Package Bees for Honey Production and Pollination

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On the modelling of isothermal gas flows at the microscale

This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case. Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers

A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flow field and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction

Capturing the Knudsen layer in continuum-fluid models of non-equilibrium gas flows

In hypersonic aerodynamics and microflow device design, the momentum and energy fluxes to solid surfaces are often of critical importance. However, these depend on the characteristics of the Knudsen layer - the region of local non-equilibrium existing up to one or two molecular mean free paths from the wall in any gas flow near a surface. While the Knudsen layer has been investigated extensively using kinetic theory, the ability to capture it within a continuum-fluid formulation (in conjunction with slip boundary conditions) suitable for current computational fluid dynamics toolboxes would offer distinct and practical computational advantages

The usefulness of higher-order constitutive relations for describing the Knudsen layer

The Knudsen layer is an important rarefaction phenomenon in gas flows in and around microdevices. Its accurate and efficient modeling is of critical importance in the design of such systems and in predicting their performance. In this paper we investigate the potential that higher-order continuum equations may have to model the Knudsen layer, and compare their predictions to high-accuracy DSMC (direct simulation Monte Carlo) data, as well as a standard result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets (Grad's 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we obtain additional boundary conditions (needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMC data is only slight

Using seismic inversions to obtain an internal mixing processes indicator for main-sequence solar-like stars

Determining accurate and precise stellar ages is a major problem in astrophysics. These determinations are either obtained through empirical relations or model-dependent approaches. Currently, seismic modelling is one of the best ways of providing accurate ages. However, current methods are affected by simplifying assumptions concerning mixing processes. In this context, providing new structural indicators which are less model-dependent and more sensitive to such processes is crucial. We build a new indicator for core conditions on the main sequence, which should be more sensitive to structural differences and applicable to older stars than the indicator t presented in a previous paper. We also wish to analyse the importance of the number and type of modes for the inversion, as well as the impact of various constraints and levels of accuracy in the forward modelling process that is used to obtain reference models for the inversion. First, we present a method to obtain new structural kernels and use them to build an indicator of central conditions in stars and test it for various effects including atomic diffusion, various initial helium abundances and metallicities, following the seismic inversion method presented in our previous paper. We then study its accuracy for 7 different pulsation spectra including those of 16CygA and 16CygB and analyse its dependence on the reference model by using different constraints and levels of accuracy for its selection We observe that the inversion of the new indicator using the SOLA method provides a good diagnostic for additional mixing processes in central regions of stars. Its sensitivity allows us to test for diffusive processes and chemical composition mismatch. We also observe that octupole modes can improve the accuracy of the results, as well as modes of low radial order.Comment: Accepted for publication in Astronomy and Astrophysic

Mode identification in rapidly rotating stars

Context: Recent calculations of pulsation modes in rapidly rotating polytropic models and models based on the Self-Consistent Field method have shown that the frequency spectrum of low degree pulsation modes can be described by an empirical formula similar to Tassoul's asymptotic formula, provided that the underlying rotation profile is not too differential. Aims: Given the simplicity of this asymptotic formula, we investigate whether it can provide a means by which to identify pulsation modes in rapidly rotating stars. Methods: We develop a new mode identification scheme which consists in scanning a multidimensional parameter space for the formula coefficients which yield the best-fitting asymptotic spectra. This mode identification scheme is then tested on artificial spectra based on the asymptotic formula, on random frequencies and on spectra based on full numerical eigenmode calculations for which the mode identification is known beforehand. We also investigate the effects of adding random frequencies to mimic the effects of chaotic modes which are also expected to show up in such stars. Results: In the absence of chaotic modes, it is possible to accurately find a correct mode identification for most of the observed frequencies provided these frequencies are sufficiently close to their asymptotic values. The addition of random frequencies can very quickly become problematic and hinder correct mode identification. Modifying the mode identification scheme to reject the worst fitting modes can bring some improvement but the results still remain poorer than in the case without chaotic modes

Coupled continuum hydrodynamics and molecular dynamics method for multiscale simulation

We present a new hybrid methodology for carrying out multiscale simulations of flow problems lying between continuum hydrodynamics and molecular dynamics, where macro/micro lengthscale separation exists only in one direction. Our multiscale method consists of an iterative technique that couples mass and momentum flux between macro and micro domains, and is tested on a converging/diverging nanochannel case containing flow of a simple Lennard-Jones liquid. Comparisons agree well with a full MD simulation of the same test case