TABLE 1. BEARING PARAMETERS FOR ANALYTICAL SOLUTIONS

Geometry:

Diameter, mm(in.) .. 2.2.2... 2.00. 25.4 (1)
Length, mm(in.) 2... 2.2... ee « . 25.4 (1)
Clearance, mm(in.).......8. 0.0254 (0.001)
Eccentricity ........2-0220008 « 0.97

Hydrodynamic:

Inlet pressure, Pin, MPa (psia) .... 13.8 (2000)
Exit pressure, Pa, MPa (psia) .... 13.45 (1950)
Maximum pressure, Pmay, MPa (psia) . . 27.16 (3938)
Minimum pressure, Poin, MPa (psia) . . 0.079 (11.5)
Inlet temperature, Tin, K (°R) eee +. 20 (36)

Speed, rad/sec (rpm) ........ 7850 (75 000)



PRESSURE, MPa

PRESSURE, MPa

RUN MASS REDUCED REDUCED REDUCED

FLOW MASS — PRESSURE, — TEMPER-
RATE, FLOW P, ATURE,
w, RATE, t
g/sec (Ib/sec) GC,
—o— 42 33 07) = 0.82 414 0.92 | PARA
aap 25257 (56) 65 297 «85 } HYDROGEN

OPEN SYMBOLS DENOTE MAXIMUM CLEARANCE
SOLID SYMBOLS DENOTE MINIMUM CLEARANCE

MAXIMUM.
CLEARANCE
(@= 7), C

MINIMUM
CLEARANCE
(8-0), C

STEP 3

~
tS
2 STEP 1 .

Po = 1.2928 MPa —:
ie 187, & psiay
oe
(c) Controlled inlet stagnation conditions.
—O— 49 366 (0. 81) 0.93 5,74 0.88
gL a 8 381 88) 7 6.35 89

MAXIMJM.
CLEARANCE
@= 7), C
‘MINIMUM
CLEARANCE
(= 0), C

Pc 1.2928 MPa
(187, 46 psial

ge i tt i pi iy J
7 6 5 4 3 2 -1 0 1
AXIAL POSITION, cm

(q) Backpressure control, repeated,
Figure 3, - Concluded,


PRESSURE, psia

600

800

600

PRESSURE, MPa

°

Ss

v
5
a

peoa

RUN

1302
12%
1294
61
1160
159
1249

MASS
FLOW
RATE,
wy,
glsec
1025
1052
nz
821
893
929
1259

INLET
PRESSURE,
Pin
MPa psia

10, 54 1528
10.45 1515
10.43 1512
6.02 873
6.9 1000
7,32 1062
10.13 149

INLET
TEMPERATURE,
Tin
K

130, 5
127.8
121.7
1168
117.0
116.0
86,2

ps 10, 45-MPa (1515-psia) STAGNATION ISOBAR

B | 117K STAGNATION
Lol ISOTHERM 10. 45-MPa (1515-psia)
/}) STAGNATION
wneks, —_/H ISOBAR
a
[~ 130, 5 Ks, -
TLTKA
L_ —
of 41
Ly Leseed
(b) Controlled inlet stagnation conditions,
38
oo © 12% 1032 «883120 119.0
0 127 «9126.39 9%.
Lg 128792573 832.2
© © 6 126 1159859 1295 85,5

AXIAL POSITION, cm

{__

-4_ 2

AXIAL POSITION, in.

(c) Controlled backpressure,

Figure 1, - Concluded,


Py Po 7? DIFFUSER

[es
1, 44)

Pop P3 Pg Ps,

14-LID TEST SECTION
USING BORDA INLET

$0, 32 (0, 125)
0.64 (0. 25)

2. 83(1.115)

7 STANDARD 3/4 AN

/ FITTING
/
0.08 STANDARD MACHINED TO
(203i ff TI4 AN CouP- 3I4AN STANDARD
1 / / LING WITH Ni . A ay
| pp, CONICAL THROAT \
bay Pe WASHER 0 ‘
|

NS$0,64 (0,25) p
~0,65 (0, 255) 4

Po Ps Pio Pie Pig

P3 \ Pr Po Pao Piz
Ve - -
Woe IP-0-p4-0.05 1. 016-0,02
b2 2 (0.895) 0.08 (0,03)
42.83 0.115) ‘PRESSURE TUBE
TO TRANSDUCER

TYPICAL PRESSURE TUBE INSTALLATION

fa) Configuration geometry.

Figure 1. - Pressure profile for nitrogen flow through high-L/D tube
with Borda inlet. (Dimensions are in centimeters (inches). )


PRESSURE, MPa

FLOW

ENLARGED VIEW OF
— == Jrlow PATH FLOW
PRESSURE TAPS AT =

0°, 90°, 180°, 270° rf
THIS POSITION ONLY HOUSING +{_f-0, 04-0.05(TYP.) J}

+ ae
q TTI | PRESSURE
|

T
3,073| | TAP (TYP. ) |

THT i!
0, 2340. 726 je

i
pad 1.334 7.8600 diam 2.769 7-987 iam |a, 382
diam | |

07.6944 diam 1,194 7.8346 diam 2.642 7. 9233 diam 4.267

ee

(a) Three-step shaft seal.

C-78-2612

RUN MASS REDUCED REDUCED REDUCED

FLOW MASS — PRESSURE, —TEMPER-
RATE, FLOW P, ATURE,
Ww, RATE, T,

r
glsec (Ibisec)

—o— 48 322 (071) 082 4,64 0.84
ap 13 34173) 83, 48 285
OPEN SYMBOLS DENOTE MAXIMUM CLEARANCE

SOLID SYMBOLS DENOTE MINIMUM CLEARANCE

MAXIMUM.

CLEARANCE

Gem, Cc

MINIMUM
CLEARANCE
@= 0), C

STEP 1 STEP 2

Pe 1.2928 MPa —
— (187. 46 psiad

se |
6 5 4 3 2 +1 0 |
AXIAL POSITION, cm ‘

(b) Applied backpressure,

Figure 3 - Pressure profile for fully eccentric, nonrotating, three-step
‘SSME seal configuration,


NASA Technical Memorandum 86980

Nested Subcritical Flows Within
Supercritical Systems

R.C. Hendricks
Lewis Research Center
Cleveland, Ohio

M.J. Braun and R.L. Wheeler III
University of Akron
Akron, Ohio

R.L. Mullen
Case Western Reserve University
Cleveland, Ohio

Prepared for the

20th Annual Cavitation and Multiphase Flow Forum
sponsored by the American Society of Mechanical Engineers
Albuquerque, New Mexico, June 24-26, 1985

NASA


2. Government Accession No. 3. Recipient's Catalog No.

"NASA TM-86980

4. Title and Subtitle 5. Report Date

Nested Subcritical Flows Within Supercritical Systems

6. Performing Organization Code

506-60-42
7. Author(s) 8. Performing Organization Report No.
R.C. Hendricks, M.J. Braun, R.L. Wheeler III, E-2518

and R.L. Mullen

10. Work Unit No.

9. Performing Organization Name and Address

National Aeronautics and Space Administration 11. Contract or Grant No.
Lewis Research Center

Cleveland, Ohio 44135

13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address Technical Memorandum
i nautics and Space Administration
» D.C.

18. Supplementary Notes
R.C. Hendricks, NASA Lewis Research Center; M.J. Braun and R.L. Wheeler III, University of Akron, Akron,
Ohio 44325; R.L. Mullen, Case Western Reserve University, Cleveland, Ohio 44106. Prepared for the 20th
Annual Cavitation and Multiphase Flow Forum sponsored by the American Society of Mechanical Engineers,
Albuquerque, New Mexico, June 24-26, 1985.

16. Abstract

In supercritical systems the design inlet and outlet pressures are maintained
above the thermodynamic critical pressure Pc. Designers rely on this simple
rule of thumb to circumvent problems associated with a subcritical pressure
regime nested within the supercritical pressure system along with the uncertain-
ties in heat transfer, fluid mechanics, and thermophysical property variations.
The simple rule of thumb is adequate in many low-power designs but is inadequate
for high-performance turbomachines and linear systems, where nested two-phase
regions can exist. Examples for a free-jet expansion with backpressure greater
than Pe and a rotor (bearing) with ambient pressure greater than Pe illus-
trate the existence of subcritical pressure regimes nested within supercritical
systems.

17. Key Words (Suggested by Author(s) 18. Distribution Statement
Two phase; Supercritical; Subcritical; Unclassified - unlimited
Flows; Cryogenics STAR Category 34
19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages 22. Price®
Unclassified Unclassified

“For sale by the National Technical Information Service, Springfield, Virginia 22161


Figure 4, - Analytical pressure map for high-speed journal bearing
With Pin, >Po>Pr. Pig = 13.8MPa (2000 psi); Pe = 13.45 MPa
(1950 pet) N= 75000; & = ey = 0,685 Tin = 20K (36 °R);
Pamp 7” Or} MPa(14.7 psi; Mh 56K (100 OR),


700

600

100

PRESSURE, psia

8

700

600

500

100

PRESSURE, MPa

°

RUN MASS REDUCED INLET
FLOW STAGNATION
L_ RATE, TEMPERATURE,
fo} Ww Tho
: glsec
b ia © 289 63467
D 2900 342 101
[— O 2921 4% a
4 o (oe © 279 4% 179
Q
R 4 in?
a
o ° = a 8 in3
aa a a
o ¢ a
ind
ie}
= ia}
°
EFFECTIVE
F sora “re
LENGTH
ooo o
| Inbal Iba tad La ir $88o,8
INLET EXIT ~ INLET EXIT * INLET EXIT “INLET EXIT.
‘SIMULATED AXIAL POSITION
{a) Controlled inlet stagnation conditions, Borda inlets.
BACKPRESSURE
\. FOR RUN =
[ Nr 397
\\ yr 2%
Sy 3195
3194
| | ! 1__,»~_1 ! | 3193
INLET EXIT INLET EXIT INLET EXIT INLET = EXIT
i] i-2 i3 i-4

SIMULATED AXIAL POSITION
(b) Controlled backpressure, orifice inlets (14),

Figure 2. - Pressure profile for flow through four sequential axially aligned inlets.


circumferential gradients are usually much larger.°
With the establishment of nested zones in seal flows,
such nested zones should occur naturally in bearings.
The two-phase zone downstream of the minimum clearance
in a bearing is well known, and the pressure and tem-
perature on the stator have been mapped for a low-
performance machine (12). It is also noted in (12)
that the two-phase zone began to collapse as system
ambient pressure was increased. However, calculations
(13) for a similar high-performance bearing in fluid
hydrogen at high eccentricity (Table 1) reveal a two-
phase zone nested within a system where Pin > Pe > Pc
(Fig. 4). Nested two-phase zones in a bearing can
lead to the onset of instabilities, contrary to the
axial flow seal. The onset of the nested zone depends
‘on the bearing parameter,© but onset is prevalent

at lower ambient pressure (e.g., one-tenth those of
Table 1), ign eccentricity, and high rotating speed
and for large geometries. This effect remains to be
verified. If it is correct, this demonstrates yet
another method of achieving nested two-phase zones,
those not requiring a sharp geometrical configuration
to "trigger" the event, spontaneous nucleation within
the metastable field being necessary and sufficient.

SUMMARY

Zones of two-phase flows have been shown to be
nested within a supercritical pressure envelope.
These zones are established by controlling inlet
stagnation conditions, exit backpressure, or combina-
tions. The zones can be "triggered" by discontinuous
changes in geometry or by significant pressure gradi-
ents. For high-performance turbomachine seals and
possibly bearings, nested two-phase zones can be found
in the circumferential and axial coordinates. The
phenomenon in bearings remains to be demonstrated
experimentally.

REFERENCES

1. Skripov, V.P., Metastable Liquids, Wiley, New
York, 1974,

2. Frenkel, J., Kinetic Theory of Liquids, Dover
Publications, New York, .

3. Hendricks, R.C., Mullen, R.L., and Braun,
M.d., "Analocy Between Cavitation and Fracture
Mechanics," ASME/JSME Thermal Engineering Conference
Proceedings, Vol. 1, ASME, New York, 1983, pp. 35-42.

5Both seals and bearings can be designed to take
advantage of these pressure gradients to provide
significant damping and stiffness, which enhances
stability (11).

Modified bearing parameter = (6nRw/sPCe)(e/C)

4. Angus, S., Imperial College, London, private
communication.

5. Hendricks, R.C., and Simoneau, R.J., “Some
Flow Phenomena in a Constant Area Duct with a Borda
Type Inlet Including the Critical Region,” ASME Paper
78-WA/HT-37, Dec. 1978.

6. Hendricks, R.C., "Some Observations of a Free
Jet Phenomenon in a 90-Degree-Sharp-Edge-Inlet

Geometry," Advances in Cryogenic Engineering, Vol. 25,
Plenum Press, New York, 1380 306 3520

> Pp. 506-520.

7. Hendricks, R.C., "Some Aspects of a Free Jet
Phenomenon to 105 L/D in a Constant Area Duct," Inter-
national Congress of Refrigeration, 15th, Vol. 2,
Organizing and Scientific Committee of the 15th Inter-
national Congress of Refrigeration, Italy, 1980,
Paper B1-78.

8. Hendricks, R.C., "A Comparison of Flow Rates
and Pressure Profiles for N-Sequential Inlets and
Three Related Seal Configurations," Advances in

Cryogenic Engineering, Vol. 30, Plenum Press, New
ork, > Pp. 846.

9. Hendricks, R.C., and Stetz, T.T., “Flow Rates
and Pressure Profiles for One to Four Axially Alined
Borda Inlets," NASA TP-2390, 1984.

10. Hendricks, R. C., “A Comparative Evaluation of
Three Shaft Seals Proposed for High Performance Turbo-
machinery," NASA TM-83021, 1982.

11. Childs, D.W., Hendricks, R.C., and Vance,
J.M., eds.: Rotordynamic Instability Problems in
High-Performance Turbomachinery, NASA CP=2133, 1980.

12. Braun, M.d., and Hendricks, R.C., "An Experi-
mental Investigation of Vaporous/Gaseous Cavity Char-
acteristics of an Eccentric Journal Bearing," ASLE
Transactions, Vol. 27, No. 1, Jan. 1984, pp. 1-14.

+ Braun, M.J., and Hendricks, R.C., "An Experi-
mental Investigation of the Effect of Pressure and
Temperature Levels on the Development and Nature of
the Cavitation Region in a Submerged Journal Bearing,"
Cavitation and Multiphase Flow Forum, ASME, New York,
T983, pp. 60-71.

14. Hendricks, R.C., and Stetz, T.T., "Flow
Through Aligned Sequential Orifice-Type Inlets," NASA
TP-1967, 1982.



of thumb is adequate in many low-power designs but,
as will be demonstrated, it is inadequate for high-
performance turbomachines end linear systems.

Global thermodynamics permits local events that
are considered unstable or unattainable when viewed in
terms of total process dynamics. It becomes a matter
of refining one's view of the black box containing the
system.! For example, local "violations" of thermo-
dynamics are termed metastabilities. Classic among
these are the work of Skripov (1) and applied work
such as fracture, boiling, and condensing (2,3). More
recently the metastable character of water was
investigated (4).

Thus the concept of a two-phase region nested
within a supercritical region would be considered not
only unstable but unrealistic. However, there is no
reason for such an exclusion as it depends on the
thermohydromechanics that exist within components (the
black box) operating at pressures above the thermo-
dynamic critical point. Such conditions do not
violate any thermodynamic hypotheses but are a source
-of incompatibility for the practicing engineer.

This paper demonstrates that two-phase regions can
be nested within a supercritical pressure system.
Furthermore conditions for the existence of nested
zones are prevalent for sharp-edge inlets and for
eccentrically loaded high-performance turbomachines
operating above the thermodynamic critical pressure.

SIMPLE GEOMETRIES

Borda-Inlet Tube
Within @ single-phase fluid, nested two-phase
flows near sharp-edge inlets are commonplace and are
in many cases represented as cavitation; however, the
ambient pressure is subcritical. Consider the pres-
sure profile of Fig. 1 (5-7). The inlet is sharp, and
the L/D can be as high as 120 (6). The working fluid
is nitrogen (Pc 3 3.417 MP2, Tc = 126.3 Ky

De = 0.3105 g/cm3). The geometry is given in

Fig. 1(a). The system was well instrumented and care
was taken to maintain an adiabatic environment. For
this configuration the inlet pressure was much greater
than Pc, but the pressure just 0.54 mm (0.020 in)
from the sharp-edge inlet was Jess than saturation
based on stagnation conditions“ P<(Sq). Downstream
there 18 an imnediete recovery toward P s(So). or
pseudocritical’ P(Sq), but full recovery could occur
anywhere between this point and the exit as illustrated
by the three different profiles. These profiles were
achieved by two methods: inlet stagnation condition
control, and exit backpressure control.

Inlet control. With controlled inlet stagnation con-
‘ditions the pressure at the exit remained subcritical,
but the pressure within the tube downstream of the
inlet was supercritical for isotherms 127.8 K and
130.5 K (Fig. 1(b)). This fully defines a two-phase
Flow nested between two zones at supercritical preg-
sure. These results are somewhat open to question

as So > Sc. However, Sq < Sc for run 1133

Perhaps as a fracture surface that when viewed from
close up appears with discontinuities everywhere yet
gppears continuous and smooth when viewed from afar.
P.(So)_ is the static pressure as a function of
gtagnation entropy.
Pseudocritical: extrapolation of the saturation
locus to the knee of the Joule-Tompson locus con-
trained by the locii of specific heat maximums.
For Sg > Sc, pseudonesting can occur, but two
phases may not occur.

(Fig. ic), where the recovery pressure was greater
than Run 1133 is inlet temperature controlled
and nested, but the nesting is marginal.

Backpressure control. For run 1248 (Fig. 1(c)) the
ackpressure was increased sufficiently to move the
pressure discontinuity ("shock") within the nozzle. A
two-phase zone occurred but was at most weakly nested
(al1_ downstream pressures were less than Pc). For
run 1547 the backpressure was increased above Poy but
there was little change in the two-phase zone within
the tube nested between Po (at -27 cm) and Pe

(at 0 cm), where Po and Pe are greater than Poe

Four Sequential Axially Aligned Borda or Orifice
Inlets

~ Amore complex flow is established by a sequence
of orifices or Borda apertures (8,9). The pressure
profiles of Fig. 2(a) are for N Bordas in sequence
with Tg approaching T. and backpressure depend-
ent on downstream losses. The pressure signature here
illustrates a nested set of two-phase zones within
Borda 2, between the supercritical pressure zones of
Borda 1 and Borda 3. With the inlet stagnation con-
ditions constant the backpressure to Borda 4 was
varied until Pe > Pc within Borda rad pre two-phase
zones remain nested Between P which are
both greater than Po. Run ano tr fo. 5 illustrates
that such zones can also exist within Borda 1,
Because of an experimental facility limitation on Po,
nested regions could be approached in Borda 3 but not
fully established; exclusion is therefore not war-
ranted for either Borda 3 or Borda 4.

For orifice flows, which may never choke, the
pressures in the nested subcritical zones are often
higher than saturation pressure. These zones shift to
higher pressures as backpressure is increased and may
not exhibit two-phase behavior (Fig. 2(b), orifice 2).

TURBOMACHINE CONFIGURATIONS

Normally seals and bearings for high-performance
turbomachines operate at small eccentricities. How-
ever, during abnormal events or even the limit-cycle
type of event, dimensionless eccentricities can
approach 1 (rubbing).

Seals

“Figure 3(a) illustrates the geometry of a high-
performance turbomachine seal such as for the space
Shuttle main engine (SSME) (8,10). The working fluid
is parahydrogen ive = 1.2928 MPa, Tc = 32.976 K,

=0. est /cm?). The pressure profiles
(fig )-ta)) are for 8 fully eccentric, nonrotat-
ing Sat The inlet pressure is greater than Po,
as is the pressure at the inlet to the third step
(Fig. 3(b)). However, immediately downstream of the
step the pressure on one “side” of the seal (@ = 0)
remains above Pc, while the pressure on the opposite
"side" (@ =) iS nearly Ps. Thus the circumferen-
tial pressure profile possesses 211 states between
Pin > Pc at @ = 0 to approximately Pc < Pe at
@=m. Furthermore the system backpressure Eould be
increased above Pc, demonstrating yet another nested
distribution - now in both e and Z (Fig. 3(c)).
To corroborate these results, the tests were repeated
(e.g., Fig. 3(d)). Thus with eccentric seals pressure
gradients of sufficient magnitude can exist to nest
two-phase zones both axially and circumferentially.

Bearings
“Sa ntike those for a seal the axial pressure
gradients for a bearing are usually small, but the


E-2518

NESTED SUBCRITICAL FLOWS WITHIN SUPERCRITICAL SYSTEMS

R.C. Hendricks
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135

M.J. Braun and R.L. Wheeler III
University of Akron
Akron, Ohio 44325

R.L. Mullen
Case Western Reserve University
Cleveland, Ohio 44106

ABSTRACT

In supercritical systems the design inlet and
outlet pressures are maintained above the thermo-
dynamic critical pressure Pc. Designers rely on
this simple rule of thumb to circumvent problems
associated with a subcritical pressure regime nested
within the supercritical pressure system along with
the uncertainties in heat transfer, fluid mechanics,
and thermophysical property variations. The simple
rule of thumb is adequate in many low-power designs
but is inadequate for high-performance turbomachines
and linear systems, where nested two-phase regions can
exist. Examples for a free-jet expansion with back-
pressure greater than Pc and a rotor (bearing) with
ambient pressure greater than P. illustrate the
existence of subcritical pressuré regimes nested
within supercritical systems.

NOMENCLATURE

c clearance, cm

°

diameter, cm

De density at thermodynamic critical point, g/cm?
i index indicating inlet number

€ eccentricity

6 mass flux, g/s cm@

G- reduced mass flux, 6/G*

G* thermodynamic parameter,
6010 g/s cm for nitrogen

L spacer length, cm
£ aperture (orifice, Borda) length, cm
P pressure, MPa

P, reduced pressure, P/Pc

R radius

g gas constant

S entropy, J/g k

T temperature, K

ry reduced temperature, T/T

Ww mass flow rate, g/sec

Z axial coordinate, cm

Z_ compressibility factor, P/oRgT
cy circumferential coordinate, rad
eo density, g/cm3

n viscosity

® — angular velocity

Subscripts
c thermodynamic critical point
e exit

in inlet

s static

0 stagnation
INTRODUCTION

Many current operational supercritical systems
have been designed on a simple rule of thumb —
maintain the design inlet and outlet pressures well
above the thermodynamic critical pressure Po to
circumvent two-phase flow and other associated
uncertainties in heat transfer, fluid mechanics, and
thermophysical property variations. The simple rule