Steam venting and condensation in a large pool of water can lead to either thermal stratification or thermal mixing. In a pressure suppression pool (PSP) of a boiling water reactor (BWR), consistent thermal mixing maximizes the capacity of the pool while the development of thermal stratification can reduce the steam condensation capacity of the pool which in turn can lead to pressure increase in the containment and thereafter the consequences can be severe. Advanced modeling and simulation of direct contact condensation in large systems remain a challenge as evident in commercial and research codes mainly due to small time-steps necessary to resolve contact condensation in long transients. In this work, effective models, namely, the effective heat source (EHS) and effective momentum source (EMS) models, are proposed to model and simulate thermal stratification and mixing during a steam injection into a large pool of water. Specifically, the EHS/EMS models are developed for steam injection through a single vertical pipe submerged in a pool under two condensation regimes: complete condensation inside the pipe and chugging. These models are computationally efficient since small scale behaviors are not resolved but their integral effect on the large scale flow structure in the pool is taken into account.
A pressure suppression pool is an important part of a BWR reactor containment safety design. It serves as a heat sink and steam condenser to prevent containment pressure buildup during loss of coolant accident (LOCA) or during safety relief valve (SRV) opening in normal operations. Steam released from the reactor vessel is vented through the blowdown pipes (in case of LOCA) or through spargers (in case of SRV operation) and condenses in the pressure suppression water pool. The temperature of the pool gradually increases as a result of condensation. This leads to a reduction of the pool’s pressure suppression capacity. Efficiency of the pool pressure suppression function is contingent upon the temperature of the pool surface, which determines the steam partial pressure in the wet well gas space. An increase of the pool’s surface temperature due to stratification can lead to a significant increase in containment pressure [
Steam injection in a pool of water is a source of both heat and momentum. A competition between heat and momentum defines the pool state whether it is thermally mixed or stratified. The heat source induces the development of thermal stratification. The configuration of the stratified layers generally depends on the spatial distribution of the heat source and history of transient heat transfer in the pool (heating and cooling phases). In a BWR pressure suppression pool operation, thermal stratification development is caused by a heat source (such as a blowdown pipe or a sparger) immersed into the pool at a certain depth. There are two typical transient stratification configurations (as shown in Figure
Typical configurations of thermal stratification in a tank (a) stratified layer and (b) thermocline layer. Note:
The momentum induced by steam condensation is capable of creating large scale circulation which can mix the pool. However, mixing of a stratified pool takes some time which generally depends on the momentum rate. The time which is necessary to achieve mixing determines how fast the suppression pool’s capacity can be restored. Thus, the characteristic mixing time scale is considered as an important parameter of the pool’s operation.
The competition between the sources of heat and momentum is determined by the steam condensation regime. Condensation regimes of steam injection into a subcooled water pool at different conditions were studied intensively in the past [
Regime map of steam condensation [
A chugging regime [
Stratification and mixing phenomena in a large pool of water with a heat source have been studied experimentally and analytically. A strong stratification above a heat source submerged in a water pool was observed in different tests [
An experimental study of thermal stratification and mixing in relatively large pools was carried out in the PUMA facility [
Similar experimental programs called POOLEX (POOL Experiment) and PPOOLEX (Pressurized POOLEX) [
It is instructive to note that flow regime domains observed in the POOLEX/PPOOLEX test agree rather well with the data from [
The POOLEX was later modified to become PPOOLEX (see Figure
(a) PPOOLEX experiment facility and examples of (b) thermal stratification development during the MIX-01 test and (c) existence of a thermocline layer during the STR-02 test [
The availability of the detailed data from the POOLEX/PPOOLEX tests was instrumental for the development and validation of the approaches described in this work.
CFD modeling of POOLEX/PPOOLEX tests has been carried out by VTT, a technical research center in Finland. The direct contact condensation in short transients is directly simulated with different heat transfer correlations and interfacial surface area between the liquid and the vapor. The results showed that the condensation rate is very sensitive to the correlations. The oscillation frequencies of the steam-water interface in the blowdown pipe were much smaller than in the experiments [
Scaling approaches for prediction of thermal stratification and mixing in pools and in large interconnected enclosures were developed and applied by Peterson and coworkers at UC Berkeley [
Gamble et al. [
Condensation and mixing phenomena during loss of coolant accident in a scaled down pressure suppression pool of simplified boiling water reactor were also studied by Norman et al. [
An experimental investigation of steam condensation and CFD analysis of thermal stratification and mixing in subcooled water of the incontainment refueling water storage tank (IRWST) of advanced power reactor 1400 (APR1400) were performed by Song et al. [
The state of the art in understanding data and modeling capabilities relevant to suppression pool stratification and mixing phenomena can be summarized as follows. Numerous experimental studies were performed in the past on stratification and mixing in a pool, but only few are large scale tests with steam injection. Tests with steam injection have been carried out mostly with small diameter pipes in order to clarify steam condensation regime and not in conjunction with mixing and stratification phenomena. Not all experimental data is readily available for model development and code validation. The POOLEX/PPOOLEX is a unique series of tests at relatively large scale which provides the most complete set of data on transient stratification and mixing caused by steam injection, which is necessary for code development and validation. System thermal hydraulic 1D codes are unsuccessful in prediction of stratification development unless expressly developed and calibrated models and closures are provided. Lumped parameter and 1D models based on scaling approaches were developed and successfully used for modeling of thermal stratification development. Unfortunately, the applicability of these methods is limited to stably stratified or well mixed conditions. The time scale of transient stratified layer erosion has not been addressed with these models. Direct application of fine resolution CFD (RANS, LES, and DNS) methods is not practical due to large uncertainty and excessive computing power in modeling of 3D high-Rayleigh-number natural convection flows in a large pool [
The objective of the present work is to propose reliable and computationally efficient methods that can predict transient mixing and stratification phenomena induced by steam injection into a large pool. These methods are necessary for safety analysis of the pressure suppression pool’s operations in different accident scenarios.
The main challenge of this work is how to take into account, in a robust and computationally efficient manner, the direct contact condensation (DCC) phenomena of steam injection into a subcooled pool that are important for development of stratification or mixing in the pool.
First, we stipulate that the goal of the analysis is to predict the stratification and mixing, and not DCC phenomena. Second, we recognize that the characteristic time and space scales of DCC phenomena are much smaller than the characteristic time and space scales of development of thermal stratification and global circulation and mixing in the pool. Third, we postulate that the individual details of small scale high frequency oscillations are lost due to the scale separation and only integral “
Thus, instead of “direct” CFD-type modeling of DCC phenomena, we propose to use the effective models (see also [
Schematic of effective heat source (EHS) and effective momentum source (EMS) models.
The EHS model provides integral heat source caused by steam injection. Its purpose is to conserve mass and thermal energy of injected steam. In Figure
A time-averaged mass flow (
The schematic illustration of the steam condensation inside the blowdown pipe is shown in Figure
Condensation inside the blowdown pipe during steam injection.
The EMS model provides time-averaged momentum source induced by steam injection. This momentum creates large scale circulation in the pool which can lead to erosion of thermally stratified layer and mixing of the pool. The effective momentum source is calculated by
For a given diameter of the blowdown pipe the condensation regime depends on the injected steam flux and pool bulk temperature (see Figure
The reason is that steam injected into a subcooled pool creates different patterns of fluid oscillations in different regimes. For instance, in the chugging regime, large amplitude periodic oscillations of the free surface inside the pipe are caused by the periodic process of (i) steam injection, (ii) expansion of the steam bubble around the pipe outlet, and (iii) volumetric condensation inside of the overexpanded steam followed by (iv) sudden bubble collapse and suction of water inside the blowdown pipe. No steam bubble plume is injected into the pool above the pipe outlet. As shown in Figure
Separate effect during chugging regime when steam is injected through vertical pipe, (a) injection phase and (b) suction phase.
In this work we consider a specific case when the momentum is generated mostly by the oscillatory flow in the blowdown pipe. The other case, when steam and possibly noncondensable gases escaping the pipe can contribute to generation of momentum in the pool due to the buoyancy force, is beyond the scope of this work.
The “synthetic jet” term was introduced to denote fluid motion which can be generated by oscillatory flow through an orifice with zero time-averaged mass flow [
(a) Schematic of a synthetic jet actuator and (b) Schlieren image of a rectangular synthetic jet [
For a single harmonic oscillation, the velocity scale based on the momentum flux [
In this work we use similarities between basic physics of synthetic jets and flow created by the free surface oscillations in the blowdown pipe in order to propose a model for effective momentum. Indeed, in case of condensation oscillations, the velocity of periodic oscillations is usually much larger than the velocity determined by the mass flow of steam, while in the synthetic jet case, the mass flow through the orifice is exactly zero. Similar to the synthetic jet, the large scale circulation in the pool does not follow the high frequency oscillations of the water level in the pipe; that is, the flow pattern in the pool is not oscillatory.
Our hypothesis, which is validated in [
The amplitude and frequency of the water level oscillations in the pipe can be obtained experimentally, for example, by temperature measurements on the pipe’s inner surface or by a level meter. Figure Convert the TC measurements to water level positions (see Figure Calculate the velocities Calculate the moving time-averaged velocities by
with an averaging time scale Calculate the effective (jet) velocity Calculate the effective momentum rate
(a) TC measurements inside the blowdown pipe and corresponding (b) water level positions for a 5 s time window and superimposed smoothed data with a moving average filter. Frequency and amplitude of oscillations can be based on the water level positions inside the pipe. The outlet of the pipe is at 0 m.
For the 5 s time window given in Figure
The ultimate goal of the EMS model is to calculate the effective momentum
Calculation diagram for the effective momentum
In order to enable sufficiently accurate and computationally affordable simulations of thermal stratification and mixing during a steam injection into a large pool of water, the concepts of effective heat source (EHS) and effective momentum source (EMS) models are proposed in this work. Specifically, the EHS/EMS models are developed for steam injection through a single vertical pipe submerged in a pool under two condensation regimes: complete condensation inside the pipe and chugging. These models are computationally efficient since small time and space scale behaviors are not resolved directly but their integral effect on the large scale flow structure in the pool is taken into account. The EMS model is based on the synthetic jet model which has to be complemented with the data about amplitude and frequency of the condensation oscillations in different flow regimes. In [
The authors declare that there is no conflict of interests regarding the publication of this paper.
Support from the NORTHNET RM3 and Nordic Nuclear Safety Research (NKS) is greatly acknowledged. The authors are grateful to Markku Puustinen (LUT) and coworkers for very fruitful discussions and providing unique experimental data for the development and validation of the models.