ML20134F235
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| Site: | 05200003 |
| Issue date: | 01/30/1997 |
| From: | Reyes J Oregon State University, CORVALLIS, OR |
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O Scaling the Depressurization Behavior of Fluids in Phase Equilibria Jos6 N. Reyes, Jr, Department of Nuclear Engineering ;
Oregon State University '
116 Radiation Center i Corvallis, OR 97331-5902, USA FAX: 541-737-4678 I
l l
1 AllSTRACT transients. The purpose of this paper is to summarize the basis for pressure scaling and the constraints associated with l In this paper, I bric0y summarize the rationale for scaling its application (Reyes, et. al. [1]).
the depressurization behavior of fluids in phase equilibria.
I begin by developing a simple depressurization rate II. CONSERVATION EQUATIONS equation from the control volume mass and energy balance equations, ne depressurization rate equation is then Let us begin our examination of depressurization presented in dimensionless fonn and an order of magnitude behavior with the fluid mass and energy conservation analysis is performed using the conditions expected for the equations. he mass conservation equation is given by:
Westinghouse Advanced Passive 600 MW(c) nuclear power plant. I then demonstrate that the key property group dM . .
goveming the depressurization rate exhibits "self-similarity" T " *= ~ *=< (1) ,
over a wide range of pressures. To assess the validity of the ;
scaling approach, I compare the test results for a counterpart i test performed both in the full pressure SPES facility in Piacenza, Italy and the reduced pressure APEX facility at where M is the fluid mass within the control volume and th the Oregon State University in Corvallis, Oregon. represents the mass flow rate entering or leaving the control !
volume. I
- 1. INTRODUCTION l The energy conservation equation for the Duid is The analysis of the depressurization behavior of nuclear expressed as follows:
reactor systems following postulated piping ruptures has dU been the focus of numerous safety studies. Because of the = (thh), - (rhh) , + 4s,, - P dV (2) significant expense involved in testing the safety systems of dt dt l full-scale nuclear power plants, the use of reduced scale test facilities offers a significant economic advantage. Scaled integral system facilities such as the Rig of Safety where U is the internal energy of the fluid within the control l Assessment (ROSA) in Japan, and the less of Fluid Test volume, h is the enthalpy of the fluid entering or leaving the l (LOFT)in the United States and scaled separate effects tests control volume,qs,, is the net energy into the system; P is have been successfully used for many years to study a the system pressure and V is the system volume.
variety of phenomena. As part of the certification effort for the AP600, Westinghouse and the U.S. Department of The specific intemal energy and the specific volume are ;
Energy recently developed the Advanced Plant Experiment defined respectively as follows:
(APEX) at Oregon State University. One of the interesting U aspects of this facility was the use of pressure scaling to simulate the behavior of portions of AP600 depressurization e"g (3) 9702070316 970130
( PDR ADOCK0520g3 t A
_ _.-.___ _ _ _ _ _ _ _ _ _ _ ._..__._____.m ..._______._._._m V which is the "depressurization rate equation." For a control v=
(4) volume with rigid boundaries, which is typically the case, equation (10) becomes:
Be' -=dP . ' -de '
M m," h" - e + v Re total change in specific internal energy can be t 6P, , di , av, ,'
written in terms of partial differentials with respect to , (11) pressure and specific volume as follows:
-sat ha - e+v b, + 4sei
' gy d P, t 1 1 %
de = - dP + - dv 2p, , (5) s $ av, , Equation (11) shall provide the basis for scaling the depressurization behavior.
Substituting equation (3) into (2) yields: 111. SCALING METHODOLOGY
= (sh), - (sh), + 4s,, - P b (6) he Hierarchical Two-Tiered Scaling (H2TS) l de di methodology (Zuber [2]) was used to scale the APEX l
facility. De basic objective of the H2TS nethodology is to develop sets of characteristic time ratios,(i.e.,11 groups),
Expanding the first term on the LHS of equation (6), for the imponant transfer processes. His is done by casting substituting equation (1) and rearranging yields: the governing control volume balance equations in I
dimensionless form. Dat is, each term of a governing Mb = s, (h, - e) - s, (h, - e) + qs,, equation is divided by its respective initial condition. Hence di all of the terms are normalized to range between zero and dy ( I unity. De equation is further normalized relative to the
-P l
7 expected dominant transport process which defines the time scale for the transient phenomenon ofinterest.
t Physically, each characteristic time ratio (R) is l Substituting equation (5) into (7), and rearranging yields: composed of a specific frequency (o,), which is an attribute l r of the specific transport process, and the residence time 0*3 d,_P M --
= s, (h, - e) - s, (h, - c) constant for the control volume,(t,,). Dat is:
i cP , dt 3
(8) U"WTi 4 ev (12)
, Se 3 dv
+ q*.*' - P dV -M dt t av; , di l
l The specific frequency defines the mass, momentum or energy transfer rate for a panicular process. De residence Using equation (4), and the mass conservation equation, the time defines the total time available for the transfer process last term on the RHS of equation (8)is written as: to occur within the control volume. A numerical value of
, Se 3 r 3 r 3 R = 1, means that only a small amount of the conserved dv de dV _ y Se h1 . propeny would be transferred in the limited time available i dv, , dt i dv, , dt i av, , for the specific process to evolve.
l As a result, the specific process would not be important l Substituting back into equation (8) yields: to the overall transient. Numerical values of R = 1 means
, that the specific process evolves at a high enough rate to M
e 3
dP
= s,h,-e+y
,A 3 permit significant amounts of the conserved propeny to be i BP; , dt i dv transferred during the time period (t,,). Such a process
, ,,l would be important to the overall transient behavior.
Se i
- s ,'h"' - e + v (10) i av; ,' in general, by writing each H group in terms of a model j
(reduced scale) to prototype (full scale) ratio and setting the
, Se , dV
' 4" , p. ratio to unity, a similarity criterion is developed. hat is:
' dt
' av' P. Un"1 (13)
q
%e geometric or operating parameters are then adjusted he characteristic time ratios are given by the following:
to satisfy the criterion. , 3 m,"" h"-e+y -
De scaling approach described in this section shall $ av, ,,
now be applied to equations (1) and (11) to obtain the II. " , , (18) characteristic time ratios and a residence time constant for s,,, h,, - e + v -
the depressurization process. t dv sp, IV. CHARACTERISTIC TIME RATIOS AND ORDER OF MAGNITUDE ANALYSIS ne mass conservation equation, equation (1), can be n*r expressed in dimensionless form by dividing each term by ' ae ' (19) its respective initial condition and further dividing by the b o=* h,, - e + v mass flow rate of the fluid leaving the break. His results in 'a the following dimensionless mass balance equation:
dM*
t,, = H , s,*, - s *, (13) II, s the energy Cow rate ratio. It represents the ratio of the dt total energy change due to fluid injection to that lost by the break flow during the residence time (t,,). IIr is the power ratio. For a fluid mixture at saturated conditions, it where the superscript "+" terms indicate normalization with represents the total vapor mass generated in the primary respect to initial conditions. The residence time constant, system during the residence time (t ,).
(t.,), for the depressurization transient is given by:
e key fluid property for the depressurization process t .
M' is the volumetric dilation, co . It is given by:
(15) eaa 1g-P*
i 6P ,,
3 and the characteristic time ratio is given by: ** * ' (20) g, t m
h,, - e + v n, . ,N "" (16) ' dv' '< a oan Equation (20) reveals that the volumetric dilation H, is the system mass flow rate ratio. For a constant couples the system intensive energy change to the intensive injection flow rate, II, represents the total liquid mass energy at the break. For high pressure systems venting to injected into the control volume during the residence time the ambient, the fluid properties at the break are determined
( t,,). at critical flow conditions. Herefore, h,,, equals b *,;
where the superscript denotes critical flow conditions.
Equation (11) can be expressed in dimensionless form by dividing each term by its respective initial condition and For saturated mixtures it can be shown that:
further dividing both sides of the equa, ion by the fluid ,
3 energy flow rate initially leaving the break. This results in Pv,,
the following dimensionless energy balance equation:
g* ,g ,'h i is t dP* ' &'
" c* M, BP,-
, dt
= II,m.,. h,, - e + v M, To determine which of the transport processes are most j
, , , important to a depressurization transient and consequently i (17)
- s"' h'-e+v c_ which parameters should be scaled in the test facility, an l i av, ,' order of magnitude analysis is performed Figure I presents i the numerical values for the characteristic time ratios
- Ilrd a presented above as evaluated for AP600 conditions. De r
4 characteristic time ratios have been evaluated at 5 percent where P is the saturation pressure, v, is the change in and 3 percent decay power using both the Henry-Fauske [3] specific volume and h 9is the latent he,at of vaporization. ,
and Homogeneous Equilibrium critical flow models to Note that the volumetric dilation for saturated mixtures estimate the break flow rates at saturated liquid conditions, depends on this group. If one graphs this quantity against The figure indicates that for break diameters greater than the corresponding saturation temperature a linear trend is approximately 5 cm (-2 inches), the depressurization observed beginning at the triple point temperature. T, and process is dominated by the mass flow rate leaving the extending nearly to the critical point temperature, T,. De system through the break. Dat is, the values for H, and Ilr saturation temperature can be expressed as a dimensionless ;
are much smaller than unity. Ilowever, as the break quantity as follows:
diameters decrease, these two Il groups become increasingly .
important and the depressurization behavior is dominated by g. - T' 0= (23) the volumetric expansion within the control volume. T, - T, 1 i
AM00 DDRIssURIZAT10N RATE EQcATION 5 Figure 2 presents a graph of $ versus 0 for water at gp -*- h DECAY Rg saturated conditions (Irey, et. al. [5] Keenan, et al. [6]).
,, httcAYR) This figure illu5trates that the data is quite linear for the
-.- W DECAY R$ range of dimensionless temperatures given by:
" "#^*
g 3- O s O s 0.8 (24) 5, 3 ' I
- i oi4 Ul Un
.. gm , , m ,s p,
0.5 5 95 14 18.5 _
BRIAE DIAMEEt(m) i Figure 1. Order of Magnitude Analysis for the Depressur. jaa j ization Rate Equation Dimensionless Groups oOV Thus, for scaling the depressurization behavior associated with breaks smaller than 1.25 cm (1 inch), the QC characteristic time ratios associated with the energy equation are most important. However, for scaling the 0 l depressurization behavior associated with breaks larger than o at 02 03 04 05 06 of os 09 i
! 5 cm ( 2 inches), scaling the break mass flow rate is most egr tytt-t))
j important.
Figure 2. Graph of Dimensionless Fluid Property $ for l V SELF SIMILARITY OF SATURATED FLUID Water l PROPERTIES The success of scaling depressurization behavior in As the critical point is approached, for values of 0 greater reduced pressure test facilities ultimately lies in the fact that than 0.8. the trend becomes non-linear. The intercept is the several properties of fluids in phase equilibria exhibit "self- value of $ evaluated at the triple point. That is:
similarity" over a wide range of conditions. As explained i by Briggs and Peat [4] in their discussion on Mandelbrot $(0)=t i (25) l fractals, self similarity is a " repetition of detail at I
descending scales." I have found this to be true for the following important property group. The slope is a constant given by:
The ratio of the pressure work associated with phase N. = ci (26) change to the total energy associated with phase change can d0 be written as follows:
Pv," Numerous fluids display the same trend as observed in
' 9 2) h,' Figure 2 and can be plotted on a single graph in terms of
($ - $,) versus 0.
1 9
Based on the results, the equation relating $ and 0 is Separating the variables and integrating both sides given by: yields an equation of state for saturation pressure in terms 9, g. of saturation temperature. That is: '
" dP dT (34)
For water, c, equals 0.0926 and $, equals 0.05038.
!P
"' " ! T(bT 7'
+ a)
- 1. Eaustion of State for Saturated Pressure and Temocrature the solution of which is:
The Clausius-Clapeyron equation is the classical ., ,
differential equation that dennes the slope dP/dT for a phase a+bT, 'TI, T ,
equilibrium curve. It is derived by assuming that the Gibb's P = P, -
(35) free energies for the two phases being considered are equal, '
e.g., lay, J.E. [7]. Using the standard deGnition for the Gibb's free energy and relating the change in entropy to the latent heat of vaporization and the saturation temperature Where P, and T, are the saturation pressure and temperature yields the well-known Clausius-Clapeyron equation: at the triple point respectively. Equation (35) is the state ,
equation that relates saturation pressure to saturatici. l dP , h,' temperature, j dT (28) v,, T i Comparisons of equation (35) to tabulated values of saturation pressure and temperature of various fluids The Clausius-Clapeyron equation can be used with indicates excellent agreement; having R2 values greater than equation (27) to obtain an equation of state for the 0.994, saturation pressure and temperature. Let us rewrite equation (27) as follows: 2. Scaled Processes Usine gun.r F%Ms in Phase Eauilibria p " = bT + a let us now turn our attention to the problem of relating (29) h,, the saturation pressure and temperature in a reduced pressure test model to the same properties in a full pressure prototype.12t us suppose that the same working fluid is where used in the model as in the prototype. We would need to relate the fluid propenies in the full pressure plant to those a = $ - bT, (30) n the reduced pressure model. If we assume that the depressurization process evolves along the saturadon curve, then equation (35) is directly applicable.
Rearranging equation (29) yields:
Equation (35) has been normalized using the saturation l
b g p pressure and temperature corresponding to the triple point i (33) f the fluid. Ilowever, the saturation pressure and v'8 (b T + a) temperature mrresponding to any point between 0 equal to ,
zero and 0.8 would serve equally well. Fordepressurization processes, it is convenient to select the initial saturation .
where: pressure and temperature as the " reference" parameters.
Thus, equation (35) becomes:
b = (r, 'T,) (32) 'r t i p , p* a+bT. ' ,T ' I (36)
,a+bT, , T,,
Substituting equation (31) into the Clausius-Clapeyron equation yields:
dP P w ere e su s pt "o' denotes a reference pmpeny
=
(33) evaluated at the initial saturated equilibrium conditions and dT T(b T + a) o
- - - . - - -. - -. .- -. .~ -. - - - _ . - -. _
i l . .
the constants "a# and "b" are as defined previously. or in terms of model parameters, denoted by the subscript Equation (36) can be written as a scaling ratio as follows: "m" and the plant parameters, denoted by the subscript "p". ,
'P' a + bT,' 'T' g p, P p
, P,, , i a+bT,,,T,,, , 6.,
Equation (41) relates the saturation pressure in the model to w here the subscript "h" denotes the ratio of model to plant the saturation pressure in the plant. His same result can be propenies. Because the same Duid is used in both cases, the obtained using the graphical approach presented by coef ficients a and b are identical in the model and the plant. Kocamustafnogullari and Ishii [8].
Substituting equation (29) into (37) and rearranging Substituting equation (40) into (37) yields an equation yields: that can be used to relate the saturation temperatures in the model to those of the plant. After some algebra, one
'P' . hr,T/v,,) .Nr obtains:
6 4R I8 f8 o R a T, =
(a + bT),(T,)R (42)
-b Figure 3 reveals that the right-hand side of equation T"(a + bT*)R (38) is essentially unity for all values of pressure ratios (P/P )in the model and the prototype. Rus:
he results herein are applicable to the range of
. breT/v,,) < ,3 dimensionless temperatures, 6, between zero and 0.8.
(39)
[,,T/v,,),A Equation (35) presents a state equation that relates saturation pressure to saturation temperature, n Equations (41) and (42) relate the saturation pressures
, , ,,, % m j and temperatures of a reduced pressure scale model to those m w= sca ; of a full pressure prototype. His allows direct data
'2'
,
- Z'0
. , comparisons when the process being examined evolves f n- along the phase equilibrium curve.
etttti i e e e l
h, The propeny of "self-similarity" is demonstrated by l } ** ' equations (39) and (40). Dat is, any continuous subset of t Os-these fluid propenies can be scaled by a single constant to
,,. re-create a " scaled" set of fluid propenies applicable to a
,, wider range of pressures.
0 OJ 04 06 08 8 msstu nno n.> VII. COMPARISONS OF A SPES AND APEX Figure 3. Effect of Pressure Scaling on the Term on the DEPRESSURIZATION TRANSIENT Right-hand Side of Equation (38)
Counterpart tests have been performed in the SPES and APEX test facilities (Hochreiter and Reyes [9]). Dese tests provide points of comparison for the facilities which enable Substituting this result into equation (38) yields: one to understand scaling and operating differences. His section examines a 2-inch small break loss of coolant
'p' "1 accident. Table i presents the general scaling ratios for the p (40) test facilities rehaive to the full-scale AP600.
iasR 1
4 h
O I
Table l' in general, the data comparisons for the 2-inch break case indicate that the agreement between SPES-2 and APEX Scaling Ratios APEX SPES-2 is very good. He timing orkey events, such as ADS valve actuation, has been preserved.
Lengths 1:4 1:1 i
Relative Elevations 1:4 1:1 !
l Flow Areas 1:48 1:395 This paper summarizes the rationale for scaling the I depressurization behavior of 0uids in phase equilibria. The !
Volumes 1:192 1:395 key scaling groups are obtained by casting the I depressurization rate equation in dimensionless fonn. l Decay Power 1:96 1:395 Performing an order of magnitude analysis on the key I I
Fluid Velocity 1:2 1:1 scaling groups reveals that pressure scaling is complicated when IIrexceeds unity. For the AP600 system, this occurs Fluid Transient Time 1:2 1:1 for breaks of approximately 2.5 cm or smaller.
Mass Flow Rate 1:96 1:395 Comparisons of the high pressure data from SPES-2 to
{'
the reduced pressure data from APEX indicate that pressure
' Note: Ratios are relative to thefull-scale AP600 scaling can be successfully implemented in reduced pressure facilities.
Scaling factors will need to be applied to the APEX and mencia osuinsu l SPES-2 results to compare time, pressure, and flowrates. +-- N*E I e' .E Z Z", 2 .mo he APEX time scale must be multiplied by a factor of two 'l , j ,
and its pressure scale normalized using the reference ,
l' pressure (maximum pressure on secondary side). Similarly, the SPES-2 pressure scale can also be normalized using the '
\'
reference pressure for the test. The Dow rate normalization j, factor in SPES-2 is the maximum flow rate for the process
'. k being examined. For example,the maximum accumulator '
)
injection Dow observed. For purposes of comparison, the ,
4'eh l
flow rate normalization factor in APEX would be the l j maximum flow rate observed for the identical process in * '
SPES-2 multiplied by the ratio 395/96. Rus, the flowrates kN can be compared on a similar basis. Figure 4. Comparison of OSU APEX and SPES-2 Two-Inch Break Pressure Ilistories l A 2 inch cold leg break was simulated in both the l APEX and SPES-2 facilities. De break location for these , ,,f57 Q"j8,* * ,,
tests was at the bottom of a single cold leg. Each system was at its steady-state initial condition at the time of break 7 " ^" " ' ' "" ~ ""
initiation. The subsequent depressurization behavior was ' .
recorded for each facility and key data plots are presented ,
herein for purposes of comparison. De vertical axis of k ,
each graph has been normalized as described previously, ne APEX time scale has been multiplied by the scaling j'
8
\
factor of two to compare with the SPES-2 time scale, ,
( -
Figure 4 compares the APEX and SPES-2 pressure histories for the reactor vessel following the initiation of the . . . , ,
simulated 2-inch cold leg break. As can be observed, the T= M trends are very similar. Figures 5 ihorugh 8 present the data Figure 5. Comparison ofOSU APEX and SPES-2 CMT-2 comparisons for the key passive safety systems. Liquid Levelliistories
- 1. \
IX. REFERENCES
?$i'"f"J."?_'ff"
"' "* * * ~ ~ " "
, 1. Reyes, J.N., Hochreiter, A.Y. Lafi, L.K. Lau, Low
,. y , Pressure Integral Systems Test at Oregon State e
a ,\ ,r M u University, Facility Scaling Report, Westinghouse dI 'N ' 'D 4
..\ .'
Zij Electric Corporation, WCAP 14270, January 1995.
~p
,I j ,
- 2. Zuber, N., " Appendix D: A Hierarchial, Two-Tiered
'!. ,. n ,*
' ' Scaling Analysis," An IntegratedStructure andScaling Afethodology for Severe Accident Technical Issue e
N * '
Resolution, U.S. Nuclear Regulatory Commission,
, Washington, DC 20555, NUREG/CR-5809, Ncrember e = = = =
1991.
Tm N
- 3. Henry, R.E. and H.K. Fauske. The Two-phase Critical Figure 6. Comparison ofOSU APEX and SPES-2 CMT-2 Flow ofone-Component Af&tures in Nozzles, Orrfices, injection Flow Rate and Short Tubes, Journal of Heat Transfer, ASME Transactions, vol. 93, ser. C, no. 2, pp.179-187, May 1971.
- 4. Briggs, John and F. David Peat. Turbulent Afirror.
. . . . on, o, .. l'S'.87.
n . .umE"f.mu80" Harper & Row Publishers, New York,1989.
..t- ~
- 5. Irey, R.K., Ansari, A., and Pohl, J.H., Thermodynamics
, for Afodular Instruction, Unit IC Properties of Pure Substances in Near Multiphase Regions, John Wiley &
, Sons, New York, IC-35,1967.
- 6. Keenan, J.H. Keyes, F.G., Hill, P.G., and Moore, J.G.,
('
Steam Tables, Wiley-Interscience, New York, 8-13, 1969.
.... .. . > . - m*., .-+-r-
, 7. Lay, J.F., Statistical Afechanics and Thermodynamics Tae N ofAfatter, Harper and Row Publishers, New York,453 l 456,1990.
Figure 7. Comparison of OSU APEX and SPES-2 ACC-1 Liquid Level Histories 8. Kocamustafaogullari,G.,and Ishii, M.,1986. " Pressure l' and Fluid-to-Fluid Scaling Laws for Two-Phase Loop Flow," NUREG/CR-4585.
1 msna m nosna mu 9. Hochreiter, L.E. and J.N. Reyes, " Comparison of SPES-
. . - T.. '"x **""'"J'"'-To 2 and APEX Tests to Examine AP600 Integral System Performance," International Joint Power Generation
, ;f '
Conference, Minneapolis, Minnesota, October 1995.
. If .
}e .
.'/
l e
a k '
'.h.s }x.
n, . . .
, . s . e. . . .n...s...
e m = = =
Tae N Figure 8. Comparison ofOSU APEX and SPES-2 ACC-1 l Injection Flow Rate 1
o l
!