NASA Technical Reports Server (NTRS) 19910013258: Development of braided rope seals for hypersonic engine applications. Part 2: Flow modeling

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by  NASA Technical Reports Server (NTRS)

NASA Techni:¢_a! Memorandum 104371
AIAA-91-2495 ................
? Development of Braided Rope Seals for
Hypersonic Engine Applications
Part II: Flow Modeling
.............R.a.j.ak.k.annu Mutharasan-- = -_:- -.......... - - _
.............D.re.x.el University
Philadelphia, Pennsylvania
Bruce M, Steinetz
Lewis Research Center
Cleveland, Ohio ....
and
Xiaorn_mg TaD and Frank Ko _ - : .
Drexel University
Philadelphia, Pennsylvania
Prepared for the
• - 27th Joint Pr0pulsion Conference -
sponsored by the A!AA,-SAE, andAS_ ....
_r ......S.a.cramento, California, June24-26, 199i
IXl/ A
N91-2257i
=..(NASA-I:M-I04371) DEVELOPMENT OF BRAIDED
ROP_ SEALS FOR HYPERSONIC ENGINE
APPLICATIONS. PAP,T 2: FLOW MODELING (NASA)
Unclas
13 p . CSCI IIA
0013495

Development of Braided Rope Seals for Hypersonic
Engine Applications Part H: Flow Modeling
By
Rajakkannu Mutharasan
Department of Chemical Engineering
Drexel University
Philadelphia, PA 19104
Bruce M. Steinetz
NASA Lewis Research Center
Cleveland, OH 44135
Xiaoming Tao and Frank Ko
Fibrous Materials Research Center
Drexel University
Philadelphia, PA 19104
NOMENCLATURE
ABSTRACT Cross sectional area of seal
A c -.-
Ay = Yarn cross-sectional area
Df -- Fiber diameter
Two models based on the Kozeny-Carmen gc = Gravitational constant
equation have been developed to analyze the fluid
Mass flow rate of gas
flow through a new class of braided rope seals under M =
development for advanced hypersonic engines. A Mw = Molecular weight of gas
hybrid seal geometry consisting of a braided sleeve Nc = Number of core yarns
and a substantial amount of longitudinal fibers with Ns = Number of sheath yarns
high packing density was selected for development Po = Pressure downstream of seal
based on its low leakage rates. The models _ = Pressure upstream of seal
developed allow prediction of the gas leakage rate Rg = Universal gas constant
as a function of fiber diameter, fiber packing T = Absolute temperature
density, gas properties, and pressure drop across the
seal. The first model treats the seal as a t,tlt2 = Seal dimensions (see Figure 4)
Superficial gas velocity
homogeneous fiber bed. The second model divides u =
Half the clearance between the seal
the seal into two homogeneous fiber beds identified Yo =
and its housing
as the core and the sheath of the seal. Flow
Porosity
resistances of each of the main seal elements are
Shape factor, defined in Equation (4)
combined to find a total flow resistance using the _ =
0 = Braid angle
electrical resistance analog. Comparisons are
Fiber density
made between measured leakage rates collected for Pf =
Gas viscosity
seal structures covering a wide range of braid _ =
Gas density
architectures and model predictions. It has been P =
found that within the experimental range, the second
model provides a satisfactory prediction of the flow
Subscripts:
for many of the cases examined. Areas where future
c Core
model refinements are required have been
e Edge
identified.
sl Seal
s Sheath
1,2...7 Flow paths (see Figure 4)
INTRODUCTION condition, the pressure drop is proportional to flow
velocity u.
In the first part of this series of papers [1], the
relationship between fiber architecture and flow In earlier studies the tortuous pore structure of
resistance was examined by an experimental study. the bed was modeled as a solid bed consisting an
A hybrid geometry consisting of a braiding sleeve assembly of capillaries with circular cross section
and a substantial amount of longitudinal fibers was [3]. The capillary model focused on the spaces or the
recommended. Critical design parameters were pores in the porous solid. The best known equation
identified: fiber diameter, yarn bundle size and proposed based on this approach is the Kozeny-
fiber packing density. The purpose of this paper is to Carman equation [4], which includes permeability
provide means of analyzing the gas flow through a coefficient as a function of porosity. One form of
braided seal and determining quantitatively the this equation is given below as:
relationship between the gas leakage rate and the
pore structure of the seal.
"(Po -Pi)g¢
u- (2)
tit (l-e2)
THEORETICAL 150(_D)2 e3
Definition of Flow Path The shape factor, ¢ is defined as :
As shown in Figure 1, the flow across a seal area of sphere equivalent to particle volume
_b- actual surface area of particle
system can be divided into two categories: (1) flow
through the seal and (2) flow around seal. The flow
in the first path is related to the packing architecture The shape factor, ¢ is unity for a sphere and 0.87 for a
of the seal itself and the flow via the second path is cylinder with its diameter equal to its length. The
dependent on the surface properties of the seal and equivalent diameter of a particle is defined as the
housing. diameter of a sphere having the same volume as the
particle. For a fiber with a diameter Deand length L,
1. Flow through seal the equivalent diameter is
Based on data from a large amount of D = (1.5D2 L) 1/3 (3)
experimental data obtained using a variety of
packing materials, both spherical and granular in and the shape factor is
shape, Ergun [2] derived the following equation:
(LID f)2/a
(4)
_b=(1.5)2_ L/Df + 0.5
-( Po" Pi )g_ (___D)e3 150(1-e)
+1.75 (1)
2
pu t 1-e (_D)pu/_
Hence, (_bD)can be expressed as
L/Df
where P denotes pressure, subscripts i the inlet and o (¢D) 1.5 (5)
= Df 1.2Df+ 0.5
the outlet, u the average velocity of the gas across the
flow area, _ the viscosity of the gas, gc the gravita-
tional constant, t the thickness of the bed and _is the If the ratio L/Dr is very large the term (¢D) will
packed bed porosity. In the above equation, if the approach the value of 1.5De. If direction of flow is
Reynolds number NRe = (_bD)pu/tt(1-e), is small, across the axis of fiber, a situation that occurs in a
then the constant 1.75 on the right side of the equation seal containing substantial amount of longitudinal
can be ignored. In the case of engine seal, the flow is fibers, the length scale, L in the above equation
expected to be laminar as the gas leakage rate and should be expected to be of the same order of
the fiber diameter are small. This implies that magnitude as the diameter of the fiber. The
viscous term dominates in the above equation and parameter (_bD) can be thought of as characteristic
the inertial term is negligible. Under such a dimension, intrinsic to flow through the fibrous seal.
2
The Kozeny-Carman equation predicts where ideal gas behavior is assumed and average
successfullythe pressuredropin packedbedswith gas density is used.
porosityrangingfrom0.3to0.6.Forporousmedia
with higher porositysuchasmostfiber bedsand
textilefabrics,a numberofauthors[forexamplesee 3. Flow resistance
ref. 5]haveshownthat predictedpressuredropis
much greater than experimentally measured Examination of Equation (6) for flow though the
values. In the currentapplication,for determining seal and Equation (9) for flow around the seal
leakagerate of a gasthrough a sealhaving low suggests the definition of flow resistance R as:
porosity, Kozeny-Carman equation is a good
startingpoint. Takingcrosssectionalareaforgas _(p 2. p.2 )
flow asAcandthe seallength asL, Equation(2) R - _ I (I0)
after multipliedbyAcP/Lcanthenberearrangedto M
expressgasleakagerateperunit lengthofsealas: L
The flow resistance, R is a function of properties of
M -(Po2-Pi2) both fluid and seal architecture and, for this
(6)
analysis, is assumed to be independent of the
L- = 300 R_:R TtL I-E)2
pressure difference across it and any compressive
Mwgc Ac £3((_D)2
pressure the seal may be subjected to.
Flow Modeling
where ideal behavior of gas is assumed. The
density of gas, p is based on an average value
In a previous paper [1], critical design
evaluated at the two end-point pressures. That is,
parameters such as fiber packing density and fiber
bundle size were identified through a combination of
(Po +P| )Mw (7) theoretical and experimental studies. It was shown
P = 2R T
that a hybrid geometry consisting of a braiding
g
sleeve and a substantial number of longitudinal
where Rg is the gas constant, Mw is molecular fibers can be employed as the fundamental structure
weight of the gas, T is the absolute temperature. for high temperature flexible fibrous seals. Since
the seal consists of both braids in the sheath and
2. Flow around seal longitudinal fibers in the core, one expects different
porosity values to be applicable in the two regions. In
Edge flow can be treated as a flow between this investigation, two models are proposed to
parallel non-porous surfaces separated by a small quantitatively evaluate the flow resistances. In the
gap. Assuming that the gap between the surfaces can first, we will consider the entire seal to have one
be considered constant equal to 2yo ,one can relate constant porosity value, while in the second model
the pressure difference across the seal to the gas we will treat the core and the sheath to have two
leakage velocity as [6] separate porosity values.
1. Model I
g_o
In the first model, the seal is assumed to be a
homogeneous fiber bed having a uniform constant
porosity regardless of the core and sheath structures.
Rearranging the above in the form of Equation (6)
Thus, only one value of porosity is used to calculate
gives
the flow resistance. As shown in Figure 2, the gas
leakage rate can be expressed as the sum of the
M _(p2.p2o i ) leakages through the seal and around the seal and is
(9)
given by
L -
M_gc Yo
3
various flow paths illustrated in Figure 4, are given
M Me Msl (Pi 2-Po 2)
(11) as:
L-L+L - R
where subscripts, sl and e refer to the seal and edge RZ =9K_3° (17)
respectively. The individual leakages are given by
t (1-_s)2
Me ( Pi2- Po2)
(12) R2 =R6 =300 K t2 £3(¢D)2 (18)
L - R_
t2 (1-£)2
M_I ( p 2. p 2)
i o (13) 1_ =R5 =300 K_ £s3(¢D)_ (19)
L - R61
The flow resistances of encountered in the flow path (1-Ec)2
through the seal is determined from Equation (6) R4 =300 K £3(_bD)2 (20)
and is given as:
R345 =R3 + R4 +R5 (21)
R 300 tt RgT t L (1-£) 2
(14) t
1= Mw g¢Ac e3(¢D)2
--3K o (22)
The edge flow consists of two parallel paths as shown
in Figure 2 and the flow resistance of each of these _ ttR3
two paths may be summed in parallel as where K=_--. The flowresistanceofthesealcan
be determined by summing the flowresistancesin
Rel Re2 (15) parallel,given as:
Re= Re1+Re2
with
1 1 1 1
R8 - R2 + R34s + R6 (23)
Rez =9 taRT t pRT t
Mwg ¢ y3o and R_=3 M gc y3o
Flow resistance of edge flow is:
where Rel is three times Re2because of the longer
path length, see Figure 2. Since the edge flow and (24)
flow through the seal occur in parallel, the overall
flow resistance of the seal system is therefore given
by The total flow resistance of the seal system is then
given by:
ReRs!
R= (16) RR
Re+R l
R= e _ (25)
Re+R_
2. Model H Calculation Basis
The second model, illustrated in Figure 3, deals One of the important parameters in determining
with a composite seal in which the sheath and core flow resistance through the seal is the characteristic
are allowed to have independent porosity values. dimension, D. Considering that the bulk of the seal
The seal has a sheath and a core with porosities es is made up of longitudinal fibers and that the
and £c, respectively. Flow resistances along the number of fiber-fiber interfaces is significantly
larger than the number of yarn-yarn interfaces, the
4
characteristic dimensionwas taken as the fiber
through H1 and their architectural parameters,
diameter,D_ Thecharacteristicdimension,(_D), braiding angle, number of longitudinal yarns and
takesonvaluesbetween1.5Deand0.75Drwhenthe number of braiding yarns, are summarized in
Table 1. Specimens G1 and H1 have the highest
ratio L/Dr is takentobelargeor 0.5, respectively.
number of longitudinal yarns while A1, B1 and C1
Thelatter valuegivesbetterfit with experimental
have the lowest longitudinal yarns.
data under a variety of situations investigated.
Therefore,all calculationspresentedin this paper
arebasedontheshapefactorvalueof0.75.It should
Flow Measurement
benotedthatthebetterfit ofexperimentadlatawith
(¢D)=0.75Dr is indicative of the fact that the
The experimental details of the flow
dominant gas flow path is across the fiber bundle measurement were described in an earlier paper by
rather than along the fiber bundle. the authors [1]. Seal specimens one foot in length
were mounted in a specially developed test fixture
Another characteristic dimension is the
and were leak tested under room temperature at
distance, Yo in calculating seal edge leakage. In the various inlet pressure conditions in the range of 5 to
present calculation, the clearance was assumed to be 60 psig. The pressure upstream of the seal was
proportional to fiber diameter. Specifically Yo is varied and the resulting leakage of gas (either air or
assumed to be 0.1 (¢D). helium) was measured. Lateral preloads were
applied uniformly to the back of the seal with an
inflatable rubber diaphragm at either 80 or 130 psig.
The cross section area of a yarn A (in 2) can be
The flow resistance of the seal was computed from
determined from its denier (grams per 9000 meters
the ratio of the difference of the squares of absolute
of fiber) and fiber density p (g/cm 3) as follows:
pressures over the mass leakage rate.
yarn denier
(26)
Ay = 5.8xl0_pf Porosity measurement
1. Sample preparation
The following are the parameters used for
calculation of various flow properties. An ultra-low viscosity embedding media
(purchased from Polysciences Inc., Warrington,
PA) was used as a rigidizing medium. The
3 denier=- 812 g/9000 m components were combined gravimetrically into an
p$ =2.54 g/cm
oven-dry beaker with a magnetic stirrer for 1-2
minutes at low speed. The components used are:
T =528 OR
Rg =1.545 x 103lb-flJ°R
Epoxy resin VCD (Vinyl Cyclohexane Dioxide) 0.5 part
Dr= 10 microns gc =32.1 lbmft/lb r sec2 Harck.ner N- Octenyl Succinic Anhydride 1.0part
Modifier 1,4-Butanediol Diglycidyl Ether 0.075 part
Catalyst DMAE(Dimethylaminoethanol) 1.0%Vol.
Mw(air) =29 lbm/lb mole Mw(He) = 4 ]bm]lb mole
After a graded series of alcohol changes
(¢D) =0.75 Dr yo=0.1 (¢D) (approximately 5 minutes each) and several 10-
minute change of 100% alcohol, the specimen was
I_of air =0.0175 cP _ofHe =0.019 cP infiltrated for 10 minutes in a 1:1 resin/100%
alcohol mix. Final infiltration consisted of 100%
embedding media for 15 minutes. Polymerization
EXPERIMENTAL
was accomplished at 70°C for 12 hours. The
specimen then was cut by a diamond saw and put
Braided Seals Specimens
into polyethylene moulding capsules containing
Lecoset 7000 cold curing resin. Curing took place at
Eight seal specimens were made using 812
room temperature for about 10 minutes. After
denier E-glass fibers (Owens Coming Glass,
demoulding, the specimen surface was polished and
Granville, Ohio). The specimens were labeled A1
5
scanning electron micrographs were taken to Flow Resistances for Different Gases
determine the dimension of the seal cross section
and packing geometry of fibers. Because of the many environments the seals are
expected to operate in, it is important to be able to
2. Determination of porosity predict the resistance to flow for various potential
coolant or leakage gases. Shown in Figure 6 is the
Porosity of the seal for calculating flow measured resistances of helium plotted against the
resistances described earlier was obtained from the resistance of air for a wide range of seal
geometry of fiber layout and is given by: architectures (specimens A1 to H1), pressure drop
conditions ( between 5 to 60 psig), and preload
A(Nc+Ns/cose) conditions (80 psig and 130 psig) investigated. If the
£--1-
t2 (27) seal's pore structure is constant, flow resistance is
directly proportional to viscosity and inversely
proportional to molecular weight of the flowing gas
where Nc and NBare the number of core and sheath
(see for example Equation 6). Hence, when we
yarns and t2 is the cross sectional area of the
compare the flow resistance of helium to that of air
installed seal and 0 is the sheath braiding angle.
in Figure 6, we expect the slope of the straight line to
Note that the seal is treated as a homogeneous fiber
be :: :
bed having a single average porosity value for
Model I.
SLOPE- (_Mw)Helium (30)
The porosity of the core and sheath sections of the (_/Mw)Ai r
specimens for Model II were determined from the
following two equations: The straight line indicated in Figure 6 is the
theoretical line with a slope of 7.87 obtained using
Equation (30). Data in Figure 6 show good
(28) agreement between the measured and the theoretical
predictions. It is important to note that for the same
seal architecture and the same pressure drop across
ANs/cose the seal the helium leakage rate is only one-eighth of
es = 1- 2 2 (29)
the air leakage rate.
t - t1
Comparison of Measured and Predicted Leakage
where t and t1are the overall width of the installed
Rates
seal, and the width of the core region, respectively
(see Figure 4).
The measured and predicted leakage rates for
two widely different seal architectures are shown in
Figures 7 and 8. Key braiding and geometry
RESULTS AND DISCUSSION
parameters of these two seal structures denoted A1
and G1 are listed in Table 1. Comparing the overall
Pressure Drop Correlations
leakage rates between specimen Al and Gl one finds
that the leakage rates for G1 are considerably less
In Figure 5, typical air leakage rates measured
than Al. Specimen G1 meets the tentative leakage
are plotted as a function of difference of the squares
limit of 0.004 lb/sec/ft [7] for air pressure
of the pressure across the seal for specimens F1 and
differentials up to -51 psi with a preload of 80 psig.
G1 at preload pressures of 80 and 130 psig. The
Specimen A1 meets the leakage limit for pressure
linear relationship between the two variables is
differentials only up to 30 psi. Measured and
indicative of the validity of the pressure dependency
predicted leakage rates for specimen A1 are shown
presented earlier in Equation (10). Although only
in Figure 7 for applied pressure differentials up to 60
two sample results are shown in Figure 5, all eight
psi for both air and helium test gases. Also shown in
specimens examined in this investigation showed
the figure are the effects of lateral preload on seal
excellent correlation with correlation coefficient
leakage. Lateral preloads of 80 and 130 psig were
lying in the range of 0.97 to 1.00. The slope of the
applied to the back of seal with a diaphragm
line in Figure 5 is equal to the inverse of flow
resistance, 1/R.
6
compressing the seal against the adjacent sidewall the porosity dependence on preload. As the backside
[see ref. 1]. preload is increased the fibers are urged closer to
one another making it more difficult for the air to
In general the more detailed model (Model II) flow around the fibers, thus increasing the
that treats the seal as a composite sheath-core resistance to flow. Neither of the models considered
structure provides a conservative leakage estimate in this paper account for this porosity-load
that agrees reasonably well with the measured data dependence since it was deemed beyond the scope of
over the full pressure range for both air and helium the immediate study. A more detailed model that
test gases. will include porosity as a function of seal preload is
presently under development.
Measured and predicted leakage rates for the
lower permeability seal G1 are shown in Figure 8 for
air and helium and for the two preload pressures SUMMARY AND CONCLUSIONS
mentioned above.
For this lower leakage seal structure both models Two analytical models have been developed for
predict higher leakage rates than the measured predicting leakage rates of braided rope seals being
values. Agreement between the measured and developed for panels of advanced hypersonic
predicted is better for the lighter 80 psig preload than engines. Both models are based on the Kozeny-
for the 130 psig preload. Carmen relations for flow through porous media,
where the characteristic size dimension is a scaled
In examining Figures 7(a) and 8(a), the fiber diameter (e.g. 0.75 Df ) based on experimental
versatility of Model II in predicting actual leakage observations. The first model treats the seal as a
rates is demonstrated. At a pressure differential of homogeneous fiber bed having a single average
40 psi the discrepancy between the measured and value for its porosity.
predicted leakage rates were only between 20 to 30
percent even though the overall leakage rates The second model treats the two-dimensional
differed by a factor of 2.50. braided seal structures as a system of flow
resistances analogous to a series of resistors in an
In all the cases, the fiber diameter was used as electrical network. For the purposes of this model
the basis of calculation. However, if yarn diameter development, resistance is defined as the ratio of the
is used as the equivalent diameter, the prediction of difference in the squares of the upstream and
the gas leakage rate is very poor as it differs from downstream pressure (e.g. the flow potential) to the
experimental observation by more than four orders mass flow per unit seal length (e.g. the current).
of magnitude. This approach allows the fundamental
inhomogeneity of the seal's core and sheath to be
Potential Sources of Modeling Discrepancy characterized. These resistances are added as in an
electrical network (e.g. resistances in series add;
Effect of shape factor resistances in parallel add by their inverses) to
form an equivalent seal resistance. Each of these
The choice of shape factor _ has a considerable resistances are made up of the product of four terms:
effect on the predicted leakage rates. For example, the first term captures the properties of the gas (e.g.
since in Equation (6) the term containing (¢D) is viscosity, gas constant, temperature and molecular
squared, reducing it from 0.75 to 0.70 reduces the weight); the second term is a ratio of the length-to-
predicted leakage by 13%. Selection of the shape thickness of that piece of seal; a term containing the
factor _ is based on experimental observations and reciprocal of (0.75 Dr)2; and a term containing a
..2
therefore some variation between widely differing
porosity factor (e.g. (-_). The porosity for the core
braids is expected. ,
£
and sheath are determined using image analyses of
epoxy-fixed seal test coupons.
Dependence of Porosity on Preload
For modeling purposes, the sheath is divided into
Another potential cause of the discrepancy
four regions of resistance depending upon the
between the measured and predicted leakage rates is
7
sheath'sbeing parallel or perpendicular to flow architectures. Agreement within 20-30% was
direction. The resistance of the core is modelled by observed for seal specimens A] and G1 whose overall
its own resistance that is markedly different from leakage rates differed by a factor of almost 2.5
those of the sheath. Surface flows between the nose of
the seal and the adjacent splitter wall and between 2. Theoretical predictions confirmed with
the top of the seal and the adjacent seal channel experimental observations for air and helium
walls are also included in the model. Adding the indicate that relative resistance to leakage flow
resistances together according to their electrical depends on the ratio of the quotients of each gas's
analog characterizes the seal for leakage viscosity and molecular weight.
predictions.
Comparisons are made between measured ACKNOWLEDGEMENT
leakage rates collected for seal structures covering a
wide range of braid architectures, and predictions The authors wish to thank Ms. Susan Marr for
made using the two models. Room temperature making most of the specimens and carrying out the
leakage measurements were collected as a function flow measurement. The financial sponsorship of
of: pressure drop applied across the seal (venting to this project from NASA is gratefully acknowledged.
atmospheric condition); backside seal preload; and
test gas (e.g. air and helium). Generally, the more
detailed flow model (Model II) is preferred since it REFERENCES
captures the significant porosity differences between
the seal's core and sheath. For modest and heavy 1. Ko, F., Steinetz, B.M., Mutharasan, R.,
preloads (e.g. 80 and 130 psi), the second model "Development of Improved Hypersonic Engine
favorably predicts the leakage flow rates for the Braided Rope Seals Part I: Design Concept and
relatively high permeability braided seal, Al. Experimental Observations," To be published as a
NASA TM.
Similar agreement between measured and
predicted leakage was observed for the low 2. Ergun, S.: "Fluid Flow Through Packed
permeability braided seal (Gl) sealing air with 80 Columns," Chemical Engineering Progress, Vol.
psig preload. Reasonable agreement between 48, No. 2, Feb. 1952, pp.89-94.
measured and predicted leakage was observed for
G1 sealing helium gas. However for the 130 psi 3. White, F. M.: Viscous Fluid Flow. McGraw Hill
preload, Model II over-predicted the measured air Book Company, New York, 1974.
leakage by as much as 100%. Model refinements in-
progress are aimed at minimizing the noted 4. Scheidegger, A. E., "The Physics of Flow
discrepancies and accounting for the effects of seal Through Porous Media," revised ed., University of
preload on seal permeability. Toronto Press, Toronto, 1960.
It is noted however, that these predictions are 5. Van Den Brekel, L.D.M. and De Jong, E.J.:
substantially closer to the measured values than Hydrodynamics in Packed Textile Beds, Textile
those obtained with the unmodified, homogeneous- Research Journal. Vol.59, no. 8, Aug, 1989, pp. 433-
porous-media predictions of the Kozeny-Carmen 440.
relations. These relations underestimate seal
leakage rates by more than several orders of 6. Bennett, C.O. and Myers, J.E: Momentum. Heat
magnitude. and Mass Transfer, Third edition, McGraw-Hill
Book Company, New York, 1982.
Based on these findings, the following results were
obtained: 7. Steinetz, B.M., DellaCorte, C. and Sirocky, P.J.,
"On the Development of Hypersonic Engine Seals,"
1. Leakage rates predicted using Model II agree NASA TP-2854, 1988.
favorably to the measured leakage rates for modest
preloads for a wide range of braided seal
8