Constitutive Equations for Magnetic Active Liquids

This article is focused on the derivation of constitutive equations for magnetic liquids. The results can be used for both ferromagnetic and magnetorheological fluids after the introduced simplifications. The formulation of constitutive equations is based on two approaches. The intuitive approach is based on experimental experience of non-Newtonian fluids, which exhibit a generally non-linear dependence of mechanical stress on shear rate; this is consistent with experimental experience with magnetic liquids. In these general equations, it is necessary to determine the viscosity of a liquid as a function of magnetic induction; however, these equations only apply to the symmetric stress tensor and can only be used for an incompressible fluid. As a result of this limitation, in the next part of the work, this approach is extended by the asymmetry of the stress tensor, depending on the angular velocity tensor. All constitutive equations are formulated in Cartesian coordinates in 3D space. The second approach to determining constitutive equations is more general: it takes the basis of non-equilibrium thermodynamics and is based on the physical approach, using the definition of density of the entropy production. The production of entropy is expressed by irreversible thermodynamic flows, which are caused by the effect of generalized thermodynamic forces after disturbance of the thermodynamic equilibrium. The dependence between fluxes and forces determines the constitutive equations between stress tensors, depending on the strain rate tensor and the magnetization vector, which depends on the intensity of the magnetic field. Their interdependencies are described in this article on the basis of the Curie principle and on the Onsager conditions of symmetry.

Experimental Study on Multi-Channel Jets in Plate Assembly Under Blockage Condition

In the nuclear field, the reactor using plate fuel assembly forms multiple jets at exit. So, it’s meaningful to study multiple jets to learn the behavior of the coolant when it leaves the core. This paper uses PIV technology to study the flow characteristics of 9 jets at low Reynolds number. Firstly, the velocity field reveals that the pressure outside the jet is greater than the inside of the jet, which causes the jet to deflect and converge inward at z/w = 0–8. Then, the velocity field with different Re number is analyzed in the center plane, and find that the flow distribution is similar. Then, a detailed analysis is performed on the jet under specific conditions, and the merge point is discussed in the paper. At the same time, the first-order velocity tensor are also calculated in this paper. In addition, this article also analyzes the jet flow field after the central narrow channel was blocked. In this experiment, a plug was used to block the No. 5 jet by 1/3. And the flow redistribution is discussed in this case. The methods of flow calculation using PIV technology is established and compared with the real number of flowmeters, it’s found that the calculation method is rather accurate. On the other hand, the experiment find that the distribution of flow in each channel is not uniform, and the blocking condition make an increase in the flow of edge channels, which leads to the decreasing of flow in the blocked adjacent channel.

CONSEQUENCES OF THE OSTROGRADSKY-GAUSS THEOREM FOR NUMERICAL SIMULATION IN AEROMECHANICS

Using the Ostrogradsky-Gauss theorem to construct the laws of conservation and replacement of the integral over the surface by the integral over the volume, we neglect the integral term outside, i.e. neglect the circulation on the sides of the elementary volume (in the two-dimensional case, this is clearly visible). Circulation means the presence of rotation, which in turn means the presence of a moment of force (angular momentum). As a result, we have a symmetric stress tensor, a symmetric velocity tensor, etc. Static pressure, as follows from kinetic theory, there is a zero-order quantity; the terms associated with dissipative effects are first-order quantities. It does not follow from the Boltzmann equation and from the phenomenological theory that the pressure in the Euler equation is equal to one third of the sum of the pressures on the corresponding coordinate axes. The inaccuracy of determining the velocities in the stress tensor in the stress tensor does not strongly affect the results at low speeds. All these issues are discussed in the work. As example in this paper suggests task of flowing liquid at little distance of two parallel plates.

Material rotating frame, rate-independent plasticity with regularization of Schmid law and study of channel-die compression

Metals often exhibit several crystallographic components that rotate when subjected to large plastic deformation. Studying their evolution constitutes a prospect to apply the finite plastic strain theory. In this respect, this research paper formulates a three-dimensional extension of Dogui’s plane kinematics to choose a material rotating frame in which deformation and velocity tensor gradients are represented by upper triangular matrices. This technique facilitates numerical calculation and renders it faster. This can prove to be useful if used for crystalline calculation. We study the kinematics of a channel-die loading to implement the material rotating frame model. The rate-independent formulation, which uses the multi-surface theory to represent the plastic flow of crystals, often leads to slip indeterminacy. Hence, we have developed a phenomenological method to solve such a difficulty using the regularization of Schmid’s yield law. As a significant application of this proposed phenomenological approach, aluminium crystal flow in channel-die compression is numerically simulated for three cases of loadings: (i) classical rolling components Cube, Goss, Brass, Copper and Dillamore orientations; (ii) {110} compression; and (iii) Strange orientation, which has no common element of symmetry with the channel-die. A good correlation between the simulation results and the available experimental ones is observed.

Turbulence characterization from a forward-looking nacelle lidar

We present two methods to characterize turbulence in the turbine inflow using radial velocity measurements from nacelle-mounted lidars. The first uses a model of the three-dimensional spectral velocity tensor combined with a model of the spatial radial velocity averaging of the lidars, and the second uses the ensemble-averaged Doppler radial velocity spectrum. With the former, filtered turbulence estimates can be predicted, whereas the latter model-free method allows us to estimate unfiltered turbulence measures. Two types of forward-looking nacelle lidars are investigated: a pulsed system that uses a five-beam configuration and a continuous-wave system that scans conically. For both types of lidars, we show how the radial velocity spectra of the lidar beams are influenced by turbulence characteristics, and how to extract the velocity-tensor parameters that are useful to predict the loads on a turbine. We also show how the velocity-component variances and co-variances can be estimated from the radial-velocity unfiltered variances of the lidar beams. We demonstrate the methods using measurements from an experiment conducted at the Nørrekær Enge wind farm in northern Denmark, where both types of lidars were installed on the nacelle of a wind turbine. Comparison of the lidar-based along-wind unfiltered variances with those from a cup anemometer installed on a meteorological mast close to the turbine shows a bias of just 2 %. The ratios of the unfiltered and filtered radial velocity variances of the lidar beams to the cup-anemometer variances are well predicted by the spectral model. However, other lidar-derived estimates of velocity-component variances and co-variances do not agree with those from a sonic anemometer on the mast, which we mostly attribute to the small cone angle of the lidar. The velocity-tensor parameters derived from sonic-anemometer velocity spectra and those derived from lidar radial velocity spectra agree well under both near-neutral atmospheric stability and high wind-speed conditions, with differences increasing with decreasing wind speed and increasing stability. We also partly attribute these differences to the lidar beam configuration.

Turbulence characterization from a forward-looking nacelle lidar

We present two methods to characterize turbulence in the turbine inflow using radial velocity measurements from nacelle-mounted lidars. The first uses a model of the three-dimensional spectral velocity tensor combined with a model of the spatial radial velocity averaging of the lidars and the second uses the ensemble-averaged Doppler radial velocity spectrum. With the former, filtered turbulence estimates can be predicted, whereas the latter model-free method allows us to estimate unfiltered turbulence measures. Two types of forward-looking nacelle lidars are investigated: a pulsed system that uses a 5-beam configuration and a continuous-wave system that scans conically. For both types of lidars, we show how the radial velocity spectra of the lidar beams are influenced by turbulence characteristics and how to extract the velocity-tensor parameters that are useful to predict the loads on a turbine. We also show how the velocity-component variances and co-variances can be estimated from the radial-velocity unfiltered variances of the lidar beams. We demonstrate the methods using measurements from an experiment conducted at the Nørrekær Enge wind farm in northern Denmark, where both types of lidars were installed on the nacelle of a wind turbine. Comparison of the lidar-based along-wind unfiltered variances with those from a cup anemometer installed on a meteorological mast close to the turbine shows a bias of just 2 %. The ratios of the unfiltered and filtered radial velocity variances of the lidar beams to the cup-anemometer variances are well predicted by the spectral model. However, other lidar-derived estimates of velocity-component variances and co-variances do not agree with those from a sonic anemometer on the mast, which we mostly attribute to the small cone angle of the lidar. The velocity-tensor parameters derived from sonic-anemometer velocity spectra and those derived from lidar radial velocity spectra agree well under both near-neutral atmospheric stability and high wind-speed conditions with differences increasing with decreasing wind-speed and increasing stability. We also partly attribute these differences to the lidar beam configuration.

A spectral model for stably stratified turbulence

A solution of the inviscid rapid distortion equations for a stratified flow with homogeneous shear is proposed, extending the work of Hanazaki & Hunt (J. Fluid Mech., vol. 507, 2004, pp. 1–42) to the two horizontal velocity components. The analytical solution allows for the determination of the spectral tensor evolution at any given time starting from a known initial condition. By following the same approach as that adopted by Mann (J. Fluid Mech., vol. 273, 1994, pp. 141–168), a model for the spectral velocity tensor in the atmospheric boundary layer is obtained, where the spectral tensor, assumed to be isotropic at the initial time, evolves until the breakup time where the spectral tensor is supposed to achieve its final state observed in the boundary layer. The model predictions are compared with atmospheric measurements obtained over a forested area, giving the opportunity to calibrate the model parameters, and further validation is provided by additional low-roughness data. Characteristic values of the model coefficients and their dependence on the Richardson number are proposed and discussed.

GEODYNAMICS

Estimated from GPS observations velocities of GPS-stations were used to obtain 2D-model velocities and strain rate field in the Eastern Europe. The study of the velocities field in the region was done in a few steps. The first one consists of the development of the finite element approach on the geosphere based on bicubic spline functions and least squares collocation method for the interpolation scattered GPS-data to the regular nodes. The second one represents the inversion of velocities from GPS-observations to the strain rate tensor. In order to test this approach we chose to apply it to an Eastern Europe where such problem was not solved before. This region is not extensively instrumented as yet but it is well studied by a geological and geophysical data. Test is based on derived in the Research Institute of Geodesy and Cartography (Kyiv, Ukraine) solution of GPS-observations data processing for the region. Finally the full eigenvalue/eigenvector solution for deformations velocity tensor of concerned territory is preformed and analyzed.

The Velocity Tensor and the Momentum Tensor

This paper introduces a new object called the momentum tensor. Together with the velocity tensorit forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are derived as well as its relation with the velocity tensor. For the sake of clarity only two-dimensional case is investigated. However, general conclusions are also valid for higher dimensional spacetimes.