Coupling Kinetic and Continuum Equations for Micro Scale Flow Computations

2011 ◽  
Author(s):  
Giulio Croce ◽  
Olga Rovenskaya
Keyword(s):  
Knudsen Number ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Physical Domain ◽  
Wide Range ◽  
Direct Numerical Solution ◽  
Conservation Of Momentum ◽  
Flow Through ◽  
Local Parameters ◽  
The Continuum

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.

Numerical Investigation of Microflow Over Rough Surfaces: Coupling Approach

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Olga Rovenskaya ◽  
Giulio Croce
Keyword(s):  
Knudsen Number ◽  
Pressure Ratio ◽  
Domain Size ◽  
Navier Stokes ◽  
Channel Height ◽  
Physical Domain ◽  
Wide Range ◽  
Conservation Of Momentum ◽  
Mach Numbers ◽  
Poiseuille Number

A numerical analysis of the flow field in rough microchannel is carried out decomposing the computational physical domain into kinetic and continuum subdomains. Each domain size is determined by the value of a proper threshold parameter, based on the local Knudsen number and local gradients of macroparameters. This switching parameter is computed from a preliminary Navier–Stokes (NS) solution throughout the whole physical domain. The solution is then advanced in time simultaneously in both kinetic and continuum domains: The coupling is achieved by matching half fluxes at the interface of the kinetic and Navier–Stokes domains, taking care of the conservation of momentum, energy, and mass through the interface. The roughness geometry is modeled as a series of triangular obstructions with a relative roughness up to a maximum of 5% of the channel height. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions 0.001 ≤ Ma ≤ 0.75 and a Reynolds number up to 170. To estimate rarefaction effect, the flow at Knudsen number ranging from 0.01 to 0.08 and fixed pressure ratio has been considered. Accuracy and discrepancies between full Navier–Stokes, kinetic, and coupled solutions are discussed, assessing the range of applicability of first order slip condition in rough geometries. The effect of the roughness is discussed via Poiseuille number as a function of local Knudsen and Mach numbers.

Numerical Investigation of Rough Surfaces: Coupling Approach

2012 ◽  
Author(s):  
Olga Rovenskaya ◽  
Giulio Croce
Keyword(s):  
Domain Size ◽  
Navier Stokes ◽  
Channel Height ◽  
Physical Domain ◽  
Switching Parameter ◽  
Wide Range ◽  
Conservation Of Momentum ◽  
Coupling Approach ◽  
Mach Numbers ◽  
Poiseuille Number

A numerical analysis of the flow field in rough microchannel is carried out decomposing the computational physical domain into kinetic and continuum sub-domains. Each domain size is determined by the value of a proper threshold parameter, based on the local Knudsen number and local gradients of macro-parameters. This switching parameter is computed from a preliminary Navier–Stokes solution throughout the whole physical domain. The solution is then advanced in time simultaneously in both kinetic and continuum domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier–Stokes domains, taking care of the conservation of momentum, energy and mass through the interface. The roughness geometry is modeled as a series of triangular obstructions with a relative roughness up to a maximum of 5% of the channel height. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions and a Reynolds number up to 100. Accuracy and discrepancies between full Navier Stokes, kinetic and coupled solutions are discussed, assessing the range of applicability of first order slip condition in rough geometries. The effect of the roughness is discussed via Poiseuille number as a function of local Knudsen and Mach numbers.

On LES Methods Applied to Seal Geometries

2012 ◽  
Author(s):  
James Tyacke ◽  
Richard Jefferson-Loveday ◽  
Paul Tucker
Keyword(s):  
Maximum Error ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Final Solution ◽  
Complex Flow ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy ◽  
Rans Models ◽  
Flow Through

Nine Large Eddy Simulation (LES) methods are used to simulate flow through two labyrinth seal geometries and are compared with a wide range of Reynolds-Averaged Navier-Stokes (RANS) solutions. These involve one-equation, two-equation and Reynolds Stress RANS models. Also applied are linear and nonlinear pure LES models, hybrid RANS-Numerical-LES (RANS-NLES) and Numerical-LES (NLES). RANS is found to have a maximum error and a scatter of 20%. A similar level of scatter is also found among the same turbulence model implemented in different codes. In a design context, this makes RANS unusable as a final solution. Results show that LES and RANS-NLES is capable of accurately predicting flow behaviour of two seals with a scatter of less than 5%. The complex flow physics gives rise to both laminar and turbulent zones making most LES models inappropriate. Nonetheless, this is found to have minimal tangible results impact. In accord with experimental observations, the ability of LES to find multiple solutions due to solution non-uniqueness is also observed.

Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1998 ◽  
Vol 120 (4) ◽  
pp. 930-936 ◽  
Author(s):  
P. Mosher ◽  
D. W. Childs
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in high-speed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to he somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

Simulation of High Knudsen Number Gas Flows in Nanochannels via the Lattice Boltzmann Method

2011 ◽  
Vol 403-408 ◽  
pp. 5318-5323
Author(s):  
A.H. Meghdadi Isfahani ◽  
A. Soleimani ◽  
A. Homayoon
Keyword(s):  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Numerical Data ◽  
Gas Flows ◽  
Wide Range ◽  
Flow Through ◽  
Boltzmann Method ◽  
Slip Transition ◽  
Pressure Driven Flow

Using a modified Lattice Boltzmann Method (LBM), pressure driven flow through micro and nano channels has been modeled. Based on the improving of the dynamic viscosity, an effective relaxation time formulation is proposed which is able to simulate wide range of Knudsen number, Kn, covering the slip, transition and to some extend the free molecular regimes. The results agree very well with exiting empirical and numerical data.

Simulation of Fluid Flow Through a Granular Bed

2006 ◽  
Author(s):  
Arezou Jafari ◽  
S. Mohammad Mousavi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Packed Bed ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Duct Geometry ◽  
Flow Through

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.

Rarefied Gas Flow Through a Circular Orifice and Short Tubes

1984 ◽  
Vol 106 (4) ◽  
pp. 367-373 ◽  
Author(s):  
Tetsuo Fujimoto ◽  
Masaru Usami
Keyword(s):  
Knudsen Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Pressure Ratio ◽  
Diameter Ratio ◽  
Empirical Equations ◽  
Rarefied Gas Flow ◽  
High Pressure Ratio ◽  
Circular Orifice ◽  
Flow Through

Rarefied gas flow through a circular orifice and short tubes has been investigated experimentally, and the conductance of the aperture has been calculated for Knudsen number between 2 × 10−4 and 50. The unsteady approach was adopted, in which the decay of pressure in an upstream chamber was measured as a function of time. For flow with high pressure ratio, empirical equations of the conductance are proposed as a function of Reynolds number, or Knudsen number, and length-to-diameter ratio of the apertures.

Pressure Ratio Effects on Rarefied Flow Through Square Tubes

1973 ◽  
Vol 95 (1) ◽  
pp. 370-372 ◽  
Author(s):  
M. W. Milligan ◽  
H. J. Wilkerson
Keyword(s):  
Experimental Data ◽  
Theoretical Model ◽  
Knudsen Number ◽  
Pressure Ratio ◽  
Semiempirical Model ◽  
Argon Gas ◽  
Rarefied Flow ◽  
Model Predictions ◽  
Number Variation ◽  
Flow Through

Experimental data are presented for the flow of argon gas through a 0.0985 in. sq tube 12 in. long. Data were obtained for pressure ratios varying between 0.943 and 0.0027. The range of Knudsen number variation was from 0.0025 (continuum) to 2.0 (near free molecular). These data are compared to existing theoretical model predictions. A simple semiempirical model is presented and compared with the data.

Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1995 ◽  
Author(s):  
Phillip Mosher ◽  
Dara W. Childs
Keyword(s):  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

Abstract This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in highspeed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to be somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

Investigation of Unsteady Flow Through a Transonic Turbine Stage: Data/Prediction Comparison for Time-Averaged and Phase-Resolved Pressure Data

1992 ◽  
Vol 114 (1) ◽  
pp. 91-99 ◽  
Author(s):  
M. G. Dunn ◽  
W. A. Bennett ◽  
R. A. Delaney ◽  
K. V. Rao
Keyword(s):  
Pressure Ratio ◽  
Design Flow ◽  
Navier Stokes ◽  
Design Stage ◽  
Pressure Data ◽  
Pressure Transducers ◽  
Data Prediction ◽  
Flow Through ◽  
Transonic Turbine ◽  
Response Pressure

This paper presents time-averaged and phase-resolved measurements of the surface pressure data for the vane and blade of a transonic single-stage research turbine. The data are compared and contrasted with predictions from an unsteady Euler/Navier–Stokes code. The data were taken in a shock-tunnel facility in which the flow was generated with a short-duration source of heated and pressurized air. Surf ace-mounted high-response pressure transducers were used to obtain the pressure measurements. The turbine was operating at the design flow function, the design stage pressure ratio, and 100 percent corrected speed. A matrix of data was obtained at two vane exit conditions and two vane/rotor axial spacings.

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