Abstracts - KTH Mechanics

Direct Numerical Simulation of Laminar Heat Transfer to a
Flat Plate affected by Free-Stream Fluctuations
J. G. Wissink ∗ and W. Rodi ∗
Free-stream turbulence in incoming flow can influence strongly heat transfer to
turbine blades. The physical mechanisms involved are only just beginning to be understood
1 . From experiments 2 , we know that 1) the affected laminar boundary layer
flow needs to be accelerating in order to observe a significant increase in ”laminar”
heat transfer - that is: the heat transfer in regions where the boundary layer is laminar
- and 2) the increase in laminar heat transfer depends on the integral length scale
of the incoming free-stream turbulence.
To further inverstigate this phenomenon, it was decided to perform a series of
Direct Numerical Simulations (DNS) of an accelerating flat plate boundary layer flow
with incoming free-stream turbulence. By varying both the Reynolds number Re
and the integral length scale Λ of the free-stream turbulence, we aim to elucidate
the physical mechanisms involved. The simulations are performed on the HP-XC1
cluster of the Scientific Supercomputing Centre in Karlsruhe (SSCK) using up to 64
processors and 135.8 Mio. grid points.
Figure 1(a) shows a cross-section of the computational domain. The contoured
upper wall induces an accelerating boundary layer flow. At the inlet, free-stream turbulence
(Tu=2.5%) - which stems from a separate simulation of isotropic turbulence
in a box - is superposed on a Blasius velocity-profile. So far, two different Reynolds
numbers, Re = 100 000 and Re = 200 000, both based on the free-stream inlet velocity
ue and the length-scale L - see Figure 1(a) - were employed. As shown in Figure 1(b),
at Re = 200 000, a significant increase in laminar heat transfer is obtained in the
presence of free-stream turbulence with an integral length-scale of Λ = 0.0830L. A
similar figure (not shown here) at Re = 100 000 shows an increase in heat transfer
which is located much farther downstream. This clearly illustrates a Reynolds number
dependence. Further studies - varying both Re and Λ - are currently performed.
We aim to present the results at the conference.
∗ Institute for Hydromechanics, University of Karlsruhe, D-76128 Karlsruhe, Germany.
1 Mayle et al, J. Turbomachinery 120, 402 (1998).
2 Junkhan and Severoy, J. Heat Transfer 17, 171 (1994).
u=u e
free-slip
Blasius
profile
Convective
outflow
no-slip
L
no-slip
0 1 2 3 4 5
x/L
(a)
Nu
1000
800
600
400
200
Re=200,000
0
0 1 2 3 4
x/L
No turbulence
Λ=0.0830
Figure 1: (a) Spanwise slice through the computational domain. (b) Local Nusselt
number along the flat plate at Re = 200 000.
(b)
43