380 research outputs found
Simulating fluid flows in micro and nano devices : the challenge of non-equilibrium behaviour
We review some recent developments in the modelling of non-equilibrium (rarefied) gas flows at the micro- and nano-scale, concentrating on two different but promising approaches: extended hydrodynamic models, and lattice Boltzmann methods. Following a brief exposition of the challenges that non-equilibrium poses in micro- and nano-scale gas flows, we turn first to extended hydrodynamics, outlining the effective abandonment of Burnett-type models in favour of high-order regularised moment equations. We show that the latter models, with properly-constituted boundary conditions, can capture critical non-equilibrium flow phenomena quite well. We then review the boundary conditions required if the conventional Navier-Stokes-Fourier (NSF) fluid dynamic model is applied at the micro scale, describing how 2nd-order Maxwell-type conditions can be used to compensate for some of the non-equilibrium flow behaviour near solid surfaces. While extended hydrodynamics is not yet widely-used for real flow problems because of its inherent complexity, we finish this section with an outline of recent 'phenomenological extended hydrodynamics' (PEH) techniques-essentially the NSF equations scaled to incorporate non-equilibrium behaviour close to solid surfaces-which offer promise as engineering models. Understanding non-equilibrium within lattice Boltzmann (LB) framework is not as advanced as in the hydrodynamic framework, although LB can borrow some of the techniques which are being developed in the latter-in particular, the near-wall scaling of certain fluid properties that has proven effective in PEH. We describe how, with this modification, the standard 2nd-order LB method is showing promise in predicting some rarefaction phenomena, indicating that instead of developing higher-order off-lattice LB methods with a large number of discrete velocities, a simplified high-order LB method with near-wall scaling may prove to be just as effective as a simulation tool
Efficient parallel solver for high-speed rarefied gas flow using GSIS
Recently, the general synthetic iterative scheme (GSIS) has been proposed to
find the steady-state solution of the Boltzmann equation in the whole range of
gas rarefaction, where its fast-converging and asymptotic-preserving properties
lead to the significant reduction of iteration numbers and spatial cells in the
near-continuum flow regime. However, the efficiency and accuracy of GSIS has
only been demonstrated in two-dimensional problems with small numbers of
spatial cell and discrete velocities. Here, a large-scale parallel computing
strategy is designed to extend the GSIS to three-dimensional high-speed flow
problems. Since the GSIS involves the calculation of the mesoscopic kinetic
equation which is defined in six-dimensional phase-space, and the macroscopic
high-temperature Navier-Stokes-Fourier equations in three-dimensional physical
space, the proper partition of the spatial and velocity spaces, and the
allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys
to improving the overall computational efficiency. These factors are
systematically tested to achieve optimal performance, up to 100 billion spatial
and velocity grids. For hypersonic flows around the Apollo reentry capsule, the
X38-like vehicle, and the space station, our parallel solver can get the
converged solution within one hour
A gas-surface interaction algorithm for discrete velocity methods in predicting rarefied and multi-scale flows
The rarefied flow and multi-scale flow are crucial for the aerodynamic design
of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete
velocity space, the discrete velocity method (DVM) and unified methods can
capture complex and non-equilibrium distribution functions and describe flow
behaviors exactly. The unified methods predict flows from continuum to rarefied
regimes by adopting unified modeling, and they can be further applied to other
multi-scale physics such as radiation heat transfer, phonon heat transfer and
plasma. In the flow field, the concrete dynamic process needs to describe the
gas-gas interaction and gas-surface interaction (GSI). However, in both DVM and
unified methods, only a simple but not accurate GSI is used, which can be
regarded as a Maxwell GSI with a fixed accommodation coefficient of 1 (full
accommodation) at the present stage. To overcome the bottleneck in extending
DVM and unified methods to the numerical experiment and investigate real
multi-scale flow physics, this paper realizes precise GSI in the DVM framework
by constructing the boundary conditions of a concrete Maxwell GSI with an
adjustable accommodation coefficient. In the constructing process, the problems
of macro-conservation and micro-consistency in the DVS at the boundary are well
solved by reflected macroscopic flux and interpolation distribution function
and interpolation error correction, respectively. Meanwhile, considering that
the multi-scale flows in the background of aeronautics and aerospace are often
at supersonic and hypersonic speeds, the unstructured velocity space (UVS) is
essential. From the perspective of generality, the GSI is forced on UVS.
Besides, by combined with the unified method (the unified gas-kinetic scheme in
the paper), the effectiveness and validity of the present GSI on the DVM
framework are verified by a series of simulations
A global adaptive velocity space for general discrete velocity framework in predictions of rarefied and multi-scale flows
The rarefied flow and multi-scale flow are crucial for the aerodynamic design
of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete
velocity space, the Boltzmann method, such as the discrete velocity method and
unified methods, can capture complex and non-equilibrium velocity distribution
functions (VDFs) and describe flow behaviors exactly. However, the extremely
steep slope and high concentration of the gas VDFs in a local particle velocity
space make it very difficult for the Boltzmann method with structured velocity
space to describe high speed flow. Therefore, the adaptive velocity space (AVS)
is required for the Boltzmann solvers to be practical in complex rarefied flow
and multi-scale flow. This paper makes two improvements to the AVS approach,
which is then incorporated into a general discrete velocity framework, such as
the unified gas-kinetic scheme. Firstly, a global velocity mesh is used to
prevent the interpolation of the VDFs at the physical interface during the
calculation of the microscopic fluxes, maintaining the program's high level of
parallelism. Secondly, rather than utilizing costly interpolation, the VDFs on
a new velocity space were reconstruction using the ``consanguinity"
relationship. In other words, a split child node's VDF is the same as its
parent's VDF, and a merged parent's VDF is the average of its children's VDFs.
Additionally, the discrete deviation of the equilibrium distribution functions
is employed to maintain the proposed method's conservation. Moreover, an
appropriate set of adaptive parameters is established to enhance the automation
of the proposed method. Finally, a number of numerical tests are carried out to
validate the proposed method
DSMC investigation of rarefied gas flow through diverging micro- and nanochannels
Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli-trials
(SBT) collision scheme has been used to study the rarefied pressure-driven
nitrogen flow through diverging microchannels. The fluid behaviours flowing
between two plates with different divergence angles ranging between 0
to 17 are described at different pressure ratios
(1.52.5) and Knudsen numbers (0.03Kn12.7). The
primary flow field properties, including pressure, velocity, and temperature,
are presented for divergent microchannels and are compared with those of a
microchannel with a uniform cross-section. The variations of the flow field
properties in divergent microchannels, which are influenced by the area change,
the channel pressure ratio and the rarefication are discussed. The results show
no flow separation in divergent microchannels for all the range of simulation
parameters studied in the present work. It has been found that a divergent
channel can carry higher amounts of mass in comparison with an equivalent
straight channel geometry. A correlation between the mass flow rate through
microchannels, the divergence angle, the pressure ratio, and the Knudsen number
has been suggested. The present numerical findings prove the occurrence of
Knudsen minimum phenomenon in micro- and Nano- channels with non-uniform
cross-sections.Comment: Accepted manuscript; 25 Pages and 11 Figures; "Microfluidics and
Nanofluidics
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