Rarefied flow between plates of finite length via the coupling approach

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.The coexistence of rarefied continuum flow regime areas and relatively small elements in which rarefaction effects become important is a typical feature of many complex gas flows micro systems. In rarefied domains, the mean free path of gas molecules is comparable or larger than a characteristic scale of the system. These domains are naturally described by kinetic equation for the velocity distribution function, which involve a considerable effort in terms of CPU time and memory requirements, due to the discretization in both physical and velocity space. The continuum domains are best described by the fluid Navier Stokes (NS) equations in terms of average flow velocity, gas density and temperature. These equations are more efficient, but less accurate in critical rarefied areas. Thus, the development of hybrid solver combining kinetic and continuum models is of great interest especially for applications range from gas flows in micro systems to the aerospace applications, such as high altitude flights. The pressure–driven gas flow of rarified monatomic gas through a two-dimensional short microchannel is considered using hybrid solver. The calculations have been carried out for pressure ratios 0.1, 0.5 and 0.9 and fixed relatively large Knudsen number. The applicability of the solver is discussed via comparison with the kinetic and NS solutions.The European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS no 215504

Balancing Ecology and Economy in Forestry: A Theoretical Investigation

While forests have traditionally been managed for wood production, there are good reasons to account also for other objectives, such as biodiversity conservation and other ecological values. In contrast to clear-cut based .normal. forestry, uneven-aged forest management can preserve a more natural structure and associated ecological values. However, due to the complex interactions among trees in such forests, optimal management modeling quickly becomes analytically intractable, and numerical investigations can prove an insuperable obstacle. A promising recent development to overcome this impasse is the perfect plasticity approximation (PPA, see below), which has opened a new avenue of ecologically realistic and analytically tractable forest models. Here we use a PPA based model to investigate the potential for combining economic and ecological values under uneven-aged forest management

Using natural selection and optimization for smarter vegetation models - challenges and opportunities

Dynamic global vegetation models (DGVMs) are now indispensable for understanding the biosphere and for estimating the capacity of ecosystems to provide services. The models are continuously developed to include an increasing number of processes and to utilize the growing amounts of observed data becoming available. However, while the versatility of the models is increasing as new processes and variables are added, their accuracy suffers from the accumulation of uncertainty, especially in the absence of overarching principles controlling their concerted behaviour. We have initiated a collaborative working group to address this problem based on a ‘missing law’ – adaptation and optimization principles rooted in natural selection. Even though this ‘missing law’ constrains relationships between traits, and therefore can vastly reduce the number of uncertain parameters in ecosystem models, it has rarely been applied to DGVMs. Our recent research have shown that optimization- and trait-based models of gross primary production can be both much simpler and more accurate than current models based on fixed functional types, and that observed plant carbon allocations and distributions of plant functional traits are predictable with eco-evolutionary models. While there are also many other examples of the usefulness of these and other theoretical principles, it is not always straight-forward to make them operational in predictive models. In particular on longer time scales, the representation of functional diversity and the dynamical interactions among individuals and species presents a formidable challenge. Here we will present recent ideas on the use of adaptation and optimization principles in vegetation models, including examples of promising developments, but also limitations of the principles and some key challenges

Исследование неустойчивости Тейлора-Гертлера в струях с помощью кинетического подхода

The aim of the paper is to study the unstable processes in free supersonic unstable jet flows. The direct method of solving a kinetic equation is used. For numerical solution the finitedifferent schemes are applied. To perform parallel computations a supercomputer MVS-100K is used. The maximum number of processors was 480. A mechanism of instability for a supercritical regime for 3D flows is investigated. Solutions of these problems are made for flows in a wide range of Knudsen number Kn with different aspect ratio of the orifice (square and rectangular forms). Mach number Ma = 1.4 and a ratio of pressure in the orifice and the background pressure np = 3.16. Comparison with results of known experiments is made. In calculations we have observed that for a subcritical regime with the large Knudsen numbers (small Reynolds numbers) a vorticity of the flow fields in the cross sections is equal zero. For supercritical regimes a system of streamwise pair vortices is obtained. That corresponds to theoretical and experimental data. The paper studies such a system of the Taylor-Görtler vortices in different cross-sections in an initial region of a jet. It presents results of numerous computations. When modeling a roughness in the nozzle orifice it has been found that the character of instability with disturbance of the symmetry in the cross-sections downstream is complicated. Based on direct method to solve the kinetic equation the paper, for the first time, studies in detail the character of 3D instability.Previously, these problems were solved by continuum methods and also for some variants of flows was used the Direct Simulation Monte Carlo method. A potential field of application of the given results is theoretical and experimental investigations with more detailed, in comparison with previous studies, description of unstable supersonic flows, which show the similar features of the Taylor-Görtler instability. Based on conducted study the paper comes to conclusion that the direct methods of the kinetic approach allow us to describe appropriately a mechanism of the transition to the unstable flows in supersonic jets. We believe that a further study will make it possible to show up the characteristics of turbulence in free supersonic jets.С помощью прямого метода решения S-модельного кинетического уравнения Больцмана численно исследуются течения в сверхзвуковых нерасчетных струях. Алгоритм ре-шения основан на явно-неявной схеме и для повышения эффективности распараллелен с помощью MPI (Message Passing Interface). Расчеты выполнены на суперкомпьютере MVS-100K. Изучается влияние геометрии отверстия и степени разреженности газа на механизм возникновения неустойчивости Тейлора-Гёртлера. Показано, что для течений при больших числах Кнудсена (малых числах Рейнольдса) неустойчивость не возникает. При переходе к закритическим режимам (малые числа Кнудсена) в поле течения возникает система продольных вихрей, соответствующая неустойчивости Тейлора-Гёртлера, что согласуется с теоретическим и опытным данными. Кроме того, при наличии дополнительного возмущающего фактора - шероховатости по периметру отверстия, обнаружена потеря поперечной симметрии струи вниз по потоку. DOI: 10.7463/mathm.0116.083362

Coupling kinetic and continuum equations for micro scale flow computations

An hybrid method, coupling the direct numerical solution of the Bhatnagar-Gross-Krook (BGK) kinetic equation and a Navier-Stokes model is presented. The computational physical domain is decomposed into kinetic and continuum sub-domains using an appropriate criteria based on the local Knudsen number and proper gradients of macro-parameters, computed via a preliminary Navier-Stokes solution throughout the whole physical domain. The coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy and mass through the interface. The proposed method is used for the simulation of the flow through a micro-slit. Outlet to inlet pressure ratio of 0.1, 0.5 and 0.9 are considered, for a wide range of Knudsen number. The local parameters (density, velocity and temperature) along symmetry axis show satisfactory agreement with those computed by the continuum model

Coupling kinetic and continuum equations for micro scale flow computations

A hybrid method, coupling the direct numerical solution of the Bhatnagar-Gross-Krook (BGK) kinetic equation and hydrodynamic (Navier-Stokes) equations is presented. The computational physical domain is decomposed into kinetic and continuum sub-domains using an appropriate criterion based on the local Knudsen number and proper gradients of macro-parameters, computed via a preliminary Navier-Stokes solution throughout the whole physical domain. The coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy, and mass through the interface. The advantage of the presented hybrid algorithm is that it easily allows the coupling of existing codes for the numerical solution of the BGK and Navier-Stokes equations. To validate and estimate the efficiency of the proposed method the simulation of the monatomic gas flow through a slit has been considered for outlet to inlet pressure ratio of 0.1, 0.5, and 0.9, and a wide range of Knudsen number. The comparison of local parameters (density, velocity, and temperature) with pure kinetic solutions shows satisfactory agreement with those computed by the hybrid solve

Three dimensional effects in compressible, rarefied gas flow in bent microchannels

Numerical investigation of pressure-driven gas flow in three-dimensional (3D) bent microchannel is carried out by the Navier \u2013 Stokes equations coupled with first order slip boundary condition. Several facets of the problem are investigated, including the influence of geometrical details such as channel aspect ratio and bend radius of curvature, as well as the impact of rarefaction and compressibility. Pressure nonlinearity, Mach number distribution, slip velocity profiles and mass flow rate are computed and commented. The results show that the additional losses induced by the bend, with respect to the straight channel, are almost negligible at high rarefaction levels. Actually, for higher values of Kn the mass flux through the bent microchannel can even be slightly larger than that through a straight microchannel of the same length and subjected to the same pressure gradient. Moreover, this increase in mass flow rate for 3D case is larger than for 2D one. Smoothed bend further reduce the effect of the bend, with respect to sharp corner geometries. Rarefaction effect on mass flow is smaller at smaller radius, nevertheless compressibility effect compensates the rarefaction resulting in a lower increase in mass flow at higher pressure ratio. Compressibility effect increases pressure losses, thus partially compensating the increase in the mass flow due to the rarefaction, at least for higher pressure ratio. For large aspect ratios flow distributions, as expected, get closer to some 2D limit lines