Page 248 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Direct numerical simulations 6.1.1

for liquid metal applications

‡
†
I. Tiselj*, E. Stalio , D. Angeli , J. Oder*
†
*Reactor Engineering Division, “Joz ˇef Stefan” Institute, Ljubljana, Slovenia, Department
of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Modena, Italy,
‡
Department of Sciences and Methods for Engineering, University of Modena and Reggio
Emilia, Reggio Emilia, Italy

6.1.1.1 Introduction

6.1.1.1.1 The Navier-Stokes equations
The phenomenon of turbulence eludes any definition and is usually introduced
through a list of typical flow features. The most relevant property of turbulence for
the present text is that it emerges as solution to the incompressible Navier-Stokes
equations:

!
r U¼ 0
! (6.1.1.1)
∂ U ! ! 1 2 !
+ U r U¼ rP + r U
∂t Re τ
where Re τ indicates the friction Reynolds number. When these equations are solved at
sufficiently high Reynolds number and using suitable numerical techniques, numer-
ical results of unsteady nature are produced, which show excellent agreement with
measurements in incompressible Newtonian fluids (Pope, 2000). This approach is
called direct numerical simulation or DNS. When we talk about “agreement,” one
should not expect the same temporal development of the dependent variables in a
selected point of computational domain and in the equivalent point of the experimen-
tal device. As solutions of Eqs. (6.1.1.1) are chaotic, only the same statistical behavior
of the numerical solution and measured signal can be observed. From the mathemat-
ical and computational point of view, any minor change in boundary or initial condi-
tions, numerical scheme, grid refinement, a different implementation of the same
algorithms, etc, will result in a different instantaneous solution of the turbulent field
after a sufficiently long time. Nevertheless, statistical properties of the solutions
remain unchanged as long as we do not significantly compromise the accuracy of
our simulations. The good thing is that statistical behavior of all these numerical solu-
tions shows close agreement with measurements.

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors. https://doi.org/10.1016/B978-0-08-101980-1.00016-8
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