scholarly journals On mathematical analysis of complex fluids in active hydrodynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yazhou Chen ◽  
Dehua Wang ◽  
Rongfang Zhang
Keyword(s):  
Weak Solution ◽  
Mathematical Analysis ◽  
Stochastic Analysis ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Complex Fluids ◽  
Strong Uniqueness ◽  
Special Issue ◽  
Survey Article ◽  
Active Liquid

<p style='text-indent:20px;'>This is a survey article for this special issue providing a review of the recent results in the mathematical analysis of active hydrodynamics. Both the incompressible and compressible models are discussed for the active liquid crystals in the Landau-de Gennes Q-tensor framework. The mathematical results on the weak solutions, regularity, and weak-strong uniqueness are presented for the incompressible flows. The global existence of weak solution to the compressible flows is recalled. Other related results on the inhomogeneous flows, incompressible limits, and stochastic analysis are also reviewed.</p>

Design of viscometers corresponding to a universal molecular simulation method

2011 ◽  
Vol 691 ◽  
pp. 461-486 ◽  
Author(s):  
Kaushik Dayal ◽  
Richard D. James
Keyword(s):  
Molecular Simulation ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Complex Fluids ◽  
Unsteady Flows ◽  
Simulation Method ◽  
Solid State Phys ◽  
Basic Theme ◽  
Conceptual Designs ◽  
Large Families

AbstractWe present conceptual designs of viscometers corresponding to our new exact molecular simulation method (Dayal & James, J. Mech. Phys. Solids, vol. 58 (2), 2010, pp. 145–163). The molecular simulation method is a generalization of the method of Lees & Edwards (J. Phys. C: Solid State Phys., vol. 5, 1972, p. 1921), and includes a three-parameter family of incompressible flows, as well as compressible flows and unsteady flows exhibiting vortex stretching. All fluids are allowed. The method gives a way to simulate these flows using relatively few molecules, in the absence of a constitutive relation describing the fluid. This paper presents conceptual designs for viscometers that produce large families of these flows. The basic theme of this paper is that the flows discussed here are a better way to characterize the properties of complex fluids than the currently available methods, such as those based on viscometric flows.

New space-averaging procedure for inhomogeneous flow fields using balance equation formulations

2006 ◽  
Vol 220 (9) ◽  
pp. 1363-1374
Author(s):  
S Wattananusorn
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Flow Fields ◽  
Coupling Factor ◽  
Balance Equations ◽  
Mean Velocity ◽  
New Space ◽  
Inhomogeneous Flow ◽  
The Mean ◽  
Dependent Flow

This paper features the possibility of averaging space-dependent flow fields using a coupling factor that links the equations of momentum and energy. The scheme is applied to the mean velocity, which is derived straightforwardly through the continuity equation. It creates a small imbalance, which can be eliminated later completely. Smaller discrepancies in the integration of systems of balance equations for inhomogeneous flow are the consequence. The procedure is verified on various flow patterns, and comparisons are made with other conventional methods and with some available experimental data. Despite investigating only numerical examples of incompressible flows here, the technique, in principle, is capable of dealing with compressible flows as well. Furthermore, the proposed method discards some variables required in other techniques while still providing useful and acceptable results for practical problems.

Effective boundary conditions for compressible flows over rough boundaries

2015 ◽  
Vol 25 (07) ◽  
pp. 1257-1297 ◽  
Author(s):  
Giulia Deolmi ◽  
Wolfgang Dahmen ◽  
Siegfried Müller
Keyword(s):  
Boundary Conditions ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Laminar Flows ◽  
Small Scale ◽  
Reynolds Number Flow ◽  
Effective Boundary ◽  
Effective Boundary Conditions ◽  
High Reynolds ◽  
Rough Boundaries

Simulations of a flow over a roughness are prohibitively expensive for small-scale structures. If the interest is only on some macroscale quantity it will be sufficient to model the influence of the unresolved microscale effects. Such multiscale models rely on an appropriate upscaling strategy. Here the strategy originally developed by Achdou et al. [Effective boundary conditions for laminar flows over periodic rough boundaries, J. Comput. Phys. 147 (1998) 187–218] for incompressible flows is extended to compressible high Reynolds number flow. For proof of concept a laminar flow over a flat plate with partially embedded roughness is simulated. The results are compared with computations on a rough domain.

Calculation of Surface Roughness Effects on Air-Riding Seals

2002 ◽  
Author(s):  
C. Guardino ◽  
J. W. Chew ◽  
N. J. Hills
Keyword(s):  
Surface Roughness ◽  
Compressible Flows ◽  
Reynolds Equation ◽  
Incompressible Flows ◽  
Numerical Solutions ◽  
Cfd Analysis ◽  
Roughness Effects ◽  
Stationary Wall ◽  
Comparative Results ◽  
Effect Of Surface

The effects of surface roughness on air-riding seals are investigated here using the Rayleigh-pad as an example. Both incompressible and compressible flows are considered using both CFD analysis and analytical/numerical solutions of the Reynolds equation for various 2D or 3D roughness patterns on the stationary wall. A ‘unit-based’ approach for incompressible flows has also been employed and is shown to be computationally much less expensive than the full-geometry solution. Results are presented showing the effect of surface roughness on the net lift force. The effects of varying the Reynolds number are demonstrated, as well as comparative results for static stiffness.

Simulation of the subsonic flow in a high-speed centrifugal compressor impeller by the pressure-based method

1998 ◽  
Vol 212 (4) ◽  
pp. 269-287 ◽  
Author(s):  
Y Wang ◽  
S Komori
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equations ◽  
Compressor Impeller ◽  
Collocated Grid

A pressure-based finite volume procedure developed previously for incompressible flows is extended to predict the three-dimensional compressible flow within a centrifugal impeller. In this procedure, the general curvilinear coordinate system is used and the collocated grid arrangement is adopted. Mass-averaging is used to close the instantaneous Navier-Stokes equations. The covariant velocity components are used as the main variables for the momentum equations, making the pressure-velocity coupling easier. The procedure is successfully applied to predict various compressible flows from subsonic to supersonic. With the aid of the k-ɛ turbulence model, the flow details within a centrifugal impeller are obtained using the present procedure. Predicted distributions of the meridional velocity and the static pressure are reasonable. Calculated radial velocities and flow angles are favourably compared with the measurements at the exit of the impeller.

scholarly journals Special Issue on Flow Phenomena of Complex Fluids

2015 ◽  
Vol 81 (823) ◽  
pp. 15-pre01-15-pre01
Author(s):  
Shigeomi CHONO ◽  
Takatsune NARUMI ◽  
Takehiro YAMAMOTO
Keyword(s):  
Complex Fluids ◽  
Special Issue ◽  
Flow Phenomena

Turbulent Flow Simulation of a Runner for Francis Hydraulic Turbines Using Pseudo-Compressibility

1996 ◽  
Vol 118 (2) ◽  
pp. 285-291 ◽  
Author(s):  
Chuichi Arakawa ◽  
Yi Qian ◽  
Takashi Kubota
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Leading Edge ◽  
Design Tool ◽  
Design Flow ◽  
Navier Stokes ◽  
Small Computer ◽  
Strong Vortex

A three-dimensional Navier-Stokes code with pseudo-compressibility, an implicit formulation of finite difference, and a k – ε two-equation turbulence model has been developed for the Francis hydraulic runner. The viscous flow in the rotating field can be simulated well in the design flow operating condition as well as in the off-design conditions in which a strong vortex occurs due to the separation near the leading edge. Because the code employs an implicit algorithm and a wall function near the wall, it does not require a large CPU time. It can therefore be used on a small computer such as the desk-top workstation, and is available for use as a design tool. The same kind of algorithm that is used for compressible flows has been found to be appropriate for the simulation of complex incompressible flows in the field of turbomachinery.

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