Investigating the effect of solid boundaries on the gas molecular mean-free-path

A key parameter for micro-gas-flows, the mean free path, is investigated in this paper. The mean free path is used in various models for predicting micro gas flows, both in the governing equations and their boundary conditions. The conventional definition of the mean free path is based on the assumption that only binary collisions occur and is commonly described using the macroscopic quantities density, viscosity and temperature. In this paper we compare the prediction by this definition of the mean free paths for helium, neon and argon gases under standard temperature and pressure conditions, with the mean free paths achieved by measurements of individual molecules using the numerical simulation technique of molecular dynamics. Our simulation using molecular dynamics consists of a cube with six periodic boundary conditions, allowing us to simulate an unconfined gas “package”. Although, the size of this package is important, since its impact on computational cost is considerable, it is also important to have enough simulated molecules to average data from. We find that the molecular dynamics method using 20520 simulated molecules yields results that are within 1% accuracy from the conventional definition of the mean free paths for neon and argon and within 2.5% for helium. We can also conclude that the normal approximation of only considering binary collisions is seemingly adequate for these gases under standard temperature and pressure conditions. We introduce a single planar wall and two parallel planar walls to the simulated gas of neon and record the mean free paths at various distances to the walls. It is found that the mean free paths affected by molecular collisions with the walls corresponds well with theoretical models up to Knudsen numbers of 0.2

An extension to the Navier-Stokes-Fourier equations by considering molecular collisions with boundaries

In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers. We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description

A Navier-Stokes model incorporating the effects of near-wall molecular collisions with applications to micro gas flows

We propose a model for describing surface effects on micro gas flows. This model consists of the Navier-Stokes equations (NS) with discontinuous velocity slip boundary conditions and a description of a geometry-dependent and effective viscosity due to special consideration of the molecular collisions with solid boundaries. By extending NS with an effective viscosity we obtain a non-linear stress/strain-rate relationship which captures some of the near-wall effects that the conventional NS are unable to describe. We show results of NS extended by using our effective viscosity applied with Maxwell's boundary condition as well as a second order boundary condition achieved by partly incorporating higher order methods, the Maxwell-Burnett boundary condition proposed by Lockerby et al. (2004). With this proposed model the simple isothermal planar channel case of 2D Poiseuille flow is solved. The results of our proposed model are compared with the conventional NS using similar boundary conditions, the BGK-method and experiments. On the one hand it is seen that our extended NS model yields results that are asymptotic to the results of conventional NS for large flow scales. On the other hand, when comparing results on the micro scale, we see that our extended NS model yields results that are closer to the results of the BGK-method and the experiments than the conventional NS. Our extended NS-model shows signs of capturing the physics of the flow to a certain rarefaction degree where it does not predict the mass flow minimum shown by the BGK-method and the experiments

An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries

We investigate a model for micro-gas-flows consisting of the Navier-Stokes equations extended to include a description of molecular collisions with solid boundaries, together with first and second order velocity slip boundary conditions. By considering molecular collisions affected by boundaries in gas flows we capture some of the near-wall affects that the conventional Navier-Stokes equations with a linear stress/strain-rate relationship are unable to describe. Our model is expressed through a geometry-dependent mean-free-path yielding a new viscosity expression, which makes the stress/strain-rate constitutive relationship non-linear. Test cases consisting of Couette and Poiseuille flows are solved using these extended Navier-Stokes equations, and we compare the resulting velocity profiles with conventional Navier-Stokes solutions and those from the BGK kinetic model. The Poiseuille mass flow-rate results are compared with results from the BGK-model and experimental data, for various degrees of rarefaction. We assess the range of applicability of our model and show that it can extend the applicability of conventional fluid dynamic techniques into the early continuum-transition regime. We also discuss the limitations of our model due to its various physical assumptions, and we outline ideas for further development

Coupling heterogeneous continuum-particle fields to simulate non-isothermal microscale gas flows

This paper extends the hybrid computational method proposed by Docherty et al. (2014) for simulating non-isothermal rarefied gas flows at the microscale. Coupling a continuum fluid description to a direct simulation Monte Carlo (DSMC) solver, the original methodology considered the transfer of heat only, with validation performed on 1D micro Fourier flow. Here, the coupling strategy is extended to consider the transport of mass, momentum, and heat, and validation in 1D is performed on the high-speed micro Couette flow problem. Sufficient micro resolution in the hybrid method enables good agreement with an equivalent pure DSMC simulation, but the method offers no computational speed-up for this 1D problem. However, considerable speed-up is achieved for a 2D problem: gas flowing through a microscale crack is modelled as a microchannel with a high-aspect-ratio cross-section. With a temperature difference imposed between the walls of the cross-section, the hybrid method predicts the velocity and temperature variation over the cross-section very accurately; an accurate mass flow rate prediction is also obtained

Molecular Momentum Transport at Fluid-Solid Interfaces in MEMS/NEMS: A Review

This review is focused on molecular momentum transport at fluid-solid interfaces mainly related to microfluidics and nanofluidics in micro-/nano-electro-mechanical systems (MEMS/NEMS). This broad subject covers molecular dynamics behaviors, boundary conditions, molecular momentum accommodations, theoretical and phenomenological models in terms of gas-solid and liquid-solid interfaces affected by various physical factors, such as fluid and solid species, surface roughness, surface patterns, wettability, temperature, pressure, fluid viscosity and polarity. This review offers an overview of the major achievements, including experiments, theories and molecular dynamics simulations, in the field with particular emphasis on the effects on microfluidics and nanofluidics in nanoscience and nanotechnology. In Section 1 we present a brief introduction on the backgrounds, history and concepts. Sections 2 and 3 are focused on molecular momentum transport at gas-solid and liquid-solid interfaces, respectively. Summary and conclusions are finally presented in Section 4

CFD model of fluid flow in reactor : A simulation of velocity and heat distribution in a channel

The basic problem of operating a boiling water nuclear reactor (BWR) is that of maximizing the power output while avoiding fuel rod over-heating (dry-out). For the safe operation of BWRs this entails a detailed understanding of the flow of water and steam through the reactor core. In a BWR the water functions not only as a coolant, but also as a moderator for the neutrons emitted in the fission process. To describe the thermohydraulic properties of the reactor a number of parameters are of common interest. Examples of such parameters are void, pressure, temperature, water and steam velocities, pressure, sheer forces and turbulent kinetic energy. There are a few ways of revealing these values such as experiments built up to behave like a reactors and computer simulations using models based on the laws of fluid dynamics and thermodynamics. This research concerns a computer based model which uses a continuous fluid dynamic, (CFD), calculation program called OpenFOAM (Open Field Operation and Manipulation). OpenFOAM uses Navier Stokes equations for continuity, momentum- and energy conservation to simulate flows. The method used in this research has been to first build a model which describes the adiabatic flow correctly by using an already existing solver which uses the continuity and momentum conservation laws. In order to achieve a model that can solve temperature distributions in the flow the energy equation is added to the program coding in OpenFOAM. There are totally 12 turbulence models. Some of the models have not produced results on account of that they either diverged or needed input that was not attainable. The models which were tested and used were four k -ε models, one RSTM model and two low-Re models. A question that is addressed in this report is which of the many turbulence models that describes the experimental flow most correctly. The low-Re model LienLeschzinerLowRe produces the results with best congruence to the experimental data. The k -ε models model RNGkEpsilon and the RSTM model LRR were also fairly close. It is found that there are a few turbulence models that describe the experimental flows sufficiently well. LaunderSharmaKe was the turbulence model which simulated the temperature distribution best and was almost within the error bar limit of 5 K in all of the plots. It is interesting that the two low-Re models show the best results if only one characteristic at the time is studied. One of the turbulence models describes only the velocity profile well and the other one oppositely describes the temperature distribution the best. It can thereby be stated that if the user wants a turbulence model that describes both velocity profiles and temperature distribution the RSTM model LRR is the best one. If on the other hand computer capacity is a limiting factor it might be profitable to use the simpler k -ε model RNGkEpsilon. An other conclusions of this thesis is that the LRR and RNGkepsilon models are suited for the simulations of the geometries described in this work provided that the channel is wide enough for the model to simulate a correct temperature profile. With the use of gmsh a case geometry with wider channel area could easily be created. It would of course be necessary to use experimental data to validate the assumption that more realistic results can be obtained on wider channels

CFD model of fluid flow in reactor : A simulation of velocity and heat distribution in a channel

The basic problem of operating a boiling water nuclear reactor (BWR) is that of maximizing the power output while avoiding fuel rod over-heating (dry-out). For the safe operation of BWRs this entails a detailed understanding of the flow of water and steam through the reactor core. In a BWR the water functions not only as a coolant, but also as a moderator for the neutrons emitted in the fission process. To describe the thermohydraulic properties of the reactor a number of parameters are of common interest. Examples of such parameters are void, pressure, temperature, water and steam velocities, pressure, sheer forces and turbulent kinetic energy. There are a few ways of revealing these values such as experiments built up to behave like a reactors and computer simulations using models based on the laws of fluid dynamics and thermodynamics. This research concerns a computer based model which uses a continuous fluid dynamic, (CFD), calculation program called OpenFOAM (Open Field Operation and Manipulation). OpenFOAM uses Navier Stokes equations for continuity, momentum- and energy conservation to simulate flows. The method used in this research has been to first build a model which describes the adiabatic flow correctly by using an already existing solver which uses the continuity and momentum conservation laws. In order to achieve a model that can solve temperature distributions in the flow the energy equation is added to the program coding in OpenFOAM. There are totally 12 turbulence models. Some of the models have not produced results on account of that they either diverged or needed input that was not attainable. The models which were tested and used were four k -ε models, one RSTM model and two low-Re models. A question that is addressed in this report is which of the many turbulence models that describes the experimental flow most correctly. The low-Re model LienLeschzinerLowRe produces the results with best congruence to the experimental data. The k -ε models model RNGkEpsilon and the RSTM model LRR were also fairly close. It is found that there are a few turbulence models that describe the experimental flows sufficiently well. LaunderSharmaKe was the turbulence model which simulated the temperature distribution best and was almost within the error bar limit of 5 K in all of the plots. It is interesting that the two low-Re models show the best results if only one characteristic at the time is studied. One of the turbulence models describes only the velocity profile well and the other one oppositely describes the temperature distribution the best. It can thereby be stated that if the user wants a turbulence model that describes both velocity profiles and temperature distribution the RSTM model LRR is the best one. If on the other hand computer capacity is a limiting factor it might be profitable to use the simpler k -ε model RNGkEpsilon. An other conclusions of this thesis is that the LRR and RNGkepsilon models are suited for the simulations of the geometries described in this work provided that the channel is wide enough for the model to simulate a correct temperature profile. With the use of gmsh a case geometry with wider channel area could easily be created. It would of course be necessary to use experimental data to validate the assumption that more realistic results can be obtained on wider channels

Extending the applicability of the Navier-Stokes equations to micro gas flows by considering molecular collisions with boundaries

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CFD model of fluid flow in reactor : A simulation of velocity and heat distribution in a channel

The basic problem of operating a boiling water nuclear reactor (BWR) is that of maximizing the power output while avoiding fuel rod over-heating (dry-out). For the safe operation of BWRs this entails a detailed understanding of the flow of water and steam through the reactor core. In a BWR the water functions not only as a coolant, but also as a moderator for the neutrons emitted in the fission process. To describe the thermohydraulic properties of the reactor a number of parameters are of common interest. Examples of such parameters are void, pressure, temperature, water and steam velocities, pressure, sheer forces and turbulent kinetic energy. There are a few ways of revealing these values such as experiments built up to behave like a reactors and computer simulations using models based on the laws of fluid dynamics and thermodynamics. This research concerns a computer based model which uses a continuous fluid dynamic, (CFD), calculation program called OpenFOAM (Open Field Operation and Manipulation). OpenFOAM uses Navier Stokes equations for continuity, momentum- and energy conservation to simulate flows. The method used in this research has been to first build a model which describes the adiabatic flow correctly by using an already existing solver which uses the continuity and momentum conservation laws. In order to achieve a model that can solve temperature distributions in the flow the energy equation is added to the program coding in OpenFOAM. There are totally 12 turbulence models. Some of the models have not produced results on account of that they either diverged or needed input that was not attainable. The models which were tested and used were four k -ε models, one RSTM model and two low-Re models. A question that is addressed in this report is which of the many turbulence models that describes the experimental flow most correctly. The low-Re model LienLeschzinerLowRe produces the results with best congruence to the experimental data. The k -ε models model RNGkEpsilon and the RSTM model LRR were also fairly close. It is found that there are a few turbulence models that describe the experimental flows sufficiently well. LaunderSharmaKe was the turbulence model which simulated the temperature distribution best and was almost within the error bar limit of 5 K in all of the plots. It is interesting that the two low-Re models show the best results if only one characteristic at the time is studied. One of the turbulence models describes only the velocity profile well and the other one oppositely describes the temperature distribution the best. It can thereby be stated that if the user wants a turbulence model that describes both velocity profiles and temperature distribution the RSTM model LRR is the best one. If on the other hand computer capacity is a limiting factor it might be profitable to use the simpler k -ε model RNGkEpsilon. An other conclusions of this thesis is that the LRR and RNGkepsilon models are suited for the simulations of the geometries described in this work provided that the channel is wide enough for the model to simulate a correct temperature profile. With the use of gmsh a case geometry with wider channel area could easily be created. It would of course be necessary to use experimental data to validate the assumption that more realistic results can be obtained on wider channels