CHT’01: ADVANCES IN COMPUTATIONAL HEAT TRANSFER
VALIDATION EXERCISE
1.
Natural convection in an air-filled cubical cavity
2.
Directional Solidification of Succinonitrile in a Horizontal Bridgman
Apparatus
3.
Confined and Submerged Liquid Jet Impingement Heat Transfer
One of the goals of CHT’01 is
to provide a mechanism for the validation of physical and computational models,
codes and solutions.
Three problems have been
chosen, for which it is felt that reliable experimental and/or computational
results are available. They encompass
laminar and turbulent flow and phase change.
The purpose of the exercise is not
to determine which is the “best” method for each problem –however “best” might
be defined. It is to provide data
against which models, methods and
codes
can be assessed, and to encourage users of both research and commercial codes
to take advantage of those data for the benefit of the computational heat
transfer community.
Contributors are invited to
submit computational solutions to one or more of these problems. We impose no limitations on physical or
computational models, methods or grid sizes.
These are at the discretion of the contributor. We will assume that the contributions
represent, in the opinions of the authors, the solution to the problem.
Contributions should contain a
summary of the assumptions, methods and grids used to obtain the solutions,
together with the results specified below in connection with each problem. The contributions will be gathered and
assessed by a Benchmark Panel including the authors of the references from
which the problems have been drawn. An
indication of the nature of the assessment may be obtained from [1].
The contributions will be
published in the Proceedings (which will be available for collection at the
Symposium), so they should be written in accordance with the Instructions to Authors. Contributors will not make an oral
presentation of their results, but are invited to prepare a poster if there are
interesting features of their work. In
addition, a summary and report of all contributions will be prepared by the
Benchmark Panel for presentation during a special session of CHT’01.
Papers are also invited which
propose additional benchmark problems for any future validation exercise. These should contain or refer to published
and accessible high quality experimental work and/or high quality computational
work. If sufficient such papers are submitted,
a special session at CHT’01
will be devoted to their presentation and discussion, apart from
discussion of the results of the present exercise.
The
contact person for each problem has been given. Enquiries may also be directed to Professor Darrell Pepper or Professor Graham de Vahl Davis.
One copy of each contribution
is to be sent no later than December 1, 2000, to
Professor Darrell
W. Pepper,
Department of
Mechanical Engineering,
University of
Nevada, Las Vegas,
4505 Maryland Pkwy,
Las Vegas, NV
89154-4027, USA.
Tel: +1 702 895
1056 Fax: +1 702 895 3936
and a second copy is
to be sent by the same date to the relevant contact person, whose
address is given below.
Department of Mechanical Engineering,
University of Waterloo,
Waterloo, Ontario, Canada N2L 3G1
Tel:
+1 519 888 4053
Fax:
+1 519 746 0852
A cubical air-filled cavity
[2, 3] is tilted at an angle to the direction of gravity such that the
gravitational vector is parallel to the x-y plane and acts in a
direction (90º -
j
) to the negative y-axis,
as shown in Figure 1. The cavity has one pair of opposing faces (x
= 0 and x = L) at temperatures Th and Tc
respectively. The temperature of the
four remaining faces varies linearly from Tc to Th.
Measured cold wall
Nusselt numbers for a range of Rayleigh numbers and box inclination angles have
been reported in Table 1 of [3], and some velocity vectors are shown in Figure
5 of [3]. These experiments were
performed in a pressure chamber with
Tc =
300 K Th =
307 K L =
0.1272 m
and the properties
of air were evaluated at Tm = (Th + Tc)/2. The Rayleigh number was varied over a range
from about 100 to about 2×108 by varying the pressure.
Further information, including
a table of experimental vcalues of Nusselt number on the cold wall, may be
found at
http://www.ryerson.ca/~weyleong/benchmark/
Solutions are invited to this
problem for the following cases:
|
Parameter values |
Results required |
|
j
= 0 Ra = 105
and 106 |
Velocity vectors
(to be presented for comparison with Figure 5 of [3]). Average Nusselt
number, and contours of local Nusselt number, on x = 0
and x = L.
|
|
j
= 45º Ra = 106
and 107 |
Average Nusselt
number, and contours of local Nusselt number, on x =
and x = L
. |
|
j
= 90º Ra = 106,
107 and 108 |
Average Nusselt
number, and contours of local Nusselt number, on x = 0
and x = L. |
NASA Glenn Research Center,
MS 105-1,
Cleveland, OH 44135, USA.
Tel: +1 216 433 5025 Fax: +1 216 433 5033
The task in this
problem is to simulate directional solidification and melting of pure
succinonitrile (SCN: NC(CH2)2CN),
which has been studied in the horizontal Bridgman apparatus [4, 5] shown in Figure 2. The ampoule in which the experiments were
conducted was made of borosilicate glass, and was square in cross-section with
dimensions 6 mm inside, 8 mm outside, and 150 mm length. Solidification was induced by controlling
the temperature of the outside of the ampoule via the heating and cooling
jackets, and by positioning the ampoule, or moving it through the apparatus, by
means of the translation mechanism. As
the heating and cooling jackets moved from right to left (as viewed in Figure 2)
over the fixed ampoule, the solid-liquid interface moved with them and
solidification of the SCN occurred.
Melting was achieved by moving the jackets in the reverse direction. A no-growth experiment was performed in
which the jackets were fixed in position.
A small gap between the jackets permitted observations to be made of the
solid-liquid interface and seed particles for velocimetry.
A Cartesian
coordinate system is used, as in Figure 3, in which the
origin is at the mid-point of the ampoule.
The x axis is directed horizontally across the ampoule; y is in the vertical (upwards)
direction and the z axis points along the ampoule from the cold to the
hot end.
The heating and cooling jackets were maintained at temperatures above and below the melting point of SCN; the temperature difference was 63°C in all experiments. Heat transfer by convection and radiation occurred across the small gap between the outside of the ampoule and the inside of the two jackets, causing a longitudinal temperature distribution to be established along the outside of the ampoule.
The outside ampoule temperatures were measured
longitudinally along the middle of the top, the bottom and one vertical side of
the ampoule, and one of the upper and lower ampoule corners.
An example of these
outside ampoule temperatures is given in Figure 4 (the corner
temperatures have been omitted for clarity), and the full sets of measurements
are shown in Table 1, Table 2 and Table 3, which are to be used
to construct boundary conditions for the respective no-growth, solidification
and melting problems. It will be
necessary to solve for conduction in the ampoule walls as well as for
solidification of the SCN.
In the no-growth
experiment, temperatures were also measured inside the SCN itself. These are given in Table 15 and should be
used for comparison with contributors’ computed values.
Although the ampoule is 150
mm long, contributors will recognize that it may not be necessary to include
the whole length in the computation zone.
No-growth
experiments started with the solid occupying about 50% of the ampoule; for
solidification and melting, the initial amounts of solid were about 33% and 67%
respectively. All experiments were
continued to steady state.
Solidification and melting experiments were stopped when the solid
occupied about 67% and 33% of the ampoule respectively.
The properties of
SCN and the ampoule material are given in Table 4.
Table 4. Properties of
succinonitrile and borosilicate glass ampoules.
|
Property |
SCN liquid |
SCN solid |
SCN interface |
Ampoule |
|
Density
r
(kg/m3) |
984. |
1016 |
|
2300. |
|
Thermal conductivity k (W/m-K) |
0.223 |
0.225 |
|
1.2 |
|
Heat capacity Cp (J/kg-K) |
2000. |
1955 |
|
753.5 |
|
Thermal expansivity
ß
(K-1) |
8.1x10-4 |
|
|
|
|
Kinematic viscosity
n
(m2/s) |
2.6x10-6 |
|
|
|
|
Melting temperature
Tm (K) |
|
|
331.34 |
|
Solutions are
invited for the following cases:
Case 1: no growth. Boundary conditions are given in Table 1.
Calculate the interface
shape on the vertical mid-plane x = 0 and the horizontal (x-z)
plane through the point of maximum horizontal deflection.
Also calculate
particle tracks and velocities for particles starting at points (0.818, 1.428, 1.868), (0.328, 1.523, 2.306)
and (0.048, 1.541, 2.109).
Case 2: solidification for a period sufficient to
reach steady state at a furnace speed V of 40 mm/s. Boundary conditions are given in Table 2.
Calculate the interface
shape on the vertical mid-plane x = 0 and the horizontal (x-z)
plane through the point of maximum deflection.
Case 3: melting for a period sufficient to reach steady state at a furnace speed V of -40 mm/s. Boundary conditions are given in Table 3.
Calculate the interface shape on the vertical mid-plane x = 0 and the horizontal (x-z) plane through the point of maximum deflection.
The results of
experiments to determine the interface shape for these
three cases are given in Tables 5 – 14, Table 15 contains two sets of
measurements of internal
SCN temperatures in the no-growth experiment, while Tables 16 – 18 contain
experimentally measured particle
tracks.
Professor Suresh V. Garimella,
School of Mechanical Engineering
1288 Mechanical Engineering,
Purdue University
West Lafayette, IN 47907-1288, USA.
Phone: +1 765 494 5621 Fax: +1
765 494 0539
A
jet of the perfluorinated dielectric liquid FC-77 flows vertically downwards
from a cylindrical plenum chamber of inner diameter 89 mm and inner height 152
mm through a cylindrical nozzle of diameter
d and length
l onto a square target plate, as shown in Figure 5 and Figure 6. Flush mounted in the target plate is a thin,
10 mm square, electrically heated foil that forms a uniform heat source over its
100 mm2 area. The plenum and
nozzle can be traversed diagonally over the heat source so that the liquid jet
can impinge at different locations defined by the radial distance r
between the axis of the jet and the centre point of the heat source. The separation H between the
nozzle plate and the target plate can also be varied. The nozzle plate is 127 mm diameter; the target plate is rectangular, 180×240 mm. Thermocouples are attached to the rear of
the heat source and by moving the heat source with respect to the jet, the
local surface temperature can be measured as a function of r.
From
a knowledge of the surface heat flux (corrected for losses) and by measurement
of the surface temperature of the heater, the local heat transfer coefficient
was measured [6, 7] as a function of position and the parameters of the
geometry and flow:
|
d |
Nozzle diameter |
|
|