Pre-Deformation Method for Manufactured Compressor Blade Based on Load Incremental Approach

The blade deformation caused by aerodynamic and centrifugal loads during operating makes blade configurations different from their stationary shape. Based on the load incremental approach, a novel pre-deformation method for cold blade shape is provided in order to compensate blade deformation under running. Effect of nonlinear blade stiffness is considered by updating stiffness matrix in response to the variation of blade configuration when calculating deformations. The pre-deformation procedure is iterated till a converged cold blade shape is obtained. The proposed pre-deformation method is applied to a transonic compressor rotor. Effect of load conditions on blade pre-deformation is also analyzed. The results show that the pre-deformation method is easy to implement with fast convergence speed. Neither the aerodynamic load nor centrifugal load can be neglected in blade pre-deformation.

Liquid toroidal drop in compressional flow with arbitrary drop-to-ambient fluid viscosity ratio

Existing experiments show that a sufficiently fat toroidal drop freely suspended in another liquid shrinks towards its centre to form a spherical drop. However, recent simulations reveal that if a liquid torus with circular cross section is embedded in a compressional same-viscosity flow that acts to expand the torus, then depending on the torus radius R and a capillary number Ca characterizing the balance between the viscous forces and the interfacial tension, the torus may either coalesce, expand indefinitely or attain a stationary shape. For each Ca less than 0.2, there is a single value of R , called the critical radius, for which the torus attains the stationary shape. Here, the drop-to-ambient fluid viscosity ratio, λ, is assumed to be arbitrary. The corresponding two-phase Stokes flow problem is solved for a liquid toroidal drop with circular cross section in terms of stream functions in the toroidal coordinates. When λ=1, the stream functions admit a closed-form integral representation for a drop of arbitrary axisymmetric shape. ‘Stationary’ circular tori minimize a certain measure of the normal velocity over the interface, and as in the case of λ=1, their radii are expected to predict the critical ones for arbitrary λ and Ca in a certain range (e.g. for Ca<0.2 when λ=1). Streamlines about ‘stationary’ circular tori are analysed for various Ca and λ.

Relaxation Estimation of RMSD in Molecular Dynamics Immunosimulations

Molecular dynamics simulations have to be sufficiently long to draw reliable conclusions. However, no method exists to prove that a simulation has converged. We suggest the method of “lagged RMSD-analysis” as a tool to judge if an MD simulation has not yet run long enough. The analysis is based on RMSD values between pairs of configurations separated by variable time intervals Δt. Unless RMSD(Δt) has reached a stationary shape, the simulation has not yet converged.

A Theoretical Description of a Dilute Emulsion of Very Viscous Drops Undergoing Unsteady Simple Shear

This theoretical work shows how the knowledge of the emulsion microscale, including drop stretching and orientation leads to a continuum description of emulsion flows. A first order small deformation theory is explored for describing the rheology of an emulsion of high viscosity drops undergoing unsteady shear flows. The stationary shape and the interfacial velocity of a drop are used in order to obtain the contribution of the drop to the effective stress tensor of the emulsion. A complex rheology including the nonlinear frequency response of the emulsion under oscillatory shear at arbitrary frequency forcing and strain amplitude is identified.

Tank-treading as a means of propulsion in viscous shear flows

The use of tank-treading as a means of propulsion for microswimmers in viscous shear flows is taken into account. We discuss the possibility of a vesicle to control the drift in an external shear flow, by locally varying the bending rigidity of its membrane. By analytical calculation in the quasi-spherical limit, the stationary shape and the orientation of the tank-treading vesicle in the external flow are determined, working to lowest order in the membrane inhomogeneity. The membrane inhomogeneity acts in the shape evolution equation as an additional force term, which can be used to balance the effect of the hydrodynamic stresses, thus allowing the vesicle to assume shapes and orientations that are impossible otherwise. The vesicle shapes and orientations required for migration transverse to the flow, together with the bending rigidity profiles leading to such shapes and orientations, are determined. Considering the variations in the concentration experienced during tank-treading, a simple model is presented, in which a vesicle is able to migrate up or down the gradient of a concentration field by stiffening or softening of its membrane.

Shape of Moving Grain Boundary and its Influence on Grain Boundary Motion in Zinc

The migration of individual special [ ] 0 1 10 tilt grain boundary (GB) with Σ =15 and misorientation angle 29° in Zn bicrystal have been investigated. The stationary shape of migrating GB has been studied and the migration rate has been measured by optical microscopy in situ between 558 and 683 K using polarized light. In certain experimental runs the migrating GB is faceted and moves thermally activated. Its kinetics follows the Arrhenius type dependence despite the fact that shape of moving GB depends on temperature. After detachment from impurity cloud the [ ] 0 1 10 tilt GB migrates activationless in the temperature interval 618÷683 K. The detachment temperature is 618 K. The non-physically high value of the apparent migration activation enthalpy can appear due to the change of GB shape from faceted to smooth and back.