Effect of Rayleigh Accelerations Applied to an Initially Moving Fluid
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EFFECT OF RAYLEIGH ACCELERATIONS APPLIED TO AN INITIALLY MOVING FLUID ROBERT F. DRESSLER NASA Headquarters, Washington, D. C. S. J. ROBERTSON AND L. W. SPRADLEY Lockheed Missiles & Space Company, Huntsville, Alabama ABSTRACT Although the instability of an initially motionless fluid subjected to a Rayleigh-type acceleration is well known, this type of excitation applied to an initially moving fluid has not been studied previously. We have therefore performed numerical analyses for two-dimensional unsteady thermal convection in circular cylinders under variable low-g conditions associated with space flight. When an acceleration vector is applied parallel to the thermal gradient for a fluid at rest, no convection results for the stable direction, and an instability leads to Rayleigh convection for the opposite direction. However, when the acceleration has a component which is orthogonal to the gradient, convection always results at any Rayleigh number; this is the usual situation during space flight. We therefore study the resultant effect on convection when both types of acceleration are applied, concurrently or sequentially, and when the resultant vector varies in direction with time. Our results indicate that for space flight conditions, the Rayleigh accelerations impose significant, but not dominating, alterations in the established convection even when the Rayleigh number is less than
critical. NOMENCLATURE Symbol
Description
D g
cylinder diameter = 2 R acceleration due to gravity (sea level)
r
radial distance
R
cylinder radius
Ra
Rayleigh number = egATD
RaH
horizontal Rayleigh number
RaV
vertical Rayleigh number
T
temperature
To0initial AT
3
3 ega0D p
mid-point temperature temperature difference across circular cylinder
204
y
R
Cgold Side
Hot Side
I
I
I
\Ig
I
I)
/
H E
T + AT
T AT
Fig. 1.
Geometry for circular cylinder enclosure (Parallel dotted lines are initial isotherms.)
y4
Fig. 2.
Geometry and computational grid for numerical simulation.
205 Ra
S1.0
= 5000
-•Cold
.o
S id e.
•
Hot S ide
S0.8 E Hg
0.6 S• S•
2000 1000 0 -IOOO
0.4 >
•
-5000
0o.2 o
Rav= 1000
0.0
2.0
1.0
0
3.0
Time, t (dimensionless) Fig. 3a.
Spatial maximum velocity for various Ra values of excitation superimposed on established'steady state flow for RaV = 1000.
0.5 -•
U) .0
••RaH
5000
0.4
(2000
5 x
1000 0
0.3 ---
-1000 -5000
S0.2
Cold Side
'5 0.1
Hot Side
RaV = 5000 En 0.0
Vg 0.25
0.5
1.0
1.25
Time, t (dimensionless) Fig. 3b.
Spatial maximum velocity history for various RaH values of excitation superimposed on previously established steady state flow for RaV = 5000.
206 Description
Symbol t t*
tdimensionless
time transient response time to reach 63% (1 steady state 2 time = vt/R
e- 1 ) of
dimensionless response time Vt /R v
velocity
vmax
spatial maximum velocity
v max
vmax for zero horizontal acceleration component
AVmax
Vmax - Vmax
v
dimensionless velocity -
0
128v D2 v
x, y
rectangular coordinates (Fig. 1)
(X
thermal diffusivity
P
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