scholarly journals Investigating the Effect of the Closure in Partially-Averaged Navier–Stokes Equations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Filipe S. Pereira ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Coherent Structures ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Auxiliary Functions ◽  
Modeling Accuracy

The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

scholarly journals Exact coherent structures at extreme Reynolds number

2016 ◽  
Vol 794 ◽  
pp. 1-4 ◽  
Author(s):  
G. P. Chini
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Wall Flows ◽  
Tollmien Schlichting ◽  
Turbulent Wall

Exact coherent structures (ECS), unstable three-dimensional solutions of the Navier–Stokes equations, play a fundamental role in transitional and turbulent wall flows. Dempsey et al. (J. Fluid Mech., vol. 791, 2016, pp. 97–121) demonstrate that at large Reynolds number reduced equations can be derived that simplify the computation and facilitate mechanistic understanding of these solutions. Their analysis shows that ECS in plane Poiseuille flow can be sustained by a novel inner–outer interaction between oblique near-wall Tollmien–Schlichting waves and interior streamwise vortices.

On the instability of vortex–wave interaction states

2016 ◽  
Vol 802 ◽  
pp. 634-666 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Time Scale ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Navier Stokes ◽  
Edge States ◽  
Asymptotic Approach ◽  
Navier Stokes Equations ◽  
High Reynolds

In recent years it has been established that vortex–wave interaction theory forms an asymptotic framework to describe high Reynolds number coherent structures in shear flows. Comparisons between the asymptotic approach and finite Reynolds number computations of equilibrium states from the full Navier–Stokes equations have suggested that the asymptotic approach is extremely accurate even at quite low Reynolds numbers. However, unlike the situation with an approach based on solving the full Navier–Stokes equations numerically, the vortex–wave interaction approach has not yet been developed to study the instability of the structures it describes. In this work, a comprehensive study of the different instabilities of vortex–wave interaction states is given and it is shown that there are three different time scales on which instabilities can develop. The most dangerous type is a rapidly growing Rayleigh instability of the streak part of the flow. The least dangerous type is a slow mode operating on the diffusion time scale of the roll–streak part of the flow. The third mode of instability, which we will refer to as the edge mode of instability, occurs on a time scale midway between those of the other two modes. The existence of the latter mode explains why some exact coherent structures can act as edge states between the laminar and turbulent attractors. These stability results are compared to results from Navier–Stokes calculations.

Low Reynolds-Number Flow in the Vicinity of Axisymmetric Constrictions

1979 ◽  
Vol 21 (2) ◽  
pp. 73-84 ◽  
Author(s):  
N. S. Vlachos ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reynolds Number Flow ◽  
Local Shear ◽  
Number Flow ◽  
Recirculation Length

Numerical solutions of the two-dimensional, Navier-Stokes equations are presented for boundary conditions corresponding to the laminar flow of Newtonian and non-Newtonian fluids in a round tube with axisymmetric constrictions. The influence of Reynolds number, blockage diameter ratio and length on the velocity components, streamlines, local shear stress and pressure drop are quantified and, in the case of the first two, shown to be large. The non-Newtonian stress-strain relationship corresponds to that for blood flowing in venules and results in an increased recirculation length and larger regions of high shear stress.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

scholarly journals Mixing of Particles in Micromixers under Different Angles and Velocities of the Incoming Water

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 577 ◽  
Author(s):  
Evangelos Karvelas ◽  
Christos Liosis ◽  
Theodoros Karakasidis ◽  
Ioannis Sarris
Keyword(s):  
Stokes Equations ◽  
Velocity Ratio ◽  
The Other ◽  
Navier Stokes ◽  
Contaminated Water ◽  
Solution Flow ◽  
Navier Stokes Equations ◽  
Inlet Velocity ◽  
Metal Capture ◽  
Discrete Motion

A possible solution for water purification from heavy metals is to capture them by using nanoparticles in microfluidic ducts. In this technique, heavy metal capture is achieved by effectively mixing two streams, a nanoparticle solution and the contaminated water. In the present work, particles and water mixing is numerically studied for various inlet velocity ratios and inflow angles of the two streams. The Navier-Stokes equations are solved for the water flow while the discrete motion of particles is evaluated by a Lagrangian method. Results showed that as the velocity ratio between the inlet streams increases, by increasing the particles solution flow, the mixing of particles with the contaminated water is increased. Thus, nanoparticles are more uniformly distributed in the duct. On the other hand, angle increase between the inflow streams ducts is found to be less significant.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

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