The analysis that has been carried out in the present paper shows the possibility to predict the onset of density wave oscillations by means of RELAP5/MOD3.3 code for simple geometry systems, whereas the difference between 1D and 3D approximations is not relevant for the purpose of the analysis; the shape of the boundary line in the stability maps is in agreement with the other authors prediction. The approximation used for helically coiled pipes in the multichannel systems seems not to affect the instability onset and the classical shape of the instability maps, that seem a powerful tool for the fluid dynamic instability predictio

De Salve, Mario

Giraudo, Matteo Giacomo

Panella, Bruno

PORTO Publications Open Repository TOrino

Politecnico di Torino
Porto Institutional Repository
[Article] Use of RELAP50MOD3.3 Code to Get Fluid Dynamic Stability Maps
Original Citation:
De Salve M.; Giraudo M.G.; Panella B. (2012). Use of RELAP50MOD3.3 Code to Get Fluid Dynamic
Stability Maps. In: TRANSACTIONS OF THE AMERICAN NUCLEAR SOCIETY, vol. 106, pp. 975-
978. - ISSN 0003-018X
Availability:
This version is available at : http://porto.polito.it/2499980/ since: July 2012
Publisher:
American Nuclear Society
Terms of use:
This article is made available under terms and conditions applicable to Open Access Policy Article
("Public - All rights reserved") , as described at http://porto.polito.it/terms_and_conditions.
html
Porto, the institutional repository of the Politecnico di Torino, is provided by the University Library
and the IT-Services. The aim is to enable open access to all the world. Please share with us how
this access benefits you. Your story matters.
(Article begins on next page)
Use of RELAP5/MOD3.3 Code to Get Fluid Dynamic Stability Maps   
M. De Salve, M. G. Giraudo, B. Panella 
 
Politecnico di Torino: Corso Duca degli Abruzzi 24, Torino, Italy, 10129 
bruno.panella@polito.it 
 
INTRODUCTION 
The study of fluid dynamic instabilities is important to 
avoid their occurrence in components like steam generators 
in nuclear and conventional power plants. Fluid dynamic 
instabilities usually arise in the heated channels 
characterized by boiling conditions either with a vertical 
layout or in case of inclined or helically coiled pipes. In 
case of parallel channels, like in the steam generators, 
oscillations determine different flow rate in different 
channels, even if the total flow rate is constant. Instabilities 
must be avoided because they may lead to  mechanical 
vibrations, to thermal crisis and heat transfer deterioration 
as well as to problems in system control and regulation.  
Several authors have studied fluid dynamic 
instabilities in the past: Kakac [1] classified them in terms 
of static and dynamic instabilities or also in terms of pure or 
composed ones: a system is subject to static instabilities if, 
when disturbed, it reaches a new operating condition in a 
succession of static working points, whereas the same 
system is subject to dynamic instabilities when there are 
feedback effects of various parameters which lead to 
oscillating transient condition.   
Density wave oscillations (DWO) were studied for the 
first time by Stenning [2]; they are dynamic instabilities 
caused by a variation of pressure drop in two-phase flow 
and, at the same time, by the delay of this effect on the 
whole system: this means that other parameters are affected 
by feedback effects in the time scale leading to flow rate 
oscillations in the system. As suggested by Fukuda [3], 
parallel channel instabilities seem to be similar to DWO in 
a single heated channel, that are always due to a variation 
of flow parameters like pressure drop. Moreover flow 
pattern instabilities are generally considered static ones and 
they usually arise during the transition from slug to annular 
flow pattern; in this case, after the transition, pressure drops 
are reduced, the flow rate increases and in turn, with a 
larger flow rate, flow pattern becomes again slug flow; very 
often the processes which occur in industrial components 
are a combination of different kind of instability.  
Stability maps are a powerful tool to predict the onset 
of instabilities in fluid dynamics systems and many authors 
have developed stability maps, either in a theoretical way or 
by experiments or by numerical way. G.Yun et al. [4] 
proposed both a theoretical and an experimental study, 
whereas Papini [5] performed a  comparison of the stability 
maps obtained experimentally with the RELAP5/MOD3.3 
[7] code prediction.  Further work is needed to increase the 
fluid dynamic instability knowledge and, in particular, the 
prediction of the phenomenon by means of fluid-dynamics 
codes.  
 
 
DESCRIPTION OF THE ACTUAL WORK 
 
In the present paper, the main goal is to study the 
possibility to predict the  density wave oscillations, flow 
pattern oscillations and parallel channel oscillations by 
RELAP5/MOD3.3 in some simple cases like a single 
vertical heated channel and in parallel channels both in 
vertical and inclined layout.  The present work concerns the 
RELAP5/MOD3.3 code ability to predict instabilities and 
to get instability maps for such simple cases; in particular  
the stability of  the helical steam generators designed for 
nuclear reactors is investigated. 
Helically coiled pipes heat exchangers are interesting 
components in many fields, in nuclear and conventional 
power plants, due to better performances regarding heat 
transfer and mechanical stresses induced by the thermal 
expansion. In order to investigate  the fluid dynamic 
instabilities by means of RELAP5/MOD3.3 code, the 
helically coiled pipes are described as inclined pipes with 
an inclination equal to the angle of the helical pipe. This 
approximation allows to take into account the gravitational 
effect and the difference between the various helically 
coiled pipes, but cannot take into account secondary flows. 
The analysis concerns a multichannel system with three 
inclined pipes with different angles. In order to describe a 
helical pipe with an inclined pipe, by considering the angle 
of the helical pipe as the angle of straight pipe inclination, 
the adopted length and the height of the pipe are the same 
as those of the helical ones. 
 
 
Stability Maps  
 
The stability maps, that were adopted the first time by 
Ishii and Zuber [6], are a powerful instrument to 
understand the physical limits of the devices you are 
dealing with. All the main parameters affecting the system 
are well represented by means of two non-dimensional 
numbers as introduced by Zuber, that is  the "Subcooling 
number" and the "Phase Change number", that  are defined 
as follows: 
௦ܰ௨௕ ൌ
ο݄௜௡
݄௙௚
ݒ௙௚
ݒ௙
ሺͳሻ 
௣ܰ௖௛ ൌ
߶
ܹ ௙݄௚
ݒ௙௚
ݒ௙
ሺʹሻ 
 
As an example, for a single heated channel, the two 
parameters can be represented in a x-y diagram, showing 
Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012
975Computational Thermal Hydraulics—I
the stability map with the classical "L- shape", where all 
the points on the right of the limit line correspond to the 
arise of instabilities as shown in Fig.1. 
 
Fig. 1. Ishii- Zuber stability maps for a single heated 
channel [6] 
 
 
RELAP5/MOD3.3 Facility Modelling 
 
The simulation of a real plant by means of  the one-D 
semi-implicit RELAP5/MOD3.3 system code, based on  a 
fluid volume model, is performed splitting up the facility 
into small volumes separated by junctions. The model 
chosen to investigate the instability phenomenon depends 
on the number of the facility channels: two time dependent 
volumes and a pipe divided in 50 volumes are used in the 
case of a single channel, whereas two branches at the inlet 
and at the outlet are added in the other cases. Two single 
junctions connect the time dependent volumes to the pipe; 
so a constant pressure difference is imposed between the 
inlet and the outlet of the system. Heat structures in 
parallel provide heat to produce the two-phase flow inside 
the pipe. The single channel simulation is presented in Fig. 
2 whereas the characteristic of the pipe are reported in 
Table I. 
 
Fig. 2. Single channel simulation 
 
TABLE I. Single channel geometrical data 
Parameters Values 
Total Length [m] 5 
Diameter [cm] 1.2 
Roughness [m] ʹǤͷ ή ͳͲିହ 
݇௟௢௖݈݅݊݁ݐ 0 
݇௟௢௖݋ݑݐ݈݁ݐ 0 
Layout Vertical 
 
In the case of multichannel system, the simulation  
has been performed with a three channel system in parallel, 
firstly with a vertical layout and secondly with three 
inclined pipes with different angles to simulate a real steam 
generator with helically coiled pipes (Fig. 3). 
 
 
Fig. 3. Scheme for multichannel systems 
 
The main variable associated with the tests is the 
pressure of the system: the steps needed to build the 
stability maps are the following: 
 
i. For each reference pressure value, the ratio 
between ݒ௙௚ and ݒ௙  is provided. 
ii. Several sample sub-cooling values are chosen 
to evaluate the Subcooling numbers. 
Subcooling values are defined as follows: 
ݔ௦௨௕ ൌ 
݄௟ǡ௦௔௧ െ ݄௜௡
௙݄௚
ൌ
ο݄௜௡
௙݄௚
ሺ͵ሻ 
where ο݄௜௡ is the inlet subcooling. 
iii. Holding a "Subcooling number" constant, 
thermal power is increased in a linear way 
until reaching the first flow rate oscillation 
(Fig. 4). Instabilities are considered fully 
developed when the amplitude of the 
Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012
976 Computational Thermal Hydraulics—I
flow rate. 
iv. Evaluating the time of the first oscillation, the 
value of the thermal power corresponding to 
the characteristic time is computed. 
v. Evaluating the flow rate as the average of the 
oscillations, the "Phase-change number" is 
found. 
vi. Plotting the Subcooling number and the Phase-
change number, a system stability boundary is 
identified. 
Fig. 4. Arising of flow oscillations 
RESULTS  
 Single channel 
 
The stability map, at three values of the pressure, is 
reported in Fig. 5. The "L-shape" can be seen and the 
region where the system is stable is on the left of the 
curves, whereas instability conditions are the ones on the 
right. The Subcooling number in correspondence of the 
slope inversion (Fig. 5) can be considered constant at 
different pressure (it is about 0.98). 
The onset of instabilities does not correspond to a 
flow regime transition, which however can be foreseen  by 
the code by means of different relationships according to 
the flow regime condition, but it is provided by dynamic 
feedback effects of system parameters in the solution of 
conservation equations. 
From the definition of the two numbers represented in 
the stability map a new relationship between Subcooling 
number and Phase-change number can be obtained: 
 
ௌܰ௎஻ ൌ ௉ܰ஼ு െ ݔ௢௨௧
ݒ௙௚
ݒ௙
ሺͶሻ 
 
 
So in correspondence of the slope inversion the  
steam quality at the outlet as a function of the pressure can 
be evaluated from eq. (4) and it is shown in Fig. 6. 
The pressure of the system is an important parameter 
to evaluate the instability and the results show that the 
pressure increase leads to a more stable system because the
 
densities of the two-phase become closer.  Such results 
agree with literature data, considering that pressure 
increase leads to a higher steam quality at the outlet 
without the arising of instabilities.  
 
Fig. 5. Stability Map for a single channel 
  
 
Fig. 6. Effects of the pressure on the steam quality at 
the outlet  
The results obtained for a single channel with vertical 
layout are consistent with the ones shown by Papini [5] 
analysis with RELAP5/MOD3.3 code in the framework of 
instability analysis at SIET Company laboratory; as shown 
in Fig. 7, for a single channel, with two pressure losses 
located at the inlet and the outlet of the pipe and for similar 
Sub-cooling numbers, the maximum error of the Phase- 
change number is about 20%. 
 
 
  
oscillations reaches the 50% of the average 
Multichannel systems  
The use of the  RELAP5/MOD3.3 code to get the 
stability maps is extended to multichannel systems. The 
Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012
977Computational Thermal Hydraulics—I
  
Fig. 7. Comparison between the present work 
(POLITO) and Ref.  [5] (POLIMI) results 
pressure chosen for the analysis is 58 bar, that is the design 
pressure for the innovative nuclear reactor IRIS steam 
generator; the procedure is the same as the previous one, 
by assuming different subcoolings and by increasing the 
thermal power in a linear way. The adopted scheme has 
been reported in Fig. 3.   
The stability map obtained by means of the 
RELAP5/MOD3.3 code is reported in Fig. 8, where there 
is a comparison  between the single vertical channel, three 
vertical channels in parallel and three inclined channel at a 
pressure of 58 bar. The results confirm the classical "L-
shape" for the boundary curve between the stable zone and 
the unstable one; the results show also that a multichannel 
system is more stable than a single one, as regards the 
density wave oscillations and in agreement with the 
literature data. In fact, the outlet steam quality at the 
instability onset for a single channel is about 30%, whereas 
it is about 40% for the multichannel system. 
 
CONCLUSION 
 
The analysis that has been carried out in the present 
paper shows the possibility to predict the onset of density 
wave oscillations by means of RELAP5/MOD3.3 code for 
simple geometry systems, whereas the difference between  
1D and 3D approximations is not relevant for the purpose 
of the analysis; the shape of the boundary line in the 
stability maps  is in agreement with the other authors 
prediction. The approximation used for helically coiled 
pipes in the multichannel systems seems not to affect the 
instability onset  and the classical shape of the instability 
maps, that seem a powerful tool for the fluid dynamic 
instability prediction.  
 
 
 
Fig. 8. Stability Maps for multichannel system 
 
NOMENCLATURE 
݄௜௡:   inlet enthalpy 
݄௟ǡ௦௔௧:   liquid saturation enthalpy 
݄௙௚:  vaporization enthalpy 
k : localized pressure loss coefficient 
Npch:  Phase change number 
Nsub:  Sub-cooling number 
ݒ௙௚:  difference between vapour and  liquid specific 
volume 
ݒ௙:  liquid specific volume 
W:  mass flow rate 
ݔ௢௨௧: outlet quality 
߶:  thermal power 
 
REFERENCES 
[1] S. KAKAC, B.  BON, "A Review of two-phase flow 
dynamic instabilities in tube boiling systems", International 
Journal of Heat and Mass Transfer, Volume: 51,  3-4,  399-
433, (2008) 
[2] A.H. STENNING, Instabilities in the flow of a boiling 
liquid ASME, Transactions, Series D-Journal of Basic 
Engineering. Vol. 86, pp. 213-217, (June 1964)   
[3] K. FUKUDA AND S. HTASEGAWA, Analysis of two 
phase flow instabilities in parallel multichannels, J. Nucl. 
Sci. Technol. 16, 190, (1979).  
[4] G.YUN,  "Experiment investigation on two-phase flow 
instability in a parallel", Annals of Nuclear Energy, 
(2010). 
[5] D. PAPINI, M. COLOMBO, A. CAMMI, M.E. 
RICOTTI, D. COLORADO, M. GRECO, G. TORTORA, 
Experimental Characterization of Two-Phase Flow 
Instability Thresholds in Helically Coiled Parallel 
Channels, Proceedings of International Congress on 
Advances in Nuclear Power Plants (ICAPP) Nice, France, 
(May 2-5 2011). 
[6] P. SAHA, M. ISHII, N. ZUBER, An Experimental 
Investigation of the Thermally Induced Flow Oscillations 
in Two-Phase Systems, Journal of Heat Transfer, Trans. 
ASME 98, 616-622, (1976). 
[7] U.S. NRC Nuclear Safety Analysis Division, 
RELAP5/MOD3.3 Code Manual, NUREG/CR-5535/Rev1 
(2001). 
Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012
978 Computational Thermal Hydraulics—I


Use of RELAP50MOD3.3 Code to Get Fluid Dynamic Stability Maps

The analysis that has been carried out in the present
paper shows the possibility to predict the onset of density
wave oscillations by means of RELAP5/MOD3.3 code for
simple geometry systems, whereas the difference between
1D and 3D approximations is not relevant for the purpose
of the analysis; the shape of the boundary line in the
stability maps is in agreement with the other authors
prediction. The approximation used for helically coiled
pipes in the multichannel systems seems not to affect the
instability onset and the classical shape of the instability
maps, that seem a powerful tool for the fluid dynamic
instability prediction

DE SALVE, Mario

GIRAUDO, MATTEO GIACOMO

PANELLA, BRUNO

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEUse of RELAP50MOD3.3 Code to Get Fluid Dynamic Stability Maps / De Salve M.; Giraudo M.G.; Panella B.. - In:TRANSACTIONS OF THE AMERICAN NUCLEAR SOCIETY. - ISSN 0003-018X. - 106(2012), pp. 975-978.OriginalUse of RELAP50MOD3.3 Code to Get Fluid Dynamic Stability MapsPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2499980 since:American Nuclear SocietyUse of RELAP5/MOD3.3 Code to Get Fluid Dynamic Stability Maps   M. De Salve, M. G. Giraudo, B. Panella  Politecnico di Torino: Corso Duca degli Abruzzi 24, Torino, Italy, 10129 bruno.panella@polito.it  INTRODUCTION The study of fluid dynamic instabilities is important to avoid their occurrence in components like steam generators in nuclear and conventional power plants. Fluid dynamic instabilities usually arise in the heated channels characterized by boiling conditions either with a vertical layout or in case of inclined or helically coiled pipes. In case of parallel channels, like in the steam generators, oscillations determine different flow rate in different channels, even if the total flow rate is constant. Instabilities must be avoided because they may lead to  mechanical vibrations, to thermal crisis and heat transfer deterioration as well as to problems in system control and regulation.  Several authors have studied fluid dynamic instabilities in the past: Kakac [1] classified them in terms of static and dynamic instabilities or also in terms of pure or composed ones: a system is subject to static instabilities if, when disturbed, it reaches a new operating condition in a succession of static working points, whereas the same system is subject to dynamic instabilities when there are feedback effects of various parameters which lead to oscillating transient condition.   Density wave oscillations (DWO) were studied for the first time by Stenning [2]; they are dynamic instabilities caused by a variation of pressure drop in two-phase flow and, at the same time, by the delay of this effect on the whole system: this means that other parameters are affected by feedback effects in the time scale leading to flow rate oscillations in the system. As suggested by Fukuda [3], parallel channel instabilities seem to be similar to DWO in a single heated channel, that are always due to a variation of flow parameters like pressure drop. Moreover flow pattern instabilities are generally considered static ones and they usually arise during the transition from slug to annular flow pattern; in this case, after the transition, pressure drops are reduced, the flow rate increases and in turn, with a larger flow rate, flow pattern becomes again slug flow; very often the processes which occur in industrial components are a combination of different kind of instability.  Stability maps are a powerful tool to predict the onset of instabilities in fluid dynamics systems and many authors have developed stability maps, either in a theoretical way or by experiments or by numerical way. G.Yun et al. [4] proposed both a theoretical and an experimental study, whereas Papini [5] performed a  comparison of the stability maps obtained experimentally with the RELAP5/MOD3.3 [7] code prediction.  Further work is needed to increase the fluid dynamic instability knowledge and, in particular, the prediction of the phenomenon by means of fluid-dynamics codes.    DESCRIPTION OF THE ACTUAL WORK  In the present paper, the main goal is to study the possibility to predict the  density wave oscillations, flow pattern oscillations and parallel channel oscillations by RELAP5/MOD3.3 in some simple cases like a single vertical heated channel and in parallel channels both in vertical and inclined layout.  The present work concerns the RELAP5/MOD3.3 code ability to predict instabilities and to get instability maps for such simple cases; in particular  the stability of  the helical steam generators designed for nuclear reactors is investigated. Helically coiled pipes heat exchangers are interesting components in many fields, in nuclear and conventional power plants, due to better performances regarding heat transfer and mechanical stresses induced by the thermal expansion. In order to investigate  the fluid dynamic instabilities by means of RELAP5/MOD3.3 code, the helically coiled pipes are described as inclined pipes with an inclination equal to the angle of the helical pipe. This approximation allows to take into account the gravitational effect and the difference between the various helically coiled pipes, but cannot take into account secondary flows. The analysis concerns a multichannel system with three inclined pipes with different angles. In order to describe a helical pipe with an inclined pipe, by considering the angle of the helical pipe as the angle of straight pipe inclination, the adopted length and the height of the pipe are the same as those of the helical ones.   Stability Maps   The stability maps, that were adopted the first time by Ishii and Zuber [6], are a powerful instrument to understand the physical limits of the devices you are dealing with. All the main parameters affecting the system are well represented by means of two non-dimensional numbers as introduced by Zuber, that is  the "Subcooling number" and the "Phase Change number", that  are defined as follows: ௦ܰ௨௕ ൌο݄௜௡݄௙௚ݒ௙௚ݒ௙ሺͳሻ ௣ܰ௖௛ ൌ߶ܹ ௙݄௚ݒ௙௚ݒ௙ሺʹሻ  As an example, for a single heated channel, the two parameters can be represented in a x-y diagram, showing Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012975Computational Thermal Hydraulics—Ithe stability map with the classical "L- shape", where all the points on the right of the limit line correspond to the arise of instabilities as shown in Fig.1.  Fig. 1. Ishii- Zuber stability maps for a single heated channel [6]   RELAP5/MOD3.3 Facility Modelling  The simulation of a real plant by means of  the one-D semi-implicit RELAP5/MOD3.3 system code, based on  a fluid volume model, is performed splitting up the facility into small volumes separated by junctions. The model chosen to investigate the instability phenomenon depends on the number of the facility channels: two time dependent volumes and a pipe divided in 50 volumes are used in the case of a single channel, whereas two branches at the inlet and at the outlet are added in the other cases. Two single junctions connect the time dependent volumes to the pipe; so a constant pressure difference is imposed between the inlet and the outlet of the system. Heat structures in parallel provide heat to produce the two-phase flow inside the pipe. The single channel simulation is presented in Fig. 2 whereas the characteristic of the pipe are reported in Table I.  Fig. 2. Single channel simulation  TABLE I. Single channel geometrical data Parameters Values Total Length [m] 5 Diameter [cm] 1.2 Roughness [m] ʹǤͷ ή ͳͲିହ ݇௟௢௖݈݅݊݁ݐ 0 ݇௟௢௖݋ݑݐ݈݁ݐ 0 Layout Vertical  In the case of multichannel system, the simulation  has been performed with a three channel system in parallel, firstly with a vertical layout and secondly with three inclined pipes with different angles to simulate a real steam generator with helically coiled pipes (Fig. 3).   Fig. 3. Scheme for multichannel systems  The main variable associated with the tests is the pressure of the system: the steps needed to build the stability maps are the following:  i. For each reference pressure value, the ratio between ݒ௙௚ and ݒ௙  is provided. ii. Several sample sub-cooling values are chosen to evaluate the Subcooling numbers. Subcooling values are defined as follows: ݔ௦௨௕ ൌ ݄௟ǡ௦௔௧ െ ݄௜௡௙݄௚ൌο݄௜௡௙݄௚ሺ͵ሻ where ο݄௜௡ is the inlet subcooling. iii. Holding a "Subcooling number" constant, thermal power is increased in a linear way until reaching the first flow rate oscillation (Fig. 4). Instabilities are considered fully developed when the amplitude of the Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012976 Computational Thermal Hydraulics—Iflow rate. iv. Evaluating the time of the first oscillation, the value of the thermal power corresponding to the characteristic time is computed. v. Evaluating the flow rate as the average of the oscillations, the "Phase-change number" is found. vi. Plotting the Subcooling number and the Phase-change number, a system stability boundary is identified. Fig. 4. Arising of flow oscillations RESULTS   Single channel  The stability map, at three values of the pressure, is reported in Fig. 5. The "L-shape" can be seen and the region where the system is stable is on the left of the curves, whereas instability conditions are the ones on the right. The Subcooling number in correspondence of the slope inversion (Fig. 5) can be considered constant at different pressure (it is about 0.98). The onset of instabilities does not correspond to a flow regime transition, which however can be foreseen  by the code by means of different relationships according to the flow regime condition, but it is provided by dynamic feedback effects of system parameters in the solution of conservation equations. From the definition of the two numbers represented in the stability map a new relationship between Subcooling number and Phase-change number can be obtained:  ௌܰ௎஻ ൌ ௉ܰ஼ு െ ݔ௢௨௧ݒ௙௚ݒ௙ሺͶሻ   So in correspondence of the slope inversion the  steam quality at the outlet as a function of the pressure can be evaluated from eq. (4) and it is shown in Fig. 6. The pressure of the system is an important parameter to evaluate the instability and the results show that the pressure increase leads to a more stable system because the densities of the two-phase become closer.  Such results agree with literature data, considering that pressure increase leads to a higher steam quality at the outlet without the arising of instabilities.   Fig. 5. Stability Map for a single channel    Fig. 6. Effects of the pressure on the steam quality at the outlet  The results obtained for a single channel with vertical layout are consistent with the ones shown by Papini [5] analysis with RELAP5/MOD3.3 code in the framework of instability analysis at SIET Company laboratory; as shown in Fig. 7, for a single channel, with two pressure losses located at the inlet and the outlet of the pipe and for similar Sub-cooling numbers, the maximum error of the Phase- change number is about 20%.     oscillations reaches the 50% of the average Multichannel systems  The use of the  RELAP5/MOD3.3 code to get the stability maps is extended to multichannel systems. The Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012977Computational Thermal Hydraulics—I  Fig. 7. Comparison between the present work (POLITO) and Ref.  [5] (POLIMI) results pressure chosen for the analysis is 58 bar, that is the design pressure for the innovative nuclear reactor IRIS steam generator; the procedure is the same as the previous one, by assuming different subcoolings and by increasing the thermal power in a linear way. The adopted scheme has been reported in Fig. 3.   The stability map obtained by means of the RELAP5/MOD3.3 code is reported in Fig. 8, where there is a comparison  between the single vertical channel, three vertical channels in parallel and three inclined channel at a pressure of 58 bar. The results confirm the classical "L-shape" for the boundary curve between the stable zone and the unstable one; the results show also that a multichannel system is more stable than a single one, as regards the density wave oscillations and in agreement with the literature data. In fact, the outlet steam quality at the instability onset for a single channel is about 30%, whereas it is about 40% for the multichannel system.  CONCLUSION  The analysis that has been carried out in the present paper shows the possibility to predict the onset of density wave oscillations by means of RELAP5/MOD3.3 code for simple geometry systems, whereas the difference between  1D and 3D approximations is not relevant for the purpose of the analysis; the shape of the boundary line in the stability maps  is in agreement with the other authors prediction. The approximation used for helically coiled pipes in the multichannel systems seems not to affect the instability onset  and the classical shape of the instability maps, that seem a powerful tool for the fluid dynamic instability prediction.     Fig. 8. Stability Maps for multichannel system  NOMENCLATURE ݄௜௡:   inlet enthalpy ݄௟ǡ௦௔௧:   liquid saturation enthalpy ݄௙௚:  vaporization enthalpy k : localized pressure loss coefficient Npch:  Phase change number Nsub:  Sub-cooling number ݒ௙௚:  difference between vapour and  liquid specific volume ݒ௙:  liquid specific volume W:  mass flow rate ݔ௢௨௧: outlet quality ߶:  thermal power  REFERENCES [1] S. KAKAC, B.  BON, "A Review of two-phase flow dynamic instabilities in tube boiling systems", International Journal of Heat and Mass Transfer, Volume: 51,  3-4,  399-433, (2008) [2] A.H. STENNING, Instabilities in the flow of a boiling liquid ASME, Transactions, Series D-Journal of Basic Engineering. Vol. 86, pp. 213-217, (June 1964)   [3] K. FUKUDA AND S. HTASEGAWA, Analysis of two phase flow instabilities in parallel multichannels, J. Nucl. Sci. Technol. 16, 190, (1979).  [4] G.YUN,  "Experiment investigation on two-phase flow instability in a parallel", Annals of Nuclear Energy, (2010). [5] D. PAPINI, M. COLOMBO, A. CAMMI, M.E. RICOTTI, D. COLORADO, M. GRECO, G. TORTORA, Experimental Characterization of Two-Phase Flow Instability Thresholds in Helically Coiled Parallel Channels, Proceedings of International Congress on Advances in Nuclear Power Plants (ICAPP) Nice, France, (May 2-5 2011). [6] P. SAHA, M. ISHII, N. ZUBER, An Experimental Investigation of the Thermally Induced Flow Oscillations in Two-Phase Systems, Journal of Heat Transfer, Trans. ASME 98, 616-622, (1976). [7] U.S. NRC Nuclear Safety Analysis Division, RELAP5/MOD3.3 Code Manual, NUREG/CR-5535/Rev1 (2001). Transactions of the American Nuclear Society, Vol. 106, Chicago, Illinois, June 24–28, 2012978 Computational Thermal Hydraulics—I

English

https://iris.polito.it/retrieve/handle/11583/2499980/57405/Transactions_0975-0978.pdf

Use of RELAP50MOD3.3 Code to Get Fluid Dynamic Stability Maps

Abstract

Similar works

Full text

Available Versions

PORTO Publications Open Repository TOrino

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)