Page 265 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Direct numerical simulations for liquid metal applications 235

1
1
0.8
Fluctuating BC 0.8 Fluctuating BC
Nonfluctuating BC
Nonfluctuating BC
0.6
0.6
R xx 0.4 R zz 0.4
0.2
0.2
0
0
–0.2 –0.2
0 1000 2000 3000 4000 5000 6000 0 500 1000 1500 2000
x + z +
Fig. 6.1.1.5 Streamwise (left) and spanwise (right) autocorrelation functions of fluctuating BC
+
(solid lines) and nonfluctuating BC (dashed lines) temperature fields at y ¼ 91 in “normal,”
“large,” and “very large” domain (Tiselj, 2014).

and nonfluctuating thermal BCs and influence of the domain size on the results, which
is visible in streamwise flux. On the other side, the wall-normal turbulent heat flux
Fig. 6.1.1.4 (right) is barely influenced by the domain size.
Influence of the long-lived large turbulent structures is seen also in the stream-
wise autocorrelation functions of the temperature fields in Fig. 6.1.1.5, which are
calculated as
+

Z
L x 0 0
θ ðξÞθ ðξ xÞdξ
0 z,t
R xx ðx,yÞ¼ + (6.1.1.15)
Z
L x
0
0
θ ðξÞθ ðξÞdξ
0 z,t
where integrals of θ are taken at fixed wall distance y while statistical averaging den-
0
oted by hi brackets is performed in spanwise direction z and time t. Similar equation is
used for spanwise autocorrelations. Autocorrelation function is a convenient quantity
than is used to determine the sufficient length of the periodic DNS domain: compu-
tational domain is sufficiently long (wide) if the autocorrelation function of all quan-
tities drops to zero at half length (width) of the domain. As shown in Fig. 6.1.1.5 in the
“normal” computational domain the streamwise autocorrelation functions drop to
about zero at the half way of the channel length, while the spanwise autocorrelations
point to nonnegligible anticorrelation at the half way of the channel width. This antic-
orrelation is more pronounced for the thermal field with fluctuating temperature BC.
In the “large” and the “very large” domains the streamwise autocorrelation functions
drop to zero, while spanwise autocorrelations are closer to zero, but still show a slight
anticorrelation. Similar profiles for autocorrelations of components of the velocity
field or pressure, which can be obtained in various DNS databases, show that
“normal” size domain is sufficient for most of the DNS simulations.
As a final remark on the size of the computational domain it should be noted that
many of the small-scale turbulent phenomena can be observed even in the very small