Accepted Manuscript Two-Phase Flow Field Simulation of Horizontal Steam Generators Ataollah Rabiee, Amir Hossein Kamalinia, Kamal Hadad PII:
S1738-5733(16)30146-2
DOI:
10.1016/j.net.2016.08.008
Reference:
NET 254
To appear in:
Nuclear Engineering and Technology
Received Date: 5 October 2015 Revised Date:
19 July 2016
Accepted Date: 9 August 2016
Please cite this article as: A. Rabiee, A.H. Kamalinia, K. Hadad, Two-Phase Flow Field Simulation of Horizontal Steam Generators, Nuclear Engineering and Technology (2016), doi: 10.1016/ j.net.2016.08.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Two-Phase Flow Field Simulation of Horizontal Steam Generators Ataollah Rabiee1*, Amir Hossein Kamalinia1, Kamal Hadad 1
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1- School of Mechanical Engineering, Shiraz University, Shiraz, Iran. *Corresponding author (Ataollah Rabiee, Email:
[email protected], P.O.B. 7193616548)
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Abstract
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The analysis of steam generators as an interface between primary and secondary circuits in light water nuclear power plants is crucial in terms of safety and design issues. VVER-1000 nuclear power plants use horizontal steam generators which demand a detailed thermal hydraulics investigation in order to predict their behavior during normal and transient operational conditions. Two phase flow field simulation on the adjacent of the tube bundles is important in
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obtaining logical numerical results. However; the complexity of the tube bundles, due to geometry and arrangement, makes it complicated. Employment of porous media is suggested to
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simplify numerical modeling. This study presents the use of porous media to simulate the tube bundles within a general-purpose computational fluid dynamics code. Solved governing
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equations are generalized phase continuity, momentum and energy equations. Boundary conditions, as one of the main challenges in this numerical analysis, are optimized. The model has been verified and tuned by simple two dimensional geometry. It is shown that the obtained vapor volume fraction near the cold and hot collectors predict the experimental results more accurately than in previous studies. Keywords: Horizontal Steam Generator, Computational Fluid Dynamics, Porous Media, Vapor Volume Fraction.
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1. Introduction The analysis and study of the steam generators is one of the more interesting and important
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subjects in the investigation of PWR nuclear power plants. The importance of these studies could be summarized in two issues: generating dry steam and avoiding the radioactive pollution boundary between primary and secondary circuits. In this study, the influence of porous media in
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order to simulate the tube bundle is investigated. The previous studies in this area are mentioned in the following.
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The importance of the tube bundle and its modeling as a porous media, Rahman et al. [1] investigated interfacial drag force in their calculations, and proposed pressure drop equations that can predict the two phase flow field reasonably. These equations have been obtained by the experimental observations in different two phase flow regimes. Bearing in mind these types of experiments, Stosic et al. [2] proposed one of the most complete numerical models that suggests
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the replacement of the tube bundle with porous media. This model, with the aim of prediction of complex geometry thermal hydraulic characteristics, has been used in the simulation of kettle reboilers [3, 4 and 5] and steam generators [6, 7 and 8]. In this research, few of the governing
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equations have been expressed based on Simovic et al. [9]. In these studies, in addition to
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reduction of the CFD execution time, compliance between obtained results and experimental results has been reported.
Bamardouf et. al. [10] carried out experimental and numerical studies in order to obtain a model to predict pressure drop in two phase flow across the horizontal tube bundle. In addition to the experimental results, different correlations have been obtained for two phase flow across the tube bundles in different flow regimes. Based on available modeling and their previous research in two phase flow, a slice of the kettle reboiler flow field has been simulated with CFX software.
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Different outlet boundary conditions have been discussed and have shown that the predicted pressure drop and vapor volume fraction distribution is in compliance with the experimental
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results as well [11, 12]. To the best of author's knowledge, there are few references on the simulation of the VVER 1000 steam generator (SG) modeled by the use of porous media. The purpose of this study is to
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evaluate the capability of the available CFD software in simulation of the SG tube bundle by comparing the results of numerical code with the available experimental results and in the
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presence of appropriate boundary conditions. In the current study, to properly simulate the two phase flow field, the change of flow regime from bubble flow to churn and finally mist flow has been considered. The details of the numerical algorithm that are important in such simulations including tube bundle pressure drop, turbulence, heat and mass transfer models are fine-tuned
2. Governing equations
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and explained in the following.
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The flow field adjacent to the tube bundle in an SG can be studied through a variety of techniques. In order to model the two phase flow field, averaged Navier-Stokes equations have
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been used with an Eulerian-Eulerian approach for each. Detailed descriptions of the mathematical models used in the available code (FLUENT) are stated in the following section [13].
• Continuity equation:
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(1)
In equation (1), subscript “q” indicates the phase, and n is the number of phases in the
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system, , , , are the volume fraction, density and velocity vector in the phase, respectively. denotes the mass transfer from to q phase, while m
!
is the mass transfer
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from to phase. is the external mass source applied on the phase and is the
• Momentum Equation:
+ ∇ ∙
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porosity coefficient of the porous media.
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= −γ ∇ + ∇ ∙ $̿ + & + '( + −
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2 34 6 67 8 + ) + ) *+,, + ) ./, + 01 + 2
(2)
In equation (2), is pressure, 9: is stress-strain tensor in the phase, '( is the interfacial
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drag force between the two phases and ) ,) *+,, and ) ./, are the external body, lift and virtual mass exchange forces, respectively.
• Energy equation:
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= −γ
+ $̿ : ∇ + − ∇.
+ > + ℎ − ℎ + >?
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ℎ + ∇ ∙ ℎ
(3)
where ℎ , S , > are the specific enthalpy of the phase, external heat source term and the
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intensity of heat exchange between the phases, respectively. ℎ , ℎ and >? are the inter-phase
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enthalpies and heat transfer between the porous media solid phase and each vapor and liquid phases, respectively.
2.1. Pressure drop
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According to Simovic et al. [9], the relations of tube bundle pressure drop has been used from Isachenko et. al. [14]. This correlation is obtained from experiments that have been performed on
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the tube bundle flow field as a two phase flow multiplier. • Liquid phase pressure drop:
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∆ = BC , C,4 D1 − FG
(4)
• Vapor phase pressure drop: ∆ 4 = BC4 H CH4 F
where F is vapor volume fraction and Eu defined by following equations [9]:
(5)
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P P 1− 1− Q Q > 0.53 MN.4O BCI = 1.93DK + 1GW 'LI . Q Q P−1 P−1
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(6)
(7)
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In equations 6 and 7: z, Re[ , D and P are the tube bundle rows in the direction of flow, Reynolds
number for liquid(k=1) or vapor (k=2) and diameter of the tubes and pitch of the tube bundles,
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respectively.
2.2. Interfacial Drag Force
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Interfacial drag force in the momentum conservation equation is crucial to predict the vapor volume fraction. Simovic et al. drag correlation has been used in this research [9].
(8)
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3 3\ ( H − ^ ( , 6^ ( H − ^ ( , '( H, = , F. 6^ 4 P]
Interfacial drag coefficient has been employed as: 4
&∆ 1 + d17.67D1 − FGe 3\ = 0.267P] a c j . F ≤ 0.3 b 18.67D1 − FGh/4 f
&∆ D1 − FGh D1 − 0.75FG4 . F > 0.3 3\ = 1.487P] a b
(9)
(10)
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It should be stated that the mentioned topological function in this simulation tries to follow the regime change from bubble flow to churn and mist flow based on the void fraction. It seems that in every computational cell, the void fraction of less than 0.3 represents the bubble flow regime.
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Otherwise churn flow plays a significant role. It is noteworthy that in the momentum equation virtual mass force has not been considered and the lift force coefficient is considered as 0.3
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based on the reference [2].
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2.3. Porosity
In the present work, according to the arrangements of the SG tube bundle as shown in figure 1,
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the porosity can be defined by equation (11) based on the McNeil et al. [12].
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a) Square (In -line)
γ1
k mn
l op oq
2.4. Interfacial phase change
b) Triangle (Staggered)
Figure 1 Tube bundle arrangement.
(11)
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Heat transfer between the first and second loop due to the enthalpy increasing and the liquid phase change to vapor, can be computed based on the interfacial phase change as in the
(1 − FG, ℎ − ℎt . ℎ < ℎt $s ℎ" − ℎ t
rw
(1 − FG, ℎt − ℎ . ℎ > ℎt و4 > 0 $w ℎ" − ℎ t
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rs
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following equations.
(12)
(13)
where rs and rw are the evaporation and condensation mass transfer and , and ℎ are the liquid
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density and liquid enthalpy respectively. $s and $w are the evaporation and condensation relaxing times [2] and ℎt and ℎ" are the saturation liquid and vapor enthalpy, respectively.
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2.5. Turbulence modeling
In this study, two regions are considered; the tube bundle and shell regions. k-epsilon equations
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are employed in the shell region to simulate the two phase flow field, while in the tube bundle zone, a porous media model is used and no turbulent model has been considered [3]. •
k-ε Model
(x) 2y + ∇ ∙ (Cx) 12 + 7 ∆x + z { bI
(14)
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({) 2y { {4 + ∇ ∙ (C{) 12 + 7 ∆{ + 3| z 3|4 b| x x
(15)
where k is the turbulence kinetic energy, ε is the dissipation rate and “G” denotes the production
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of turbulence kinetic energy. The model closure coefficients employed here are the ’standard’ ones (see, e.g., [13]): 3} = 0.09, bI = 1.0, b| = 1.3, 3| = 1.44, and 3|4 = 1.92.
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2.6. Heat transfer of primary to secondary loops
reported in Stosic et. al. [2] as follows: ~ = ℎ_ − I
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The primary circuit is modeled by taking inspiration from the energy source term that has been
(16)
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_ is the tube bundle wall temperature and I is the temperature of the fluid that is placed
around the tubes. The heat transfer coefficient can be computed as follows: ℎ = D G~
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D G = 4.32D N.l + 1.28 × 10M4 4 G
= 0.7
(17) (18)
P is the pressure (MPa), ~ is the surface heat flux and n is the constant equal to 0.7. It should be noted that the flow in the tube bundle is a kind of single phase flow that transfers heat from the primary side of the SG to the secondary side.
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To computethe wall temperature, the following methodology is used. The water temperature at the inlet and outlet is set at 321 and 291 Celsius respectively (VVER 1000 SG characteristics). Due to the fact that boiling occurs on the outer side of the tube wall, the temperature in this zone
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(not tube wall temperature) is fixed. As a result, figure 2 is obtained numerically for the wall
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temperature:
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Figure 2 Wall temperature distribution along the tube length
According to the stated equations, the wall heat flux would decrease along the tube bundle. It is
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noteworthy to say that this procedure has been employed for VVER440 SG by considering its inlet and outlet temperatures.
3. Results and Discussion
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This section presents the results of the modeling of the two phase flow field accompanied by porous media for a reboiler for validation of the available CFD code (FLUENT) and simulation
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of the VVER 1000 SG.
3.1. Results of the Kettle Reboiler Thermal-Hydraulic Characteristics
The kettle reboiler as a special reboiler with the horizontal tube bundle has been considered to
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validate the CFD code. According to the available experimental results [4, 5] two arrangements have been considered. Figure 3 and 4 and table 1 depict the geometry, boundary condition and
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characteristics of the kettle reboiler, respectively.
Figure 3 Kettle reboiler tube bundle arrangements.
The inlet mass flow rate is based on the vapor generation on the reboiler as follows: m
Q h
(19)
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Q is the tube bundle heat power (W) and hfg is the difference between the saturation vapor
Arrangement 2
Tube diameter
19 mm
15.9 mm
Tube pitch
25.4 mm
Radius of the shell
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Arrangement 1
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Table 1 Kettle reboiler characteristics
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enthalpy that exits the kettle reboiler and the saturation liquid which enters the kettle reboiler.
23.88 mm 0.254 m
Level of fluid from center of the shell
0.21 m
0.17 m
Distance between center of the tube bundle and the shell
0.114 m
0.0714 m
Tube numbers
241
75
Tube arrangement
Square
Square
Working fluid
R113
R113
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0.368 m
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Figure 4 Kettle reboiler boundary conditions.
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The tube bundles are simulated using the porous media and outlet boundary conditions with a vapor volume fraction equal to 90 percent as reversed flow [12]. Figure 4 depicts the schematic of the kettle reboiler boundary conditions. It is noteworthy that the computational domain could
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be generated simply by using the tube bundle as porous media. According to arrangement 1
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which is mentioned in table 1, pressure drops in different rows are depicted in figures 5 and 6. As can be seen, the pressure drop profiles are in reasonably good agreement with the experiment and an increase in the heat flux level reduces the pressure drop in every row, correspondingly.
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Figure 5 Kettle reboiler (arrengement 1) pressure drop in heat flux 10 kW/m2.
Figure 6 Kettle reboiler (arrengement 1) pressure drop in heat flux 20 kW/m2.
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According to table 1 and arrangement 2, the description of both liquid and vapor phases vectors
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in heat flux 10 kW/m2 have been depicted in figure 7 and 8, respectively.
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Figure 7 Description of kettle reboiler (arrengement 2) liquid phase vectors in heat flux 10 kW/m2
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Figure 8 Description of kettle reboiler (arrengement 2) vapor phase vectors
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in heat flux 10 kW/m2
As can be seen from these figures, natural circulations have taken place in the kettle reboiler, due to the hot tube bundle which is placed in the middle of the shell reboiler and leads to a reverse
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flow, particularly at the boundary conditions. The direction of the reverse flow, due to natural
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circulation, would be clockwise in the computational domain which blocks the vapor phase flow that is exiting the flow field, near the curved reboiler wall (Figure 7). It seems that due to flow at the opening outlet boundary conditions, with vapor void fraction equal to 0.9, reverse flow can take place in these boundary conditions and some of the vapor can be trapped, due to the curvature of the reboiler shell wall (Figure 9).
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Figure 9 kettle reboiler (arrengement 2) vapor void fraction contours in heat flux 10 kW/m2.
In the following vapor volume fraction, distributions in different rows are shown in Figure 10 to 13 for a wall heat flux equal to 10 kW/m2. In this case, inlet and outlet boundary conditions are
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considered as mass flow inlet and pressure outlet, respectively [3]. It could be concluded that the
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obtained results, based on the outlet boundary conditions, have better agreement with the measurements compared to the similar CFD simulation of Pezo et. al. [3].
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Figure 10 Kettle reboiler (arrengement 2) void fraction distribution in heat flux 10 kW/m2 between 1st
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and 2nd rows.
Figure 11 Kettle reboiler (arrengement 2) void fraction distribution in heat flux 10 kW/m2 between 4th and 5th rows.
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Figure 12 Kettle reboiler (arrengement 2) void fraction distribution in heat flux 10 kW/m2 between 8th
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and 9th rows.
Figure 13 Kettle reboiler (arrengement 2) void fraction distribution in heat flux 10 kW/m2 between 13th and 14th row.
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3.2. Results of the BNPP SG Thermal-Hydraulic Characteristics The SG vapor volume fraction could affect the design and the vapor quality that transfers to the
3.2.1. Geometry and boundary conditions
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turbine. Results of the BNPP SG thermal-hydraulic characteristics are reported in the following.
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The steam generators of the BNPP are the type of steam generators with horizontal tube bundles.
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Table 2 and Figure 14 depict geometry and characteristics of BNPP SG, respectively. Table 2 Bushehr NPP SG Characteristics.
Parameter Thermal power ( MW)
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Steam capacity (t/h)
Value 753 1470 6.27
Coolant inlet tempreture (ºC)
321
Coolant outlet tempreture (ºC)
291
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Outlet pressure (MPa)
Feedwater tempreture (ºC)
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Coolant flow rate (m3/h)
220 21200
Nominal secondary side level (m)
2.6
Distance between axes of rows (mm)
19
Distance between tubes axes in a row (mm)
23
Total heat transfer area (Secondary side) (m2)
6.115
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1-Housing 2-Heat Exchanger Surface 3-Collector 4-Feed Water Collector 5-Emergency Feed Water Collector 6Steam Perforated Plate 7-Perforated Plate
Figure14 Bushehr NPP SG [15].
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Feed water nozzles inject water from a collector that includes perforated tubes above the hot side of the SG. In normal operations, the average mass of the feed water injection is equal to generation vapor. In this study, according to Figure 15, feed water is simulated by the five feed
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boundary is set at the nominal level of the SG.
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water sources above the tube bundle. In order to reduce the computational cell, the outlet
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Figure 15 Schematic of feed water in computational domain.
The grid dependency has been investigated based on average relative pressure along the height of the SG. The following figure depicts the grid dependency analysis. It is obvious that the three grids return similar solutions, indicating mesh-independency has been achieved.
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Figure 16 Grid-independence examinations.
3.2.2. Results and Discussion of Bushehr Steam Generator The Eulerian - Eulerian approach is employed to predict vapor volume fraction distribution in
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computational fluid dynamics modeling. Obtained results in this research have been compared
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with similar research [7 ,8]. Table 3 and Figure 17 show the criterion points At which measurements have occurred.
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Table 3 Criterion points. Distance from Perforated Plate (mm)
، ، ، ، ، ، ، ، ،
350
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70
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Point
Figure 17 Positions of criterion points.
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In order to reduce the computational cell, the outlet boundary has been set at the nominal level of the SG and reversed flow has been considered as the 80 percent vapor volume fraction. Figure 18 and table 4 show the vapor volume fraction and the comparison between current and similar
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studies with the measurements, respectively. Although, as can be seen from table 4,
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predicted vapor volume fractions in some points such as 12 and 14 are slightly under-predicted, vapor volume fractions are in reasonably good agreement with the experiments in comparison
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with previous numerical studies [7, 8].
Figure 18 SG vapor volume fraction at different sections.
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Table 4 Comparison of the vapor volume fraction in different studies.
F2 F3 F4 F6
0.43
0.63
0.49
0.45
0.54
0.76
-
0.32 0.43
0.50
0.41
0.64
0.72
0.77
0.68
0.69
0.55
0.53
0.51
0.56
0.54
0.40
0.51
0.51
0.44
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0.55
Current Study
0.50
0.63
0.57
0.46
0.52
0.54
0.48
0.48
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F14
0.45
0.45
F12 F13
0.55
0.55
F10
al. [8]
0.30
0.70
F8
Safavi et.
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F1
Melikhov et al. [7]
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EXP. [16]
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point
Basically, achieving an accurate solution in multiphase flows, particularly in a two phase flow,
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demands tuning the available code based on the various models, such as heat and mass transfer models, lift and drag, and coupling these models with turbulent models, spatial discretization and adjusting proper boundary conditions. The distributions of averaged void fraction in the vicinity of the hot and cold legs at the different elevations are shown in Figures 19 and 20. In addition to the higher value of the vapor volume fraction at hot side of the steam generator, it is observed that the void fraction increases with the
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elevation and relatively has good agreement with the measurements in comparison with drift flux numerical model [17] as well as the RELAP numerical simulations [18, 19]. Three – dimensional simulation in the current study in comparison with the one dimensional simulations in the
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previous works, is one of the main reasons for improved agreement with experimental results.
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Figure 19 Distribution of cold leg void fraction.
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Figure 20 Distribution of hot leg void fraction.
4. Conclusion
In this research, an effort is made to simulate the BNPP SG tube bundles using the porous media
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model within the general-purpose computational fluid dynamics codes. Simulation of the flow field is carried out using averaged Navier-Stokes equations with the Eulerian - Eulerian approach for each phase and optimized boundary conditions. To validate and tune the available
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computational fluid dynamic code, a two dimensional analysis of a typical kettle reboiler has been considered (Figures 5 to 13).
A point to point comparison of the obtained results in
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various parts of BNPP SG indicates better agreement with the experimental data than previous studies (Table 4). Averaged void fractions calculated near the walls of the cold and hot legs at different elevations signifies that the amount of vapor volume fractions at SG hot side is higher than the cold one due to more heat flux in the hot side (Figures 18 to 20) and the location of the feed water nozzle that leads to an increase in turbulence as well.
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Inertial resistance coefficient [m-1]
3\
Drag coefficient
P
Tube diameter [m]
P]
Average bubble dimeter [m]
)*+,
Lift force [N]
)
Virtual mass force [N]
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Nomenclature
Gravitional accelaration [m s-2]
ℎ,
Enthalpy of saturated Liquid [j kg-1]
ℎH
Enthalpy of saturated vapor [j kg-1]
ℎ,H
Difference of enthalpy between saturated liquid and vapor [j kg-1]
Length [m]
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&
Mass flow rate between phases [kg s-1]
H
Vapor mass flow rate [kg s-1]
'(
Interfacial drag force [N]
Source
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Tube bundle pitch [m]
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Q
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Time [s]
Tempareture [K]
^,
Liquid velocity [m s-1]
^H
Vapor velocity [m s-1]
1/
Viscous resistance coefficient [m-2]
F
Vapor Volume Fraction
,
Liquid density [kg m-3]
H
Vapor density [kg m-3]
2
Dynamic Viscosity [Pa s]
b
Surface tension [N m-1] Liquid Tube Bundle Pressure Drop [Pa]
∆ H
Vapor Tube Bundle Pressure Drop [Pa] Condensation mass transfer [kg s-1]
rs
Evaporation mass transfer [kg s-1]
$w
Condensation relaxing time [s]
$s
Evaporation relaxing time [s]
Porosity
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References
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rw
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∆ ,
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vertical two-phase cross-flow past horizontal in-line and staggered tube bundles, Int. J. Multiphase Flow 22, pp. 753–766, 1996 [2] Z.V. Stosic, V.D. Stevanovic, Advanced three-dimensional two-fluid porous media method for transient two-phase flow thermal-hydraulics in complex geometries, Numer. Heat Transfer B: Fundam. 41 (3-4), pp.263–289, 2002. [3] M. Pezo, V. Stevanovic, Z. Stevanovic, A two-dimensional model of the kettle reboiler shell side thermal–hydraulics, Int. J. Heat Mass Transfer 49 (7–8) , pp . 1214–1224, 2006.
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and design 256 249-255, 2013.
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across tube bundle, Int. J. Multiphase Flow 33 , pp. 217–226, 2007. [10] K. Bamardouf, D. A. McNeil, Experimental and numerical investigation of two-phase pressure drop in vertical cross-flow over a horizontal tube bundle, Applied Thermal Engineering, Volume 29, Issue 7, May 2009, pp. 1356-1365, 2009. [11] D.A. McNeil, K. Barmardouf, B.M. Burnside, M. Almeshaal, Investigation of flow phenomena in a kettle reboiler, Int. J. Heat Mass Transfer 53 pp. 836–848, 2010.
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[12]D.A. McNeil, K. Bamardouf, B.M. Burnside, Two-dimensional flow modelling of a thin slice kettle reboiler, Int. J. Heat Mass Transfer 54, pp. 1907– 1923, 2011. [13] K. Vafai, Handbook of porous media, Second Edition, Ch1, Taylor & Francis, 2005.
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[14] Isachenko, V.P., Osipova, V.A., Sukomel, A.S., Heat Transfer, Third edition. Mir Publishers, Moscow, pp. 473–474, 1980..
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