Total Body Force Research Articles

On pressure robustness and independent determination of displacement and pressure in incompressible linear elasticity

We investigate the possibility to determine the divergence-free displacement uindependently from the pressure reaction p for a class of boundary-value problems in incompressible linear elasticity. If not possible, we investigate if it is possible to determine it pressure robustly, i.e. pollution free from the pressure reaction.For convex domains there is but one variational boundary value problem among the investigated that allows the independent determination. It is the one with essential no-penetration conditions combined with homogeneous tangential traction conditions.Further, for the investigated cases, the weakly divergence-free displacement can be computed pressure robustly provided the total body force is decomposed into its direct sum of divergence- and rotation-free components using the Helmholtz decomposition. The elasticity problem is solved using these components as separate right-hand sides. The total solution is obtained using the superposition principle.We employ a (u,p) higher-order finite element formulation with discontinuous pressure elements. It is inf–sup stable for polynomial degree p≥2 but not pressure robust by itself. We propose a three step procedure to solve the elasticity problem which includes by the Helmholtz decomposition of the total body force. The extra cost for the three-step procedure is essentially the cost for the Helmholtz decomposition of the assembled total body force, and the small cost of solving the elasticity problem with one extra right-hand side. The results are corroborated by theoretical derivations as well as numerical results.

The role of nonlinear body force in production of electric wind in an asymmetric surface dielectric barrier discharge

The electrohydrodynamic body force produced in an asymmetric surface dielectric barrier discharge is widely utilized in flow control applications. The mechanism of body force production has a key role in the performance of plasma actuators. In this paper, a novel supplementary theory of body force production, named ‘nonlinear force’, is described as a new interesting component of total body force. This force is distinct from the well-known body force with a Coulomb origin, and also acts through a different mechanism. The theory of nonlinear force shows that it is unidirectional and pushes all particles towards the lower electrode irrespective of the charge sign and variations in electric field polarity.

Modular Integrated Longitudinal, Lateral, and Vertical Vehicle Stability Control for Distributed Electric Vehicles

There is a nonlinear coupling relationship between the vehicle in the longitudinal, lateral, and vertical directions, which brings great difficulties to the design of the controller. To tackle the chattering problem, a hierarchical integrated controller for distributed electric vehicle is proposed to improve driving safety, handling stability, ride comfort, and road tracking capabilities. The proposed algorithm has been developed to overcome a major challenge of the conventional method, which can improve only partial dynamic performance of the vehicle. The optimal pre-pointing lateral acceleration model is used to simulate the operator's expected reaction to the vehicle. The body control layer decouples complex problems to achieve multi-target independent tracking through a nonlinear sliding-mode control algorithm, and calculates the expected total body force to meet the upper level instructions. The tire force distribution layer is designed to optimize the function by reducing the tire load ratio and balancing the vertical dynamic load coefficient to improve the vehicle's driving stability and ride comfort. The lower actuator control layer controls the corresponding actuator to achieve the optimal tire force output from the middle layer. Finally, the effectiveness of the chassis integrated control system is verified in CarSim and MATLAB co-simulation.

On basic equations and kinematic-wave theory of separation processes in suspensions with gravity, centrifugal and Coriolis forces

Neglecting inertial and viscosity effects in the bulk flow is a common assumption in the analysis of separation processes in suspensions under the action of gravity or centrifugal and Coriolis forces. While there is a number of examples of particular solutions, the general form of the basic equations for three space dimensions, together with the appropriate boundary and initial conditions, is still uncertain and, with regard to certain aspects, even controversial. An essential point is a proper choice of the variables. Here it is proposed to introduce the mass density of the mixture, the mean mass velocity of the mixture and the total volume flux as a set of dependent variables. After some manipulations, a complete set of basic equations is obtained. It consists of two continuity equations, a generalized drift-flux relation, and two linearly independent components of a vector equation describing the total body force as irrotational. Then, by eliminating the mean mass velocity of the mixture from the set of unknowns, a generalized kinematic-wave equation is derived. It describes kinematic waves that are embedded in a bulk flow that may be one-, two- or three-dimensional. Concerning boundary conditions at solid walls, one has to ascertain whether the total body force at the wall points into the suspension or out of it. In the former case, a thin boundary layer of clear liquid is formed at the wall, whereas in the latter case a thin sediment layer may either stick at the wall or slide along it. Each of those three possibilities leads to a particular boundary condition for the bulk flow in terms of the dependent variables. In addition, initial conditions and kinematic shock relations are briefly discussed. Finally, the application of the kinematic-wave theory to the settling process in rotating tubes is outlined.

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).

Using Parabolic Flights to Examine Quantitatively the Stability of Liquid Bridges under Varying Total Body Force

Liquid bridges were flown aboard a Boeing 727-200 aircraft in a series of parabolic arcs that produced multiple periods of microgravity. During the microgravity portion of each arc, geff, the effective total body acceleration due to external forces became negligibly small so that cylindrical liquid bridges could be suspended across two coaxial support posts. Near the bottom of each arc, geff slowly increased to a maximum of 1.84g, causing the liquid bridges to deform and in some cases collapse. Although the physics of liquid bridges subject to varying total body force is well-established and has been analyzed extensively both theoretically and experimentally, specific hardware was designed to vary geff in a precise way that overcomes the gravity-related limitations and high g-jitter associated with parabolic flights. Bridge-stability was examined for axial and lateral orientations with respect to geff by measuring the slenderness ratio as a function of Bond number at the instant of bridge collapse. Results exhibit remarkable agreement with theory as well as with the experimental results obtained in a magnetic levitation-based experiment. The parabolic flight method offers technical originality and provides experimental insights for researchers in the microgravity field. Here we present hardware development, experimental considerations, and results, and demonstrate that parabolic flight is a viable alternative to extant techniques for quantitative experiments on fluids.

Galerkin Boundary Elements for a Computation of the Surface Tractions in Exterior Stokes Flows

In the computation of a three–dimensional steady creeping flow around a rigid body, the total body force and torque are well predicted using a boundary integral equation (BIE) with a single concentrated pair Stokeslet- Rotlet located at an interior point of the body. However, the distribution of surface tractions are seldom considered. Then, a completed indirect velocity BIE of Fredholm type and second-kind is employed for the computation of the pointwise tractions, and it is numerically solved by using either collocation or Galerkin weighting procedures over flat triangles. In the Galerkin case, a full numerical quadrature is proposed in order to handle the weak singularity of the tensor kernels, which is an extension for fluid engineering of a general framework (Taylor, 2003, “Accurate and Efficient Numerical Integration of Weakly Singulars Integrals in Galerkin EFIE Solutions,” IEEE Trans. on Antennas and Propag., 51(7), pp. 1630–1637). Several numerical simulations of steady creeping flow around closed bodies are presented, where results compare well with semianalytical and finite-element solutions, showing the ability of the method for obtaining the viscous drag and capturing the singular behavior of the surface tractions close to edges and corners. Also, deliberately intricate geometries are considered.

Interaction Body Force Density and Mechanical Deformation in Soft Magnetic Materials With External Field by Freezing Procedure of Magnetization

The quantitative interaction body force density was calculated in soft magnetic materials by using a freezing procedure of magnetization and virtual air-gap scheme, which were implemented by using the Finite Element Method. Until now, the virtual air-gap concept has been successfully applied to evaluating contact force and body force density in soft magnetic materials. When the generalized methods, methodologies with virtual air-gap scheme, are introduced, one can have an irregular force field, which seems to be random distribution of body force density. Even though this irregular pattern generates a correct global force and reasonable trend of mechanical deformation, it is quite difficult to predict the resultant deformation by the irregular force field. This irregular force field pattern is originated from the field direction to the finite element edge where the virtual air gap is inserted and an additional strong force arises with the outward normal direction. To remove this irregular pattern and evaluate an interaction body force density, the self-force density by the frozen magnetization should be withdrawn from the total body force density. To verify the proposed method, first, a critical magnetic system, which cannot be solved by the equivalent magnetizing source methods, were tested for evaluating the interaction body force density corresponding to the resultant mechanical deformations. After confirming the interaction force, two additional specific models were tested with the resultant mechanical deformations due to the different local force densities.

Evaluation of Magnetic Force Distribution and Torque Due to Smooth Interaction Body Force Density in Permanent-Magnet Materials

A smooth interaction body force density and torque were evaluated in permanent-magnet (PM) systems by using the virtual air-gap scheme coupled with the finite-element method. The virtual air-gap method has been successfully applied to soft magnetic materials for evaluating the force density, global contact force, and optimal shape design. These force-calculating methods employing the virtual air-gap scheme have been called generalized methods. Unlike the soft magnetic materials, there have been few research works related to force density and global force in PMs. We evaluated the interaction body force density, which represents the smooth and pure interacting force field between PMs and other magnetic components, by withdrawing the self-body force density from the total body force density. From this result, the smooth interaction body force density can explicitly show the trend of resulting mechanical torque. The torque by the self-body force density, of course, was zero and the torque, here, was evaluated by using the total body force density. From the previous results, the torque by total body force density shows some numerical instability, and we used edge-force components in each element for removing the numerical instability. Finally, the global quantities, such as global force from the smooth interaction body force density and torque from the total body force density, were successfully evaluated and verified by the conventional force calculating methods, such as the Maxwell stress tensor method and the virtual work principle method.

Partial Segment Force on Ferromagnetic Material of High-Field Magnetic System

The electromagnetic total force and body force density distribution in the high-field magnetic system are important factors for mechanical deformation or vibration, electromechanical-coupled phenomenon, behavior of ferromagnetic material, etc. Since the high-field magnetic system, such as the transformer, electric motor, and generator with magnetic core are driven by very high magnetic flux density, the resulting electromagnetic force is so large that it causes serious mechanical problems. Therefore, accurate analysis of the distribution of force density and the partial forces on segment parts is helpful for the mechanically solid design of machine structures of ferromagnetic part and superconducting windings. In this paper, the body force density distribution and the partial forces over the ferromagnetic core are presented by using the recently developed body force calculation methods, which are based on the virtual airgap scheme. The presented method is applied and tested for four examples of a transform, a dipole magnet, a quadrupole magnet, and an induction motor.

Optimization of Dielectric Barrier Discharge Plasma Actuators for Active Aerodynamic Flow Control

This paper presents the results of a parametric experimental investigation aimed at optimizing the body force produced by single dielectric barrier discharge plasma actuators used for aerodynamic flow control. A primary goal of the study is the improvement of actuator authority for flow control applications at higher Reynolds number than previously possible. The study examines the effects of dielectric material and thickness, applied voltage amplitude and frequency, voltage waveform, exposed electrode geometry, covered electrode width, and multiple actuator arrays. The metric used to evaluate the performance of the actuator in each case is the measured actuator-induced thrust which is proportional to the total body force. It is demonstrated that actuators constructed with thick dielectric material of low dielectric constant produce a body force that is an order of magnitude larger than that obtained by the Kapton-based actuators used in many previous plasma flow control studies. These actuators allow operation at much higher applied voltages without the formation of discrete streamers which lead to body force saturation.

Numerical simulation for separation of multi-phase immiscible fluids in porous media

Based on a lattice Boltzmann method and general principles of porous flow, a numerical technique is presented for analysing the separation of multi-phase immiscible fluids in porous media. The total body force acting on fluid particles is modified by adding relative permeability in Nithiarasu's expression with an additional surface tension term. As a test of this model, we simulate the phase separation for the case of two immiscible fluids. The numerical results show that the two coupling relative permeability coefficients K12 and K21 have the same magnitude, so the linear flux-forcing relationships satisfy Onsager reciprocity. Phase separation phenomenon is shown with the time evolution of density distribution and bears a strong similarity to the results obtained from other numerical models and the flows in sands. At the same time, the dynamical rules in this model are local, therefore it can be run on massively parallel computers with well computational efficiency.

Magnetic levitation-based Martian and Lunar gravity simulator

Missions to Mars will subject living specimens to a range of low gravity environments. Deleterious biological effects of prolonged exposure to Martian gravity (0.38 g), Lunar gravity (0.17 g), and microgravity are expected, but the mechanisms involved and potential for remedies are unknown. We are proposing the development of a facility that provides a simulated Martian and Lunar gravity environment for experiments on biological systems in a well controlled laboratory setting. The magnetic adjustable gravity simulator will employ intense, inhomogeneous magnetic fields to exert magnetic body forces on a specimen that oppose the body force of gravity. By adjusting the magnetic field, it is possible to continuously adjust the total body force acting on a specimen. The simulator system considered consists of a superconducting solenoid with a room temperature bore sufficiently large to accommodate small whole organisms, cell cultures, and gravity sensitive bio-molecular solutions. It will have good optical access so that the organisms can be viewed in situ. This facility will be valuable for experimental observations and public demonstrations of systems in simulated reduced gravity.

Resonance behavior of liquid bridges under axial and lateral oscillating total body forces

Cylindrical liquid bridges that are magnetically levitated in air against gravity are subjected to either axial or lateral oscillations of the total body force. It was found that the frequency of the first resonance peak is maximum when the total body force is zero and decreases with increasing total body force for both axial and lateral oscillations. The experimental results for the axially symmetric case are compared to theoretical calculations using the one-dimensional slice model.

Stability of connected cylindrical liquid bridges.

Two cylindrical liquid bridges, with a conduit to facilitate flow of liquid from one bridge to the other, were levitated against gravity in a magnetic field gradient. The stability limit of the bridges subjected to near zero total body force was measured as a function of their slenderness ratios, and found to be in good agreement with theoretical predictions.

Collapse dynamics of liquid bridges investigated by time-varying magnetic levitation

Using a novel technique that facilitates temporal control over the total body force on a liquid, an unexpected scaling relationship was discovered for the collapse time of a liquid bridge. A paramagnetic liquid was suspended between the tips of two collinear rods in a strong magnetic field gradient that was adjusted to compensate gravity. A sudden change of the magnet current, corresponding to a change of Bond number, resulted in a deformation and ultimate collapse of the liquid bridge. The collapse time was found to be independent of the bridge length when other parameters were held constant.

On singular integral equations and fundamental solutions of poroelasticity

This paper presents a unified formulation of the various singular integral equations used in the boundary element methods (BEM) for the solution of linear, quasi-static, anisotropic poroelasticity. In particular, a derivation is provided that connects the "direct method" with the "indirect methods". The presentation begins with an alternative derivative of the time and space dependent reciprocal integral. The Somigliana-type integral equations for the direct BEM are first constructed. By summing integral equations representing an interior and an exterior domain problem, the Somigliana (displacement discontinuity) and Volterra (stress discontinuity) type dislocation equations for indirect BEM are obtained. An extension to the edge dislocation method is discussed. These stress and displacement discontinuity equations are then combined to construct a symmetric Galerkin integral equation system. Through such construction, many intriguing connections among Green|s functions of fluid source, dipole, dilatation, fluid body force, total body force, and displacement discontinuity are revealed. Finally, a complete compilation of fundamental solutions for the isotropic case is provided.

The Stratopause Semiannual Oscillation in the Berlin Troposphere–Stratosphere–Mesosphere GCM

Abstract The tropical stratopause semiannual oscillation (SAO) in the Berlin troposphere–stratosphere–mesosphere general circulation model (TSM GCM) is investigated. The model is able to produce a semiannual oscillation that is properly located in time and space in comparison with observations; however, the westerly phase is 10–15 m s−1 too weak while the second easterly phase of the year is about the same amount too strong. A case study is performed to examine the westerly forcing of the SAO in detail. At 1 hPa in one particular March, when the strongest westerly acceleration of the year takes place, only 18% of the forcing is due to the dissipation of Kelvin waves, whereas 72% of the forcing is due to the dissipation of other slow eastward propagating planetary-scale waves and 10% is due to the dissipation of eastward propagating inertio–gravity waves. Throughout the year the Kelvin wave contribution to the total body force is below 50%. The modeled Kelvin waves are dissipated at higher altitudes than o...

Gravity‐driven groundwater flow and slope failure potential: 1. Elastic Effective‐Stress Model

Hilly or mountainous topography influences gravity‐driven groundwater flow and the consequent distribution of effective stress in shallow subsurface environments. Effective stress, in turn, influences the potential for slope failure. To evaluate these influences, we formulate a two‐dimensional, steady state, poroelastic model. The governing equations incorporate groundwater effects as body forces, and they demonstrate that spatially uniform pore pressure changes do not influence effective stresses. We implement the model using two finite element codes. As an illustrative case, we calculate the groundwater flow field, total body force field, and effective stress field in a straight, homogeneous hillslope. The total body force and effective stress fields show that groundwater flow can influence shear stresses as well as effective normal stresses. In most parts of the hillslope, groundwater flow significantly increases the Coulomb failure potential Φ, which we define as the ratio of maximum shear stress to mean effective normal stress. Groundwater flow also shifts the locus of greatest failure potential toward the slope toe. However, the effects of groundwater flow on failure potential are less pronounced than might be anticipated on the basis of a simpler, one‐dimensional, limit equilibrium analysis. This is a consequence of continuity, compatibility, and boundary constraints on the two‐dimensional flow and stress fields, and it points to important differences between our elastic continuum model and limit equilibrium models commonly used to assess slope stability.

The influence of gravitational force on gas absorption in a packed column

AbstractCarbon dioxide was desorbed from water in a packed column mounted on a large centrifuge. By varying the centrifuge rotational speed, the total body force acting upon the liquid was varied from 1 to 6.4 times the normal gravitational force. The results, obtained for ¾ in. Rasching ring packing, showed kLa varying with the body force to a power between 0.41 and 0.48, the exponent being larger at lower liquid flow rates. This effect of gravity is compared with penetration theory predictions and with those inferred from dimensional analysis and the effect of packing size.