The thermal-hydraulic computer code ATHLET is an advanced best-estimate one-dimensional two-phase system code. ATHLET has been developed by the Gesellschaft fur Anlagen und Reaktorsicherheit (GRS), Germany, for the analysis design basis and beyond design basis accidents (without core degradation) in light water reactors. The ATHLET structure is highly modular, and allows an easy implementation of different physical models. The code is composed of several basic modules for the calculation of different phenomena involved in the operation of light-water reactors:

— thermo-fluid dynamics,

— heat transfer and heat conduction,

— neutron kinetics,

— general control simulation module,

— specific modules as valve, pump, steam generator, pressurizer, leak and break, accumulator, quench front, feel, charge, boron concentration, non-condensable gases.

ATHLET provides a modular network approach for the representation of a thermal-hydraulic system. A given system configuration is simulated by a net of basic fluid dynamic elements, called objects. Their geometry and connections are done in an input deck. There are several object types, each of them applying for a certain fluid dynamic model.

ATHLET offers the possibility of choosing between different models for the simulation of fluid dynamics. In the current released code version, the basic fluid-dynamic option is a five — equation model, with separate conservation equations for liquid and vapour mass and energy, and a mixture momentum equation, accounting for thermal and mechanical non-equilibrium, and including a mixture level tracking capability.

As an option, there is a possibility to use a six-equation model, with completely separated conservation equations for liquid and vapour mass, energy and momentum, taking into account also non-condensable.

The spatial discretization is performed on the basis finite-volume approach. It means, the mass and energy equations are solved within control volumes, and the momentum equations are solved over flow paths — or junctions — connecting the centres of control volumes. The solution variables are the pressure, vapour temperature, liquid temperature and mass quality within a control volume, as well as the mass flow rate at a junction.

Two types of control volumes are available. Within the so-called ‘ordinary’ control volume a homogenous mass and energy distribution is assumed. Within the ‘non-homogenous’ control volume a mixture level is modelled. Above the mixture level steam water droplets, below the mixture level liquid with bubbles may exist. The combination of ordinary and non­homogenous control volumes provides the option to simulate the motion of mixture level through a vertical component.

A full-range drift-flux model is available for the calculation of the relative velocity between phases for the five-equation model. The model comprises all flow patterns from homogeneous to separated flow occurring in vertical and horizontal two-phase flow. It also takes into account counter-current flow limitations in different geometry.

Moreover, this fluid-dynamic option allows for the simulation of non-condensable gases, on the basis of the ideal gas formulation.

Another fluid-dynamic option in ATHLET consists of a four-equation model, with balance equations for liquid mass, vapour mass, mixture energy and mixture momentum. It is based on a lumped-parameter approach. The solution variables are the pressure, mass quality and enthalpy of the dominant phase within a control volume, and the mass flow rates at the junctions. The entire range of fluid conditions, from sub-cooled liquid to superheated vapour, including thermodynamic non-equilibrium is taken into account, assuming the non-dominant phase to be at saturation. The option has also a mixture level tracking capability.

For pipe-objects, on the basis of either a 5-equation or a 4-equation model, there is also the possibility to use method of integrated mass and momentum balances an option for fast­running calculations. With the application of the method, the solution variables are now the object pressure, the mass flows at pipe inlet and outlet, and the local qualities and enthalpies (4-equation model) or temperatures (5-equation model). The local pressure and mass flow rates are obtained from algebraic equations as a function of solution variables.

Furthermore, an additional mass conservation equation can be included for the description of boron transport within a coolant system.

This system is commonly used in most existing BWR plants. However, the system used in the SWR 1000 features some differences to previous standard designs:

■ Three of the six valves work on the pressurization principle and the other three on the depressurization principle, so a common mode failure is not possible due to diversity;

■ The quenchers are located in the flooding pool (instead of the condensation pool) at a comparably high elevational position (about 2.5 m below the water level);

■ The main valves are activated passively for automatic depressurization by means of diaphragm pilot valves, which in turn are activated by passive pressure pulse transmitters.

On the primary side a forced-flow condition prevails as long as the RPV pressure is more than 0.25 bar higher than the pressure in the drywell. In the pool there would normally be a forced — flow condition near the quenchers and natural circulation at distances greater than 1 m away from the quenchers. With an arrangement such as that in existing BWR plants, only the pool water above the quenchers (or only about 40% of the water inventory) could be used as a heat sink due to the stratification of the warm water above the cold. In the SWR 1000, the quenchers have been modified to prevent this limitation. The quenchers are mounted to the wall of the flooding pool and the more than 2000 quencher holes are directed solely towards the center of the pool. This gives a maximum pulse of about 50 kN for each quencher directed into the pool. These enormous forces lead to forced convection in the pool and to a complete mixture of the water inventory. Restrictions due to natural convection are thus eliminated entirely.

1.1. Main design characteristics of AC600/1000

145 fuel assembly and 3658 mm active section core is used in AC600. 177 fuel assembly and 4267mm active section core is used in AC1000. Neutron instrumentation system inserts into core from top of pressure vessel so that there is not any penetration in the bottom head of reactor pressure vessel. Steel water reflector is used to save neutron and to reduce neutron fluency on wall of reactor pressure vessel. Modularization construction, advanced digital instrumentation and control system are considered in AC600/1000 design. Passive safety systems including passive emergency residual heat removal, passive safety injection and passive containment cooling sub-systems are very important for AC600/1000 design.

No any penetration below top of reactor core is useful to reduce core melt frequency. Integral reactor top structure and large size reactor vessel are also used in AC600/1000 design. The inner diameters of reactor pressure vessels are 4000mm for AC600 and 4340 mm for AC1000. Low power density of reactor core, low neutron leakage, 80% stainless steel +20% water reflector and large size reactor pressure vessel are able to assure 60 year life time of plant. Gray rods are used in AC600/1000 to achieve daily load follow. Linear power density of core is 134.2/140W/cm for AC600/1000 respectively, much lower than current PWR nuclear power plant so that AC600/1000 reactor core has larger safety margin.

The main problem in the first two test series in PACTEL was the rapid condensation in the CMT, which temporarily stopped the ECC water injection. The condensation took place when the saturated water layer in the CMT broke down, and the steam got into contact with cold ECC water. This happened when water flowed to the CMT after the level in the tank has already dropped. In the tests the water level in the CMT started to drop almost immediately after the opening of the break and the period of single phase natural circulation through the cold leg pressure balancing line to the CMT was very short. Due to this the saturated water layer in the CMT separating cold water from steam remained thin. For the third series, a flow distributor called sparger has been added to the CMT. The purpose of the sparger is to diminish possibilities of rapid condensation in the CMT. Further, the experiment procedure included filling of the PBL with hot water before the break opening. The CMT and the IL was full of cold water. All the earlier experiments begun with cold water in the CMT, PBL and IL. The main objective of the third series was to investigate the influences of break size and the removal of the pressurizer PBL on the CMT behaviour in cold leg SBLOCA’s. The tests run with four different break sizes (from I to 5 mm) including reproducibility studies. Like in the earlier tests the main objective of the tests was to simulate the PSIS behaviour and not to try to simulate any proposed ALWR reactor concept in particular.

The main results of the third series can be summarised as the following:

• the recirculation phase was much longer than in the earlier experiments with two PBL’s and without PBL heating,

• the recirculation phase was longer; and the resulting hot liquid layer, thicker in the experiments with smaller break size;

• the analyses of the test data supported using the McAdams correlation for calculating the heat transfer from the hot liquid layer to the CMT wall, as the Westinghouse suggested [11]. The use of the Nusselt film condensation correlation for the condensation in the CMT walls seems correct, although the correlation gave high values for the heat transfer coefficient;

• the oscillation phase between the injection and recirculation phases was longer in the experiments with small break size; and

• local wall heat flux to the CMT wall was higher in the experiments with larger break size.

In all experiments the CMT ran as planned. There were no problems with rapid condensation in the CMT, such as was seen in the earlier passive safety injection experiments in PACTEL. The main reason was the new CMT arrangement, with a flow distributor (sparger) installed to the CMT. The sparger spread incoming flow to the CMT horizontally, and the breakdown of the saturated water layer due to incoming water was not possible. The hot liquid layer between the steam and cold water in the CMT remained stable, even in the experiments where the hot liquid layer was less than 5 cm thick.

The design of the Isolation Condenser in the Dodewaard Reactor is shown in Fig. 9. Some operational tests have been performed as well as some sequences occurred where the isolation condenser was used to cope with transients.

Because the operational instrumentation did not completely cover the phenomena needed for a detailed analysis and because some manual operation (not documented in detail) was used to cope with the transient a detailed evaluation of the operational data is not possible. Therefore, in Fig. 10 calculated values for the Dodewaard Isolation Condenser is given. One power level could be compared with a TRAC calculation; the agreement is good.

FIG. 7. Arrangement of the PANDA-IC in the pool.

FIG. 8. Power levels of the PANDA-IC calculated with ATHLET as a function ofpressure for the pure steam tests.

FIG. 9. Arrangement of the isolation condenser in the condenser tank of the Dodewaard nuclear power plant.

3. DISCUSSION AND CONCLUSIONS

The requirements from licensing bodies for the acceptance of experimental and analytical data in a licensing process are quite higher now than 10 or 20 years ago.

To the extend possible original geometries and materials should be used; if this is not possible, reliable scaling rules should exist.

For the Emergency Condenser (EC) and the Dodewaard Isolation Condenser (IC) original geometries and materials were used. The Isolation Condenser in PANDA is a scaled-down test section. However, the components with original geometries and materials have been tested in the PANTHERS facility; the data are not publicly available except for the licensing bodies.

The equivalent thermal-hydraulic initial and boundary conditions should be used.

This is the case for the EC and the Dodewaard IC. The PANDA IC was limited to 1 MPa, but the full pressure has been used in PANTHERS.

To the extend possible the components should be tested also with beyond-design thermal — hydraulic conditions and for low-power or shutdown situations.

The EC and PANDA IC have also been tested with non-condensables in the inlet flow. The EC has been tested with shutdown situations.

The data and procedures should be documented; an uncertainty analysis should be available.

With the exception of the Dodewaard IC those requirements could be met.

The sequences tested should be simulated with at least one computer code and the results compared with the experimental data.

This has been extensively done for the EC and PANDA IC test series.

In conclusion, tests as well as related calculations with several computer codes have been performed for passive decay heat removal systems. The spectrum tested and the quality should allow its use in a licensing process.

The NOKO test facility located at the Institute for Safety Research and Reactor Technology of the Research Center Jiilich is a thermal hydraulic test rig, which was constructed within the framework of a research task in a joint project of the Research Center Jiilich (FZJ) and SIEMENS AG, Power Generation Division (KWU), with support from the German Federal Ministry of Education, Science, Research and Technology and German utilities. The facility is suited for a broad spectrum of experiments in the field of thermodynamics and fluid dynamics of water, water vapor and non-condensable gases. Different passive safety systems can be investigated with only minor modifications.

The parameter limits given by the design are:

• maximum primary pressure: 7 MPa;

• maximum secondary pressure: 1 MPa;

• maximum power: 4 MW.

The maximum temperatures are the corresponding saturation temperatures.

The NOKO facility is composed of three sections. The first section is the primary circuit with the pressure vessel, the bundle of the emergency condenser and the associated connecting lines. The second section is the secondary side with condenser tank, relief lines and relief tank. The system of steam generation with electric boiler, separator and the associated lines forms the third section. The arrangement and linkage of the individual sections can be seen from Figure Al.

The steam-water mixture produced in the electric boiler is passed into the water — steam separator where the steam is separated from the water. The water is pumped back into the electric boiler. The separated steam is either passed into the pressure vessel or — if more steam was produced than is needed — the excess steam blown off into the relief tank. The steam is condensed in the relief tank which is cooled by an external cooling circuit. The components are made of austenitic steel. An exception is the condenser tank, which consists of ferritic steel and is internally coated with XYVADUR 569 for reasons of corrosion protection. This coating is resistant up to 200°C.

The PANDA test facility was erected in the early 1990s within the framework of the so-called ALPHA Program (Advanced Light Water Reactor Passive Heat Removal and Aerosol Retention Program) at the Paul Scherrer Institute. The PANDA test facility is a large-scale thermal hydraulic low-pressure test facility for investigating passive decay heat removal systems for the next generation of Light Water Reactors. In the first instance, PANDA is used to examine the integral long-term performance of the Passive Containment Cooling System for the Simplified Boiling Water Reactor (SBWR). The facility is an approximately 1:25 volumetric, full-scale height simulation of the SBWR containment system.

Within the project here, experiments with newly developed components were carried out in the PANDA test facility. This included the PANDA isolation condenser, the SWR-1000 building condenser and a plate condenser. All three components serve for heat removal from the containment after a serious accident.

The PANDA test facility is of modular design. It consists of a pressure vessel simulating the reactor pressure vessel, two dry-well and two wet-well containers as well as a Gravity Driven Cooling System (GDCS) pool. The facility has two separated water pools. In a water pool two passive containment coolers (PCC) are installed. In the other pool one PCC which was also used as an isolation condenser (IC) was placed. The condensers are full-scale mock-ups which only differ from those projected for the SBWR by the number of tubes. The setup of the facility is shown in Figure B1 comprising also the connections between the containers, which are not described here in detail.

The PANDA-PCC consists of 20 vertically arranged tubes connected at their ends with drum — type headers. The upper header has a connection for steam supply, the bottom header has a drain for the condensate produced and a drain for non-condensable gases. The tubes of the PCC have an outside diameter of 50.8 mm and a wall thickness of 1.65 mm. They are made of austenitic steel.

The PCC as well as the IC are passively acting components. They are heat exchangers serving to condense steam. The gas flows to the condensers without the use of pumps. It enters into the upper drum and most of the steam is condensed in the vertical tubes. The condenser pool has a ground surface of 1.5 m x 2 m and a height of 5 m. The water level is approx. 4.50 m.

In many new concepts, the containment consists of an inner steel shell for providing leak tightness and an outer reinforced concrete shell for protection against external hazards. It should be noted that compared to the concrete wall the steel shell is more sensitive to the fast or local thermal loads which can be produced by direct containment heating or fission product deposition phenomena. For this containment configuration, the passive containment cooling system (PCCS) utilises the steel shell as a heat transfer surface. In case of an accident the inner containment shell will heat-up and drive an air flow, that enters the gap between inner and outer containment shell through windows at a lower position and leaves for the environment through filtered air outlet at the top. The air-flow will cool the steel shell by natural convection. Steam produced inside the containment due to accident conditions will be condensed on the inner surface of the steel shell and the condensate will collect in the containment sump.

In some PWRs (e. g. AP600, EP1000, AC600/1000), between the inner steel shell of the containment and the outer reinforced concrete shell an air baffle forms an annular wind duct. The PCCS utilises the steel shell as a heat transfer surface. In case of an accident the containment heats up and drives an upward air-flow in the gap between the steel shell and the air baffle [5]. Water from a water storage tank is sprayed onto the top of the steel shell. It flows down the outer surface as a water film counter-current to the air, intensifying heat removal by evaporation. Steam will be condensed on the inner surface of the steel shell with the condensate being collected in the containment sump. The capacity of the water storage tank is sufficient for 72 hours [6]. In the very unlikely case that the operator would not be able to replenish the water in the water tank when it empties after 72 h, the natural convection of air will be sufficient to prevent containment failure although the design pressure will be slightly exceeded [4]. A similar PCCS concept without the seismic issue of an elevated tank utilises an external ground level water storage tank with an insulated floating lid on the water level. The top of this tank is connected to an internal vessel with a low boiling point fluid. If the containment heats up this fluid starts to boil and pressurises the external tank by pushing the floating lid. Therefore the coolant is sprayed onto the top of the containment [7]. Another concept uses the lower part of the annulus between the steel and concrete shell as a water pool. Air enters the gap trough windows above the water level and leaves it at the top. When the steel shell heats up, the temperature of water will increase up to boiling. The heat will be removed by single-phase convection of water and air or by evaporation, depending on the containment conditions [7].

In Russian WWER-640/V-407 concept [8], at the outer surface of the containment steel shell, rectangular pockets are arranged in rows and columns. The pockets of each column are inter­connected by vertical lines. A NC flow of cooling water from an external pool near the roof will be established. Steam is condensed at the cooled parts of the inner surface of the steel shell. The condensate is collected in the sump to allow for post accident recirculation.

A passive containment cooler (PCC) which is used in some designs primarily for severe accident prevention purposes will also mitigate severe accident consequences as it is foreseen in the design of the ESBWR, and some advanced PWR and CANDU designs. The PCC is a condenser immersed in a special PCC pool above the containment, using the design principles of an isolation condenser. It consists of a tube bundle connecting inlet (top) and outlet (bottom) collectors. The steam-gas mixture from the containment enters the inlet collector of the PCC and will be condensed inside the tubes. The condensate drains towards the RPV and the wet well [9].

In a PCC system for an advanced heavy water reactor design the condensate is collected in a water storage tank for gravity driven injection, and non-condensables are vented to a suppression pool [10]. A PCC proposed for application in a PWR (e. g. the CP-1300) utilises an external pool in a high elevation as a heat sink. The steam-H2 mixture passes H2-ignitors before entering the heat exchanger. The condensate is collected in the IRWST and/or used for passive containment spray [7].

In some designs (e. g. some BWRs and PWRs with double concrete containment) a building condenser (BC) is used for passive containment cooling. A BC consists of an internal (inside containment) heat exchanger (HX) in combination with an external (outside containment) pool containing the cooling water. The HX is composed of a number of finned condenser tubes between an inlet — and an outlet collector. It is placed at an upper position inside the containment. The HX tubes are slightly inclined. Thus the outlet is somewhat higher than the inlet. The collectors are connected with the external pool (penetrations). The outlet line ends at a higher elevation in the pool than the inlet line. Cooling water will flow by natural circulation from the pool through the BC back to the pool. The condensate drops down from the outer surface of the HX to a core flooding pool (BWR) or to the containment sump (PWR). A skirt is used in PWR design to separate the condensate from non-condensable gases. As a kind of BC, the modular PCCS [11] can be considered for PWRs with double concrete containment. Modular PCCS uses an internal HX with a skirt (similar to BC) connected with a pool in the gap between the containment shells. Before the cooling water enters the pool it passes through an external HX where heat is transferred to an air-flow. The air-flow will enter the gap through outer concrete shell windows, pass the HX, move over the water surface in the pool and leave the building through a chimney. Condensation of steam and separation of non-condensables functions as in a BC system.

Passive containment cooling can also be ensured by internal plate condensers (PCs) that are fitted to the containment wall and connected with an external heat sink. One example for a PC utilises cooling elements made from ductile cast iron, containing fins at the side facing the containment atmosphere. These fins can absorb loads from fragments impact without any effects on the cooling system. The cooling water flows through steel pipes in bores along the fins. Natural circulation is established by an external draught cooling tower. PCs were found to be a valuable passive energy sink particularly under convective heat transfer conditions, i. e. beyond its design conditions [12].

Containment spray systems are widely used in current reactor designs as well as in future concepts to reduce the concentration of fission products (e. g. for iodine precipitation and aerosol wash out). Containment spray systems also contribute to containment pressure and temperature reduction. Although containment spray systems in most cases utilise pumps (active), at the secondary side of the cooler natural circulation driven systems can be used. Nevertheless, there are completely passive concepts with a spray water supply from elevated [7] or pressurised [4] tanks, that can contain special chemicals e. g. for iodine precipitation. Another passive concept uses the condensate of a PCC system to feed the spray [7]. An alternative passive system to drive a spray mass flow uses an ejector-condenser (E-C) system [13]. Its principle is based on the dynamic form of natural convection utilising inertia forces instead of gravity for fluid circulation. Steam speeds up to a high velocity in a Laval nozzle. Then it mixes in a mixing chamber with cold water that takes off its mass, heat and kinetic energy. The resulting two-phase mixture gets a supersonic flow, the kinetic energy of which turns into potential form in a diffuser. Thus the outlet pressure can exceed essentially the inlet steam and water pressure. In containment spray application water is taken from the sump, cooled by an external cooler (e. g. draught cooling tower) and fed by the E-C to the spray nozzles. The driving steam for the E-C is taken from a heat exchanger that evaporates part of the supplied water mass flow (bypass) by the heat of the containment atmosphere [14]. For start of the system an external start-up tank is necessary.

A Technical Committee Meeting on Natural Circulation Data and Methods for Innovative

Nuclear Power Plant Design was held at in Vienna in July 2000.

The meeting presentations and discussions were directed toward three related aspects of

natural circulation phenomena:

(a) Design considerations for development and deployment of innovative concepts using natural circulation phenomena;

(b) Computer codes and incorporated models for analysis of natural circulation phenomena;

(c) Experimental facilities and data for support of concept design and analysis.

Within the area of computer codes and models, two classes of models were discussed:

(a) Systems codes — Established systems codes are used to model complete plant systems, including instrumentation and control. These are typically one dimensional (1D) models with multi-dimensional phenomena addressed within component models where necessary;

(b) Multi-dimensional generic flow models — Two types of models were discussed:

— Computational fluid dynamic (CFD) models

— Large eddy simulation (LES) models.

Following the meeting presentations, a general discussion of the subject was held among

participants, resulting in the following conclusions and recommendations.

Functional and structural diversity of WWER-1000/V-392 safety systems provide deep protection against common-course failures, and application of passive systems and active systems actuation without personnel interference yield deep protection against human errors. These engineering solutions used in NVAES-2 design enable the attainment of increased safety level, compared to the existing WWER-1000 plants.

For existing plants where the most of safety functions are ensured by active systems, the electric power supply is an important precondition for the successful operation of the safety systems. In spite of the very reliable emergency power supply from diesel-generators, loss of offsite power remains to be very essential contributor to the estimated core melt frequency from the internal initiating events (for example, more than 80% for unit 4 of Balakovo NPP [6]). For NVAES-2 with V-392 reactor plant, this figure is reduced to about 30% at absolute value 7.91 x 10-9 As a whole, total core melt frequency for NVAES-2 is about three orders of magnitude less than for Balakovo-4 which is the latest WWER-1000/V-320 unit commissioned in Russia.

Passive residual heat removal system from the core via steam generators to the atmosphere as the ultimate heat sink (so called SPOT) plays an important role in the core melt frequency reduction mentioned above. The design basis for this system is that in case of station blackout during the most unfavorable atmosphere conditions the heat removal capacity with account for the failure of one channel shall amount to not less than 2% of the reactor rated power. The heat removal at the initial stage of the accident is performed due to partial water evaporation from the secondary side via steam generator relief valves to the atmosphere.

The SPOT system consists of four groups (corresponding to the number of reactor coolant system loops) of closed natural circulation circuits. In the ribbed tubular air-cooled heat exchanger (four heat exchangers for each of these circuits), steam extracted from the steam generator condenses, and the condensate flows by gravity to the steam generator boiler water volume. Under normal reactor plant operation, the SPOT system is under standby when all the SPOT circuits are in the warmed-up state. In case of plant blackout, the SPOT state changes from the standby to the operating condition. In addition to its main purpose (core decay heat removal in case of complete loss of a. c. power), the SPOT system can maintain the hot standby parameters of the reactor plant; for this purpose the SPOT has a special controller. The system is thermally insulated, so the heat losses in standby conditions are less than 0.1% of reactor rated power. Natural circulation in the SPOT system is provided by the corresponding layout of the steam generator, heat exchanger and draught air duct.

The steam circuit pipeline runs from fresh steam line to collector which distributes the steam by smaller tubes to four heat exchanger. The condensate from each heat exchanger is supplied by tubes to the collecting receiver and then by pipeline to the steam generator. Two isolation valves are installed at heat exchanging module inlet and outlet to isolate it in case of damage or maintenance. Small diameter pipelines with valves installed on them are provided for removal of air from heat exchanger when filling them with water during hydrotest and for periodical removal of non-condensables under standby conditions. Cooling air is taken from the atmosphere outside the reactor building. Air goes through the protective net and enters the annular corridor located around the reactor building and then to the heat exchanging modules. The air takes the heat from the steam and goes to the draught air ducts, which have the common outlet collector-deflector. Inlet and outlet gates and controller are installed on the airside of each heat-exchanging module. The gates open to switch on the heat exchanging

module to operation. The controller can be used to change the airflow rate to ensure additional SPOT system functions (for example, to maintain the reactor plant in the hot standby conditions).

Under standby conditions, the I&C system ensures for each heat exchanging module the measurements of the air inlet and outlet temperature, outlet air humidity, water level and temperature in the condensate lines. Information on the air humidity is especially important to detect a leak in due time. For this aim, humidity measurement is installed close to the upper part of the air space of the heat exchanger. Under accident conditions, power supply to the instrumentation is ensured by the sources of category 1. Under these conditions the number of measured parameters is reduced to condensate and air temperature and air humidity at the heat exchanger outlet.

Equation (14) has shown that simulation of the steady state behaviour is possible by simulating Grm/NG for any natural circulation loop. The transient and stability behaviour, however, are described by equations (8) and (10). Substituting the steady state solution, the transient momentum equation can be rewritten as

From equations (17) and (8), it is obvious that the transient and stability behaviours are governed by the physical parameters Grm, St and the geometric parameters of NG, g, Vt/Vh, PcLt/Ac and the area ratio ai. To reduce the number of independent parameters, it is customary to combine St and PcLt / Ac into a single dimensionless parameter called Stm. Similarly, Grm and NG can be combined as Grmb/3-b/NG3/3-b so that the transient and stability behaviour can be expressed as

Further reduction in the number of independent parameters is possible for special cases. For example, with a uniform diameter loop, (Vt / Vh ) = (Lt / Lh), ai=1 and NG = Lt / D so that

In addition to Lt/Lh other length scales also affect the stability behaviour. This can be established by carrying out a linear stability analysis. In this method, the loop flow rate and temperature are perturbed as

ю = rnss + rose111 and 9 = 9ss + 9senx

Where e is a small quantity, w and в are the amplitudes of the flow and temperature disturbances respectively, and n is the growth rate of the perturbations. Substituting Eq. (20) in equations (10) and (17), and using the continuity of temperature perturbation in various segments as the boundary condition, the characteristic equation for the stability behaviour can be derived. The characteristic equation for a uniform diameter loop with horizontal heat source and sink can be expressed as Y(n)=0 (Vijayan and Austregesilo (1994)), where

-L{p(- nLh/Lt)-1} + (exp{- n(sc — St — Sh)h )Lt}-1

nLh

and D = ex p{StmLc/Lt}- exp(- n) Where St=Lt/H and Sx =sx/H. Sc, St and Sx are the

dimensionless distances from the origin (i. e. S=0 in Fig. 1) in anticlockwise direction. It is obvious from equation (21) that, apart from the parameters listed in (19), the ratios of the lengths are also required to be preserved to simulate the stability behaviour.

All following results are from the transient calculation and are time averaged over two minutes, like in the experiment. The calculated temperature field is shown in Fig. 5. Despite a careful and detailed 3d modeling of the geometrical and thermal characteristics of the SUCOS-3D ex­periment, the calculated pool temperature (Tp. cai = 29.2°C) is lower than the measured one Tp. exp 32.6 C. the corresponding deviation is (Tp_i-Тр_иЧр) (Тр_иЧр-"I/0oi ) = 34%.

In order to find possible reasons for this deviation one should compare the calculated flow field to the experimental one. The calculated flow field for SUCOS-3D is very similar to the ex­perimentally found and calculated one for SUCOS-2D. A stable natural convection loop devel­ops, Fig. 6: the heated fluid rises from the copper plate through the chimney to the covered water level; here the warm flow turns right to the horizontal side area and flows on without an intensive contact to the horizontal cooler; the water is mainly cooled in the vertical side area from where it returns to the pool where it is heated again; part of the cold water from the hori­zontal coolers moves from time to time in form of cold plumes against the mean flow down­wards through the chimney and mixes with the rising heated water. These non-stationary plumes cause the strong time dependence of the heat flux on the copper plate, Fig 4. Accord­ing to this flow field, the temperatures in the horizontal side area of SUCOS-2D are higher than the ones in the pool under the tilted roof, similar to the temperatures in Fig. 5.

The flow field in the experiment SUCOS-3D must be reconstructed from the measured tem­peratures because no velocity measurements were performed. Other than in SUCOS-2D here we find in the experiment the highest temperatures not in the horizontal side area, but below the tilted roof, Fig. 7. Therefore, a different behavior of the natural convection has to be de­duced: We have at least to expect stronger mixing between cold counter-current downward flow with hot rising fluid in the chimney.

—► 0.01 m/s

Possible reasons for the disagreement in the pool temperature and in the natural convection loop were investigated. Since SUCOS-2D calculations showed a high sensitivity of the natural convection on thermal disturbances, the thermocouple support structure installed in the chim­ney was additionally modeled as a thermally interacting structure. Unfortunately, the exact po­sition of the movable probe is not known. Nevertheless, the new results with probe support structure are better than the previous ones and bring the calculated pool temperature to the right direction but not yet enough to achieve a satisfactory agreement.

So far, the cooling performance of the vertical coolers was overestimated by all previous calcu­lations. Therefore, a further numerical study was performed changing the kind of the thermal boundary conditions for the active vertical coolers: values for the wall heat fluxes deduced from the experiment were pre-set instead of using surface temperatures. Then, the calculated pool temperature Tp, cai= 32.8 °С agrees well with the experimental one, Fig. 8: the deviation is reduced from 34% to only 2%. Despite of this positive result, qualitatively the same natural convection loop is obtained like in the previous calculations. This means, the calculated flow field still shows no agreement with the reconstructed one in the experiment.

The differences between experiment and calculation in the behavior of the flow field were fur­ther analyzed by means of vertical temperature distributions, which were measured in the chimney and in the vertical side area (Carteciano et al. 2000). The amount of water flowing down from the horizontal cooler to the vertical one was much less in the experiment than cal­culated, which causes reduced heat fluxes at the outermost section of the vertical coolers. An other significant difference between calculation and experiment can also be found in the chim­ney: recirculation of cold water flowing back from the horizontal cooler to the chimney is cal­culated, while cold water was registered in the experiment in the plane of measurements only under the tilted roof. The origin of the cold water under the roof in the experiment was recon­structed by analyzing the cooling performance of the horizontal coolers which are divided into two big and two small ones. The cooling performance of one small cooler is in the experiment as high as the one of a big cooler despite the cooling surface ratio of about 1:2. Therefore, a stronger water flow was obviously present over the small cooler. This cold flow returns to the corners of the chimney (Fig. 9) and is recorded only when it reaches the thermocouples at posi­tion R below the chimney.

A decisive conclusion on the disturbance responsible for the experimental flow behavior was not found in all previous calculations and studies. Further deviations in the modeling or bound­ary conditions used in the simulations from those in the experiments have to be considered. One example, which would explain the unexpected results from the SUCOS-3D experiment, is to postulate that one of the horizontal coolers was slightly tilted against the main flow direc­tion.

Additional calculations with a 2d slab model similar to SUCOS-2D were performed with dif­ferent inclinations of the horizontal coolers from 0 to 4 mm, corresponding respectively to 0 and 1.04 % slope. The mass flow of the cold water going back to the chimney from the hori­zontal coolers increases due to this measure by about 70% and the corresponding heat removal by this flow increases by about 55%! Therefore, the mixing between the cold water and the heated water rising through the chimney is strongly increased like in the experiment. These re­sults show that a very small slope of the horizontal coolers can influence the flow behavior in a drastic way and would explain the experimental flow field, but a final check is not possible be­cause the experimental facility is already disassembled.