The Experts below are selected from a list of 1959 Experts worldwide ranked by ideXlab platform
David R Emerson - One of the best experts on this subject based on the ideXlab platform.
-
linearized moment analysis of the temperature jump and temperature defect in the Knudsen Layer of a rarefied gas
Physical Review E, 2014Co-Authors: David R EmersonAbstract:Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen Layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen Layer are derived with the linearized 26 moment equations.
-
modelling thermal flow in the transition regime using a lattice boltzmann approach
EPL, 2007Co-Authors: Yonghao Zhang, Robert W Barber, David R EmersonAbstract:Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen Layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen Layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen Layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58.
-
capturing Knudsen Layer phenomena using a lattice boltzmann model
Physical Review E, 2006Co-Authors: Yonghao Zhang, Robert W Barber, David R EmersonAbstract:In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in microscale and nanoscale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques such as the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen Layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations. In this paper, we propose an effective mean-free path to address the Knudsen Layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.
-
on hydrodynamic predictions of near wall effects in rarefied gases some phenomenological and modelling approaches
International Conference on Heat Transfer and Fluid Flow in Microscale, 2005Co-Authors: Jason M Reese, Duncan A Lockerby, David R EmersonAbstract:Methods for simulating the critical near-wall region in hydrodynamic models of gas micro-flows are discussed. Two important non-equilibrium flow features - velocity slip at solid walls, and the Knudsen Layer (which extends one or two molecular mean free paths into the gas from a surface) - are investigated using different modelling approaches. In addition to a discussion of Maxwell's slip boundary condition, a newly implemented 'wall-function' model that has been developed to improve hydrodynamic simulations of the Knudsen Layer is described. Phenomenological methods are compared to physical modelling and it is shown that, while both simulation types have merit, and both can quantitatively improve results in most cases, there are drawbacks associated with each approach. Phenomenological techniques, for example, may not be sufficiently general, whilst issues with applicability and stability are known to exist in some physical models.
Lajos Szalmás - One of the best experts on this subject based on the ideXlab platform.
-
variable slip coefficient in binary lattice boltzmann models
Central European Journal of Physics, 2008Co-Authors: Lajos SzalmásAbstract:We present a new method in order to obtain variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. We present the Boundary Layer theory. We study both the single-and multi-fluid BGK-type models as well. The boundary slip and the Knudsen Layer are analyzed in detail. Benchmark simulations are carried out in order to compare the analytical derivation with the numerical results. Excellent agreement is found between the two analytical formalism and the numerical simulations.
-
variable slip coefficient in binary lattice boltzmann models
arXiv: Computational Physics, 2008Co-Authors: Lajos SzalmásAbstract:We present a new method in order to get variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. Boundary Layer theory is presented. We study both the single- and multi-fluid BGK-type models as well. The boundary slip and the Knudsen Layer are analyzed in detail. Benchmark simulations are carried out in order to compare the analytical derivation with the numerical results. Excellent agreement is found between the two situations.
-
lattice boltzmann method with optimized boundary Layer at finite Knudsen numbers
International Journal of Modern Physics C, 2008Co-Authors: Lajos SzalmásAbstract:We present an optimization procedure in high-order lattice Boltzmann models in order to fine-tune the method for micro-channel flows in the transition region. Both the first and second slip coefficients are tunable, and the hydrodynamic and Knudsen Layer solutions can be tailored. Very good results are obtained in comparison with the continuous solution for hard sphere molecules. For the first time, we provide an accurate description of Poiseuille flow in the transition region.
-
Knudsen Layer theory for high-order lattice Boltzmann models
EPL, 2007Co-Authors: Lajos SzalmásAbstract:A Knudsen Layer theory is presented within the framework of a high-order lattice Boltzmann model obtained from the fourth-order Gauss-Hermite quadrature. The Kramers problem is analyzed in detail. We employ a multi-relaxation collision operator which is shown to permit a variable Layer width. Computer simulations are performed which give excellent agreement with the theoretical derivations. Good qualitative agreement is achieved with the accurate numerical solution of the Boltzmann equation for hard sphere molecules. Our theoretical result clearly indicates that the lattice Boltzmann models with high symmetric velocity sets naturally develop to physically relevant Knudsen Layers due to the discrete ordinate origin of the method.
Yonghao Zhang - One of the best experts on this subject based on the ideXlab platform.
-
modeling of Knudsen Layer effects in micro nanoscale gas flows
Journal of Fluids Engineering-transactions of The Asme, 2011Co-Authors: Nishanth Dongari, Yonghao Zhang, Jason M ReeseAbstract:We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen Layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime.
-
Lattice Boltzmann modelling Knudsen Layer effect in non-equilibrium flows
EPL (Europhysics Letters), 2008Co-Authors: Gui-hua Tang, Yonghao Zhang, David EmersonAbstract:Due to its intrinsically kinetic nature, lattice Boltzmann (LB) approach to simulating non-equilibrium gas flows has recently attracted significant research interest. Compared with other kinetic methods, it can offer a significantly smaller computational cost. To capture the nonlinear high-order rarefaction phenomena in gas flows, a geometry-dependent gas local mean free path has been proposed to be implemented in our "high-order" LB model. A series of tests on rarefaction effects and the Knudsen Layer interference have been carried out and the simulation results demonstrate our LB model's capability for highly non-equilibrium flows.
-
modelling thermal flow in the transition regime using a lattice boltzmann approach
EPL, 2007Co-Authors: Yonghao Zhang, Robert W Barber, David R EmersonAbstract:Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen Layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen Layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen Layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58.
-
capturing Knudsen Layer phenomena using a lattice boltzmann model
Physical Review E, 2006Co-Authors: Yonghao Zhang, Robert W Barber, David R EmersonAbstract:In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in microscale and nanoscale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques such as the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen Layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations. In this paper, we propose an effective mean-free path to address the Knudsen Layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.
Nishanth Dongari - One of the best experts on this subject based on the ideXlab platform.
-
implementation of Knudsen Layer phenomena in rarefied high speed gas flows
Journal of Aerospace Engineering, 2019Co-Authors: Apurva Bhagat, Harshal Gijare, Nishanth DongariAbstract:AbstractA numerical investigation of Knudsen Layer effects in high-speed flows in a rarefied flow regime has been carried out. The conventional compressible flow computational fluid dynamics (CFD) ...
-
the effect of Knudsen Layer on rarefied hypersonic gas flows
31ST INTERNATIONAL SYMPOSIUM ON RAREFIED GAS DYNAMICS: RGD31, 2019Co-Authors: Harshal Gijare, Apurva Bhagat, Nishanth DongariAbstract:Effect of the Knudsen Layer (KL) on surface and bulk flow properties is investigated for the hypersonic flow applications in the slip flow regime. Knudsen Layer formulation is incorporated within an open source computational fluid dynamics framework, OpenFOAM. Navier-Stokes (N-S) constitutive relations, and first order slip and jump boundary conditions are modified based on the effective mean free path, which is dependent on the geometry of an obstacle and local flow gradients. This new approach is evaluated for three configurations: (1) the flate plate with M = 6.1 and Kn = 0.004, (2) the sharp wedge, with M = 10 and Kn = 0.01, and (3) the cylinder, with M= 10 and Kn = 0.05, with argon and nitrogen as working gases. Simulation results are validated against published Direct Simulation Monte Carlo (DSMC) and experimental results. The surface velocity predicted by new formulation give good agreement with the DSMC data especially for the flat plate case. It has also shown maximum improvement of 47 % at θ = 90◦ for cylinder case over a conventional solver. Knudsen Layer formulation have improved the results in the bulk flow region as well. Simulation results convey that our approach greatly improves the predictive capabilities of the compressible N-S-F solver upto early transition flow regime. The current work is significant from the perspective of accurate thermal design of hypersonic vehicles.Effect of the Knudsen Layer (KL) on surface and bulk flow properties is investigated for the hypersonic flow applications in the slip flow regime. Knudsen Layer formulation is incorporated within an open source computational fluid dynamics framework, OpenFOAM. Navier-Stokes (N-S) constitutive relations, and first order slip and jump boundary conditions are modified based on the effective mean free path, which is dependent on the geometry of an obstacle and local flow gradients. This new approach is evaluated for three configurations: (1) the flate plate with M = 6.1 and Kn = 0.004, (2) the sharp wedge, with M = 10 and Kn = 0.01, and (3) the cylinder, with M= 10 and Kn = 0.05, with argon and nitrogen as working gases. Simulation results are validated against published Direct Simulation Monte Carlo (DSMC) and experimental results. The surface velocity predicted by new formulation give good agreement with the DSMC data especially for the flat plate case. It has also shown maximum improvement of 47 % at θ = 9...
-
effect of Knudsen Layer on the heat transfer in hypersonic rarefied gas flows
International Journal of Thermal Sciences, 2019Co-Authors: Harshal Gijare, Apurva Bhagat, Nishanth DongariAbstract:Abstract Effect of the Knudsen Layer on the surface heat transfer is investigated for the hypersonic flow applications in the slip and early transition flow regime. Knudsen Layer formulation is incorporated within an open source computational fluid dynamics framework, OpenFOAM. Navier-Stokes-Fourier constitutive relations, and first order slip and jump boundary conditions are modified based on the effective mean free path, which is dependent on the geometry of an obstacle and local flow gradients. The modified solver is validated against benchmark cases of low-speed Couette gas flow and hypersonic flow over a flat plate. Investigation is further extended to the high speed flow over a wedge and a circular cylinder covering a wide range of Knudsen numbers within the slip and early transition flow regime. Effect of Knudsen Layer on the surface heat transfer is examined, and maximum improvement of 27 % is achieved for a wedge case. Moreover, results show excellent agreement with the DSMC data, especially for the cylinder cases with high Knudsen numbers, Kn = 0.05 and 0.25. The simulation results convey that our approach greatly improves the predictive capabilities of the compressible N-S-F solver up to early transition flow regime (Kn ∼ 1). The current work is significant from the perspective of accurate thermal design of hypersonic vehicles.
-
Modeling of Knudsen Layer Effects in the Micro-Scale Backward-Facing Step in the Slip Flow Regime
Micromachines, 2019Co-Authors: Apurva Bhagat, Harshal Gijare, Nishanth DongariAbstract:The effect of the Knudsen Layer in the thermal micro-scale gas flows has been investigated. The effective mean free path model has been implemented in the open source computational fluid dynamics (CFD) code, to extend its applicability up to slip and early transition flow regime. The conventional Navier-Stokes constitutive relations and the first-order non-equilibrium boundary conditions are modified based on the effective mean free path, which depends on the distance from the solid surface. The predictive capability of the standard `Maxwell velocity slip-Smoluchwoski temperature jump' and hybrid boundary conditions `Langmuir Maxwell velocity slip-Langmuir Smoluchwoski temperature jump' in conjunction with the Knudsen Layer formulation has been evaluated in the present work. Simulations are carried out over a nano-/micro-scale backward facing step geometry in which flow experiences adverse pressure gradient, separation and re-attachment. Results are validated against the direct simulation Monte Carlo (DSMC) data, and have shown significant improvement over the existing CFD solvers. Non-equilibrium effects on the velocity and temperature of gas on the surface of the backward facing step channel are studied by varying the flow Knudsen number, inlet flow temperature, and wall temperature. Results show that the modified solver with hybrid Langmuir based boundary conditions gives the best predictions when the Knudsen Layer is incorporated, and the standard Maxwell-Smoluchowski can accurately capture momentum and the thermal Knudsen Layer when the temperature of the wall is higher than the fluid flow.
-
implementation of Knudsen Layer effects in open source cfd solver for effective modeling of microscale gas flows
2015Co-Authors: Shashank Jaiswal, Nishanth DongariAbstract:We incorporate the power law (PL) based geometry de- pendent mean free path (MFP) model into the open-source computational fluid dynamics (CFD) software OpenFOAM. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to model the flow behavior in the Knudsen Layers close to surfaces. The velocity slip and temperature jump boundary condi- tions are also modified in the rhoCentralFoam solver. We carry out numerical simulations in order to accuarately cap- ture the Knudsen-Layer effect in microscale gas flows. Our model implementation is validated against the direct sim- ulation Monte-Carlo (DSMC) data. The modified rhoCen- tralFOAM solver is applied to low and high mach number velocity-driven (Couette) flow and Fourier heat transfer in microchannels. The results show that our solver greatly im- proves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime. The importance of this paper stems from the numerical simulation point of view, as OpenFOAM tool is open source, parallel-friendly, and able to solve flows involving complex geometries and unstructured mesh.
Duncan A Lockerby - One of the best experts on this subject based on the ideXlab platform.
-
computing the near wall region in gas micro and nanofluidics critical Knudsen Layer phenomena
Journal of Computational and Theoretical Nanoscience, 2007Co-Authors: Jason M Reese, Yingsong Zheng, Duncan A LockerbyAbstract:In order to capture critical near-wall phenomena in gas micro- and nanoflows within conventional CFD codes, we present scaled Navier-Stokes-Fourier (NSF) constitutive relations. Our scaling is mathematically equivalent to applying an 'effective' viscosity to the original constitutive relations. An expression for this 'effective' transport coefficient is obtained from the half-space Kramer's flow problem. The advantage of our model over the traditional NSF equations is that the non-equilibrium flow near to the wall (the momentum Knudsen Layer) can be described. Its advantage over higher-order hydrodynamic models for gas micro- and nanoflows is that the boundary conditions remain the same as required for the traditional NSF equations, so modifications to current CFD codes (provided they are already capable of modelling slip at solid surfaces) would be minimal. As an application example, we apply our model to the isothermal problem of a micro sphere moving through a gas: we show that our model gives excellent results in the Knudsen number range Kn<0.1 and acceptable results up to Kn=0.25. This is much better than the traditional NSF model with non-scaled constitutive relations.
-
the usefulness of higher order constitutive relations for describing the Knudsen Layer
Physics of Fluids, 2005Co-Authors: Duncan A Lockerby, Jason M Reese, Michael A GallisAbstract: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.
-
capturing the Knudsen Layer in continuum fluid models of nonequilibrium gas flows
AIAA Journal, 2005Co-Authors: Duncan A Lockerby, Jason M Reese, Michael A GallisAbstract: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.
-
capturing the Knudsen Layer in continuum fluid models of non equilibrium gas flows
AIAA Journal, 2005Co-Authors: Duncan A Lockerby, Jason M Reese, Michael A GallisAbstract: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.
-
on hydrodynamic predictions of near wall effects in rarefied gases some phenomenological and modelling approaches
International Conference on Heat Transfer and Fluid Flow in Microscale, 2005Co-Authors: Jason M Reese, Duncan A Lockerby, David R EmersonAbstract:Methods for simulating the critical near-wall region in hydrodynamic models of gas micro-flows are discussed. Two important non-equilibrium flow features - velocity slip at solid walls, and the Knudsen Layer (which extends one or two molecular mean free paths into the gas from a surface) - are investigated using different modelling approaches. In addition to a discussion of Maxwell's slip boundary condition, a newly implemented 'wall-function' model that has been developed to improve hydrodynamic simulations of the Knudsen Layer is described. Phenomenological methods are compared to physical modelling and it is shown that, while both simulation types have merit, and both can quantitatively improve results in most cases, there are drawbacks associated with each approach. Phenomenological techniques, for example, may not be sufficiently general, whilst issues with applicability and stability are known to exist in some physical models.
