ML20027E824

To Mark I Vacuum Breaker Improved Valve Dynamic Model - Model Development & Validation

ML20027E824
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Site:	Fermi
Issue date:	09/30/1982
From:	Sullivan J CONTINUUM DYNAMICS, INC.
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82-31, NUDOCS 8211160216
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C.D.I. TECH NOTE 82-31 I

l MARK I VACUUM BREAKER IMPROVED VALVE DYNAMIC MODEL - MODEL DEVELOPMENT AND VALIDATION Revision 0 Prepared by CONTINUUM DYNAMICS, INC.

for GENERAL ELECTRIC COMPANY September 1982 Oyj6 hhdsan 0

09 4

PDR L

q V-C.D.I. TECH NOTE 82-31 MARK I VACUUM BREAKER IMPROVED VALVE DYNAMIC MODEL - MODEL DEVELOPMENT AND VALI.DATION Revision 0 Prepared by John M. Sullivan CONTINUUM DYNAMICS, INC.

P.O. BOX 3073 PRINCETON, NEW JERSEY 08540 Prepared Under Purchase Order No. 205-XJ102 For THE GENERAL ELECTRIC COMPANY 175 CURTNER AVENUE SAN JOSE, CALIFORNIA 95125 Approved by A

_(

A~t (

/

h Alan J. Bilanin August, 1982

l DISCLAIMER OF RESPONSIBILITY Neither the General Electric Company nor any of t,he contributors to this document makes any warranty or representation (express or implied) with respect to the accuracy, completeness, or usefulness of the information contained in this document or that the use of such information may not infringe privately owned rights; nor do they assume any responsibility for liability or damage of any kind which may result from the use of any of the information contained in this document.

i

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9 CONTENTS Section M

Stannary iv 1

Introduction 1.1 2

Valve Model - Analysis 2.1 3

Valve Model - Verificati;n 3.1 4

References 4.1 l

l t

I v

i au

ILLUSTRATIONS Figure

Page, 1

Schanatic of a vacuum breaker valve.

1.2 2

Measured ring header pressure during run S-DA 1.4 with linear trend removed. Submergence head removed.

3 Comparison of experimental and predicted closing 1.10 disk impact velocities for run S-DA.

Hydrodynamic torque computed from Eq. (1.1).

4 Single valve model geometry.

2.3 5

Schematic of fluid flow field in the vicinity 2.4 of the valve disk.

6 Measured vacuum breaker disk angle during run S-DA 3.2 7

Comparison of experimental and predicted closing 3.7 impact velocities for run S-DA 8

Predicted vacuum breaker disk angle for run S-DA 3.8 (using model with flow effacts f = 2.25) 9 Comparison of experimental and predicted closing 3.13 impact velocities for run S-DA.

1 11

TABI.ES Table g

1 GPE 18" Internal Valve Characteristics 1.9 2

CPE Valve Response to S-DA Measured Pressure Signal 3.14 iii l

SUMMARY

Earlier studies of Mark I vacuum breaker dynamics to determine valve impact velocities used an overly conservative analytic valve model. Com-parison of its predictions with measured valve position from FSTF run S-DA showed that valve velocities were overpredicted ' y 150%. This report des-b cribes the development of a new valve dynamic model which computes the spatial harmonics of the pressure field around the vacuum breaker to determine the flow past the valve. This allows the pressure reduction, due to dynamic effects, to be calculated. A parameter study was undertaken to fix the value of a model parameter by comparisons against experimental data. The adjusted model is shown to provide accurate, but still conservative, estimates of valve impact velocities.

iv

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I 1

t

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r NOMENCLATURE i

a chamber radius A

disk area c

speed of sound I

f model parameter adjusting strength of Bernoulli torque term H(A) height of gap around valve disk 1

angular moment of inertia of valve disk J

Bessel function of order n L

disk pressure moment ann D

L system gravitational moment arm g

mg system weight p(t) pressure field around valve disk P (w) frequency components (Fourier transform) of p P,

coefficient of nmth spatial harmonic of P e efficients of left and right travelling one-dimensional 00 ' 00 pressure waves respectively q

fluid speed on upstream and downstream sides of valve disk Q(e,t) flow past valve (fluid volume per unit time per unit distance in 6 direction)

(r,9,z) right-handed cylindrical coordinate system based at center of closed valve disk t

time v

axial fluid velocity axial fluid velocity due to flow around the valve disk vg x

pressure reduction factor to account for upstream dynamic pressure 8

valve coefficient of restitution 6,,

value of the argument at the mth positive zero of J'

op(t)

Pressure difference across the valve l

v aw w

WZ NTe AMA

e

'}

l f

A valve disk opening angle measured from the closed position t

opening an8 e measured from the closed position 1

A, ma.._.

A angle between valve center of mass and vertical with valve g

in the closed position p

fluid density 0,

orifice ceafficients for positive and negative flow T

Berneulli torque reduction term B

T t tal hydrodynamic torque H

w circular or angular frequency of pressure signal components vi Jo l

R 1

• h

?

i

.,I j

1.

INIRODUCTION I

1 During the Mark I Full Scale Test Facility (FSTF) containment loads i

program, a GPE wetwell to drywell vacuum breaker was observed to cycle.1 j

In order to assess the structural adequacy of wetwell to drywell vacuum breakers under these cycling conditions, it is necessary to determine the cycling velocities of the valve disk, particularly when and if the valve disk strikes the full open stop or seat. These impact velocities art then either used by a structural analyst to assess the resulting stresses or may

'a be used to define a test program from which the stresses may be measured directly.

In an earlier study, the dynamics of a wetwell to drywell vacuum breaker j

was simulated by assuming that the hydrodynamic torque T about the valve H

i shaft which results as a consequence of a differential pressure t.p across the valve disk'was given by

=gAapcos(7j g A (1.1)

TH max where I is the distance from the shaf t to the center of the valve disk g

of area A (see Fig. 1).

The cosine factor was introduced as an approximate reduction of the hydrodynamic torque with valve opening angle A.

Assuming i

that Sp(t) is prescribed say from measured test data, the valve motion is estimated by integrating I dA*L mg sin (A + A )

- T (1.2) 2 G

g H

de 1.1

T

• }

t M

C L

[~

p I +

c s g ~.G.

^G l

..ain vent or Wetwell side l

header side g

i I

I I

I Figure 1.

Schematic of a vacuum breaker valve.

1.2 a

subject to the conditions that at i

A - A,. h

-Sh A-0 or (1.3)

The constant 8 is a coefficient of restitution and fixes the fraction of kinetic energy lost during impact.

i I

During FSTF run S-DA, a GPE vacuum breaker mounted on the ring header was instrumented such that valve displacement and pressure differential across the valve disk were recorded as a function of time. This test (S-DA) per-mitted a comparison to be made between predictions of valve displacement / velocity and actual measured displacement / velocity. Predictions were made by specifying the measured differential pressure across the valve (shown in Figure 2) and integrating in Eq. (1.2) with the valve geometric and inertial parameters speci-fied in Table 1.

The result of this comparison is summarized in Figure 3 where measured closing impact velocities are compared to predicted impact velocities.

}

(No impacts of the valve displacement with the full open stop were observed or predicted.)

The scatter plots in Figure 3 and later figures were generated by consider-ing the 28 chugs in run S-DA, during which all significant valve actuation took place. These chugs were distributed through 50 seconds of the S-DA run. During many of these chugs, there were a number of seat impacts, because the valve I

bounced.

In such cases, the maxistan impac"t velocity was used. Thus, each symbol on the scatter plot graphs the maximum predicted impact velocity during a parti-cular chug against the maximum experimental impact velocity for the same chug.

The particular geometric symbol used for a given point shcas which 10 second time 1.3

S-DA MEASURED RING HEADER PRESSURE 3

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TABLE 1 GPE 18" Internal Valve Characteristics GPE 18" INTERNAL 2

I, system moment of inertia (1b-in-s )

20.38 Lg, system moment arm (in) 10.71 Lp, disk pressure moment arm (in) 11.47 m, system mass (1b) 50.9 A, disk area (in )

375.82 Ag, rest angle (rad) 0.0 A,,x, maximum opening angle (rad) 1.32 8, coefficient of restitution (seat and body) 0.6 4

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l Figure 3.

Comparison of experimental and predicted closing disk impact velocitics for run S-DA.

Hydrodynamic torque computed from Eq. (1.1) 1.10 A

9 period of run S-DA the corresponding impact was within, as indicated in the plot label.

(No correlation between impact velocities and run time was observed.)

It should be noted that the experimental velocities used were derived from measured digitized time history of valve position by a two peint nethod

- A +1)

A + - (A (1.4) n at which provides a considerably more constzw tiva suu piu'ua'uly sl:o more accurate estimate of impact velocities than a three-point parabolic fit method would.

As can be seen, the predicted impact velocities were greater than the expertnental impact velocities by an average factor of more than 2. For this reason, an analytic effort described below was initiated to develop a valve dynamic model which would more realistically estimate actuation velo-cities of vacuum breaker disks under transient loading conditions.

1.11 l

2.

VALVE MODEL - ANALYSIS-The very conservative prediction of valve actuation velocities results 6

from the f act that flow across the valve disk reduces the hydrodynami:

torque generated on the disk to less than that estimated from Eq. (1.1).

In order to more appropriately account for this reduction of hydrodyna=ic torque resulting from flow through the valve it is proposed to estimate the actual pressure distribution on the valve disk by analytically computing the fluid velocity distribution about the valve disk and then estimating the corresponding pressure and int (.jrarfr: this pra==nra ever th. valve stea to compute hydrodynamic torque. The analysis will be to compute the hydrodynamic torque T such that H

p( ) - T TH" D

B

(*

The quantity L Aap(t) is the estimate of hydrodynamic torque which results D

when no credit is taken for the reduction of static pressure across the valve disk as a consequence of flow. The quantity T is the torque reduction B

which results as a consequence of flow through the valve and will be estimated from an analysis which assumes that the valve disk undergoes small displacements.

For this reason, a factor f is introduced which will be fixed by comparison of the model predictions against data.

In the function T the subscript B denotes Bernoulli since the 3

reduction of torque results primarily from a reduction of the static pressure by dynamic pressure. This result is a consequence of the fact that although the valve disk may be in motion, the fluid flow field is approximately quasi-l steady.

It may be shown that the reduced frequency for the valve motion l

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considered here is indeed small and hence fluid acceleration effects may be neglected. Therefore, the Bernoulli torque is given by 2

2 B"

(9+ ~ 9-)(a - r c s 6)rdrds (2.2)

T r<a 2

2 where q,

and q,

are the fluid velocity squared on the upstream and downstream sida of the valve disk (as shown in Figure 4) respectively.

2 The task now is to estimate

q.. This is accomplished by noting that the fluid is nearly incompressible and hence the pressure field 2

satisfies 7p=0.

General solutions to this equation are found up-stream and downstream of.the valve disk with the boundary condition at the valve disk that the fluid velocity v along the valve axis is w=

(a - r cos 0) + v (2.3) g where wg is the flow velocity through the valve shown in Figure 4 The flow velocity through the valve is estimated from 2 c.H(A)f ~2 l0pl Q(0.t) =

(2.4) where Q is the volumetric leakage flow per unit circtanferential length areund the valve body and H(A) is the height of the annular flow

~*

2 area with the valve open. The factor a is an orifice coefficient and is left as model parameter. o has been taken to be 1.0 for positive flow and 0.6 for negative flow. The x factor is used to account for the reduction I

of upstream pressure due to nonnegligible upstream flow velocity at large 2.2 6

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2.3 m

VALVE MOTION:

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CIRCUMFERENTIAL LINE SOURCE / SINK NORMAL VELOCITY DTSTRIBUIION Figure S.

Schematic of fluid flow field in the vicinity of the valve disk.

2.4

valve opening angles. This factor may be shown to be equal to 2

f-x=

1-(2.5)

The volunetric flow through the valve Q is related to v by f

distributing the flow as an annular source as sketched in Figure 5. The flow field at the valve disk is related to the pressure field by

-w-f-(2.6) where the general solution for pressure is

=

=

P (w) = P O

c s nG 00*

00*

n nm

,,, y

-S,z/a gg P e e

(2.7) for one frequency component. With the orifice coefficients fixed the above model has one free modeling constant, f.

This constant is deter-mined by comparison against full scale test data.

+,

2.5

3.

VAI.VE MODEL - VERIFICATION As discussed in the Introduction, FSTF run S-DA was instrtsnented to obtain valve displacement data as well as to measure the differential pres-sure across the valve disk. By driving the valve dynamic model with the measured differential pressure across the valve, predictions of valve dis-placacient versus time are made and compared against measured data. Referring back to Firure 2, the pressure measured in the ring header curing FSTF run S-DA is shown over a 50 second interval during which strong pressure oscil-lations were observed. The mean has been removed from this data. The measured valve displacement over this time interval is shown in Figure 6 where a maximum valve displacement of 18* is observed to occur at time 19.5 seconds.

The valve model impact velocity predictions with f=1 are compared with measured data in Figure 7.

As can be ssen, the predicted impacts are still very conservative with regard to measured closing impact data. To reduce this conservatism further, a parameter study was undertaken and it was determined that with f = 2.25 predicted valve impact velocities would still bound all test impact data with approximately a 12% margin. The predicted valve displacement versus time is shown in Figure 8.

These pre-I dictions may be compared to the measured displacements shown in Figure 6 from which it will be seen that the comparisons are very favorable.

In Figure 9 is shown the predicted and measured closing inpact velocities which illustrate that conservatism in the analytic valve dynamic model has been minimized. Lastly, in Table 2 the results of model i.omparisons with data are summarized. It should be noted that this valve dynamic model with 3.1

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S-DA, f = 2.25,

impact velocities for run adjusted model with minimized conservatism.

3.13

i o.

^

TABLE 2 GPE Valve Response to S-DA Measured Pressure Signal Maxim a Seat Naber of Maximum Impact Velocity Impacts above Open (rad /sec)

-7.5 rad /sec (rad)

Original Model (f = 1.00)

-14.35 25 0.73 Adjusted Model (f = 2.25)

-9.31 8

0.42 GPE Measured Impact Velocities

-8.06 2

0.34 l

l 1

3.14

f = 2.25 over predicts the maxiassa observed closing impact velocities by approximately 12%.

It is concluded that the valve dynamic model results in realistic yet conservative predictions of valve actuation velocities and is there-fore appropriate for the analysis and/or qualification of Mark I wetwell to drywell vacuum breakers.

1 l

l 1

l 3.15 l

4.

REFERENCES 1.

" Mark I Containment Program; Full Scale Test Program; Final Report,"

l NEDE-24539-P, Class III, General Electric Ccxspany, April 1979.

I l

l l

4 e

4.1 t

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a t

CO NTIN U U M DYN AMICS, INC.

P.O. Box 3073, Princeton, NJ 08540

-