Numerical Investigation on the Long-term System Transient Response ...

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 40, No. 10, p. 871–880 (October 2003)

ORIGINAL PAPER

Numerical Investigation on the Long-term System Transient Response of a SWR Event in a LMR Jae-Hyuk EOH* , Eui-Kwang KIM and Seong-O KIM Fluid Engineering Division, Korea Atomic Energy Research Institute, 150 Dukjin-dong, Yusong-Gu, Taejon, Korea, 305-353 (Received March 7, 2003 and accepted in revised form May 30, 2003) In order to investigate the later phase of a sodium-water reaction (SWR) event, the code SELPSTA (Sodium-water reaction Event Later Phase System Transient Analyzer) has been developed and the analysis for the long-term system dynamic responses of a SWR event in KALIMER (Korea Advanced LIquid MEtal Reactor) has been made. The SELPSTA code uses the very simple analysis model applied only to the reaction period characterized by a bulk motion, and makes the very quick and concise computation possible. The code reasonably predicts the quasi-steady system transients and has the superiority in the aspect that the various design parameters or operational characteristics are flexibly applicable. In the long-term period of a SWR event, the system dynamic responses analyzed by the code totally depend on the system design parameters such as the breaking pressure of the rupture disk, the variation of the steam injection rate and the sodium drain tank pressure, etc. Based on these analyses results, it is expected that the numerical quantification method of the SELPSTA code is practicable for the long-term system transient analysis and also makes the design of a pressure relief system against a SWR event in a liquid metal reactor (LMR) possible. KEYWORDS: sodium-water reaction, KALIMER, spike pressure, quasi-steady state, water/steam leak rate, simple analysis model, steam to hydrogen molar conversion ratio, cover gas, SWRPRS

I. Introduction A sodium water reaction is an important issue on the design of a steam generator and related systems of a liquid metal reactor (LMR). The system dynamic response during a sodium water reaction event shows very different characteristics between the initial stage of an acoustic wave propagation and the long-term period of a bulk motion. Accordingly, the analysis of a sodium-water reaction, hereafter called SWR, can also be classified by two major events in general. One is the very initial stage of peak pressure and acoustic wave propagation caused by the reaction itself, and the other is the bulk motion including the mass transfer phase in the quasi-steady state of the reaction period during several second or minute orders after leak initiation. Although a numerical analysis of the long-term system transient behavior of a SWR event has been performed in many preceding works, complex modeling and numerical schemes have been applied to the analysis because it has been treated as an extended work of the initial wave propagation stage. However, a complicated method for the analysis of long-lasted reaction phenomena may not be necessarily required in a design purpose if the characteristics of the event and consistency with the initial wave propagation stage are well considered and reflected. Therefore, in this study, only the main characteristics of the long-term reaction period are selected through the review of previous studies and the simple numerical quantification method has been developed by using them with careful considerations of the reaction phenomena. In the long-term period of a SWR event, acoustic wave propagation effects of a sharp and short-lived pressure pulse is ∗

Corresponding author, Tel. +82-42-868-8970, Fax. +82-42-8617697, E-mail: [email protected]

subsided and the system dynamic response depends on characteristics of the bulk motion with quasi-steady pressurization of the system due to a continuous chemical reaction. Since the intermediate heat transport system (IHTS) is a closed loop before the rupture disk breakage, the system pressure response in the quasi-steady state of a SWR can be determined by analyzing the pressure behavior of cover gas space in a steam generator. In order to simplify the very complex phenomena of a SWR, the analysis model can also be simplified by using the assumption that the cover gas space experiences the pressure and temperature transient by an inflow of hydrogen gas and exothermic energy from a leak site. Based on the very concise approach for the later phase of a SWR, a new computer code, SELPSTA (Sodium water reaction Event Later Phase System Transient Analyzer) has been developed by using the simple analysis model and the system dynamic responses including the sodium-water reaction pressure relief system (SWRPRS) behavior are also investigated in the present study.

II. Sodium Water Reaction in KALIMER Design 1. System Description of KALIMER Korea Advanced Liquid Metal Reactor (KALIMER) is a liquid metal sodium cooled fast reactor plant.1) The major systems of KALIMER are a reactor, reactor coolant system and connected systems, engineered safety features, instrumentation and control systems, electric power systems, auxiliary systems, and steam and power conversion systems. The overview of a nuclear steam supply system (NSSS) of KALIMER is shown in Fig. 1. The IHTS includes the sodium drain piping, the sodiumwater reaction pressure relief subsystem (SWRPRS), and vent

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after exchanging energy in the tube bundle region. Sodium free surface level is maintained above the sodium distributor to avoid gas entrainment from the argon cover gas space. 2. Large-leak Reaction Phenomena When a large quantity of steam or water is suddenly injected into the shell-side sodium caused by defects or ruptures of heat transfer tubes in a steam generator, the sodium water reaction will occur and large amounts of hydrogen gas and exothermic heat will be generated in the system. Though various chemical reactions occur competitively during the reaction period, it is very difficult to consider all of these possible reactions. Therefore, to analyze the system pressure transient during the reaction period, it needs to simplify the complex reaction phenomena using the representative reaction equation. The reaction between sodium and water/steam can be expressed as the following general form of the chemical reaction equation,2, 3) A·Na + H2 O → B·Na2 O + C·NaOH + D·NaH Fig. 1 Overview of the KALIMER plant

piping from the steam generator. Each IHTS loop including steam generator (SG) has its own SWRPRS, which consists of the sodium dump tank (SDT), separator, rupture disk, backpressure rupture disk, and piping, and it provides pressure relief and gas venting capability to mitigate the effects of tube failure in the steam generator. A rupture disk is installed at the piping located at the bottom of the steam generator, and will burst by an excessive pressure in the steam generator caused by a large sodium-water reaction event. In a case of the burst of the rupture disk, the shell-side sodium and the sodium slugs are dumped to the dump tank through the rupture disk line. The dumping of the sodium and sodium slugs can be accelerated rapidly by the increased cover gas pressure resulting from the continuous sodium-water reaction in the steam generator. The dump tank normally contains fresh sodium about 0.5 m in depth for make-up and for protection from thermal shock in case of quick hot sodium dump, and it is always controlled at 200◦ C same as other sodium piping systems. The dump tank can accommodate the SWR products and all sodium of IHTS including the steam generator and its free volume is 150 m3 , and it is also connected to the IHTS sodium purification system. Thermal expansion and/or contraction of the sodium in the IHTS loop or steam generator is accommodated by the cover gas space in the steam generator and the sodium level control system. In KALIMER design, the argon cover gas space located in the top of the steam generator is also designed to mitigate pressure spikes in a SWR event instead of using an additional surge tank in the loop and it simplifies system design and arrangement, e.g. reducing the number of component and structures, etc. In the steam generator, intermediate sodium heated in the intermediate heat exchanger (IHX) flows through the IHTS piping and enters at the top of the unit through the sodium distributor, and then leaves the steam generator unit through a central nozzle on the bottom head

+ αH2 + Q.

(1)

In this equation, A, B, C and D are the reaction constant, Q is an exothermic reaction energy produced by the reaction and α is a molar conversion ratio of unit mole of water/steam to hydrogen gas. Sodium reacts with unit mole of water/steam, as shown in Eq. (1), and then various reaction products such as NaOH, NaH, Na2 O and hydrogen gas are produced with an exothermic reaction heat. In these main reaction products, it is well known that the gaseous product like hydrogen gas plays an important role in a system pressure transient.2, 3) The molar conversion ratio (α) of steam to hydrogen gas is one of the most important factors in the analysis of a SWR event, therefore, it should be defined quantitatively to verify the system pressure transient caused by hydrogen gas and exothermic heat generation. From previous researches conducted in various organizations such as PNC in Japan, GE in USA, and EDF in France, etc., the value of α is reported experimentally as about 0.5–0.7, and the absolute temperature of the hydrogen gas produced by the reaction has a value between 1,000 K and 1,660 K in a large-leak SWR analysis.3–5) For a large safety margin in view of system design, the molar conversion ratio is set up as 0.7 and the absolute temperature of hydrogen gas is assumed as the constant value of 1,300 K in this study. Accordingly, the generation quantity of hydrogen gas can be considered totally as a function of the existent quantity of water/steam in the shell-side sodium and the steam to hydrogen conversion ratio. 3. Backgrounds of the Code Development The analysis of the system pressure and temperature responses during a SWR event in KALIMER has been performed using the SPIKE code2) and the SELPSTA code developed in this study. The SPIKE code is developed only for the prediction of the system transient behavior of the very initial stage of peak pressure, called as a spike pressure, incurring acoustic wave propagations in the system. The SPIKE code is based on the numerical scheme of MOC (Method of Characteristics) for solving wave equations. Since the scheme,

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however, is only used to solve an acoustic wave propagation phenomena, it does not have a proper method for solving the mass transfer phenomena in the quasi-steady pressure transient. Figure 2, for example, shows the pressure variation of the rupture disk line mounted on the lower part of the steam generator as results of the SPIKE calculation. As shown in this figure, the pressure variations are independent of a specific design feature, such as the cover gas volume, in the very initial stage of acoustic wave transfer regime, and this well shows the characteristics of the acoustic wave propagation. On the other hand, they seem to be strongly dependent on design features in the mass transfer regime, but the use of the SPIKE code in these quasi-steady pressure transients just after the subsidence of the acoustic wave propagation phenomena may incur the improper or unreasonable prediction because the SPIKE code has a drawback in mass transfer calculation. The SPIKE code has been developed under the assumptions that the pressure wave is generated only by single hydrogen gas bubble formed by the reaction and that the initial spike pressure behavior totally depends on the single bubble growth.2, 6) As the reaction is progressed, the bubble size increases rapidly and is finally bigger than the diameter of the steam generator, therefore the SPIKE calculation has the difference from the practical phenomena of quasi-steady system transients of a SWR event. This is the reason that the SPIKE code predicts physically unreasonable calculation results in the longer term period of a SWR event.6) That is, the system design features in mass transfer phase cannot be properly reflected in the SPIKE calculation and, from this reason, the applicable range of the SPIKE code should be limited just for the very initial wave propagation stage up to 100 ms– 1 s.6) Accordingly, it is suitable for using the SELPSTA code rather than the SPIKE code in the quasi-steady state, and the SELPSTA code has the feasibility for reasonable analysis during the long-term period of a SWR to reflect system design features, effectively. In the SELPSTA code, to simplify complex phenomena of a SWR in the mass transfer phase, it is assumed that all the hydrogen gas and exothermic energy due to the sodium-water reaction merged into the cover gas region in the steam generator, and the system pressure transient could be regarded as the

cover gas pressure transient. This is extremely concise and quick calculation method to investigate the system pressure transient for an extended time period. Since the SELPSTA code, however, does not have a suitable function for analyzing the pressure wave propagation, the initial conditions for the code calculation such as system pressure and temperature should be needed. In view of the consistency between the initial stage and the mid/long term period of the reaction, the calculation results of the SPIKE code are used as the initial conditions of the SELPSTA code. This is the very feasible approach to have a consistency in the analysis of a SWR event in KALIMER design for an extended time period including acoustic wave propagation phenomena and quasi-steady system transients. The detail descriptions for the SELPSTA code are provided in the following section.

Fig. 2 Pressure variation in R/D line (SPIKE calculation)

Fig. 3 Schematic drawing for a simple analysis model of a SWR

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III. Description of the Code SELPSTA 1. Simple Analysis Model The analysis of the later phase of a SWR event is mainly treated as none acoustic wave propagation during several milli seconds but the quasi-steady pressure transient including the rupture disk breakage and pressure relief system behavior during several seconds or minutes up to the ending time of the reaction. Based on these features, the system pressure variation is regarded as the cover gas pressure variation since the shell side sodium is assumed as an incompressible liquid and the mass and energy transferred from the reaction site flow into the cover gas region. The schematic drawing of the simple analysis model for the later phase of a SWR is shown in Fig. 3. To simplify complex phenomena of a SWR event in the steam generator, it is assumed that (1) the reaction occurs instantaneously if a water/steam leaks into a sodium phase, (2) non-reacted quantity of water/steam in the sodium phase is negligible, (3) the generation quantity of hydrogen totally depends on the steam to hydrogen conversion ratio, (4) all of the hydrogen gas and exothermic energy due to the reaction itself flow into the cover gas space. Using this brief analysis model for the long-term period of

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a SWR event, the SELPSTA code has been developed and it calculates system pressure and temperature, sodium drain tank pressure, sodium discharge flow rate, sodium free surface level in the shell side of the steam generator, and termination time of the reaction, etc. Figure 4 shows the flow chart of the code calculation. The code is based on the following simplifications and assumptions; – flow is one-dimensional. – shell side sodium is incompressible. – gas phase in the system is an ideal gas. – system is totally adiabatic. – no mixing between liquid and gas phase is existed. From the above assumptions, the energy balance between the cover gas and the shell side sodium can be described as shown in Fig. 5 and the energy balance presented here does not contain terms representing the phase change of the reaction products such as Na2 O and NaOH for simplification of the phenomena. The water/steam leak rate into the sodium phase is used as a source term for computation in the code, and the initial conditions of system parameters such as pressure and temperature of the cover gas region are cited from the results of the SPIKE code calculation at 1 s after the water/steam leak initiation, which will be mentioned in the later section in this paper. 2. Mathematical Model (1) Governing Equation The energy transfer process between the cover gas and the shell-side sodium can be expressed by the equation

Fig. 4 Computation flow chart of the code SELPSTA

Fig. 5 Energy balance around the cover gas region

∂E = Q gen − Q sin k − W˙ + Q i n − Q out . (2) ∂t Equation (2) is for the energy variation in a cover gas region, and the first term in right hand side of Eq. (2) becomes zero since no heat generation source in the cover gas region exists, and the last term of the equation is also decayed out since the system is completely adiabatic condition as mentioned above. The total stored energy in cover gas region can be expressed as the equation m i (h i − h io ), i = g, l, H. (3) Eg = i

According to the previous study, the multiplying term of m˙ l · h l can be negligible since a sodium vapor existed in the cover gas region is less than 1%.7) Accordingly, the total energy variation in cover gas region corresponding to the time can be described as shown in the equation ∂ Eg ∂m H = c p,H ∆Tg ∂t ∂t ∂ Eg ∂m H dt . (4) + m g c p,g + c p,H ∂t ∂t Each term in the right hand side of Eq. (2) can be expressed by the following equations. Equation (5) means the energy inflow term from the leak site to the cover gas region, and the heat transfer is carried out between hydrogen gas generated by the exothermic reaction and cover gas. Equation (6) represents the heat sink term of the cover gas region, which means the heat transfer process from the cover gas to the shell-side sodium, thus the sodium temperature increases in this mechanism: ∂m H (5) Q i n = (h H − h g ) ∂t ∂m g Q sin k = (h g − h l ) . (6) ∂t Equation (7) means work done by cover gas expansion to the system, and two independent boundary conditions of the rigid and the moving boundary condition are applied. The rigid boundary condition can be applied to the pre-stage of rupture disk breaking and, therefore, V˙ , which means the time derivative term, goes to zero since the free surface level of the shell-side sodium is fixed before the initiation of sodium discharge through the rupture disk line mounted on the lower part of the steam generator. After the bursting time of the rupture disk, the free surface level of shell side sodium is decreased


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due to the sodium discharge, the moving boundary condition should be applied for the post-stage of rupture disk breakage related to the cover gas expansion ∂ (7) W˙ = {Pg · Vg }. ∂t From Eqs. (4)–(7), we can obtain the differential form of the governing equation used in the computation as shown in the equation ˙ c p,H m˙ H ∆Tg + m acc H c P,H Tg = c p,H m˙ H ∆TH − m˙ g c p,g ∆Tg − (Pg V˙g + V˙g Pg ). (8) In this equation, the upper dot represents the time derivative term. Using Eq. (8), the temperature variation in cover gas region can be determined by the equation ∂ Tg mH = [c p,H (TH − Tg ) − c p,g (Tg − Tl )] ∂t m g,tot c p,g −

W˙ m g,tot c p,g

.

(9)

Where subscript tot means the total mass of each component such as cover gas and hydrogen existed in cover gas region. Also, using the state equation for the cover gas region regarded as an ideal gas such as helium or argon, Eq. (8) is rewritten as Eqs. (10) and (11) for numerical computation of cover gas pressure variations: R¯ j +1 j (m − m H )Tgj +1 Pgj +1 = Pgj + o Vg M H H j +1 j o m m acc g H ¯ (Tg − Tg ) + (10) R o + MH Mgo Vgo j +1

j ¯ gj +1 V − V RT g g j +1 j (m H − m H ) + Pgj +1 = Pgj 1 − j +1 j +1 Vg M H Vg j +1 j o m T m acc − T g g g H + o R¯ . (11) + j +1 M Ho Mg Vg Equation (10) describes the pressure variation of cover gas for the pre-stage of rupture disk breaking and Eq. (11) includes the depressurization term of cover gas region due to the sodium discharge in the post-stage of rupture disk breaking. From the energy balance between the cover gas and the shell-side sodium represented in Eq. (6), the sodium temperature can be determined as shown in Eq. (12) as the form of a numerical computation: Tl

j +1

= Tl + (Tgj +1 − Tgj ) + j

j +1

ml

j

− ml j

ml

j

(Tgj − Tl )

j

−

Q sin k ∆t j

m l c P,l

.

(12)

Where ∆t is the time difference between previous and current time step. (2) SDT and Sodium Discharge Model The sodium drain tank (SDT) is normally filled with an inert gas to avoid the possibility of a hydrogen explosion in the system after a sodium discharge from the system to the


SDT. The inert gas is maintained above atmospheric pressure so that oxygen will not leak into the tank. In order to maintain an inert gas in the SDT, a low-pressure rupture disk is installed in the pipe to the stack, and this rupture disk is quickly broken or ejected after a small pressure increase in the SDT. In order to model the SDT in the SELPSTA code, the inert gas in the tank is assumed as an ideal gas such as helium or argon; therefore, the pressure variation of gas space in the SDT is expressed by Eq. (13) as the differential form for numerical computation:

j +1 j VSDT − VSDT j +1 j PSDT = PSDT 1 − j VSDT +

m oSDT R¯ j +1 j · j (TSDT − TSDT ). o MSDT VSDT

(13)

Where subscript SDT means the gas filled in the upper part of the sodium drain tank. If the SDT pressure increases, the rupture disk mounted on the stack line is broken, and the SDT pressure suddenly decreases to the atmospheric pressure. The shell-side sodium is drained when the main rupture disk mounted on the lower part of the steam generator breaks, and then the free surface level decreases corresponding to the increase of the amount of discharged sodium. The mass flow rate of discharged sodium can be determined by the pressure difference between the system and the SDT pressure and flow resistance term of discharge pipe line as shown in the equation PSYS (t) + Pst,l (t) − PSDT (t) . (14) m˙ ex (t) = C R/D,pipe The term of Pst is the static pressure formed by the remaining sodium in the shell-side of the steam generator, and the value of C R/D,pipe means a flow resistance in the discharging pipe line from the steam generator to the sodium drain tank with its dimension defined as [Pa·s2 ·kg−2 ]. These two variables can be written as the equations Pst (t) = ρl (Tl )g Hl (t)

L pipe 1 +K C R/D,pipe = f . Dpipe 2ρl (Tl )Apipe

(15) (16)

Through these relations, the sodium discharge flow rate can be calculated and it is also used to determine the free surface level of shell-side sodium by using the relation t

˙ ex dt 1 Vl (t) t0 m o = Hl (t) = Vl − . (17) Aeff (H ) Aeff (H ) ρl (Tl ) The integrated term of the sodium discharge flow rate from the time t0 to the time t means the total venting volume of sodium with the dividing the sodium density. Also, Aeff means the effective sodium flow area defined as a function of sodium level in the shell-side steam generator. Since the rate of sodium level decrease is varied in each vertical position of the shell-side steam generator due to the flow area change caused by the complex inner structures such as the tube bundle and spacer grid, etc. (3) Steam Injection and Hydrogen Generation Model The steam injected into the shell-side sodium causes the exothermic chemical reaction, therefore, this injected steam

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is the reaction source term in the analysis of a SWR event. Since the pressure difference between tube-side steam and shell-side sodium is very large, the injection rate of steam can be assumed as a critical flow. Accordingly, using the choking flow correlation of steam,8) the steam injection rate can be determined as follows, 0.53 × Ptube , (18) m˙ crit = 1.62708 × (h s − 430.195) where m˙ crit is the critical mass flow rate per unit area with the dimension of [kg·s−1 ·m−2 ], and the tube-side steam pressure (Ptube ) is 15.5 MPa1) in the normal operation condition. Here, using Eq. (18), we can obtain the critical mass flow rate of steam injected into the shell-side sodium by multiplying the ruptured tube area. In this study, it is assumed that the event is three double-ended guillotine tube breaks (DEGB) as a design basis event in KALIMER,1) the mass flow rate of steam injection can be determined by the equation m˙ oleak = 3 × (2 × Aleak )m˙ crit .

(19)

Using Eqs. (18) and (19), the yielding rate of hydrogen gas can also be determined as follows. In this study, the molar conversion ratio is set up as 0.7 and hydrogen gas temperature is assumed as 1,300 K in a conservative sense as mentioned above. From the definition of steam to hydrogen conversion ratio, therefore, the rate of hydrogen gas generation in mass unit can be expressed as Eq. (20) using the molecular weight of hydrogen gas and water/steam: MH end m˙ leak exp[−γ (t − tleak )]. (20) m˙ PRH = α Ms The exponential decay term in right-hand side of Eq. (20) means the leak inertia term for a stability of computation proend means the ending time of the chemical reaction cess. Also tleak due to the reactants isolation, and γ is a constant for the leak inertia control. 3. Initial Conditions of the Code SELPSTA The SELPSTA code requires the initial conditions for the calculation of quasi-steady system transients as mentioned above. In view of the consistency with the initial stage of a SWR, the steam injection in the long-term period of the reaction should be modeled as follows. Since the design basis leak in KALIMER design is defined as three double-ended guillotine tube breaks at 1 s after leak initiation1) as shown in Fig. 6, it is feasible to carry out the SPIKE calculation up to that time in order to consider the consistency between the two codes and meet the design basis leak rate of KALIMER. The design basis tube leak rate maintains up to the ending time of the reaction, and the termination of the reaction is accomplished by either tube-side steam isolation or shell-side sodium clearing. Accordingly, the steam injection rate can be set up as design basis leak at 1 s after leak initiation using Eqs. (18) and (19), and this value is the initial flow rate of the tube leakage in the SELPSTA code regarded as a source term of the code calculation. Also, one more requirement to satisfy an analytic agreement between the earlier and later phase of a SWR event is the thermal hydraulic data such as the system pressure and

temperature at 1 s after leak initiation. Since the SELPSTA code solves the energy equation using the energy balance between the cover gas space and the shell-side sodium from the added energy caused by the reaction, these values are important parameters for the code calculation with other KALIMER design data. Accordingly, based on these steam injection profile and thermal hydraulic data, the initial conditions of the SELPSTA code can be provided using the results of the SPIKE calculation carried out up to the time of 1 s after tube leak initiation. In the SPIKE calculation, since the SPIKE code solves the wave equation using the numerical scheme of MOC, the system pressure behavior shows a very different trend according to the location in the steam generator as shown in Fig. 7. This figure shows the pressure variations of the system up to 1 s after leak initiation as results of the SPIKE calculation. As shown in this figure, the pressure variations in the cover gas space located in the top of the steam generator and the rupture disk line mounted on the lower part of the steam generator show a reversible behavior due to the wave propagation effect as mentioned above. In other words, the pressure increase in the cover gas region means the pressure decrease in the rupture disk line and this is the typical characteristics of the acoustic wave propagation stage of a SWR event. Accord-

tLEAK,END

Fig. 6 Variation of steam injection rate

Fig. 7 System pressure variation in earlier stage (∼1 s)


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ingly, to set up the overall initial conditions of the SELPSTA code for solving the system dynamic responses in the mass transfer phase showed a bulk motion, we should take the average value of system pressure. The straight line in Fig. 7 means the average system pressure, and the value at 1 s after leak initiation can be chosen as the initial system pressure for the SELPSTA calculation. Through these efforts, the representative initial conditions of the SELPSTA code for analyzing the long-term period of a SWR event in KALIMER can be provided as shown in Table 1.

IV. Results and Discussions Sample analysis results of the long-term period of a SWR event in KALIMER steam generator and related systems are given in this chapter to check the capabilities of the simple numerical quantification method used in the SELPSTA code. To analyze the quasi-steady system transient during a SWR event, the systems and components including the faulted steam generator, IHTS, rupture disk mounted on the lower part of the steam generator, and SWR pressure relief system (SWRPRS) are considered and modeled in this study using the design data of KALIMER.1) Figure 8 shows the yielding rate of hydrogen gas corre-

Table 1 Major design parameters for input deck of the code SELPSTA Parameters System pressure at normal operation Initial cover gas volume Initial sodium temperature in SG (average value) Cover gas pressure (at 1 s) Water/steam injection rate (design basis leak in KALIMER) Hydrogen gas temperature (constant) SDT free volume Initial SDT gas temperature R/D bursting pressure

Fig. 8 Variation of H2 generation rate


Value 0.1 MPa 9.23 m3 400◦ C 0.78 MPa 21.57 kg/s 1,300 K 150 m3 200◦ C 1.5 MPa

sponding to the steam injection with the steam to hydrogen molar conversion ratio of 0.7. As shown in Fig. 8, the initial yielding rate of hydrogen gas is maintained at a constant value of the design basis leak, and it can be seen that the ending time of the hydrogen gas generation is different between the tube-side steam isolation and the shell-side sodium clearing. This is because the steam isolation time is faster than the sodium clearing time, quantitatively about 3 min,1, 9) since the feed water isolation system will be activated as soon as the sodium-water reaction is detected. On the other hand, the shell-side sodium clearing is strongly dependent on design features, such as a pressure difference between system and sodium drain tank and geometric effects in the shell-side of steam generator, etc., therefore, it can be said that the sodium side isolation model is more conservative than the steam-side isolation model in the aspect of the system design. Based on these features, it will be expected that the system pressure response is also different in these two steam injection models. For a more conservative approach, however, it is assumed that the tube-side steam injection is maintained up to the ending time of the reaction and the reaction is terminated only by the shell-side sodium clearing related to the sodium free surface level decrease in the steam generator. In this study, accordingly, the system dynamic responses are analyzed only for the shell-side sodium clearing model using the system design parameters as shown in Table 1. The temperature variations of the cover gas region and the shell-side sodium are shown in Fig. 9. In order to simplify the analysis of the long-term period of a SWR characterized by a bulk motion, the shell-side sodium temperature should be considered as an average value between the upper and lower plenum sodium temperature. This is the reason that the initial temperature difference between the cover gas region and shell-side sodium exists. As shown in this figure, the cover gas temperature rapidly increased up to the rupture disk bursting time since the cover gas volume is fixed before the rupture disk breakage. In other words, since the rigid boundary condition is applied to the cover gas region and the exothermic reaction energy flows into the fixed volume with the mass inflow of hydrogen gas, a compressible gas in the cover gas region, therefore, experiences a drastic pressure and tempera-

Fig. 9 Temperature variations of cover gas and sodium

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ture transient. This is the reason for the initial rapid temperature increase of the cover gas region. After the bursting time of the rupture disk, the cover gas region is expanded and the moving boundary condition is applied to the region, so the temperature is almost the same or very slowly increases due to the net effects between the energy term added by hydrogen gas and the volume expansion term in an adiabatic system, in view of thermodynamics as mentioned in previous section. The shell-side sodium temperature also increases rapidly corresponding to the cover gas temperature increase as the heat transfer rate from the cover gas region to the shell-side sodium increases. In particular, the sodium temperature increases rapidly compared to the cover gas temperature variation as the remaining quantity of shell-side sodium in the steam generator is decreased. From this reason, the sodium temperature is nearly equal to the cover gas temperature at the end of the reaction period, which does not have, however, a physical meaning but is just the numerical computation results related to the lack of the remaining sodium quantity in the shell-side SG. Figure 10 shows the pressure variations during the longterm period of a SWR event. As shown in this figure, the system pressure is rapidly increased up to the rupture disk bursting pressure, and suddenly decreased to the normal transient system pressure range with some pressure oscillations. The bursting time of the rupture disk is about 2 s after the leak initiation. A relatively small pressure increase is shown just after the rupture disk bursting time since the continuous steam injection of the initial leak rate is still maintained during this time period. The sodium drain tank pressure remains at a constant value of the initial SDT pressure before the rupture disk bursting, and slowly increases corresponding to the system pressure decrease after the rupture disk bursting. This is because the free volume of an inert gas in SDT is sufficiently large enough to hold the total sodium volume of IHTS loop including the steam generator, therefore, the pressure variation is relatively small compared to the system depressurization. At the end of the reaction period about 4 min after the leak initiation, the SDT pressure is nearly equal to the system pressure since the shell-side sodium in the steam generator is almost discharged and the pressure difference between the

Fig. 10 Pressure variations of the system and the SDT

system and the SDT becomes very small. Figure 11 shows the variations of the sodium discharge flow rate and the accumulated venting volume of the shellside sodium after the rupture disk bursting. The sodium discharge flow rate is instantaneously peaked and promptly decreased corresponding to the system pressure variation just after the rupture disk bursting time. This instantaneous peak value of the discharge flow rate is extremely high, which does not have, however, a physical meaning but is just the numerical computation results caused by the initial high pressure difference between the system and the SDT. After this initial period of the discharging process, the flow rate shows a secondary increase, that is reasonable, corresponding to the pressure difference between the system and the SDT, and then is slowly decreased. On the other hand, the accumulated volume of the shell-side sodium is steadily increased and becomes nearly saturated at the end of the reaction period since the sodium discharge flow rate decreases rapidly in this time period. Figure 12 shows the trend of the cover gas volume increase and the shell-side sodium free surface level decrease corresponding to the sodium discharge shown in Fig. 11. In this figure, the sodium level decrease shows a little bit different trend from the discharged sodium or cover gas volume in-

Fig. 11 Variations of discharge flow rate and accumulated sodium venting volume

Fig. 12 Variations of CG Volume and sodium free surface level


879


crease, since the sodium level is determined by the relation between the discharged volume and the effective flow area related to the complicated geometric effects in the shell-side steam generator as represented in Eq. (17). Accordingly, the ending time of the reaction defined as the time that the shellside sodium is completely cleared is about 4 min after the rupture disk breakage. Actually, in the aspect of the design, a reduction of termination time of the reaction can be accomplished by the tube-side water/steam isolation, and its reduction is about 23%9) in time, quantitatively. In the SELPSTA code, the tube-side isolation model can be selected optionally according to the purpose of the analysis. It should be reminded, however, that the termination of a SWR event in this study was assumed only by the shell-side sodium clearing as mentioned above. It is concluded that the SELPSTA code can simulate the long-term system transient of a SWR phenomena with respect to the various design conditions associated with the pressure relief system and operational strategy against a SWR event in KALIMER design. The numerical quantification method used in the SELPSTA code is very practicable to the system design purpose. Through the further experimental study, the code verifications will be accomplished and then it is expected that the enhancement of the reliability of the SELPSTA code is possible.

V. Conclusions Using the developed code SELPSTA, the analysis of the long-term system dynamic response of a SWR event in KALIMER (Korea Advanced Liquid Metal Reactor) IHTS and related systems has been made. The SPIKE and SELPSTA computer codes complement each other to provide a feasible analytic capability and a design tool to investigate the initial and the long-term system dynamic responses to a SWR event in KALIMER. Through this study, we can get a very easy analysis method for the long-term period of a SWR event which has physically reasonable calculation results, and also it has the superiority in the aspect that the various design parameters or operational characteristics are flexibly applicable. In contrast with the previous studies using a very complicated analysis method for a SWR, the simple approach using in the SELPSTA code makes the very quick and concise computation possible. Based on this study, it is expected that the code has reasonable capability to predict the quasi-steady system transients according to the system design purpose, and feasible calculation results can be provided to design the IHTS and related systems of KALIMER. Further experimental verifications of the SELPSTA code are in progress for enhancement of the code capability. Nomenclature Aeff : Aleak : Apipe : C: cp: D: E: f:

Effective flow area (m2 ) Tube leak area (m2 ) Flow area of sodium discharge line (m2 ) Flow resistance (Pa·s2 /kg2 ) Heat capacity (kJ/kg·K) Hydraulic diameter (m) Energy (kJ) Friction factor


g: H: h: K: L: M: m: m: ˙ m˙ crit : m˙ ex : m˙ PRH : P: PSDT : PSYS : Pst : Q: Qi n : Q gen : Q out : Q sin k : ¯ R: T: t: end : tleak V: W˙ :

Gravitational acceleration (m/s2 ) Level or elevation (m) Enthalpy (kJ/kg) Form loss coefficient Length (m) Molecular weight (kg/kmole) Mass (kg) Mass flow rate (kg/s) Critical mass flux of steam (kg/m2 ·s) Mass flow rate of discharged sodium (kg/s) Production rate of hydrogen gas (kg/sec) Pressure (Pa) Sodium drain tank pressure (Pa) System pressure (Pa) Static pressure (Pa) Rate of heat transfer (W) Rate of heat transfer into a cover gas space (W) Rate of heat generation (W) Rate of heat transfer out of a cover gas space (W) Rate of heat sink (W) Universal gas constant (8.314 kJ/kmole·K) Temperature (◦ C) Time (s) Ending time of the chemical reaction (s) Volume (m3 ) Rate at which work is performed (W)

(Greek letters) α: Steam to hydrogen molar conversion ratio γ : Flow inertia control factor ρ: Density (kg/m3 ) (Subscripts) g: H: s: l: tot:

Inert gas (cover gas) Hydrogen gas Steam or water Liquid sodium Total value

(Superscripts) acc: Cumulative value o: Reference or initial state

Acknowledgment This study has been carried out under the national nuclear mid and long-term R&D program which is supported by the Ministry of Science and Technology of Korea. References 1) D. H. Hahn, et al., KALIMER Conceptual Design Report, KAERI/TR-2204/2002, Korea Atomic Energy Research Institute (KAERI), (2002). 2) J. H. Park, et al., Development of the SPIKE code for Analysis of the Sodium Water Reaction, KAERI/TR-1123/98, Korea Atomic Energy Research Institute (KAERI), (1998). 3) M. Hori, “Sodium/water reactions in steam generators of liquid metal fast breeder reactors,” At. Energy Rev.–Austria, 18[3], 707–778 (1980). 4) D. A. Greene, “Steam generator vessel pressures resulting from a sodium/water reaction: a computer analysis with the SWEAR code,” Nucl. Technol. USA, 14[3], 218–231 (1972). 5) G. Vambenepe, “Liquid metal fast breeder reactor steam generator survey of the consequences of large scale sodium water reac-

880 tion,” ENS/ANS Int. Topical Meeting on Nuclear Power Reactor Safety, Brussels, Belgium, Oct. 16–19, 1978, (1978). 6) Y. S. Kim, Y. S. Sim, E. K. Kim, et al., “Evaluation of the SWR’s early pressure variations in the KALIMER IHTS,” J. Energy Eng., 11[2], 122–129 (2002). 7) J. H. Eoh, Y. S. Sim, Y. S. Kim, et al., “Assessment of analysis model for longer-term effects of SWR in LMR,” Proc. Korean Nuclear Society (KNS), 2001 Spring Meeting, Che-Ju, Korea, May 23–25, 2001, (2001).

J. H. EOH et al. 8) A. N. Nahvandi, M. Rashevsky, Computer Program for Critical Flow Discharge of Two Phase Steam-Water Mixtures, CVNA-128, Westinghouse Electric Corporation, Atomic Power Division, (1962). 9) J. H. Eoh, E. K. Kim, S. O. Kim, “Development of tube leak model for analysis code of SWR in LMR,” Proc. Korean Nuclear Society (KNS), 2002 Autumn Meeting, Yong-Pyong, Korea, Oct. 23–25, 2001, (2001).
