NUMATH

Turbulent Channel Flow – Re_T = 200

Description of the Re_τ = 200 turbulent channel flow database

Jesús Garicano-Mena^a,∗, Binghua Li^a,b, Eusebio Valero^a

^a Departmento de Matemática Aplicada a la Ingeniería Aeroespacial, ETSI Aeronáutica y del Espacio Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros, 3, E 28040, Madrid, Spain
^b Center for Engineering and Scientific Computation, School of Aeronautics and Astronautics – Zhejiang University, Zhejiang 310027, China

Abstract

In this document we describe a Re_h ≈ 3600, Re_τ ≈ 200 turbulent channel flow database. This database has been investigated in _[1].

Database Description

A turbulent channel flows database has been generated by the incompressible DNS solver described in _[2]. The code follows the paradigm introduced in _[3]: it solves for the wall-normal components of velocity v and vorticity η. This quantities are Fourier transformed (de-aliased using the 3/2 rule) along the homogeneous directions, and discretized using explicit compact ﬁnite-differences along the wall normal direction. Both the streamwise u and spanwise w velocity components are retrieved using the continuity equation with the relation η = ∂w ∂x − ∂u ∂z . Time integration is accomplished by an explicit third order, low-storageRunge–Kuttamethod, combined with animplicit second-order Crank–Nicolson scheme.

The channel walls are planar and the simulations have been conducted under the assumption of constant mass ﬂux.

The spatial resolution for the standard channel ﬂow mesh is ∆x⁺ = 6.54 and ∆z⁺ = 3.27 along the homogeneous directions and ∆y⁺ ∈ (0.95,5.18).
The time-stepenforced in the simulation is in both cases ∆t = 0.015625, which corresponds to ∆t⁺ ≈0.1.

Table 1 summarizes the characteristics of the database.

Table 1: Auxiliary database description.

The database consists of the following ﬁles:

xyz.dat: This ﬁle contains the locations (x,y,z) of the nodes.
SnapAvgXZN.dat: Each of these ﬁles is a snapshot of the u^~ (tk) ﬂow velocities.
dUdyN.dat: Each of these ﬁles contains the d ¯ U dy (tk) proﬁle.
mean.dat: This ﬁle contains the average y proﬁles.

The associated matlab script loadDB.m illustrates how to load the database in memory.

References

[1] J.Garicano-Mena,B.Li, E.Ferrer, and E.Valero. A composite dynamic mode decomposition analysis of turbulent channel ﬂows. Physics of Fluids, 31(11):115102, 2019.
[2] P.Luchini and M.Quadrio. A low -cost parallel implementation of direct numerical simulation of wall turbulence. J. Comput. Phys., 211(2):551–571, January 2006.
[3] J. Kim, P. Moin, and R. Moser. Turbulence statistics in fully developed channel ﬂow at low Reynolds number. J. Fluid Mech., 177:133–166, 1987.