Application of a High-Order Macroscopic Approach to Force-Driven Poiseuille Flow in the Slip and Transition Regimes

2008 ◽  
Author(s):  
Simon Mizzi ◽  
Xiao-Jun Gu ◽  
David R. Emerson ◽  
Robert W. Barber ◽  
Jason M. Reese
Keyword(s):  
Boundary Conditions ◽  
Poiseuille Flow ◽  
Solid Wall ◽  
Moment Equation ◽  
Moment Equations ◽  
Molecular Collision ◽  
Macroscopic Models ◽  
Gaseous Flows ◽  
Wall Interaction ◽  
The Moment

In this paper various extended macroscopic models are described and applied to force-driven Poiseuille flow. In particular, details are given for the regularized Grad 13- and 20-moment equations. Extended macroscopic models have, until recently, been limited by the uncertainity surrounding the prescription of boundary conditions on solid-walls. The gas-solid wall interaction plays an important role in describing the dynamics of confined gaseous flows. This problem is tackled in the context of the moment equations whereby the simplified Maxwell microscopic formalism is used to derive boundary conditions for a given moment equation set. The proposed governing equations and boundary conditions are applied to force-driven Poiseuille flow where anomalous thermal behavior is observed as the Knudsen number increases. Results are compared to DSMC data and it is established that the proposed extended macroscopic models can capture this non-intuitive behavior. However, the models show some quantitative disparity in representing this behavior. It is proposed that this is addressed by development of a consistent theory of molecular collision geometries in the extended hydro-dynamic model or by the utilization of more extended moment sets.

A Generalized Integral Computation Technique for Nonequilibrium Compressible Turbulent Boundary Layers Using Moment Equations

1972 ◽  
Vol 39 (3) ◽  
pp. 667-672 ◽  
Author(s):  
J. P. Lamb ◽  
L. J. Hesler ◽  
J. H. Smith
Keyword(s):  
Boundary Layers ◽  
Mechanical Energy ◽  
Moment Equation ◽  
Turbulent Boundary Layers ◽  
Moment Equations ◽  
Governing Equations ◽  
Starting Conditions ◽  
The Moment ◽  
Momentum Integral ◽  
Layer Concept

Computation of nonequilibrium compressible turbulent boundary layers using Coles’ three-parameter representation for the layer (cf, δ, Π) is discussed. Governing equations include momentum integral, skin friction, and an integral moment equation. It is shown that the hypothetical equilibrium layer concept employed by Alber to determine the dissipation integral of the mechanical energy equation can be utilized to estimate similar auxiliary parameters in the entrainment and moment-of-momentum integral equations. A series of comparisons of experimental data and predictions, using each of the moment equations shows that all combinations yield very similar results which are in general agreement with measurements. Some sensitivity to starting conditions was observed with the moment-of-momentum and entrainment relations.

Evaluation of moment equation in the 2000 Canadian highway bridge design code for soil–metal arch structures

2004 ◽  
Vol 31 (2) ◽  
pp. 281-291 ◽  
Author(s):  
Dong-Ho Choi ◽  
Gi-Nam Kim ◽  
Peter M Byrne
Keyword(s):  
Finite Element ◽  
Moment Equation ◽  
Finite Element Analyses ◽  
Moment Equations ◽  
Metal Structures ◽  
Maximum Moment ◽  
Design Variables ◽  
Arch Structures ◽  
The Moment ◽  
Soil Metal

This paper evaluates the moment equation in the 2000 Canadian highway bridge design code (CHBDC) for soil–metal arch structures. This equation is adopted from Duncan's moment equation (1978), which is based on his finding from finite element analyses that the maximum moment occurs at the quarter point of soil-metal structures. However, finite element analyses carried out for this study demonstrate that the maximum moment in soil–metal arch structures with spans greater than approximately 11 m occurs at the crown point. In this study, the location and magnitude of the maximum moment was examined for soil–metal arch structures having spans of 6–20 m under three construction stages; backfill up to the crown, backfill up to the cover depth, and live loading. Based on the location of the maximum moment, two sets of moment equations dependant on span length were found necessary. Moment coefficients and moment reduction factors in moment equations are proposed from the results of numerous finite element analyses for semi-circular arch and part-arch types of soil–metal structures considering the various design variables, such as span length, structural shapes, section properties, and backfill conditions. The validity of the coefficients and reduction factors in the moment equation of the 2000 CHBDC is investigated by comparison with those proposed in this study. The comparison demonstrates that the moment equation of the 2000 CHBDC is still valid and a little conservative. The effects of design variables on the variations of moments of soil–metal arch structures during construction stages are also examined.Key words: soil–metal arch structures, moment equations, CHBDC, soil-structure interaction.

scholarly journals The Solvability of Mixed Value Problem for the First and Second Approximations of One-Dimensional Nonlinear System of Moment Equations with Microscopic Boundary Conditions

2022 ◽  
Author(s):  
Auzhan Sakabekov ◽  
Yerkanat Auzhani
Keyword(s):  
Distribution Function ◽  
Nonlinear System ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Collision Operator ◽  
Maxwell Distribution ◽  
Moment Equations ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
The Moment

AbstractThe paper gives a derivation of a new one-dimensional non-stationary nonlinear system of moment equations, that depend on the flight velocity and the surface temperature of an aircraft. Maxwell microscopic condition is approximated for the distribution function on moving boundary, when one fraction of molecules reflected from the surface specular and another fraction diffusely with Maxwell distribution. Moreover, macroscopic boundary conditions for the moment system of equations depend on evenness or oddness of approximation $${f}_{k}(t,x,c)$$ f k ( t , x , c ) , where $${f}_{k}(t,x,c)$$ f k ( t , x , c ) is partial expansion sum of the molecules distribution function over eigenfunctions of linearized collision operator around local Maxwell distribution. The formulation of initial and boundary value problem for the system of moment equations in the first and second approximations is described. Existence and uniqueness of the solution for the above-mentioned problem using macroscopic boundary conditions in the space of functions $$C\left(\left[0,T\right];{L}^{2}\left[-a,a\right]\right)$$ C 0 , T ; L 2 - a , a are proved.

scholarly journals R13 moment equations applied to supersonic flow with solid wall interaction

2019 ◽  
Author(s):  
Maksim Timokhin ◽  
Henning Struchtrup ◽  
Alexey Kokhanchik ◽  
Yevgeniy Bondar
Keyword(s):  
Supersonic Flow ◽  
Solid Wall ◽  
Moment Equations ◽  
Wall Interaction

scholarly journals Compartor: a toolbox for the automatic generation of moment equations for dynamic compartment populations

2021 ◽  
Author(s):  
Tobias Pietzsch ◽  
Lorenzo Duso ◽  
Christoph Zechner
Keyword(s):  
Stochastic Dynamics ◽  
Moment Equation ◽  
Automatic Generation ◽  
Moment Equations ◽  
Biochemical System ◽  
Biochemical Processes ◽  
Stochastic Population Models ◽  
Living Organisms ◽  
The Moment ◽  
Python Package

Abstract Summary Many biochemical processes in living organisms take place inside compartments that can interact with each other and remodel over time. In a recent work, we have shown how the stochastic dynamics of a compartmentalized biochemical system can be effectively studied using moment equations. With this technique, the time evolution of a compartment population is summarized using a finite number of ordinary differential equations, which can be analyzed very efficiently. However, the derivation of moment equations by hand can become time-consuming for systems comprising multiple reactants and interactions. Here we present Compartor, a toolbox that automatically generates the moment equations associated with a user-defined compartmentalized system. Through the moment equation method, Compartor renders the analysis of stochastic population models accessible to a broader scientific community. Availability and implementation Compartor is provided as a Python package and is available at https://pypi.org/project/compartor/. Source code and usage tutorials for Compartor are available at https://github.com/zechnerlab/Compartor.

The moment equations for three-group systems

1981 ◽  
Vol 43 (1) ◽  
pp. 40-48
Author(s):  
P.L Corio ◽  
M.L Trover
Keyword(s):  
Moment Equations ◽  
The Moment

Electromagnetic wave backscattering across a magnetic field in a bounded plasma

1979 ◽  
Vol 22 (1) ◽  
pp. 85-96
Author(s):  
Joseph E. Willett ◽  
Sinan Bilikmen ◽  
Behrooz Maraghechi
Keyword(s):  
Magnetic Field ◽  
Numerical Study ◽  
Magnetized Plasma ◽  
Absolute Instability ◽  
Moment Equations ◽  
Homogeneous Plasma ◽  
Coupled Equations ◽  
Bounded Plasma ◽  
The Moment ◽  
The Magnetic Field

The stimulated backscattering of electromagnetic ordinary waves from extraordinary waves propagating normal to a magnetic field in a plasma of finite length is studied. A pair of coupled differential equations for the amplitudes of the backscattered and scatterer waves is derived from Maxwell's equations and the moment equations for an inhomogeneous magnetized plasma. Solution of the coupled equations for a homogeneous plasma yields an expression for the growth rate of the absolute instability as a function of plasma length and damping rates of the product waves. The convective regime in which only spatial amplification occurs is discussed. A numerical study of the effects of the magnetic field on Raman and Brillouin backscattering is presented.

scholarly journals A convergence study for the Laguerre expansion in the moment equation method for neoclassical transport in general toroidal plasmas

2010 ◽  
Vol 17 (8) ◽  
pp. 082510 ◽  
Author(s):  
S. Nishimura ◽  
H. Sugama ◽  
H. Maaßberg ◽  
C. D. Beidler ◽  
S. Murakami ◽  
...  
Keyword(s):  
Moment Equation ◽  
Equation Method ◽  
Laguerre Expansion ◽  
Toroidal Plasmas ◽  
Neoclassical Transport ◽  
Convergence Study ◽  
The Moment

Fluid-Dynamic Loading on a Tilted Rectangular Cylinder Near a Solid Wall

2006 ◽  
Author(s):  
Stefano Malavasi ◽  
Emanuele Zappa
Keyword(s):  
Boundary Conditions ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Solid Wall ◽  
Large Body ◽  
Experimental Results ◽  
Different Boundary Conditions ◽  
Force Coefficients ◽  
Rectangular Cylinder ◽  
The Impact

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder. We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number due to the proximity of the cylinder to a bottom plate (placed at various distances from the cylinder) at different angles of attack. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 200 mm. The effects of the different boundary conditions on the vortex shedding phenomenon are investigated by considering the Strouhal number of the vortex shedding as the key controlling parameter. The experimental results mimicking the unbounded conditions (relative large elevation of the cylinder above the solid wall) are in close agreement with those already found in literature. On the contrary, remarkable differences occur when the elevation of the cylinder is decreased. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.

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