Study on Influencing Factors of Helicopter Brownout Evolution Based on CFD-DEM

The gas-solid two-phase flow model is constructed based on the Euler-Lagrangian framework. The SST k−ω two-equation turbulence model and the soft ball model are coupled by computational fluid dynamics (CFD) and a discrete element model (DEM). Brownout is then simulated by the above method with sliding mesh. As the calculation examples show, the simulations and experiments of the Lynx rotor and the Caradonna–Tung rotor are compared. The coupling method is verified through calculation of the rotor lift coefficient, blade section pressure coefficient and tip vortex shedding position. The results show that when the helicopter is hovering at a height of 0.52R from the ground, it will cause brownout and the pilot’s vision will be obscured by sand. When the hovering height is 1R, the phenomenon of brownout is not serious. The movement speed of most sand dust is about 12 m/s, and the height of the sand dust from the ground will gradually increase over time. Large particles of sand are more difficult to be entrained into the air than the small particles, and the particles with a radius of 50 um are basically accumulated on the ground. Moreover, the slotted-Tip rotor has an effect on restraining brownout.

Conserved momenta of ferromagnetic solitons through the prism of differential geometry

The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This makes canonical momenta gauge-dependent and requires a careful application of Noether’s theorem. We show that Cartan’s theory of differential forms is a natural language for this task. We use it to derive conserved momenta of the Belavin–Polyakov skyrmion, whose symmetries include translation, global spin rotation, and dilation.

Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity

PurposeThe goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.Design/methodology/approachThe authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.FindingsThe authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.Originality/valueIn contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

Coupled Eulerian-Lagrangian Simulation of Indexable Drilling

This paper presents finite element simulations of indexable drilling of AISI4140 workpieces. The Coupled-Eulerian-Lagrangian framework is employed and the focus is to predict the drilling torque around the hole axis, thrust force, temperature distributions and chip geometries. The cutting process is modelled separately for peripheral and central insert. Then, the total thrust force and torque are predicted by superposing the predicted result for each insert. Experiments and simulations are conducted at a constant rotational velocity of 2400 rpm and feed rates of 0.13, 0.16 and 0.18 mm/rev. While the predicted torques are in excellent agreement, the thrust forces showed discrepancies of 12 - 20% to the experimental measured data. Effects of the friction modelling on the predicted torque and thrust force are outlined and possible reasons for the thrust force discrepancies are discussed in the paper. Additionally, the simulations indicate that the tool and workpiece temperature distributions are virtually unaffected by the feed rate.

Mass-Zero constrained dynamics and statistics for the shell model in magnetic field

In several domains of physics, including first principle simulations and classical models for polarizable systems, the minimization of an energy function with respect to a set of auxiliary variables must be performed to define the dynamics of physical degrees of freedom. In this paper, we discuss a recent algorithm proposed to efficiently and rigorously simulate this type of systems: the Mass-Zero (MaZe) Constrained Dynamics. In MaZe, the minimum condition is imposed as a constraint on the auxiliary variables treated as degrees of freedom of zero inertia driven by the physical system. The method is formulated in the Lagrangian framework, enabling the properties of the approach to emerge naturally from a fully consistent dynamical and statistical viewpoint. We begin by presenting MaZe for typical minimization problems where the imposed constraints are holonomic and summarizing its key formal properties, notably the exact Born–Oppenheimer dynamics followed by the physical variables and the exact sampling of the corresponding physical probability density. We then generalize the approach to the case of conditions on the auxiliary variables that linearly involve their velocities. Such conditions occur, for example, when describing systems in external magnetic field and they require to adapt MaZe to integrate semiholonomic constraints. The new development is presented in the second part of this paper and illustrated via a proof-of-principle calculation of the charge transport properties of a simple classical polarizable model of NaCl.

Lagrangian Strain- and Rotation-Rate Tensor Evaluation Based on Multi-pulse Particle Tracking Velocimetry (MPTV) and Radial Basis Functions(RBFs)

Physical conservation laws are inherently Lagrangian. However, analyses in fluid mechanics using the Lagrangian framework are often forgone in favor of those using the Eulerian framework. This is perhaps due to a lack of experimental techniques with high temporal and spatial resolution that track the movement of fluid tracers in a flow domain. The development of time-resolved Particle Tracking Velocimetry/Accelerometry (TR-PTV/A) that measures flows with high seeding density has made the use of the Lagrangian framework more accessible. A challenge facing PTV/A is the need for robust mesh-free numerical schemes that handle random particle locations. Such a scheme can be created with high-order accuracy using Radial Basis Functions (RBFs). RBFs allow direct evaluation of derivatives of vector and scalar fields at random locations with infinite-order smoothness. The current work uses RBF-based differential schemes to develop a post-processing tool for PTV/A data, which can accurately evaluate spatial derivatives directly from Lagrangian particle tracks. This RBF-based strain/rotation-rate tensor evaluation tool is validated with two and three-dimensional flows from analytical solutions and is then tested with experimental data measured by a multi-pulse PTV/A system.

Downscaled surface mass balance in Antarctica: impacts of subsurface processes and large-scale atmospheric circulation

Antarctic surface mass balance (SMB) is largely determined by precipitation over the continent and subject to regional climate variability related to the Southern Annular Mode (SAM) and other climatic drivers at the large scale. Locally however, firn and snow pack processes are important in determining SMB and the total mass balance of Antarctica and global sea level. Here, we examine factors that influence Antarctic SMB and attempt to reconcile the outcome with estimates for total mass balance determined from the GRACE satellites. This is done by having the regional climate model HIRHAM5 forcing two versions of an offline subsurface model, to estimate Antarctic ice sheet (AIS) SMB from 1980 to 2017. The Lagrangian subsurface model estimates AIS SMB of 2473.5 ± 114.4 Gt per year, while the Eulerian subsurface model variant results in slightly higher modelled SMB of 2564.8 ± 113.7 Gt per year. The majority of this difference in modelled SMB is due to melt and refreezing over ice shelves and demonstrates the importance of firn modelling in areas with substantial melt. Both the Eulerian and the Lagrangian SMB estimates are within uncertainty ranges of each other and within the range of other SMB studies. However, the Lagrangian version has better statistics when modelling the densities. There is a mean bias in modelled density of −24.0 ± 18.4 kg m−3 and −8.2 ± 15.3 kg m−3 for layers less than 550 kg m−3 for the Eulerian and Lagrangian framework, respectively. For layers with a density above 550 kg m−3 the bias is −31.7 ± 23.4 kg m−3 and −35.0 ± 23.7 kg m−3 for the Eulerian and Lagrangian framework, respectively. The mean firn 10 m temperature bias is 0.42–0.52 °C. Further, analysis of the relationship between SMB in individual drainage basins and the SAM, is carried out using a bootstrapping approach. This shows a robust relationship between SAM and SMB in half of the basins (13 out of 27). In general, when SAM is positive there is a lower SMB over the Plateau and a higher SMB on the westerly side of the Antarctic Peninsula, and vice versa when the SAM is negative. Finally, we compare the modelled SMB to GRACE data by subtracting the solid ice discharge, and find that there is a good agreement in East Antarctica, but large disagreements over the Antarctic Peninsula.There is a large difference between published estimates of discharge that make it challenging to use mass reconciliation in evaluating SMB models on the basin scale.