Category Archives: Natural circulation data and methods for advanced water cooled nuclear power plant designs

Models for 1-D thermalhydraulic analysis

(a) Homogeneous equilibrium model:

This is the simplest model for analysing the thermal hydraulic phenomena in a two-phase system. This considers one conservation equation each for the mass, energy and momentum of the mixture. Hence, it assumes complete thermal and mechanical equilibrium between the phases. This model is also referred to as Equal Velocity and Equal Temperature (EVET) model. Here, the mixture is considered to behave as a single fluid. An equation of state takes into account the variation of fluid properties. To take into account the differences in velocity between the phases, empirical slip models are used. The success of the model depends on the accuracy of the empirical relationships used in the code for the wall friction and wall heat transfer. Use of computer codes based on the homogeneous equilibrium model for accident and safety analysis of nuclear reactor systems is perhaps becoming a thing of the past. However, in the earlier design stages, codes based on this model are still extensively used. Further, most analyses to generate the stability behaviour (basically codes used to generate stability maps) of natural circulation systems are based on the homogeneous equilibrium model.


We have derived two results, which enable both the stability and natural circulation characteristics to be evaluated analytically and with the minimum of computation.

The requirement for both dynamic and static instabilities is that the increase in the two-phase pressure drop should be either equal to or greater than the decrease in the single-phase pressure drop as the inlet flow decreases. The relevant limit is actually the static (non-linear) instability boundary, which may lead to CHF, has been called the "zeroth mode" of dynamic instability. Thus, in dynamic dispersion-type analysis, it corresponds to the time-independent, zero-frequency (or infinite wave number), real wave number case which, corresponds precisely to the homogeneous equilibrium limit for the flow. In non-linear (called “excursive instability”), the channels could switch from one flow rate to another while maintaining the same total pressure drop. When non-linearly unstable, the channel flow fluctuates, or reverses, and dryout can ensue.

Подпись: <9AP ~dG Подпись: 0 Подпись: (7)

The static limit is the non-linear limit of conditionally instability, where departure from nucleate boiling or critical heat flux will occur at low and high qualities, respectively. There are sufficient data in the literature which show that instability in multiple channels precedes the limit of classic single channel (mass-flow controlled) dryout (Mathison, 1967); (D’Arcy, 1967). This differs from the result for the zero frequency condition, which can only be written as a cubic in, (Ns / Np), and does not give a critical subcooling number. The condition of static instability in parallel channels is the Ledinegg condition (Saha et al, 1976); (Duffey and Hughes, 1991),

This condition, when applied to Equation (1) and with the vapor to liquid density ratio being small, leads to the following characteristic Equation (8), which is derivable after many pages of straightforward but extensive algebra:


where Nf, Ns, Nfr, and Np are again the Froude, Subcooling, Friction and Phase Change numbers, respectively. In addition, the k-parameters are loss coefficients normalized with the Friction Number. (The last term in brackets is corrected for a typographical error in the earlier paper (Rohatgi and Duffey, 1994) which omitted the number 2.)

It is important to note that arising naturally from the analysis, the instability region is bounded by the two roots of Equation (8), where the pressure drop versus flow rate is a minimum, maximum or point of inflection. The region of instability for a parallel channel system as bounded by these roots, which correspond to low (subcooled boiling) and high (saturated boiling) vapor qualities. This result has been rederived and confirmed by (Babelli et al, 1995), who retained the vapor to liquid density ratio, and the convective acceleration term, to derive
a "corrected result" more complex than Equation (8). The overall effect of the corrections is generally small. The two roots of the quadratic have been termed the first and second analytic instability lines by (Babelli et al, 1995), corresponding to the low and high quality flow states respectively.

The conditions for existence of positive real solution in Equation (8) which is quadratic in Np and Ns, are as follows:

image017Подпись: and (9)


image019 Подпись: (11)

The above equation is also quadratic in Ns and provides a lower bound for the static instability. For large values of Np and Ns, the asymptotic form of Equation (8), has the limits, for small,


Nr_n N?_ — — Qor—— 2

Reflux Condensation (RCNC)

At ‘low’ mass inventories of primary coolant and/or at low core power, steam velocities in the upper part of the system including hot legs and steam generator entrance are low. Weak interactions occur at the steam-liquid interface that are not enough to cause CCFL. In these conditions, the liquid that is condensed or entrained in the ascending side of the U-Tubes may flow back to the hot leg and to the core. Stratified countercurrent steam and liquid flow simultaneously in the hot legs. Mass flowrate at core inlet is close to zero, although a ‘minor’ natural circulation path may establish between core and downcomer inside the vessel. However, upward two-phase mixture and downward liquid flows occur at the core outlet. Core thermal power can be removed by boil-off in the saturated nucleate boiling heat transfer regime.


3.1. Experiments with naturally-induced flow

From the results of the commissioning tests with pumped flow presented in preceding section, it was clear that the test facility was operating satisfactorily. Accordingly, a detailed programme of experiments was carried out with naturally-induced flow and uniform wall temperature. The power control and measurement system was used to achieve uniform values of wall temperature ranging from 60 to 300°C. Corresponding experiments with uniform wall heat flux were also performed keeping the total heat input the same as in the uniform wall temperature experiments. The matrix of conditions covered was as follows.

Wall temperature Tw (°С)








Corresponding wall heat flux qw (W/m2)








Uniform heat flux boundary condition Re=29085 Qw=1910 W/m 2


FIG. 4(a). Commissioning test results with uniform heating for forced convection

Uniform heat flux boundary condition
Re= 10261 Qw=913 W/m2


FIG. 4(b). Commissioning test results with uniform heating for mixed convection with impaired heat transfer

In these experiments the flow rate induced through the system increased systematically as the thermal loading was increased. The variation of dimensionless flow rate (characterised by Reynolds number) with dimensionless heat loading (characterised by Grashof number) is shown in Figures 5(a) and 5(b) for the uniform wall heat flux and uniform wall temperature cases, respectively. The physical properties in these dimensionless parameters were evaluated at the inlet temperature and the characteristic dimension used was the tube diameter.

Подпись: 12000
Подпись: 10000
Подпись: О.ООВ-ОО 5.00В07 1.00Е+08 1.50В08 2.00В08
Подпись: 2000

FIG. 5. Relationship between flow rate and thermal loading for naturally induced flow with (a) uniform heat flux, (b) uniform wall temperature

Figures 6(a) to 6(f) show the axial distributions of Nusselt number obtained in these experiments. The flow rates induced through the test section were used to determine the Reynolds numbers shown on the figures. In each case a curve is presented for forced convection with uniform heat flux evaluated at the Reynolds number for that case using the equation of Petukhov et al [5]. The main points to note are:

(i) The experimental values of Nusselt number all follow a similar general pattern. They lie well below the curves for forced convection calculated using the Petukhov equation.

(ii) The values of Nusselt number for the uniform wall temperature case are slightly lower than those for uniform wall heat flux in spite of the fact that the flow rates induced through the system are greater.

(iii) The Nusselt number curves for forced convection calculated using the Petukhov equation decrease slowly at a steady rate in the thermally fully developed region. This is due to the fact that the Reynolds number decreases as the bulk viscosity increases due to the rise of bulk temperature.

Figures 7(a) and 7(b) show the experimental results plotted in terms of local values of local Nusselt number, Nux, and Grashof number, Grx (evaluated using the distance x from the start of heating as the characteristic dimension). The fluid properties were evaluated at the local bulk temperature, calculated knowing the air temperature at inlet, the heat input and the flow rate of air induced through the system. As can be seen, this method of presenting the results does enable a good correlation of the data to be achieved.

The main conclusions which can be drawn from the naturally-induced flow tests are as follows:

image230Even though the flow rates achieved were such that in the absence of buoyancy influences the flow would have been turbulent, the effectiveness of heat transfer was seriously impaired in relation to that expected for conditions of turbulent forced convection at those flow rates. It is clear that under the conditions of all the experiments performed the turbulence structure was


significantly modified by buoyancy. In the experiments with uniform wall temperature the heat transfer behaviour did not change much as the temperature was increased. Furthermore, the behaviour was very similar in the corresponding experiments with uniform wall heat flux. Clearly, the results obtained in this study highlight the need for care to be exercised in the design of systems for cooling a steel containment shell by naturally-induced flow of air so as to ensure that the kind of buoyancy-influenced conditions which prevailed in the present experiments are avoided.

FIG. 6(b). Heat transfer results for naturally induced flow with Tw = 100°C



3.2. Experiments with pumped flow

After completing the naturally-induced flow experiments reported in the preceding sub-section, a programme of pumped flow experiments with uniform wall temperature was carried out. The conditions of heat transfer achieved in those experiments varied from forced convection with negligible influences of buoyancy to mixed convection with very strong influences of buoyancy. Inlet Reynolds number was varied in steps from about 30,000 down to 3,500 and values of wall temperature from 75°C to 300°C were covered. Again, corresponding experiments were performed with uniform heat input.


FIG. 7. Correlation of heat transfer results for naturally induced flow with (a) uniform wall heat flux, (b) uniform wall temperature

Some sample results for a wall temperature of 150°C are shown in Figures 8(a) to 8(d) along with the corresponding ones for uniform heat flux. The Reynolds numbers at inlet were about 29,000, 10,500, 5100 and 3500. The main points to note are:

(i) The heat transfer mechanism at the highest Reynolds number is turbulent forced convection. As can be seen from Figure 8(a), the results for the uniform heat flux case lie very close to the curve calculated using the Petukhov equation. Thus there are no significant influences of buoyancy. As expected, the results for uniform wall temperature lie slightly below those for uniform wall heat flux.

(ii) At the Reynolds number of 10,500, Figure 8(b), the mechanism of heat transfer is mixed convection with serious impairment of heat transfer due to influences of buoyancy on turbulence. The effect is much greater for uniform wall temperature than for uniform heat flux. The results for uniform wall temperature are similar to those obtained for naturally-induced flow with a wall temperature of 200°C (Figure 6(d)).

(iii) In the case of the experimental results shown in Figures 8(c) and 8(d) the conditions are those of mixed convection with progressively stronger influences of buoyancy leading to recovery and enhancement of heat transfer. Concentrated non-uniformities appear in the distributions of Nusselt number as a consequence of the development of the flow along the tube under the influence of strong buoyancy forces.

Figures 9(a) and 9(b) shows results from the pumped flow experiments for a large value of x/D presented in terms of Nusselt number ratio and buoyancy parameter. Experimental data for naturally induced flow are also included (in these cases the Reynolds number was evaluated using the value of flow rate induced through the system). The impairment of heat transfer which develops with increase of buoyancy parameter is strikingly apparent in both cases, as also is the recovery of heat transfer (in relative terms) when buoyancy influences become strong enough to restore turbulence production. As can be seen, when presented in this form the naturally-induced flow results map directly onto the pumped flow results.

Although the results obtained in the pumped flow experiments confirm that the general pattern of behaviour in buoyancy-aided mixed convection is the similar with uniform wall temperature and uniform wall heat flux, the impairment of heat transfer which develops with onset of buoyancy influences does occur more readily in the case of uniform wall temperature. The results highlight the fact that care is needed in the design of containment cooling systems to avoid conditions under which buoyancy-induced impairment of heat transfer might occur.

Energy Balances

In Section 2.3 it was shown that — in principle — 3 different loops exist in the NOKO facility. For the tests with the emergency condenser as the test section this configuration allowed the

evaluation of the energy transferred by the emergency condenser by three different and independent balances:

I) The steam flow to the condensers was measured with an orifice.

II) The steam flow to the condensers was calculated from the power input by the boiler and

pumps, the heat losses and the energy removal by cooling.

III) If the water pool was at saturation temperature, the steam was measured using an orifice.

The comparison of these three balances increased the confidence in accuracy of the results.


FIG. 3. Structure of the NOKO-Data in the Internet.

NC simulation in PWR and WWER-440 ITF

NC experiments have been conducted in all ITF for characterizing the loop features and for constituting databases suitable for code assessment. NC experiments have been conducted in the Lobi, Pkl, Bethsy Pmk and Pactel facilities, the first three simulators of PWR and the last two simulators of WWER-440. In relation to all the ITF, NC experiments with decreasing mass inventories of the primary coolant system have been carried out. The electrical power supplied to the core simulator corresponded to the decay power and ranged between 1.5% and 5%, roughly of the nominal core power. In these situations the NC scenario can be characterized by a diagram showing the core power as a function of the primary system mass inventory.

The applications of system codes have been of help for interpreting the experimental scenarios, for optimizing the features of the nodalizations and for characterizing the code capabilities. A list of significant achievements is given below together with references where details of the analyses can be found.

a) The codes have been used to distinguish five main NC flow patterns depending upon the value of the mass inventory of the primary loop (see also Ref. [7]):

— Single phase NC with no void in the primary system excluding the pressurizer and the upper head;

— Stable co-current two-phase NC with mass flow rate increasing when decreasing primary system fluid inventory;

— Unstable two-phase NC and occurrence of siphon condensation;

— Stable reflux condensation with liquid flowing counter-current to steam in the hot legs: flow-rate is sufficient to remove core power till loop mass inventory achieves values as low as 30-40% of the nominal values;

— Natural circulation with part of core rods in dry-out condition not favorable from the current technological and safety point of view.

b) The code has been used for characterizing the oscillations (third dashed item in the list above), showing the different role of the counter-current flow limitation (CCFL) at the entrance of the U-tubes, the siphon effect and the steam condensation both in the rising part of the U-tubes. The flow reversal and the different behaviour of parallel groups of U- tubes could also be observed by the help of the code, Ref. [8].

c) Different codes used by different European organizations have been applied to the comparative analysis of the A2-77 experiment carried out in Lobi facility. Capabilities of the codes were characterized as well as the influence upon the results that should be expected owing to the code-user effect, Ref. [9]. Deficiencies were observed in the predictions of pressure drops at low value of the Reynolds number.

d) The application to the study of NC in WWER-440 showed the code capability in predicting the flow stagnation and the consequent rise in system pressure caused by the loop sealing present in the hot leg of this reactor type, Ref. [10]. Clearing of loop seal occurs before dangerous situation for the system are reached and is also predicted by the code.

e) The code has been used to determine the maximum core power at which the PWR systems or PWR simulators can be operated in NC keeping sub-cooled the core. The limit was found close to 10% of the core nominal power, Ref. [11]. Higher limits were found fixing different thresholds for the system operation.

f) The code has been successfully used in predicting NC phenomena measured in systems that are relevant to the AP-600, including NC across the PRHR (pressurized residual heat removal), and the CMT (core make-up tank) systems, Refs [12] and [13].

. Results processing and computer models validation

Every transient was graphically display as a verification procedure, in order to identify anomalies that could lead to reproduce a test. The deviations in transients were numerically processed and presented as trend graphs. A sensitive analysis was performed and most sensitive parameters were identified.

A representative group of transients were selected, in order to check computer models.

Simulation models are in current development against a reference transient, without adjustment. When this contrast is clear, models will be compared against the representative group of transients. The information on specific models should be fed in CAREM modeling.

New dynamical experiments are planned, but the final selection will be based on the results of the contrast of the computer models against the representative group of transients.


An overview of the thermal hydraulic aspects of CAREM reactor was presented. The analytical dynamical studies and experimental facility, studies and results were briefly presented.

It was observed that around the operating point self-pressurized natural circulation was very stable, even with important deviation on the relevant parameters.

Results of correlations

Using UCB condensation data base [7] for both pure and steam/air mixture available, the unknown parameters of the correlations have been estimated by using Marquardt-Levenberg non-linear parameter estimation method [8] which provides quicker convergence than alternative methods. Results of present correlations are given in Table I.

PACTEL passive safety injection experiments and APROS code analysis

J. Vihavainen

Lappeenranta University of Technology

J. Tuunanen

VTT Energy


Abstract. VTT Energy in Finland and Lappeenranta University of Technology (LTKK) have run several experiments with the PACTEL (Parallel Channel Test Loop) facility to investigate the performance of Passive Safety Injection System (PSIS) of Advanced Light Water Reactors (ALWRs) in Small Break Loss-Of-Coolant Accident (SBLOCA) conditions. PACTEL is full-height medium scale (1:305) integral test facility originally designed to simulate thermal-hydraulic phenomena of the Finnish Loviisa PWR of WER-440 type. The passive safety injection experiments in Lappeenranta started already in 1992 with a series of five experiments. These experiments simulated hot leg SBLOCA’s. The PSIS included a Core Make-up Tank (CMT), two pressure balancing lines (PBL) and an injection line (IL). The second series included similar PSIS as in the first series. The European Commission 4th Framework Programme project “Assessment of Passive Safety Injection Systems of Advanced Light Water Reactors Reactors” involved experiments on the PACTEL test facility and computer simulations of selected experiments. The project involved 15 experiments in three series. The experiments provided information about condensation and heat transfer processes in the CMT, thermal stratification of water in the CMT, and natural circulation flow through the PSIS lines. The EC project included validation of three thermal-hydraulic computer codes. The APROS analyses were performed at LTKK. The analyses showed that the codes are capable of simulating the overall behaviour of the transients. The codes predicted accurately the core heat-up, which occurred when the primary coolant inventory was reduced so much that the core top became free of water. The detailed analyses of the calculation results showed that some models in the codes still needed improvement. Especially, further development of models for thermal stratification, condensation and natural circulation flow with small driving forces would be necessary for accurate simulation of the phenomena in the PSIS. The modelling of thermal stratification has already been improved and also tested with the APROS code. The new calculation results have showed significantly better behaviour in PSIS operation.


PACTEL (Parallel Channel Test Loop) [1, 2] is a full height, medium-scale integral test facility (volumetrically scaled 1:305) designed to simulate the thermal-hydraulic phenomena characteristic of the Finnish Loviisa PWR. VTT Energy together with the Lappeenranta University of Technology run the facility. PACTEL has three primary coolant loops with pressurizer, primary coolant pumps and horizontal steam generators, high-pressure emergency core cooling system (ECCS), and low pressure ECCS with two accumulators. The peak operating pressures in the primary and secondary sides are 8 MPa and 4.6 MPa, respectively. The reactor vessel is simulated with a U-tube construction consisting of separate downcomer and core sections. The core comprises of 144 full length, electrically heated fuel rod simulators with a heated length of 2.42 meters. The maximum total core output is 1 MW, or 22% of scaled full power. The three coolant loops with double capacity steam generators model the six loops of the reference power plant. Each steam generator has 118 U-tubes with an average length of 2.8 m.

The passive safety injection experiments in Lappeenranta started already in 1992 with a series of five experiments. These experiments simulated hot leg SBLOCA’s. The PSIS included a


CMT and two PBL’s. The second series included four cold leg SBLOCA experiments in 1993. These experiments used similar PSIS as in the first series. In 1996, a new project of passive safety injection experiments with a CMT and one PBL started. The new experiments are a part of the European Commission 4th Framework Programme Nuclear Fission Safety program. Within this new project, two series of five experiments have been completed so far, and the third series is scheduled on September 1997. The project continues until September 1998. See Fig. 1 for a general view of PACTEL and Fig. 2 in the passive safety injection system in the fourth experiment series.


The main objective of the tests was the overall simulation of the PSIS behaviour. The experiments demonstrated the capability of PACTEL for the simulation of PSIS’s. The data did not provide very detailed information about phenomena in the CMT. The instrumentation of the CMT in the first test series was limited. The tests were partially aimed for investigation of possibilities to run passive safety injection tests on PACTEL. The experience gathered during this first series was then used in the specification of the test parameters and instrumentation of the second series.


FIG. 2. General view of the PACTEL experiment facility and the passive safety injection system in the fourth experiment series.

Passive decay heat removal from the core region

E. F. Hicken, H. Jaegers

Institute for Safety Research and Reactor Technology, Forschungszentrum Julich Germany

Abstract. The decay heat in commercial Light Water Reactors is commonly removed by active and redundant safety systems supported by emergency power. For advanced power plant designs passive safety systems using a natural circulation mode are proposed; several designs are discussed. New experimental data gained with the NOKO and PANDA facilities as well as operational data from the Dodewaard Nuclear Power Plant are presented and compared with new calculations by different codes. In summary, the effectiveness of these passive decay heat removal systems have been demonstrated; original geometries and materials and for the NOKO facility and the Dodewaard Reactor typical thermal-hydraulic inlet and boundary conditions have been used. With several codes a good agreement between calculations and experimental data was achieved.


The decay heat in commercial Light Water Power Reactors is commonly removed by active safety systems which require redundant systems as well as emergency power. This is expensive and requires time for maintenance and testing.


Therefore — when studying advanced power plant designs — the decay heat removal by passive safety systems was re-evaluated. In Fig. 1 some passive safety systems under consideration are shown.

For PWR the use of heat exchangers submerged in a large water pool (up to several thousand m3) is evident. The working principle is well known and can be calculated with well validated codes. However, to avoid heat losses during normal operation in the range of several per cent of the total thermal power valves have to be installed in the pipes to and/or from the heat exchanger. This definitely reduces the reliability of the decay heat removal as well as it results in additional costs. The expensive valves can be avoided if the principle used for the so-called
"Thermal Valve" is applied: the heat exchanger — now without valves in the high-pressure lines — is installed within a bell-shape volume. On signal by the reactor protection system or by manual operation a valve at top of the volume opens allowing heat removal by water circulation. This proposed design, however, has to be validated against experiments and related code calculations.

The principle already used in BWR’s and again proposed for advanced BWR designs is the Evaporation — Condensation mode: water in the core region is evaporated by decay heat and condensed within a heat exchanger placed in a water pool, the condensate returns to the core region.

This principle has been used in the Dodewaard Reactor and some other reactors already decommissioned. This principle has been proposed for the advanced BWR, the SBWR and the SWR 1000. Experimental results and comparison with code calculations will be given below.

The two new designs — for the SBWR and the SWR 1000- show some remarkable differences; some will be discussed below.

1) Both designs need a large water pool. Due to the fact that the heat exchanger for the SWBR can be placed above the Reactor Pressure Vessel (RPV) — thus allowing more flexibility in the design — valves are needed in the lines to and from the heat exchanger. Therefore, the heat exchanger can also be placed outside the containment. The heat exchanger and the water pool of the SWR 1000 have to be placed at the elevation of the core and within the containment.

2) The operation of both designs is quite different. When opening the valves in the connecting lines the full heat exchanger capacity is available from the beginning while the heat exchanger of the SWR 1000 will start slowly from zero to full capacity.

3) These passive heat exchangers are mainly designed to be used for a decay heat removal without a loss-of-coolant sequence; for some time they assist the heat removal in case of small breaks — for large break LOCA they are of no benefit.

4) The modelling of the phenomena and system behaviour with these designs is not always easy as it will be shown below, because the condensation behaviour inside the heat exchanger tubes — including the presence of non-condensables — as well as the heat transfer from these tubes to the water pool has to be considered.

5) Heat exchangers using condensation of steam are always sensitive to the accumulation of non-condensables. If no venting capability is installed the concentration has to be kept below a value, where the non-condensables can be dissolved in the condensate.

6) There exists some operating experience mainly in the Dodewaard Reactor.