Adiabatic versus conductive heat transfer in off-critical SF
6
in the absence of convection
T. Fro ¨hlich, P. Guenoun, M. Bonetti, F. Perrot, and D. Beysens*
Commissariat a ` l’Energie Atomique (CEA), Centre d’Etudes de Saclay, Service de Physique de l’Etat Condense ´ (SPEC),
F-91191 Gif-sur-Yvette Cedex, France
Y. Garrabos
Institut de Chimie de la Matie `re Condense ´e de Bordeaux (ICMCB), Universite ´ Bordeaux I, F-33600 Pessac, France
B. Le Neindre
Laboratoire d’Inge ´nierie des Mate ´riaux et des Hautes Pressions (LIMHP), Universite ´ de Paris Nord, F-93430 Villetaneuse, France
P. Bravais
L’Air Liquide, F-38360 Sassenage, France
Received 27 December 1995; revised manuscript received 13 March 1996
The process of adiabatic heating of compressible fluids piston effect PE has been investigated in SF
6
at
off-critical density 1.27
c
near the coexistence temperature in the absence of convection. The temperature
response of the fluid to an internal heat pulse has been recorded at different distances from the heat source
confirming a spatially homogeneous temperature rise outside an expanding boundary layer during heating.
This process can be distinguished from the following conductive heat transfer when the energy contained in the
boundary layer diffuses. This observation is confirmed by both experiment and calculations. During and after
the heating process, ( P , , T ) data of the fluid behaves according to a given equation of state at equilibrium
because hydrodynamic velocities remain small. The isentropic character of the PE was confirmed by both
calculations from the pressure and density measurements. The presented experimental results were obtained on
ESA’s critical point facility CPF during the Spacelab IML-2 mission in July 1994. S1063-651X9604507-2
PACS numbers: 44.10.+i, 05.70.Jk, 66.10.Cb
I. INTRODUCTION
The transport of heat in dense pure fluids classically in-
volves the mechanisms of convection, diffusion, and radia-
tion. Recently, the understanding of thermal equilibration of
a pure fluid near its gas-liquid critical point CP has evi-
denced a fourth mechanism, the so-called ‘‘piston effect’’
PE1–7. Although it is also present in an ideal gas 4, it
is emphasized near the CP where the compressibility of a
fluid diverges. This high compressibility leads to an unstable
character of supercritical fluids which induces buoyancy-
driven convection in the presence of an accelerating field
gravitation, rotation, . . . . To suppress these perturbing
convective flows and carry out a proper experimental analy-
sis of the different modes of heat transfer, a microgravity
environment has been used.
When such a supercritical homogeneous fluid enclosed in
a sample cell is suddenly heated from one wall, a diffusive
thermal boundary layer ‘‘hot boundary layer’’ HBL
forms at this wall-fluid interface. Due to the high compress-
ibility of the fluid outside the layer ‘‘bulk’’, the fluid layer
expands and acts as a piston, generating an acoustic wave
which propagates in the bulk and which is reflected on the
second wall enclosing the fluid. Thermal conversion of this
pressure and density rise is, in turn, able to heat the fluid in
an adiabatic way. As a result, spatially uniform heating of
the bulk fluid occurs on an acoustic time scale t
a
=L / c with
L the characteristic sample dimension and c the sound ve-
locity in the fluid. During repeated travels of the pressure
wave in the fluid, the bulk temperature progressively rises to
reach thermal equilibrium. At the same time, heat starts to
diffuse from the fluid into the nonheated walls, if these are
not perfectly isolating. In this case, a ‘‘cold’’ boundary layer
CBL is formed at this interface, where the fluid contracts
and thus decompresses the bulk. It is then the competition
between the HBL and the CBL which rules the evolution of
the bulk fluid state.
When deriving the energy balance for heat transfer in a
compressible medium, the pressure term has to be taken into
account and we obtain
T
t
=
1
c
P
1
r
n
r
r
n
T
r
+
1 -
c
v
c
P
T
P
dP
dt
. 1
Here, is the thermal conductivity and c
P
and c
v
are the
heat capacities at constant pressure and volume, respectively.
The parameter n indicates the geometry of the considered
process and equals 0 for plane, 1 for cylindrical, and 2 for
spherical geometry. Critical divergence of these properties
induces a nonlinear diffusion process 5 coupled with adia-
batic heating. In fact, this form of the energy equation
stresses the two different types of heat transfer, which are the
nonisentropic heat diffusion first right-hand term and the
temperature variation due to isentropic compression second
term.
*Present address: Commissariat a ` l’Energie Atomique CEA,
Centre d’Etudes de Grenoble, De ´partement de la Recherche sur la
Matie `re Condense ´e DRFMC, F-38054 Grenoble Cedex 9, France.
PHYSICAL REVIEW E AUGUST 1996 VOLUME 54, NUMBER 2
54 1063-651X/96/542/15446/$10.00 1544 © 1996 The American Physical Society