Bader, Michel

Carlson, William C A

English

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NATIONAL ADVISORY COMMITTEE %i 
FOR AERONAUTICS 
TECHNICAL NOTE 4274 
MEASUREMENT OF THE EFFECT OF AN AXIAL MAGNETIC FIELD 
ON THE REYNOLDS NUMBER OF TRANSITION IN MERCURY 
FLOWING THROUGH A GLASS TUBE 
By Michel Bader and William C. A. Carlson 
Ames Aeronautical Laboratory 
Moff ett Field, Calif. 
Washington 
May, 19 58 
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TECH LIBRARY KAFB, NM 
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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICE 00bb9L4 
TECHNICALNOTE 4274 
MEASUREMENTOFTHEEFFECTOFANAXIALMAGNEZICFIEl3 
ONTBBREYNOLDSNUMBER OF TRANSITION IN MERCURY 
FLOWINGTHROUGHAGlXSSTUBE 
By Michel Bader and William C. A. Carlson 
Experiments were conducted to determine the effect of a strong axial 
mametic field on the flow of mercury through a circular channel. The 
magnetic induction was 15,000 gauss, and the channel was a pyrex tube 
17-l/4 inches long and 0.027 inch inside diameter. Application of the 
magnetic field produced very little change in Reynolds number of transi- 
tion when large Initial disturbances were introduced at the entrance to 
the flow.tube. However, the magnetic field increased the Reynolds number 
of transition by as much as 10 percent at Reynolds numbers between 5,000 
and 8,000 when only slight instabilities were present; at lower Reynolds 
numbers this increase was not observed. 
INTRODUCTION 
The possibility of stabilizing the flow of a conducting fluid by 
means of a magnetic field has been the subject of considerable specula- 
tion. In particular, it has been suggested that a parallel field (lines 
of magaetic flux along lines of flow) could be used to dsmp out small 
oscillations from which turbulence develops, thus increasing the Reynolds 
numbers of transition on airframes. 
. 
It was first demonstrated experimentally by Hartman and Lazarus 
(ref. 1) and again by Shercliff (ref. 2) that a transverse magnetic field 
has the effect of raistig.the Reynolds number at which transition from 
laminar to turbulent flow occurs. The stability of flow between parallel 
plates has been investigated theoretically for a coplanar field by Stuart 
(ref. 3) and for a-transverse field by Lock (ref. 4). Much larger effects 
are predicted for transverse than for parallel fields. Theoretical cal- 
culations for two-dimensional flow predict easily detectable effects when 
the ma@petic parameter Q = 
fields (ref. 4) and 3~10~~ 
uB2d/pu reaches the value 10B4 for transverse 
for parallel fields (ref. 31. 
The present qeriment was undertaken to provide experimental data 
on the effect of a parallel magnetic field on the Reynolds number of 
transition. Mercury flow through a circular pipe was chosen because of 
2 NACA TN 4274 
the relative simplicity of the experiment. -It should'be recognized, 
however, that pipe flow is of a fundsmentally different character from 
flow over airframes., so that no direct quantitative inference can be 
made concerning the latter. 
Q ma@petic parameter, - uB2d, dimensionless 
PU 
Re Reynolds number, @, dimensionless 
u 
B 
d 
electrical conductivity of the fluid 
applied magnetic Fnduction 
characteristic dimension (diameter in case of circular flow tube) 
density of the fluid 
velocity of the flow 
viscosity of the fluid 
SYMBOLS 
APPARATUS AND PROCEDURE 
A mercury reservoir (see fig. 1) 4 inches in diameter and 52 inches 
high was made from Lucite tubing with provisions near the bottom for 
attaching the flow tube and for draining the reservoir. The flow tube 
used had an internal diameter of 0.027 inch and was 17-l/4 inches long; 
its entrance was flared in order to allow high Reynolds numbers with 
laminar flow. The pressure drop across the flow tube was adjusted by 
changing the height of the mercury in the reservoir. The flow rates for 
a given pressure were determined by weighing samples of mercury collected 
over timed Intervals. The Reynolds numbers Were computed from the aver- 
age flow rates thus obtained. 
The electromagnet consisted of 14 layers of copper tubing wound on 
a s/k-inch core of laminated mica tube I6 inches long. The inner six 
layers were l/&inch O.D. tubing and the outer eight layers were 5/16-inch 
O.D. tubing. The layers were separately water cooled and were connected 
in series-electrically. A direct current of 750 amperes was used 5.n all 
tests. The coils were encased in iron with a pole piece opposite the exit 
end in an attempt to make the ma@petic induction along the axis as nearly 
constant as possible. A plot of the magnetic induction along the axis of 
the magnet is given in figure 2. 
NACA TN 4274 3 
Additional cooling along the flow tube was provided by a stream of 
air gently blown down the center of the electroma@pet. The mercury tem- 
perature was thus stabilized near 70' F, the exact temperature being 
recorded for each test. The flow rate was determined alternately with 
and without magnetic field in rapid succession. The air and cooling 
water flows were continued during the tests without current in the mag- 
net in order to duplicate conditions- as closely as possible. Cross 
hairs were installed at the entrance end of the flow tube in order to 
introduce the slight amount of disturbance necespary to induce turbulent 
bursts. The flow tube was cleaned with concentrated nitric acid after 
approximately every 20 minutes of running time. Cleanliness was found 
to be very essential for reproducibility. Vibration of the apparatus, 
on the other hand, did not seem to affect the flow. A qualitative esti- 
mate of the amount of turbulence could be made visually by observing the 
jet of mercury at the exit end of the flow tube. The jet was steady and 
uniform when the flow was 7r but showed considerable irregularity 
during increasingly frequent turbulent bursts as the flow became more 
turbulent. 
EWERIMENTAL REsuLTs 
The results of the test are shown in figure 3. The ordinate indicates 
the pressure difference required between the ends of the tube to obtain 
a given flow rate which is represented by the Reynolds number, pud/l. As 
noted in the figure, the open and solid symbols are test results obtained 
with no magnetic field and with a field of 15,000 gauss, respectively. 
The data on the right of the figure show that at high Reynolds numbers 
(where the flow consisted of turbulent bursts ti otherwise leminar flow) 
the magnetic field was able to shift the flow to fully laminar. This 
effect was observed at Reynolds numbers from approximately 5,000 up to 
8,ooO, the lknit obtainable with the apparatus. The resultFng increases 
in average flow velocity increased the Reynolds numbers up to 10 percent. 
At lower Reynolds numbers, and for the more turbulent flow conditions at 
higher Reynolds numbers, the effect of the magnetic field was observed 
to decrease rapidly. The shift dropped to approximateu 2 percent almost 
mediately when the flow could no longer be shifted to laminar, and 
eventually to approximately zero when the flow was fully turbulent. 
The bounding lines drawn in figure 3 for lsminarflow and fully 
turbulent flow were determined experimentally. The laminar plot agrees 
approximately with the predicted theoretical. value and is an extension 
of the curve for Reynolds numbers under 1,800 where only leminar flow is 
possible. The laminar conditions were characterized by a steadiness of 
flov which could be visually observed. The fully turbulent flow was 
obtained by mesns of a sharp entrance endto the flow tube. The result- 
.ing pressure+rop.curve deparfcs from the laminar flow relation near 
Re = 1,800. With-a .sharp entrance-to the tube, the magnetic field did 
not stabilize!the- flow a~noticeabie~anknt (see-the. symbols near the 
fully turbulent curve). The entrance to the tube was then smoothed, and 
NACA TN 4274 
separate tests were made for different tripping conditions and are shown 
plotted in figure 3. The tripping conditions for only slight turbulence # 
were extremely critical and were not reproducible. It was found that a , 
slight amount of contamination was more effective in inducing turbulence 
than the cross hairs which were installed. 
As can be seen from figure 2, a certain amount of transverse compo- 
nent of the field was present at the ends of the magnet. This cross 
field was small and is believed to have had a negligible effect; indeed, 
with a magnetic parameter Q as small as 0.01, laminar flow is detect- 
ably slowed down by a transverse field. No such slowing down was observed 
here. A further test was made by placing the entrance of the flow tube in 
a transverse field of the same order of magnitude as that present in the 
main mamet. This field had no observable effect on the flow. 
CONCLUDING REMARKS 
The magnetic parsmeter Q, in this experiment, ranged from 0.09 at 
Re m 8,000 to 0.4 at Re z 1,800, as is indicated in figure 3. These 
were the highest values of Q and Re obtainable with the apparatus. 
The results indicate that the stabilizing effect occurred only at 
Reynolds number above about 5,000, so that the region of practical appli- 
cability seems to be at fairly high Reynolds numbers and when there are 
only slight disturbances in the flow. The parallel magnetic field was 
ineffective in stabilizing highly turbulent tube flow. Unfortunately, 
no quantitative inference can be made from pipe flow to flow over air- 
frames; however, it would be of interest to perform similar experiments 
on the flow of ionized gases around bodies in a magnetic field nearly 
parallel to the lines of flow. 
Ames Aeronautical Laboratory 
National Advisory Committee for Aeronautics 
Moffett Field, Calif., Feb. 19, 19% 
NACA TN 4274 
REFEEENCES 
5 
1. Hartmann, Jul., andLazmus,Freimut: Hg-Dynamics II - ExperWental 
Investigations on the Flow of Mercury in a Homogeneous Ma@petic 
Field. Denmark, Kgl. Danske Videnskabernes Selskab, Mathematisk- 
fysiske Meddelelser, vol. 15, no. 7, 1937. (English text) 
2. Shercliff, J. A.: The Flow of Conducting Fluids In Circular Pipes 
Under Transverse Magnetic Fields. Jour. Fluid Mech., vol. 1, 
pt. 6, Dec. 1956, pp. 644-666. 
3. Stuart, J. T.: On the Stability of Viscous Flow Between Parallel 
Plases in the Presence of a Co-planar Magnetic Field. Proc. 
Roy. Sot. London, ser. A, vol. 221, no. 1145, 21Jan. 1954, 
pp. Mg-a6. (AILS o available as British A.R.C., Fluid Motion 
Sub-Cam. Rep. 15,903, FM 1898, May 13, 1953) 
4. Dock, R. C.: The Stability of the Flow of an Electrically Conducting 
Fluid Between Parallel Planes Under a Transverse Magnetic field. 
Proc. Roy. Sot. London, ser. A, vol. 233, no. l.lp, Dec. 6, 1955, 
pp. 105-125. 
. 
. 
: 
1- 
. 
.I -’ ‘- 
- 
I 
- . 
/Mercury 
reservoir 
t- 16” I 
Section of magnet 
” Figure l..- Schai5c di~am of the appratus. 
i- 
1 f 
I 5 Air supply 
c’ l v” t 
l . . 8 d 
Flow tube 
01 2 4 
Distance Ir 
0 IO 
3 magnet along axis, Inches 
12 14 16 
Figure 2.- Value ofthemsgmtlc induction almgthe axis of the elect- t and relative 4 
position of the flow tube. 
NACA TN 4274 
36- 
32- 
28 - 
24 - 
16- 
8- 
4- 
L 
Fully 
Different open symbols with their associated 
full symbols represent tests performed 
under different operating conditions 
Open symbols: B ‘0, Q = 0 
Full symbols: B = 15,000 gauss, 
Q given on scale below 
Magnetic parameter, Q 
/ I I I I I I I I 
I 2 3 4 5 6 7 8 xl03 
Reynolds number, Re 
Figure 3.- Effect of an axial magnetic field on the Reynolds number at 
various values of pressure drops akoss the flow tube. 
NACA - Lendey Field, Va. 


Measurement of the effect of an axial magnetic field on the Reynolds number of transition in mercury flowing through a glass tube

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