NASA/CR.--_"_,--.-- 207909 Final Report 1 i/# - / Microgravity Science and_ Applications Division Fluid Physics Program The Circular Hydraulic Jump in Microgravity NASA Grant NAG 3-1627 Principal Investigator: Period: C. Thomas Avedisian Sibley School of Mechanical and Aerospace Engineering Cornell University 193 Grumman Hall Ithaca, New York 14853-7501 phone: 607-255-5105 FAX: 607-255-1222 email: cta2 @ cornell.edu June 24, 1994 to June 23, 1996 Cost: https://ntrs.nasa.gov/search.jsp?R=19980048927 2018-04-26T21:53:11+00:00Z
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NASA/CR.--_"_,--.-- 207909
Final Report
1
i/# - /
Microgravity Science and_ Applications Division
Fluid Physics Program
The Circular Hydraulic Jump in Microgravity
NASA Grant NAG 3-1627
Principal Investigator:
Period:
C. Thomas Avedisian
Sibley School of Mechanical and Aerospace EngineeringCornell University193 Grumman HallIthaca, New York 14853-7501
thannormalgravity,andthecurvatureacrossthejump is lessin microgravitythannormalgravity.
At G=0,Dhis infinite byeq. 1andthusshouldnotbeobserved,but this limit is animpracticalone
becauseof the impossibilityof experimentallycreatingpreciselytheG=0condition.
SinceG changesabruptly in thepresentexperiments,the suddendecreasein _ canbe the
sourceof wavesthat are clearly evident in fig. 5, 8, and 10 for hoo=2mmand t=O.2sin the
downstreamflow in microgravity.
Thequalitativetrendof how Dhdependsonh,,ofor givenG that ispredictedby eq. 1 is not
confirmedby the G<<I measurementsreportedhere. Fig. 13showsthat Dhexhibits at mosta
weakvariationwith hooashooincreasesin G<<I while eq. 1showsthat Dh shouldasymptoteto
infinity asG is reduced.This limit G is not followed by themeasurementsandthe discrepancy
couldbedueto neglectingfriction.
An extension of eq. 1 to include friction in the upstream fluid was first reported by Watson
(1964) who uses a boundary layer model to predict the velocity profile across the upstream film.
The results show that the flow becomes self-similar at some radial position away from the
stagnation point. This theory has the essential features of more advanced treatments (e.g., Bowles
and Smith 1992; Higuera 1994) and is applied to the present data. The result can be expressed in
non-dimensional form by introducing the parameters (Middelman 1995) Y -= RH/Froo+I/(2RH),
R-Dh/DjRe-I/3, the Reynolds number Re- 4Q/(rcDjv), H-2h,,JDj Re 1/3 and Froo-Uj2/(Ggohoo):
11
Y =.26/(R3+.287)
where the approximation hoo>>h has been made. The viscous limit is R---)0 in eq. 3. Y and R are
known from the experimental results: Dh as discussed previously, and hoo and Q as input
parameters (Uj=Q/[r_Dj2/4]). A reference location of 2Dj above the target surface was used to
measure Dj. For the water kinematic viscosity at 300°K we took v--8.95x10-7m2/s (Keenan et al.
1969). An average G of 1.1xl0 -2 is used over the free-fall distance for the unshielded falling
package.Thougheq.3 is notexplicit in thejump radius,it canbeusedto determinetheextentof
agreementbetweenmeasuredandpredictedCHJradii.
Fig. 15showsthevariation of Y with R. The inviscid limit (dotted line) clearly does not
predict our measurements while all of the G= 1 data are predicted reasonably well when viscosity
effects are included (eq. 2). On the other hand all of the measurements of Dh for G<< 1 are not well
predicted by eq. 3. These observations suggest that a physical process which is masked at G=I
may become dominant at G<< 1. Candidate processes include flow separation downstream of the
jump and the nonuniform downstream velocity that is not included in the analysis, or neglect of
viscous drag at the surface of the plate.
6. Conclusions
The major conclusions from this nominal one-year preliminary study are the following:
1) a steady CHJ can be established in microgravity;
2) the CHJ in microgravity is larger than at normal gravity, other flow conditions being
the same;
3) the fluid response time to re-establish a CHJ at G<<I from a jump at G=I is on the
order of 200ms;
4) the transition of the fluid film thickness across the CHJ boundary is more gradual in
microgravity than at normal gravity due to the reduction in hydrostatic pressure in the downstream
film;
5) the G=I measurements are well correlated by an existing formulation but the
microgravity measurements are not well predicted;
6) the CHJ diameter shows no clear trend with hoo in a microgravity environment; and
7) All G<<I downstream flow patterns showed capillary ripples.
12
Publications/Presentations:
The Circular Hydraulic Jump in Microgravity, Journal of Fluid Mechanics, submitted
13
7. References
Allen, T. and Ditsworth, R.L. (1972) Fluid Mechanics, pp. 291-291, McGraw-Hill, New York.
Avedisian, C.T., Yang, J.C and Wang, C.H. (1988) Proc. R. Soc. Lond A420, 183.
Bowles, R.I. and Smith, F.T. (1992) J. Fluid Mechanics. 242, 145.
Chaudhury, Z.H. (1964) J. Fluid Mechanics. 20, 501.
Craik, A.D.D., Latham, R.C., Fawkes, M.J. and Gribbon, P.W.F. (1981) J. Fluid Mechanics
112, 347.
Errico, M. (1986) "A Study of the Interaction of Liquid Jets with Solid Surfaces," Ph.D. Thesis,
University of California, San Diego.
Fox, R.W. and McDonald, A.T. (1992) Introduction to Fluid Mechanics, 4th edition, pp. 525-530,
John Wiley, New York.
Gajjar, J.S.B. and Smith, F.T. (1983) Mathematika 30, 77.
Higuera, F.J. (1994) J. Fluid Mechanics. 274, 69.
Jackson, G.S. and Avedisian, C.T. (1994)Proc. R. Soc. Lond., A446, 257-278.
Keenan, J.H., Keys, F.G., Hill, P.G., and Moore, J.G. (1969) Steam Tables, p. 114, John
Wiley, New York.
Labus, T.L. (1976) "Liquid Jet Impingement Normal to a Disk in Zero Gravity," Ph.D. Thesis,
University of Toledo.
Liu, X. and Lienhard, J.H. (1993) Exp. Fluids, 15, 108.
Middelman S. (1995) Modeling Axisymmetric Flows, Chapter 5, New York, Academic Press.
Nirapathdongporn, S. (1968) "Circular Hydraulic Jump", M.Eng. Thesis, Asian Institute of
Technology, Bangkok, Thailand.
Thomas, S., Hankey, W.L., Faghri, A., and Rahman, M.M. (1990) J. Heat Transf 112, 728.
Tani, I. (1948) J. Phys. Soc. Japan 4, 212.
Watson, E.J. (1964) J. Fluid Mechanics 20, 481.
D O
gj
liquid jet
hydraulic jumpcontrol volume
h(r)U2
stagnation_ _"
region _
Figure 1
r o
r
rh
steel aluminumtop
plate
105mmlens plexiglasssidewalls ..... ==
lens support
35 mm /_
camera body hoo
plenum
water level,
electromagnet
steel plate
hydraulic jump
halogen lamp
electronic flowmeter
28 mm aluminum
supportbracket
mirror
Figure 2
drain valve
flow controlvalve
--- aluminum
plate
waterinlet
flangeweld
lassbeads(3.5dia.)
152.40
meshscreen
-- PVCsleeve
O-rin< orificeplate(seebelow)
Plenum Design[numbers in mm; not to scale]
Figure 3
6-32 clearance
. (6 reqd.)
J
DO (= 1.22, 2.56 ,3.83, 5.08) O-ring groove
j.il L_"-'
57.15
! !
63.50
Detail of orifice plate[numbers in mm; not to scale]
Figure 4
G=I; h_o=4mm; Q=9.32ml/s
(a)
G<<I
(b)figure 5
!I
Figure 6
D o = 2.56 mm Q = 9.932 ml/s h_ = 4 mm(View from underneath traget plate)
t=0G=I
k
t = 0. 2 secG<<I
40 mmI I
t = 0.4 secG<<I
waves
figure 7
D O = 1.22 mm
hoo = 2 mm
Q = 6.32 ml/s
hoo = 4 mm
t=OG=I
t=0G=I
t = 0.2 secG<<I
t = 0.2 secG<<I
t = 0.4 secG<<I
t = 0.4 secG<<I
I I40 mm
figure 8
t = 0.6 secG<<I
Photograph of a CHJ taken 200ms after the period of microgravity. The flowconditions are identical to figure 5. The 'hump' just downstream of the jump is
caused by the rapid increase of curvature from G=I to G<<I.
Figure 9
hoo
D o = 1.22 mm
=2mm
Q = 2.39 ml/s
hoo = 4 mm
t=0G=I
40 mm
t=0G=I
t = 0.2 secG<<I
t = 0.2 secG<<I
t = 0.4 secG<<I
t = 0.4 secG<<I
figure 10
100
80
6O
40Oq
20
D = 2.56 mmo
' ' ' ' ' ' I _ ' _ I ' ' ' I ' ' ' I ' ' ' I ' ' '
G=I _ G<<I
-00-0-_0000000000-00-0
0 o
---0000 ....
transienl period
Q = 26.47 mils
• Q = 9.93 ml/s
••00•00000000-•0/
0 L I i I i _ i I i , I I l i L I i i , I , , * I J l l
-0.2 0 0.2 0.4 0.6 0.8 1 i.2
Time (sec)
Figure 11
80
70
6O
50
E
40e..
30
20
10
0-0.2
OOO O
h =4 mm; U.=3.1 _sj
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
D =3.83mmo
D =2.56 mmo
O., O _1, 41. _1' _, 41. 41, # O. • O _. O # _. _' _1, # • 41, _1, • 41, • O _ O _
41, #
##,### D =1.22 mmo
i i i I i i i I _ r i I i i i I i i i I i t , I _ i i
0 0.2 0.4 0.6 0.8 1
Time (sec)Figure 12
.2
e-
60
5O
4O
3O
20
10
00
Q=6.32 ml/s
........ G<<I
+ G=I
i no jump observed at G=I
t I I [ I ' J J t I B r l I I ] I I a ] i r r I j i i I t I i
2 4 6 8 10 12 14
h(mm)
Figure 13
16
3.5
3
2.5
_ 2E 1.5>- 1
0.5
0
-0.5
3.5
3
2.5
2
E 1.5
>- 1
0.S
0
-0.5
3.5
3
2.5
2E
E 1.5>- 1
0.5
0
-0.5
3.5
3
2.5
E 1.5
>- 1
0.5
0
-0.5
3.5
3
2.5
1.5
0.5
0
-0.5
3.5
3
2.5
P 1.5
>" 1
0.5
0
-O.S
_ .......... __qi__.___- .O.j _ _---_'_- Time ffi 0 ms