======2D Channel Flow with/without Thermal Field======
=====DNS by Kasagi, Tomita, Kuroda, Ohtsubo=====

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====Description====

The cases here consist of DNS studies of fully developed plane channel flow, as shown in
<imgref cas45-geom>. The dynamic field is reported at two Reynolds numbers (\(Re_{\tau}=100\)
and \(150\)). For the higher Reynolds number case the fully developed thermal field is also
reported, for molecular Prandtl numbers of 0.71 an 0.025. These conditions are summarized in 
the table below.

^    ^   Cases   ^^^
| \(Re_{\tau}\)    |  100   |        150       ||
| \(Re_{bulk}\)   |  2980  |        4560      ||
| \(Pr\)           |   -    |   0.71  |  0.025  |

For the thermal field calculations isoflux conditions were imposed on the two walls, so the 
local mean temperature increased linearly in the streamwise direction. With any buoyancy 
effect neglected, temperature was considered as a passive scalar. 

<imgcaption cas45-geom| Flow configuration>{{ figs:case045:chan-geom.png |Flow configuration}}</imgcaption>

====Simulation Details====

The flow geometry and the co-ordinate system are shown in <imgref cas45-geom>. 
Note that \(y\) denotes the distance from the bottom wall normalised by the channel 
half width \(\delta\); i.e., \(y = 0\) and \(2\) at the two walls. 

The Reynolds number \(Re\), based on the wall friction velocity \(u_{\tau}\) and \(\delta\) was 
set to be 100 and 150 in the two cases. The resultant bulk Reynolds numbers \(Re_{bulk}\) were
approximately 2980 and 4560 respectively. 

Referring to the numerical procedure used by 
Kim et al. (1987), a fourth-order partial differential equation for \(v\), a second-order partial 
differential equation for the wall-normal component of vorticity \(\omega_y\)
and the continuity equation were used to solve the flow field.

A spectral method with Fourier series in the \(x\) and \(z\) directions and a Chebyshev polynomial 
expansion in the wall-normal direction were used. 
For the \(Re_{\tau}=150\) case the computational periods were chosen to be \(5\pi\delta\) and 
\(2\pi\delta\) (2356 and 942 in wall units) in the \(x\) and \(z\) directions, respectively. 
\(128 \times 128\) Fourier modes and Chebyshev polynomials up to the order 96 in wave number space were 
used in order to resolve all essential turbulent scales on the computation grid. The collocation 
grid used to compute the nonlinear terms in physical space had 1.5 times finer resolution in 
each direction to remove aliasing errors. This resulted in effective grid spacings of:
\(\Delta x^+ \approx 18.4\), \(\Delta y^+ = 0.05\) to \(4.9\), and \(\Delta z^+ \approx 7.4\)
in the three directions.

For time integration, the second-order Adams-Bashforth and Crank-Nicolson schemes were adopted for the nonlinear and viscous terms, respectively.

====Available Data====

The available data include:

\(Re_{\tau}=100\) Case:
  * Mean velocity and Reynolds stress profiles across the channel
  * Skewness and flatness factors
  * Turbulent kinetic energy budget

\(Re_{\tau}=150\) Case:
  * Mean velocity and Reynolds stress profiles across the channel
  * Mean temperature, turbulent heat fluxes and temperature variance profiles
  * Skewness and flatness factors
  * Budgets of Reynolds stresses, turbulent kinetic energy and its dissipation rate
  * Budgets of turbulent heat fluxes, temperature variance and its dissipation rate
  * One dimensional energy spectra at selected \(y^+\) locations
  * Two-point correlations at selected \(y^+\) locations

[[case045-plots|Sample plots]] of selected quantities are available.

The data can be downloaded as compressed archives from the links below, or as individual files.

  * {{cdata:case045:chtp-allfiles.zip|chtp-allfiles.zip}}
  * {{cdata:case045:chtp-allfiles.tar.gz|chtp-allfiles.tar.gz}}


|          |  \(Re_{\tau}=100\)  |  \(Re_{\tau}=150\)  |
| Dynamic field  |  {{cdata:case045:ch12_pg_wl2.dat|ch12_pg_wl2.dat}}   |   {{cdata:case045:ch12_pg_wl1.dat|ch12_pg_wl1.dat}}   |
| Thermal field, \(Pr=0.71\)    |         |   {{cdata:case045:ch122_pg_wl1.dat|ch122_pg_wl1.dat}}   |
| Thermal field, \(Pr=0.0.25\)  |         |   {{cdata:case045:ch122_pg_wl2.dat|ch122_pg_wl2.dat}}   |


====References====

  - Kasagi, N., Tomita, Y., Kuroda, A. (1991). Direct numerical simulation of the passive scalar field in a two-dimensional turbulent channel flow.  //Proc. 3rd ASME/JSME Thermal Engineering Joint Conference//.
  - Kasagi, N., Tomita, Y., Kuroda, A. (1992). [[https://doi.org/10.1115/1.2911323|Direct numerical simulation of passive scalar field in a turbulent channel flow]]. //ASME J. Heat Transfer//, Vol. 114, p. 598.
  - Kasagi, N.,  Ohtsubo, Y., Tomita, Y. (1991). Direct numerical simulation of the low Prandtl number scalar field in a two dimensional turbulent channel flow.  //Proc. 8th Turbulent Shear Flow Symposium//, Munich, Germany.
  - Kim, J.,  Moin, P., Moser, R. (1987). [[https://doi.org/10.1017/S0022112087000892|Turbulence statistics in fully developed channel flow at low Reynolds number]]. //J. Fluid Mech.//, Vol. 177, pp. 133-166.

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Indexed data:
<data dbcase confined_flow>
case       : 045
title      : 2D Chanel Flow with/without Thermal Field
author*    : Kasagi, Tomita, Kuroda, Ohtsubo
year       : 1992
type       : DNS
flow_tag*  : scalar, constant_cross_section, channel_flow
</data>