Analysis and extension of the quadratic constitutive relation for RANS methods

2021 ◽  
Vol 125 (1292) ◽  
pp. 1746-1767
Author(s):  
K. Sabnis ◽  
H. Babinsky ◽  
P.R. Spalart ◽  
D.S. Galbraith ◽  
J.A. Benek
Keyword(s):  
Boundary Layers ◽  
Constitutive Relation ◽  
Stress Distributions ◽  
Duct Flow ◽  
Turbulent Stress ◽  
Streamwise Vorticity ◽  
Mean Flow ◽  
Square Duct ◽  
Flow Equilibrium ◽  
New Formulation

AbstractThe quadratic constitutive relation was proposed as an extension of minimal complexity to linear eddy-viscosity models in order to improve mean flow predictions by better estimating turbulent stress distributions. However, the successes of this modification have been relatively modest and are limited to improved calculations of flow along streamwise corners, which are influenced by weak secondary vortices. This paper revisits the quadratic constitutive relation in an attempt to explain its capabilities and deficiencies. The success in streamwise corner flows cannot be entirely explained by significant improvements in turbulent stress estimates in general, but is instead due to better prediction of the particular turbulent stress combinations which appear in the mean streamwise vorticity equation. As a consequence of this investigation, a new formulation of turbulent stress modification is proposed, which appears to better predict the turbulent stress distributions for a variety of flows: channel flow, equilibrium boundary layers, pipe flow, separated boundary layers and square duct flow.

Direct numerical simulation of turbulent duct flow with inclined or V-shaped ribs mounted on one wall

2021 ◽  
Vol 932 ◽  
Author(s):  
S.V. Mahmoodi-Jezeh ◽  
Bing-Chen Wang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Secondary Flows ◽  
Wall Turbulence ◽  
Spanwise Direction ◽  
Duct Flow ◽  
Mean Flow ◽  
Square Duct ◽  
Turbulence Structures ◽  
The Mean

In this research, highly disturbed turbulent flow of distinct three-dimensional characteristics in a square duct with inclined or V-shaped ribs mounted on one wall is investigated using direct numerical simulation. The turbulence field is highly sensitive to not only the rib geometry but also the boundary layers developed over the side and top walls. In a cross-stream plane secondary flows appear as large longitudinal vortices in both inclined and V-shaped rib cases due to the confinement of four sidewalls of the square duct. However, owing to the difference in the pattern of cross-stream secondary flow motions, the flow physics is significantly different in these two ribbed duct cases. It is observed that the mean flow structures in the cross-stream directions are asymmetrical in the inclined rib case but symmetrical in the V-shaped rib case, causing substantial differences in the momentum transfer across the spanwise direction. The impacts of rib geometry on near-wall turbulence structures are investigated using vortex identifiers, joint probability density functions between the streamwise and vertical velocity fluctuations, statistical moments of different orders, spatial two-point autocorrelations and velocity spectra. It is found that near the leeward and windward rib faces, the mean inclination angle of turbulence structures in the V-shaped rib case is greater than that of the inclined rib case, which subsequently enhances momentum transport between the ribbed bottom wall and the smooth top wall.

scholarly journals Turbulence and secondary motions in square duct flow

2018 ◽  
Vol 840 ◽  
pp. 631-655 ◽  
Author(s):  
Sergio Pirozzoli ◽  
Davide Modesti ◽  
Paolo Orlandi ◽  
Francesco Grasso
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Good Accuracy ◽  
Streamwise Velocity ◽  
Secondary Flows ◽  
Duct Flow ◽  
Streamwise Vorticity ◽  
Square Duct ◽  
Developed Turbulence ◽  
Number Variation

We study turbulent flows in pressure-driven ducts with square cross-section through direct numerical simulation in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). Numerical simulations are carried out over very long integration times to get adequate convergence of the flow statistics, and specifically to achieve high-fidelity representation of the secondary motions which arise. The intensity of the latter is found to be on the order of 1 %–2 % of the bulk velocity, and approximately unaffected by Reynolds number variation, at least in the range under scrutiny. The smallness of the mean convection terms in the streamwise vorticity equation points to a simple characterization of the secondary flows, which in the asymptotic high-$Re$ regime are approximated with good accuracy by eigenfunctions of the Laplace operator, in the core part of the duct. Despite their effect of redistributing the wall shear stress along the duct perimeter, we find that secondary motions do not have a large influence on the bulk flow properties, and the streamwise velocity field can be characterized with good accuracy as resulting from the superposition of four flat walls in isolation. As a consequence, we find that parametrizations based on the hydraulic diameter concept, and modifications thereof, are successful in predicting the duct friction coefficient.

Post-transitional periodic flow in a straight square duct

2018 ◽  
Vol 859 ◽  
pp. 731-753
Author(s):  
S. Gavrilakis
Keyword(s):  
Friction Velocity ◽  
Reynolds Numbers ◽  
Dynamical Process ◽  
Streamwise Vorticity ◽  
Transition Flow ◽  
Mean Flow ◽  
Square Duct ◽  
The Mean ◽  
Secondary Velocity ◽  
Incompressible Turbulence

Direct numerical simulation of incompressible turbulence in a straight square duct finds the post-transition flow evolving substantially, and for Reynolds numbers based on the friction velocity and duct hydraulic radius greater than 600 a two-structure secondary flow regime has been established, suggesting the coexistence of two distinct sources of mean streamwise vorticity. The nominal source terms in the equation for the mean streamwise vorticity involve turbulent variables only, that allow us to identify the dominant dynamical process that marks and/or sustains the transverse mean flow. Close to the corner a mean profile instability is dominant, while farther away turbulent streamwise vorticity intensification is broadly distributed near the duct walls. The instability-driven secondary velocity maximum on the duct diagonals scales with the friction velocity. There is limited scaling of turbulent intensities on the wall bisectors.

scholarly journals On the role of secondary motions in turbulent square duct flow

2018 ◽  
Vol 847 ◽  
Author(s):  
Davide Modesti ◽  
Sergio Pirozzoli ◽  
Paolo Orlandi ◽  
Francesco Grasso
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Streamwise Velocity ◽  
Normal Velocity ◽  
Duct Flow ◽  
Mean Flow ◽  
Square Duct ◽  
The Mean ◽  
Wall Shear

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number $Re_{b}=40\,000$ to quantitatively analyse the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIK), which allows one to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute approximately 6 % of the total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress non-uniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions are artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses.

Optimal linear growth in magnetohydrodynamic duct flow

2010 ◽  
Vol 653 ◽  
pp. 273-299 ◽  
Author(s):  
DMITRY KRASNOV ◽  
OLEG ZIKANOV ◽  
MAURICE ROSSI ◽  
THOMAS BOECK
Keyword(s):  
Magnetic Field ◽  
Boundary Layers ◽  
Linear Growth ◽  
Rectangular Cross Section ◽  
Flow Direction ◽  
Duct Flow ◽  
Mean Flow ◽  
Optimal Linear ◽  
Magnetohydrodynamic Channel ◽  
The Magnetic Field

Transient linear growth in laminar magnetohydrodynamic duct flow is analysed. The duct is straight with rectangular cross-section and electrically insulating walls. The applied uniform magnetic field is oriented perpendicular to the mean flow direction and parallel to one of the walls. Optimal perturbations and their maximum amplifications over finite time intervals are computed. The optimal perturbations are increasingly damped by the magnetic field, localized in the boundary layers parallel to the magnetic field irrespective of the duct aspect ratio. Typically, the optimal perturbations have non-vanishing streamwise wavenumber as found in magnetohydrodynamic channel flow with spanwise magnetic field. The Hartmann boundary layers perpendicular to the magnetic field do not contribute to the transient growth.

scholarly journals Effects of Curvature on Unsteady Solutions through a Curved Square Duct Flow

2013 ◽  
Vol 56 ◽  
pp. 217-224 ◽  
Author(s):  
Md. Saidul Islam ◽  
Rabindra Nath Mondal
Keyword(s):  
Duct Flow ◽  
Square Duct

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

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