ML19284A739
| ML19284A739 | |
| Person / Time | |
|---|---|
| Site: | Susquehanna  |
| Issue date: | 03/29/1972 |
| From: | Schall, Weisshaupl PENNSYLVANIA POWER & LIGHT CO. |
| To: | |
| Shared Package | |
| ML17138A531 | List: |
| References | |
| 2208, NUDOCS 7903150315 | |
| Download: ML19284A739 (31) | |
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S O U R C:5 : AEG-TELEFUi1KEil REPORT No. 2208 8e 29 MARCH 1972 sh g;
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PROPRIETARY INFORMATION This document has been made NON-PROPRIETARY by the deletion of that information which was classified as PROPRIETARY by KRAFTWERK UNION AG (KWU).
The PROPRIETARY information deletions are so noted throughout the report where indicated by a) Use of the term KRAFTWERK UNION AG PROPRIETARY INFORMATION.
b) Use of blocked out areas by cross hatch bands in the report text and figures / tables, e.g.
i) ...." with a mass flow density ofBi% W K;'n2s...";
ii) _
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Ffm., 29 March 1972 AEG-TELEFUNKEN Dr. Wei/ru Report No. 2208 NUCLEAR REACTORS E 3/E 2-SI CALCUIATION MODEL TO CLARITY THE PRESSURE OSCILLATIONS IN THE a SUPPRESSION CHAMBER AFTER "ENT CLEARING u
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Dr. Weissh5upl/Schall E3/E 2 353IPrepared: /s/
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Dr. Koch, E 3/E 2-SI ggyoggChecked:
Kasper, E 312 Classified: /s/
Class II 2-1
Distribution list:
E 3/ v 4.Ew (22 x)
E3 E 3A*
I 3/E E 3/R E 3A'4 E 3 A'3 E 3A' 1 E SA't E 3/E 2 E3 /E 2-SI (3 x)
E 3/E 1 E 3/R 1 E 3/R 1.AB E 3/R 1. ABS E 3/R 1-ABB E 3/R 1 E 3/E 3 Eg/E3vsr iblio[hek TT-F e
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NONLIABILITY CLAUSE This report is based on the latest state of science and technology as achievable by our best efforts. It makes use of the knowledge and experience of AEG-TELYTJNKEN.
However, AEG-TELETUNKEN and all persons acting in its behalf make no guarantee. In particular, they are not liable for the correct-ness, accuracy and co=pletaness of the data contained in this report nor for the observance of third party rights. ,
AEG-Tr'frUNTIN reserves all rights to the technical information
~
contained in this report, partiedarly the right to apply for patents.
Further dissocination of this report and of the knowledge contained therein requires the written approval of AEG 'tEIZTUNKEN. Moreover, thi.s report is c-ainated under the assumption that it will be banM1ed confidentially.
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Table of contents Page
- 1. Introduction 2-6
- 2. Oscillation of the air bubble - water mass syste:a 2-E 2.1 Equation of motion 2-8 2.2 Performance of the nurserical calculation 2-11 2.2.1 Data 2-11 2.2.2 Paraneter calculation 2-12 2-14
- 3. Discussion
- 4. Conclusion 2-16 Figures 2-18 9 @
2-4
su:=arv To explain the periodic pressure variations observed in KW Andarneath the relief pipe of the suppression chamber and in GwH in the scran tank, a physical model is set up. This model consists of the assumption that during the vent clearing process in the relief pipe the air cushion situated between the outflowing strim and the water slug is highly compressed and, when it emerges fra the pipe, begins to expand suddenly because of its over-pressure. It is then compressed again by the pressure of the water mass loading it frcxs above, etc. , thereby creating an oscillation process.
The excellent qualitative and quantitative agreement between the theoretical and experimental pressure variations allows us to concluda that the observed periodic pressure fluctuations can be described by ths assumed physical model of the oscillation of the system consisting of air bubble and water aass loading it from above.
~
2-5
- 1. Introduction Before the steam " braid" is produced during clearing through tha relief pipe, the water slug situated in the pipe is first expelled, forming a highly compressed air cushion between the water slug and the af terflowing steam. When that air cushion amerges from the pipe, it begins to expand again suddenly in order to come into equilibrium with the surrounding pressure (which is composed of the pressure in the suppression chamber and the hydrostatic pressure).
The suppr4ssion chamber water mass loaded by the emerging air cushion li, driven upward until the influence of the gravitational force and of the unde.. pressure forming in the air bubble as time passes (which is produced by the continued upward movement of the water resulting from the mechanical inertia principle) leads to a revarsal of the process and the air but'.'.e is compressed again by downward sotion of the water mass. That is followed by renewed expansion, etc., etc. The air bubble - water mass system undar consideration thus represents an oscillatory system whose oscillation persists until the air bubble has risen to the water's surface and breaks there or until the oscillstion amplitude becomes negligibly sc.all due to strong damping and lateral outflow of the water that is thrown upward. -
In the following we now set up a highly simplified model of this oscillation process and compare the results obtaaned frcan it with 2-6
the periodic pressure variations observed experimentally in KW and in GMI [1].
[1] Rupp, Eismar, Pohl: KW - Pasults of the relief valve tests with the special instrumentation. AEG-E3-1160 2-7
Oscillation of the air bubble - water mass syste.,
2.1 h tion,gf, mom on To calculate the oscillatory behavior of the air bubble and the water mass loading it from above, we make the following highly simplified assumptions:
a) Af ter emerging from the relief pipe, the air bubble has the shape of a flat-cylinder (see Figure below).
Pk Pn I J pg = pressure in 3 ,
g r suppression chamber lt o unter 'p i, hine s LaQAir P Y, T Matar blup*
b) The air bubble does not rise to the surf ace of the water during the oscillation process (the influence of this process is taken into consideration by a parametrization of the air bubble's subnargence).
c) The air bubble expands only in the vertical direction (assuming a flat cylinder, the horizontal espansion is approximately negligible relative to the vertical expansion). _.
d) The water mass lying above the bubble does not change its shape during the oscillation process (thus, no water flows 2-8
sway Jaterally during the lift, and no water flows in frers the side during the drop).
From the center-of-uss theoreri we obtain the equation of motion of the water mass:
(1) m x" - - m g + (p pa) F ,
The acceleration of the water mass m is maintained by gravitation, the pressure p of the air bubble on the water mass a'.rve it, and the su;pressicn cha=ber pressure p.
g x is the coordinate of the center of mass of the water mass, F is the boundary surface area between the air bubble and water mass.
Since the oscillation proceeds rapidly enough, we can assume an aM ahatic change of state of the gas. Therefore, the relation between the instantaneous state (p, V, T) and the initial state (p,, V,, T,) which prevails immediately after the expulsion of the air- bubble fren the relief pipe reads:
~
p V * , p, . \t,
- For air, c = M The change of the gas volume from V, to V corresponds exactly to the lift of the water mass. Thus:
~
(3)
V = V, +F.x, from which we obtain for the pressure from Eq. (2):
2-9
P.
y)* (4)
P " (4 +
If we now express the state variable V, in terms of the state variables p,, V, for the initial state of the quantity of air which is present before the beginning of the vent clearing process:
(5)
Pr V * = p, V, x o ,
then we get for the pressure p:
P*
x - (6) p = I 4 + (p,/p.)'^ .g V, /F If we insart this expression into the dif ferential equation (1) we finally obtain for the equation of motion:
.. P,e p, - Ff x ~*
x s y fw A+f,A{4+[F,I V./F (1) in which we have set m = p/h for the mass a of the uter (o g is the density of the water, h is the subsergence of the air bubble) .
In this dif f erential equation of second order, the variables po ,
= kg/cm ).
b, F and V , appear as parameters (p, = p kg/cm , pK The equation can be solved readily by a numerical method (Runge-Kutta, Euler, etc.) and leads to the cantar-of-mass b tion of the water mass as a function of times x = x (t) . The dependence of the pressure on time, p = p(t), can finally be determined frcus Eq. (6).
2-10
2.2 Enfo,rmance of the meerical calculation The input quantities in Eq. (7) consist of assasurable data (maximum pressure, normal air volume) and also of data resulting from the assumption of the calculated model. In order to include quantitatively the effect of those calculatien assumptions, parameter calculations were performed starting from a reference case.
2.2.1 Data The data for the reference case were:
a) Initial pressure p,3 k%%%%%%
oorresponding to a measuremant of the mavimum pressure b) specific weight of the waters oy= &%1 kg/m 3 c) Beight of the water cushion h:
h = k%%T The air bubble was assumec to be at the height of the end of the relief pipe. There f ore ,
ha subnergence of the relief pipe d) Surf ace area of the cylindrical steam bubble: -
It was assumed that the steam bubble expands cylindrically as far as the* edge of the suppression chamber. Therefore:
2-11
r - i e' VM#/#E li V A !
e) Normal air volume V, The air volume in the relief pipe was determined in AEG-E3/
E2-2160 to be With this data we obtain for the constant:
The numerical evaluation was acccs:plished by using the Runge-Kutta method with a time sharing system. The result of the cal-culation is illustrated in Figure 2. A comparison with the measured pressure variation (Figura 'l) reveals good qualitative agreement and thus provides the sought proof that the observed oscillations were interpreted correctly.
Fo.e a quantitative interpretation it is necessary to perform several (parameter) calculations to exhibit the influence of the various influential parvaeters on the oscillation data.
2.2.2 gagaggggg_calgulation The input quantitier into the oscillation model are bas,ed partially on measurements and partially on assumptions concerning the shape of the air bubble. To detemine the influence of this " arbitrary" initial data, it is necesrary to perferm a parameter calculation.
2-12
The following quantities were varied ja the parameter calculation:
Po
- Pressure ratio of the blow-out process P,
h a Distance of the air bubble from the water surface v
[ : This quantity represents a form factor, since, in addition to the known quantity V,, it also contains an assumption concerning -:he spreading of the surf ace area (cylindrical).
A survey of the calculations performed is given in Table 1.
The variation of the pressure in the air bubble and the displace-ment amplitude of the water layer for a half oscillation period are illustrated for the various calculations in Figures 3-11.
From them we can determine the various charactaristic magnitudes characterizing the oscillation:
Maximum vertical displacement Minimum pressure ratio (Half) oscillation period and oscillation frequency The corresponding values for the con.putation runs are listed in Table 1.
A graphical evaluation was perform M in Figure 12. _
2-13
- 3. Discussion The frequency is of primary interest in connection with the measured pressure oscillations, since only through it is it pos-sible to confira quantitatively the calculation results. (The maximum pressure is an input quantity into the calculation; the vertical displacament of the water was not measured.)
The only
- arbitrary" input quantity into the computation model was the bubble's surf ace area T, which contair.ed a hypothesis con-cernin; the (cylindrical) shape of the air bubble. The influence of the corresponding parameter (it involves the parameter V,/T) on the frequency therefore provides an indication of a possible As quantitative agreement between calculation and measurement.
follows fran Figure 12a, such agreement- does exist for a relatively flat air-bubble shape with a diameter of d= 4 k, T
KRAFTWERK UNION AG PROPRIETARY INF)RMATION 2-14
This result is confirmed qualitatively by the observed rapid spreading of the air expelled during the blow-out.
The bubble's subnergence h decreases during the oscillation process.
It follows from Figure 12a that this (as in the tests) is asso-ciated with a sharp increase of the frequency and therefore pro-vides another confirmation of the correctness of the physical model. The maximum pressure p, (or the ratio p,/p,) is fixed by the blowdown process and can only be changed by design measures.
As expected, this quantity influences primarily the minimum pres-sure ratio and the maximum vertical displacement (Figures 12b and 32c).
2-15
- 4. Conclusion The purpose of the study was to provide computational proof that the pressure oscillations occurring in the condensation u sts are related to the amount of air expelled at the beginning of the blowdown.
A physical model was set up and calculated in accordance with the concept that the expelled air, which is at an overpressure relative to the steady-state conditions, forms a cylindrical bubble and
- represents an oscillatory structure together with the water layer lying above it.
Using this simplified model and the measurable input magnitudes, and assuming a particular dimension of the cylindrical air bubble, both qualitative and quantitative agreement was found between the measured and calculated oscillation mode and the frequency behavior of the oscillation was correctly predicted.
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