing which model best predicted the actuator effects. The algebraic Dual Potential Model provided a good agreement between experimental and simulated results, in terms of flow velocities and thickness of the induced wall-jet. The downstream decay of the wall-jet velocity, experimentally observed, was also successfully predicted. A maximum induced velocity of ≈2 m/s was obtained and a jet thickness of ≈3 mm.