High Reynolds number separated flow solutions using Navier-Stokes and approximate equations

AIAA Journal ◽  
1987 ◽  
Vol 25 (2) ◽  
pp. 260-265 ◽  
Author(s):  
M. Napolitano
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Separated Flow ◽  
Navier Stokes ◽  
High Reynolds ◽  
Approximate Equations

scholarly journals The emergence of localized vortex–wave interaction states in plane Couette flow

2013 ◽  
Vol 721 ◽  
pp. 58-85 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall ◽  
Andrew Walton
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Critical Layer ◽  
Navier Stokes ◽  
Turbulent Spots ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractThe recently understood relationship between high-Reynolds-number vortex–wave interaction theory and computationally generated self-sustaining processes provides a possible route to an understanding of some of the underlying structures of fully turbulent flows. Here vortex–wave interaction (VWI) theory is used in the long streamwise wavelength limit to continue the development found at order-one wavelengths by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). The asymptotic description given reduces the Navier–Stokes equations to the so-called boundary-region equations, for which we find equilibrium states describing the change in the VWI as the wavelength of the wave increases from $O(h)$ to $O(Rh)$, where $R$ is the Reynolds number and $2h$ is the depth of the channel. The reduced equations do not include the streamwise pressure gradient of the perturbation or the effect of streamwise diffusion of the wave–vortex states. The solutions we calculate have an asymptotic error proportional to ${R}^{- 2} $ when compared to the full Navier–Stokes equations. The results found correspond to the minimum drag configuration for VWI states and might therefore be of relevance to the control of turbulent flows. The key feature of the new states discussed here is the thickening of the critical layer structure associated with the wave part of the flow to completely fill the channel, so that the roll part of the flow is driven throughout the flow rather than as in Hall & Sherwin as a stress discontinuity across the critical layer. We identify a critical streamwise wavenumber scaling, which, when approached, causes the flow to localize and take on similarities with computationally generated or experimentally observed turbulent spots. In effect, the identification of this critical wavenumber for a given value of the assumed high Reynolds number fixes a minimum box length necessary for the emergence of localized structures. Whereas nonlinear equilibrium states of the Navier–Stokes equations are thought to form a backbone on which turbulent flows hang, our results suggest that the localized states found here might play a related role for turbulent spots.

Fine Structure of Vortex Sheet Rollup by Viscous and Inviscid Simulation

1991 ◽  
Vol 113 (1) ◽  
pp. 31-36 ◽  
Author(s):  
G. Tryggvason ◽  
W. J. A. Dahm ◽  
K. Sbeih
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Flow Region ◽  
Vortex Sheet ◽  
Navier Stokes ◽  
Vortex Sheets ◽  
Limiting Behavior ◽  
High Reynolds

Numerical simulations of the large amplitude stage of the Kelvin-Helmholtz instability of a relatively thin vorticity layer are discussed. At high Reynolds number, the effect of viscosity is commonly neglected and the thin layer is modeled as a vortex sheet separating one potential flow region from another. Since such vortex sheets are susceptible to a short wavelength instability, as well as singularity formation, it is necessary to provide an artificial “regularization” for long time calculations. We examine the effect of this regularization by comparing vortex sheet calculations with fully viscous finite difference calculations of the Navier-Stokes equations. In particular, we compare the limiting behavior of the viscous simulations for high Reynolds numbers and small initial layer thickness with the limiting solution for the roll-up of an inviscid vortex sheet. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. Our results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.

S0550204 LES of turbulent-separated flow controlled by DBD plasma actuator at high Reynolds number

2014 ◽  
Vol 2014 (0) ◽  
pp. _S0550204--_S0550204-
Author(s):  
Makoto SATO ◽  
Kengo ASADA ◽  
Taku NONOMURA ◽  
Hikaru AONO ◽  
Aiko YAKENO ◽  
...  
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Separated Flow ◽  
Plasma Actuator ◽  
Dbd Plasma ◽  
High Reynolds ◽  
Turbulent Separated Flow

scholarly journals Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

2013 ◽  
Vol 729 ◽  
pp. 285-308 ◽  
Author(s):  
Maciej J. Balajewicz ◽  
Earl H. Dowell ◽  
Bernd R. Noack
Keyword(s):  
Reynolds Number ◽  
Galerkin Method ◽  
Stokes Equation ◽  
High Reynolds Number ◽  
Transient Flow ◽  
Navier Stokes ◽  
Power Balance ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
High Reynolds

AbstractWe generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results.

The rise of a gas bubble in a viscous liquid

1959 ◽  
Vol 6 (1) ◽  
pp. 113-130 ◽  
Author(s):  
D. W. Moore
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Viscous Liquid ◽  
High Reynolds Number ◽  
Separated Flow ◽  
Gas Bubble ◽  
Bubble Shape ◽  
Spherical Cap ◽  
Spherical Bubbles ◽  
High Reynolds

The rise of a gas bubble in a viscous liquid at high Reynolds number is investigated, it being shown that in this case the irrotational solution for the flow past the bubble gives a uniform approximation to the velocity field. The drag force experienced by the bubble is calculated on this hypothesis and the drag coefficent is found to be 32/R, where R is the Reynolds number (based on diameter) of the bubbles rising motion. This result is shown to be in fair agreement with experiment.The theory is extended to non-spherical bubbles and the relation of the resulting theory, which enables both bubble shape and velocity of rise to be predicted, to experiment is discussed.Finally, an inviscid model of the spherical cap bubble involving separated flow is considered.

scholarly journals RANS study of very high Reynolds-number plane turbulent Couette flow

2020 ◽  
Vol 14 (2) ◽  
pp. 6663-6678
Author(s):  
Akshay Sherikar ◽  
P. J. Disimile
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
High Reynolds Number ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Sensitivity Testing ◽  
Wall Functions ◽  
High Reynolds ◽  
Very High

The objective of this study is to expound on the deliverables of a steady-state RANS (Reynolds Averaged Navier Stokes) simulation in one of the simplest flows, Couette flow, at a very high Reynolds number. To that end, a process to perform better grid sensitivity testing is introduced. Three two-equation turbulence models ( , , and ) are compared against each other as well as pitted against formal literature on the subject and core flow velocities, slopes, wall-bounded velocities, shear stresses and kinetic energies are analyzed.  applied with enhanced wall functions is consistently found to be in better agreement with previous studies. Finally, plane turbulent Couette flow at  51,099, the range at which it has not been studied experimentally, numerically or analytically in former studies, is simulated. The results are found to be consistent with the trends asserted by literature and preliminary computations of this study.

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