An Approach to Physics Based Surrogate Model Development for Application with IDPSA

Transcription

1 An Approah to Physis Based Surrogate Model Development for Appliation with IDPSA Ignas Mikus a*, Kaspar Kööp a, Marti Jeltsov a, Yuri Vorobyev b, Walter Villanueva a, and Pavel Kudinov a a Royal Institute of Tehnology (KTH), Stokholm, Sweden b Mosow Power Engineering Institute, Mosow, Russia Abstrat: Integrated Deterministi Probabilisti Safety Assessment (IDPSA) methodology is a powerful tool for identifiation of failure domains when both stohasti events and physial time dependent proesses are important. Computational effiieny of deterministi models is one of the limiting fators for detailed exploration of the event spae. Pool type designs of Generation IV heavy liquid metal ooled reators introdue importane of apturing intriate 3D flow phenomena in safety analysis. Speifially mixing and stratifiation in 3D elements an affet effiieny of passive safety systems based on natural irulation. Conventional 1D System Thermal Hydraulis (STH) odes are inapable of prediting suh omplex 3D phenomena. Computational Fluid Dynamis (CFD) odes are too omputationally expensive to be used for simulation of the whole reator primary oolant system. One proposed solution is ode oupling where all 1D omponents are simulated with STH and 3D omponents with CFD odes. However, modeling with oupled odes is still too time onsuming to be used diretly in IDPSA methodologies, whih require thousands of simulations. The goal of this work is to develop a omputationally effiient surrogate model (SM) whih aptures key physis of omplex thermal hydrauli phenomena in the 3D elements and an be oupled with 1D STH odes instead of CFD. TALL-3D is a lead-bismuth euteti thermal hydrauli loop whih inorporates both 1D and 3D elements. Coupled STH-CFD simulations of TALL-3D typial transients (suh as transition from fored to natural irulation) are used to alibrate the surrogate model parameters. Details of urrent implementation and limitations of the surrogate modeling are disussed in the paper in detail. Keywords: IDPSA, Dynami PSA, Surrogate Model, TALL-3D. 1. INTRODUCTION Generation IV nulear reator designs often inorporate pool type onfigurations with passive safety features whih depend on omplex physial interations and loal flow onditions. Lak of operation on large sale means the pre-knowledge of suh systems performane, their safety and failure modes is sare. The IDPSA methodology is proposed in suh ases for a omprehensive safety analysis. It is a powerful tool to identify failure domains when both stohasti events and physial time dependent proesses are important [1]. This method relies less on expert knowledge of the system and more on the deterministi odes to explore the event spae. Several thousands of alulations need to be run for a suessful analysis of a given design. Pool type nature of the designs requires a 3D simulation ode to be used as 1D system odes fail to apture omplex flow phenomena e.g. mixing and stratifiation during transient onditions. However, appliation of a CFD ode for the full model of the reator design is not feasible due to unreasonably long alulation time. To avoid this, approahes for oupling STH and CFD odes have been proposed, whih retain auray as well as effiieny [2]. However, oupled STH-CFD simulations are still too omputationally expensive for IDPSA appliations. Here another approah is to use alulation results from a CFD ode to reate a physisbased Surrogate Model (SM) whih would give omparable outome. Suh SM ould be used oupled * mikus@kth.se

2 with an STH ode instead of CFD. Using a surrogate model would onsiderably derease the alulation time and allow IDPSA methodology to be applied more effiiently. 2. TALL-3D FACILITY DESCRIPTION Both separate models, alulation odes, and oupled ode approahes need to be validated against real-world experimental data. This requires omplex and highly speifi experimental equipment. Therefore a lead-bismuth euteti (LBE) thermal hydrauli test faility TALL-3D was built at the Royal Institute of Tehnology (KTH). The loop is designed to provide experimental data for single STH, CFD and oupled STH/CFD ode validation with the aim to study omplex feedbaks between the 3D and system sale phenomena [3]. The layout of the faility is shown in Figure 1. The loop is omposed of 3 setions: the main heater leg (left); the 3D test setion leg (enter); and the heat exhanger leg (right). Total height of the faility is 6980 mm whereas the height of the loop piping is 5830 mm. The width of the loop is 1480 mm. The pipes have internal diameter of mm and outer diameter of 33.4 mm. The main heater leg ontains a 25 kw rod type eletrial heater whih is 8.2 mm in diameter and the heated part has a length of 870 mm. An expansion tank is installed on the top of the main heater leg. The 3D leg ontains a heated pool type test setion in its lower part. The test setion heater power is 15 kw. The heat exhanger leg ontains a heat exhanger in the top part and an eletromagneti pump below it. The seondary loop utilizes DOWTHERM RP as ooling fluid and a fan is used as a seondary heat exhanger. The LBE is stored in the sump tank loated at the lower left orner of the loop. Three ball valves (one per setion) are installed for fine tuning of the flow. This enables equalizing the flow rates in the main heater and 3D legs in natural irulation mode, thus allowing the mass flow rates to be brought out of balane by a relatively small effort, leading to flow osillations in the two hot legs [3]. All parts of the faility in ontat with the LBE are manufatured of SS-316L stainless steel to ensure orrosion and erosion resistane. Stainless steel is haraterized by a relatively high thermal expansion oeffiient, therefore the effets of thermal deformation must be onsidered. For this purpose TALL- 3D was designed with a system of expansion joints, anhored fixation points and pipe guides to preserve the loop geometry, aount for different thermal expansion of different legs, damp possible vibrations, and preserve a strit vertial position of the 3D test setion. An extensive amount of instrumentation is installed in both loop type omponents and the 3D test setion to provide suffiient information for single STH, oupled STH/CFD ode validation, and investigation of isolated physial phenomena. This inludes two Coriolis flow meters on the primary loop; a five-group differential pressure measurement system, enabling measurements of total 15 differential pressures around the loop; and numerous thermoouples positioned in the flow, on the pipe walls as well as on the walls of the insulation. The instrumentation is onneted to the Data Aquisition System (DAS) and is operated via a LabView interfae. Most of the faility an be represented as a 1D model sine small diameter pipes have negligible 3D flow tendenies. Pool type test setion in the middle leg introdues omplex axisymmetri geometry and requires full three dimensional flow solution in transient onditions for orret outlet temperature estimation. This means there is a lear separation between the STH ode domain and the CFD ode domain for the TALL-3D faility.

3 Figure 1: Shemati view of the TALL-3D faility Expansion tank Expansion ompensator Ball valve with position ontrol 1 2 Oxygen meter Heat exhanger 11 Straight run Differential pressure group DP2 Loop support frame 3 Flow diretion Coriolis flow meter TC D Test setion 9 Eletri-Permanent Magnet pump Main heater 8 Radial TCs setup around main heater 5 Sump tank 7 6

4 2.1. 3D test setion TALL-3D design inorporates a 3D test setion to introdue flow onditions that annot be properly aptured by 1D STH odes. It is an axisymmetri ylindrial vessel with an outlet at the top and an inlet at the bottom. A 15 kw rope heater is installed at the upper part around the lateral wall. The heater is used to failitate stratifiation development in the pool, and allows outlet flow temperatures of up to 500 C. The shematis of the test setion are shown in Figure 2. Internal diameter and height of the test vessel are 300 and 200 mm respetively. A irular plate of 200 mm diameter is installed inside, orthogonal to the flow diretion. The purpose of the plate is to reflet the upward LBE jet towards the walls of the vessel, thus enhaning mixing in the pool at high inlet mass flows. At low flows the jet does not penetrate all the way to the plate and stratified layer forms in the upper setion of the pool. The temperature distribution is measured by thermoouples installed in-flow, and on internal and external walls of the test setion. Figure 2: Shematis of the TALL-3D test setion vessel 450 Outlet ID 27.8 mm Rope heater, 10 kw External on-wall TCs 122 Inner plate OD 200 mm 78 In-flow TCs Internal on-wall TCs Test setion ID 300 mm H 200 mm 250 Inlet ID 17 mm CFD analysis was performed in the 3D test setion design proess for hoosing the proper inlet pipe diameter, test setion height, heater power and geometry. The aim of the design is to ensure, that if the whole loop is lose to instability in natural irulation onditions, the 3D test setion would be the omponent responsible for 1D/3D feedbaks. Namely the pool should be mixed at high flow rates and stratified at low flow rates. The seletion of parameters was done using the saling analysis developed for buoyant jets in pool-like geometries [4]. The onfiguration was seleted in suh way that stratifiation is allowed to develop in the pool at flow rates up to 0.65 kg/s. Figure 3 shows the results of pre-test CDF modelling. The pool is mixed when the inlet mass flow rate is 1 kg/s and stratified when the inlet mass flow rate is 0.2 kg/s.

5 Figure 3: CFD simulation results for the 3D test setion. Temperature is shown on the left and veloity on the right of the pool for flow rate 1.0 kg/s and 0.2 kg/s The effets resulting from suh 3D omponent introdution into the loop design were demonstrated in pre-test STH and oupled STH-CFD simulations of the TALL-3D faility. The presene of the test setion auses non-linear interations between 3D and 1D loop omponents, whih result in osillations, not properly resolved by single STH ode, as shown in Figure 4. Figure 4: LBE temperatures at the bottom and top of 3D test setion [2] 3. SURROGATE MODEL DEVELOPMENT APPROACH Surrogate Model (SM) is neessary when using original multi-dimensional high resolution odes beomes too omputationally expensive. For example, a TALL-3D transient simulation using oupled STH-CFD approah takes several days of omputing. Suh approah is not suitable in the IDPSA methodology, where large numbers of alulations need to be run to identify failure domains and perform sensitivity and unertainty analysis. Therefore we seek to develop a surrogate model to replae the CFD part in oupled alulations to derease the omputational time, and make the oupled alulation suitable for IDPSA. The aim of the SM is to reprodue only a limited set of results with aeptable auray, while disregarding the detailed modelling of the atual physial system, thus avoiding the diret

6 onsideration of physial proesses whih would introdue omplexity and inrease omputational effort (ex. solution of 3D onservation equations whih leads to a CFD approah). However the SM needs to give better results than urrently available models implemented in STH odes to resolve previously identified 3D effets. Thus the riterion of a suessful SM development is to obtain a more aurate solution, than ahievable by a single STH ode, and ahieve better omputational performane ompared to CFD or oupled STH-CFD approahes. One of the more popular method for surrogate model development depends on an advaned approximation of a omplex funtion whih is represented by a database of full model solutions e.g. appliation Neural Networks (NN). However, this way no atual physis modelling is involved in the SM, and the proedure is essentially a fitting proess. This approah requires large number of data alulated by the original model, so the atual gain in omputational effiieny an even deline in the proess of SM development and appliation. Furthermore, it results in a SM that annot be assumed reliable outside of the domain of parameters overed in the database of the original model solutions, sine no physial reasoning is applied to the extrapolation [5]. Our approah is to apture the most important physial phenomena in the surrogate model itself. Then, a proess of alibration is applied to determine the parameters whih represent the physial proesses not diretly modelled in the SM. Sine a limited set of SM output results is desired, only few parameters need to be onsidered for alibration. These SM losures an be dedued by standard fitting proedures, or by more advaned appliation of Neural Networks. Therefore our goal is to seek for an intermediate approah in between a pure NN appliation and a pure analytial solution. The proess an be summarized as shown in Figure 5. These steps form an iterative proess, whih is ontinued until the desired SM preision is reahed. Figure 5: Surrogate model development proedure Identifiation of physis to be resolved by the SM Identifiation of physis to be resolved by alibration Identifiation of data neessary for alibration Generation of neessary data Calibration of SM against generated data SM assessment The SM should orretly reprodue the history of the system, so temporal evolution equations have to be solved expliitly. However the exhange rates in these equations are of loal nature, and do not depend on history effets. Therefore they an be determined by applying empirial losures. In this work we develop the surrogate model based on pre-alulated CFD solutions. Currently an idealized CFD model is utilized, and no heat losses are onsidered. We believe that CFD appliation will give us the general form of losures, whih will be later adjusted in aordane with the experimental results.

7 4. DEVELOPMENT OF SM FOR TALL-3D The ultimate goal of SM development for the TALL-3D test setion is to ouple the SM with a STH ode to be used for IDPSA. The surrogate model will use the inlet mass flow, inlet temperature and pool heater power values to estimate outlet temperature of the 3D pool at given moment. This value will be used in turn in STH ode in the same way as in STH-CFD oupling [2]. Four CDF transients were run to gather insight about the mixing and stratifiation phenomena (see Table 1). LBE temperature at the test setion inlet and the test setion heater power were kept onstant at 425 K, and 5 kw respetively. The transition from fully mixed to fully stratified states was seen in CFD results in the dereasing mass flow rate transients, while the stratified pool was fully mixed in the inreasing mass flow rate ases. The test setion outlet temperature and total momentum values were monitored in CFD solution and analyzed. Table 1: Parameters of CFD transient ases run for mixing/stratifiation analysis Transient Initial m (kg/s) Final m (kg/s) d m / dt (kg/s 2 ) The most straight-forward approah to evaluate the outlet temperature omes from a simple energy balane over the 3D test setion. Assuming the LBE pool as a homogeneous ontrol volume, the outlet temperature T an be alulated as follows: d( mpt) m p ( Tin T) Q h dt (1) Here m is the mass of LBE in the test setion, m is the mass flow, T in is the inlet temperature, the heater power, and p is the average isobari speifi heat, whih an be evaluated as: 1 p pdt T T T in T where the isobari speifi heat orrelation is given as [6]: in p T T (3) (2) Q h is Solving equation (1) gives good agreement with CFD simulation results when prediting steady state outlet temperature values. However, it fails to predit the transient behavior as shown in Figure 6, as expeted. Suh disrepanies are aused by 3D effets in the test setion, namely the inlet jet wall jet, and the inlet jet stratified layer interations. Therefore the 3D test setion annot be modelled as a homogeneous ontrol volume.

8 Figure 6: Test setion outlet temperature during dereasing mass flow transients (1 kg/s to 0.2 kg/s) at two rates - slow (0.005 kg/s2) and fast (0.01 kg/s2) Without going into detailed investigation of the 3D phenomena, the additional effets may be inluded in equation (1) by adding a 3D term Q, to aount for the observed disrepanies: d( mpt) m p ( Tin T) Q h dt Q (4) Figure 7: Q term orrelation with total pool momentum for dereasing mass flow transient Taking the test setion outlet temperature data from the CFD solution, the Q term an be alulated diretly from equation (4). The evolution of this term (adjusted for different rates of hange of mass 1/ 4 flow Q r ) during the dereasing mass flow transient (stratifiation development in the pool) was found to orrelate with the instantaneous pool momentum values, as shown in Figure 7.

9 Figure 8: Q term as alulated by CFD and from the orrelation with the total pool momentum for dereasing mass flow transient Here r denotes the rate of hange of mass flow ( d m / dt ). Approximating the observed trend, the Q term evolution during the transient an be reprodued reasonably well, as shown in Figure 8. Substituting the reprodued Q values bak into eq. (4) a signifiant improvement over the mixed pool temperature predition is ahieved, as shown in Figure 9. Figure 9: Test setion outlet temperature values alulated by CFD and by solving eq. (4) using the Q approximation for dereasing mass flow transient The same approah, however, does not yield a good orrelation between Q and pool momentum values during the inreasing mass flow (mixing of the stratified pool) transient, as shown in Figure 10. The orretion of the Q 0.67 term by r allows mathing the amplitude, but the pool momentum value at whih the 3D effets have the highest influene seems to be dependent on the rate of hange of mass flow (flow aeleration), ontrary to what was found in the stratifiation development ase.

10 Figure 10: Q term orrelation with total pool momentum for inreasing mass flow transient Roughly approximating the observed trend, and substituting the temperature predition as shown in Figure 11. Q values into eq. (4) results in Figure 11. Test setion outlet temperature values alulated by CFD and by solving eq. (4) using the Q approximation for inreasing mass flow transient Better agreement ould be ahieved by diretly interpolating the Q values in the form as shown in Figure 10. This would require running CFD ases of limiting flow aeleration that ould be expeted in the TALL-3D loop. Furthermore, despite it was shown that 3D effets an be orrelated with the pool momentum, the pool momentum itself must be alulated from the known inlet mass flow rate and flow aeleration values, for the surrogate model to be fully self-suffiient. Currently pool momentum values were taken diretly from CFD alulations therefore the momentum modelling is still to be resolved. However, after identifying the relation between the 3D effets and the total pool momentum value, Neural Network approximation approah ould be applied to link the Q values with the pool momentum, and the pool momentum with the known parameters of LBE mass flow rate and flow aeleration.

11 6. CONCLUSION We an onlude from the results shown in this paper that the 3D effets present in the TALL-3D test setion pool an be orrelated with the total momentum in the pool and that the test setion outlet temperature an be predited reasonably well in ase of transient with mass flow derease (stratifiation development), but further effort is needed to link pool momentum with inlet mass flow and flow aeleration. Also, further work inluding analysis of additional transients, onfirmation of the stratifiation transient SM results as well as development of an approah for momentum predition is foreseen. Aknowledgements This work has been arried out under the support of European 7 th framework projet THINS. Referenes [1] Y. Vorobyev, P. Kudinov. Development of methodology for identifiation of failure domains with GA-DPSA, 11th International Probabilisti Safety Assessment and Management Conferene and the Annual European Safety and Reliability Conferene (PSAM, ESREL) (2012) [2] M. Jeltsov, K. Kööp, P. Kudinov and W. Villanueva. Development of a Domain Overlapping Coupling Methodology for STH/CFD Analysis of Heavy Liquid Metal Thermal-Hydraulis, NURETH-15, Pisa, Italy, May (2013) [3] M. Jeltsov, K. Kööp, D. Grishhenko, A. Karbojian, W. Villanueva, P. Kudinov. Development of TALL-3D Faility Design for Validation of Coupled STH and CFD Codes, NUTHOS-9, Kaohsiung, Taiwan, September 9-13 (2012) [4] P. F. Peterson. Saling and analysis of mixing in large stratified volumes International Journal of Heat and Mass Transfer, Vol. 37, no. 1, pp (1994) [5] P. Kudinov, M. Davydov. Development of Surrogate Model for Predition of Corium Debris Agglomeration, ICAPP 2014, Charlotte, USA, April 6-9 (2014) [6] OECD/NEA. Handbook on Lead-bismuth Euteti Alloy and Lead Properties, Materials, Compatibility, Thermal-hydraulis and Tehnologies, OECD (2007)