draft validation of trio_u for transient accident

th

12 International Conference on Nuclear Engineering Washington D.C., USA, April 25-29 2004 ICONE12-49487

DRAFT

VALIDATION OF TRIO_U FOR TRANSIENT ACCIDENT SCENARIOS – NUMERICAL SIMULATIONS OF A ROCOM BUOYANCY DRIVEN TEST CASE T. Höhne Phone: (+49) 351 260 2425 e-mail: [email protected]

U. Bieder Phone: (++33) 4387 89514 e-mail: [email protected]

Forschungszentrum Rossendorf - Institute of Safety Research P.Box 510119 D-01314 Dresden Germany Fax:(+49) 351 260 3440

Laboratoire de Developpements en Thermohydraulique Avancee (LDTA), CEA Grenoble, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France

KEYWORDS: BORON DILUTION, COOLANT MIXING, ROCOM TEST FACILITY, COMPUTATIONAL FLUID DYNAMICS, LES, TRIO_U ABSTRACT

The results of the experiment as well as of the numerical calculations show, that a streak formation of the water with higher density is observed. At the upper sensor, the ECC water covers a small azimu thal sector. The density difference partly suppresses the propagation of the ECC water in circumferential direction. The ECC water falls down in an almost straight streamline and reaches the lower down comer sensor position directly below the affected inlet nozzle. Only later, coolant containing ECC water appears at the opposite side of the downcomer. The study showed, that density effects play an important role during natural convection with ECC injection in pressurized water reactors. Furthermore it was important to point out, that Trio_U is able to cope the main flow and mixing phenomena.

A generic investigation of the influence of density differences between the primary loop inventory and the ECC water on the mixing in the downcomer was made at the ROCOM Mixing Test Facility at Forschungszentrum Rossendorf (FZR)/Germany. ROCOM is designed for experimental coolant mixing studies over a wide variety of possible scenarios. It is equipped with advanced instrumentation, which delivers high-resolution information characterizing either temperature or boron concentration fields in the investigated pressurized water reactor. For the validation of the Trio_U code an experiment with 5% constant flow rate in one loop (magnitude of natural circulation) and 10% density difference between ECC and loop water was taken. Trio_U is a CFD code developed by the CEA France, aimed to supply an efficient computational tool to simulate transient thermal-hydraulic mono-phase turbulent flows encountered in the nuclear systems as well as in the industrial processes. For this study a LES approach was used for mesh sizes between 300000 – 2 million control volumes.

1.

INTRODUCTION

During a loss-of-coolant accident in a nuclear power plant, the injection of relatively cold emergency core cooling (ECC) water can induce buoyancy-driven stratification. This can cause thermal loads on the reactor pressure vessel (RPV). Additionally, in the case of inadvertent injection of low borated ECC wa ter, a

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boron dilution transient would be initiated. The transient is then depending on the resulting boron concentration distribution at the core inlet. Neutron kinetic simulations have shown [1], that a uniform distribution of the perturbation at the core inlet of pressurized water reactors (PWR), i.e. the assumption of an ideal mixing, does not deliver conservative results. The remaining uncertainties were too large to be acceptable for safety analyses. There are numerous postulated accident scenarios, where in case of uniform mixing the core survives without consequences or even without reaching criticality, while neglecting the mixing leads to the prediction of severe fuel rod failures. In reality, a partial mixing takes place. In the result, the real distribution of the parameter at the core entrance is situated in-between the two extreme cases both concerning shape and amplitude of the perturbation. To make realistic predictions about the consequences it is necessary to study the coolant mixing, which is a complicated three-dimensional fluid dynamic problem. Modern CFD codes running on powerful computers became available to model the coolant flow in the complex geometry of a PWR a couple of years ago [i.e. 2-7]. Nevertheless the use of CFD for this complicated task is a challenge still today. Due to the high safety relevance of the coolant mixing phenomenon it is necessary to validate computer codes and to verify computational results using experimental data. The literature reports about a number of test facilities to study mixing of cold ECC water injected into the cold leg of a PWR [i.e. 8-11]. In order to study coolant mixing under this conditions inside the RPV of a German type PWR the test facility ROCOM (Rossendorf Coolant Mixing Model) was used. The facility represents a 1:5 scaled Konvoi type PWR (1300 MWel). For the comparison with the Trio_U code an experiment with a constant flow rate in one loop (magnitude of natural circulation) and 10% density difference between ECC and loop water was taken.

cold legs, which are closest to the reactor inlet, the geometrical similarity between model and original reactor is respected until the core inlet. The core itself is excluded from the similarity; a core simulator is used to keep the Euler-number constant (similar pressure drop model/prototype). The reactor model is manufactured from Plexiglas © (Fig. 1). A total view of the test facility is given in Fig. 2. The reactor model describes the geometry of the original PWR with respect to the design of the nozzles (diameter, curving radii, diffuser parts), the characteristic extension of the downcomer cross section below the nozzle zone, the so-called perforated drum in the lower plenum and the design of the core support plate with the orifices for the coolant. The flow rate in the loops is scaled according to the transit time of the coolant through the reactor model. Since the geometrical scale of the facility is 1:5, the transition time of the coolant is identical to the original reactor, when the coolant flow rate is scaled down by 1:5, too.

2.

Fig. 1

ROCOM TEST FACILITY

Reactor model of the test facility ROCOM

The nominal flow rate in ROCOM is therefore 185 m³/h per loop. Since the viscosity of water is much higher at low temperature compared to the hot coolant, the Reynolds numbers, which can be achieved in the test facility, are by factor of 100 lower than those in the original reactor. The geometrical scaling causes a factor of five; another factor of five by the scaling of the flow rate, the rest is an effect of the increased viscosity. The facility is operated with water at room temperature and ambient pressure. Since the coolant mixing is mainly based on turbulent dispersion it is possible to use a tracer substance to model differences

The Mixing Test Facility ROCOM consists of a reactor pressure vessel model (Fig. 1) with four inlet and four outlet nozzles. The Facility is equipped with four fully operating loops (Fig. 2), i.e. it has four circulation pumps, which are driven by motors with computer controlled frequency transformers. As a result, a wide variety of flow rate regimes, such as four-loop operation, operation with pumps off, simulated natural circulation modes and flow rate ramps can be realized. For natural circulation conditions the corresponding pumps are operated at low rotation speed by means of the frequency transformer system. Beginning from the bends in the

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of either boron concentration or coolant temperature. The coolant in the disturbed loop was labeled by injecting a sodium chloride solution into the main coolant flow in front of the affected reactor inlet nozzle. Magnetic valves controlled start and stop of the injection process.

Loop 4

Loop 1

Loop 2

low viscosity is re placed by a function, which is additionally dependent on the normalized viscosity. The viscosity itself depends linearly from the density of the glucose-water mixture (Fig. 3). This correlation has been proved by special mixing tests prior to the experiments, where the conductivity was measured for given values of the mixing scalar adjusted artificially by diluting the tracer solution with desalinated water. The results for two bounding initial conductivity values are shown in Fig. 4.

RPV

Pump Loop 3

Fig. 2

ROCOM test facility with four loops and individually frequency controlled circulation pumps

In case of the experiments on ECC injection, an injection nozzle was used, which was geometrically similar to the original Konvoi reactor. The higher density of the cold ECC water was simulated by adding sugar (glucose), since density gradients cannot be created by temperature differences, because the facility cannot be heated up. Fortunately, the viscosity of glucose solution becomes large only at concentrations, where the relative density increase is well above the 10 % necessary for the experiments. A sugar solution with the corresponding density of 1100 kg/m³ has a viscosity, which is still just by factor of about 3 higher than that of pure water. The tracer can therefore still be envisaged as a low-viscous fluid.

Fig. 3

Fig. 4

3.

Influence of the viscosity on the dependency of the conductivity from the degree of mixing for two bounding initial conductivity values

INSTRUMENTATION

The tracer distribution in the reactor model was observed by so-called electrode-mesh sensors, which measure the distribution of the electrical conductivity over the cross section of the flow duct. The own development was aimed at a direct conductivity measurement between pairs of crossing wires to avoid tomo graphic reconstruction algorithms [13] and to reach a time resolution of up to 10 000 frames per second [14]. Two crossing grids of electrodes insulated from each other are placed across the flow duct. The electrodes of the first grid (transmit ter electrodes) are supplied with short voltage pulses in a successive order. The currents arriving at the electrodes of the second grid are recorded (re ceiver electrodes). After a complete cycle of transmit ter activation a complete matrix of local conductivities is obtained. Special methods of signal acquisition [13] guarantee that each value of the matrix depends only on the local conductivity in the immediate vicinity of the corresponding crossing point between transmitter and receiver electrodes. Measured local conductivities are afterwards related to reference values. The result is a so-called mixing scalar that characterizes the instantaneous share of coolant originating from the disturbed loop (i.e. where the tracer is injected) at a given location inside the flow

Comparison of the normalized viscosity of water and of the glucose-water mixture used in the ROCOM experiments

The linearity between the tracer concentration and the measured local conductivity is the basis for the transformation of the obtained results into dimensionless mixing scalars (1). The increase of the viscosity by adding sugar changes the relation between tracer concentration and conductivity. The linear correlation typical for salt solutions at

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field. The scalar is dimensionless. Assuming similarity between tracer field and the temperature and boron concentration fields it can be used to apply the experimental results to the original reactor. The re ference values correspond to the unaffected coolant (index 0) and the coolant at the disturbed reactor inlet nozzle (index 1). The difference between the two reference values is the magnitude of the perturbation. The mixing scalar Θ is defined as follows: θ x ,y ,z ,t =

σ x,y,z ,t − σ0 σ1 − σ 0

≅

Tx,y,z ,t − T0 T1 − T0

≅

C B, x , y , z , t − C B, 0 C B,1 − C B,0

phenomena were not requiring a higher sampling frequency. 4.

The goal of the experiments presented was the generic investigation of the influence of density differences between the primary loop inventory and the ECC water on the mixing in the downcomer. To separate the density effects from the influence of other parameters, a constant flow in the loop with the ECC injection nozzle was assumed in this study. The mass flow rate was varied between 0 and 15 % of the nominal flow rate, i.e. it was kept in the magnitude of natural circulation. The other pumps were switched off. The density difference between ECC and loop water was varied between 0 and 10 %. Fig. 6 summarizes the boundary conditions of the experiments. Altogether 18 experiments have been carried out (dots in Fig. 6). In all experiments, the volume flow rate of the ECC injection system was kept constant at 1.0 l/s. The normalized density is defined as the ratio between ECC water density and density of fluid in the circuit. All other boundary conditions are identical. Based on the observations [5], the set of experiments conducted according to Fig. 6, was divided into three groups: density dominated flow (?), mo mentum dominated flow (?) and the transition re gion (*). The conditions at the inlet into the down comer were used to calculate Froude-numbers of the experiments according to the formula (2) [8]:

(1)

Here, σ is the electrical conductivity, T is the temperature and CB the boron concentration. Which of the two parameters temperature or boron concentration is represented by the measured mixing scalar depends only on the right choice of the reference values and the set-up of the boundary conditions in the experiment.

Fig. 5

ECC WATER INJECTION WITH DENSITY EFFECTS

Mesh sensor for measuring tracer distributions in front of the reactor inlet nozzle

Fr =

Mesh sensors are placed at four positions of the flow path. The first sensor (Fig. 5) is flanged to the reactor inlet nozzle (Figures 1 and 2) in loop CL1. It is aimed at the observation of the distribution at the reactor inlet. The second and the third sensors are located in the downcomer. The downcomer sensors consist of radial fixing rods with orifices for four circular electrode wires. Small ceramic insulation beads separate rods and wires electrically. The rods are acting as radial electrodes, i.e. each rod corresponds to an azimuthal measuring position. The fourth sensor is integrated into the core support plate. 2 x 15 electrode wires are arranged in a way that the wires of the two planes cross in the centers of the coolant inlet orifices of each fuel ele ment. In this way, the tracer concentration is measured at each fuel element inlet. In total, about 1000 measuring points are recorded, the measuring fre quency is 200 Hz. In most of the cases 10 successive measurements were averaged and the result was stored with a fre quency of 20 Hz, because the characteristic frequency of the observed

v in g ⋅s ⋅

? in − ? a ? in

(2)

where vin is the velocity at the reactor inlet (combined loop and ECC flow), g is the gravitational accele ration, s is the width of the downcomer, ρ in the density of the incoming flow, calculated with the assumption of homogeneous mixing between ECC and loop flow, and ρ a the density of the ambient water in the downcomer. Lines of constant Froude-numbers calcula ted by means of this formula are shown in Fig. 6. All experiments, identified as density dominated are located in the region left of the iso-line Fr = 4.0 and all momentum dominated points are found right of the iso-line Fr = 7.0. These two numbers are critical Froude numbers separating the two flow regimes for the ROCOM test facility. Between the two criterial values a transition region is located. The experiment with 5% constant flow rate in one loop and 10% density difference between ECC and loop water was analysed in detail (Table 1). The Froude number is Fr=1.62, it is identified as density dominated (in Fig. 6 on the upper left side).

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• •

Fig. 6

The VDF method consists in integrating the conservation equations over the cells of an orthogonal-structured mesh grid. This method was not used in the present calculations. The VEF method is a “hybrid” method, which merges the finite volumes and the finite elements approaches. In fact, the domain is discretised in elements (which are triangular and tetrahedrical for 2D and 3D problems respectively), and the conservation equations are integrated over control volumes associated to those elements. The unknown continuous variable is expressed as a combination of a base of form functions that is assigned to each element and that depends on the nodal values. Different element “types” are used, depending on the variables arrangement on the grid and on the form functions. The ones used in Trio_U are briefly described below:

Test matrix of ECC injection experiments, indication of observed flow regime [5]

Table 1 Experiment chosen for code validation

•

V& (ECCS) V& (CL1) / Density difference Fr / m3 /h

m3 /h

Loop / ECC water (DC)

3.6

9.25

1:1.1

1.62 •

5.

VDF (Finit Vo lu me Method ) VEF (Finit Element based Finite Volume Method)

TRIO_U

5.1 THE IMPLEMENTED NUMERICAL METHODS The discretisation method for the conservation equations implemented in the Trio_U codes are based on the finite volumes approach: this means that the differential equations, written in the conservative form, are integrated over the control volumes which constitute the discretised domain; then the volume and surface integrals are approximated as functions of the values of the unknown variable at the grid nodes, in order to obtain a system of linear equations [12]. This approach has the advantage that the fluxes through the surfaces of the cells are always continuous “by construction”, so the conservation of the physical properties to conserve is guaranteed both locally and globally. This is not the case, for instance, of the finite elements methods, which are methods that integrate the conservation equations in the weak form (that is non-conservative), thus not allowing for the continuity of the fluxes at the interfaces between the elements. This explains why the finite elements methods have not encountered great success in the CFD, since it is necessary, in order to obtain “physical solutions”, to respect the conservation of mass, momentum and energy. In Trio_U, two methods are available [16]:

•

P0 : the unknown variable is calculated at the center of the element, and it is assumed to be constant over the entire element (then the center value is considered a mean value); the control volume coincides with the element itself. The variable is discontinuous at the interfaces. P1 -NC: the unknown variable is calculated at the midpoints of the element faces, and is assumed to be a linear function of the coordinates (than its gradient is constant); it is discontinuous at the interfaces, but the continuity of the fluxes is respected. A control volume corresponds to each face, which is defined by the centers of the two adjacent elements and their common vertexes. P1 -bulle: the unknown variable is calculated at the vertex and at the center of the element and is still assumed to be a linear function of the coordinates. A control volume is assigned to each center (defined by the midpoints of the element faces) and to each vertex (defined by the midpoints of the faces of the elements concurring to that vertex).

Thus two discretisation methods on non-structured grids are available in Trio_U depending on the degree of velocity-pressure coupling: • •

P1 -NC/P0 for a weak coupling applicable for RANS calculations P1 -NC/P1-bulle for a strong coupling indispensable for LES calculations

5.2 THE SOLUTION METHODS Once the equations have been discretised, a system of algebraic equations is obtained whose

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unknown are the discrete physicals variables. It should be remarked that the Navier-Stokes equations are not linear, as well as the discretised equations which they yield. Concerning the pressure calculation, two different methods are available to solve the corresponding system: • •

the used methods for the present CFD calculations with Trio_U. Table 2 Used numerical methods for code validation Discretisation method

Hybrid finite volume-finite element

The Cholesky method: it is a direct method, but it requires an amount of memory proportional to the number of cells. The Preconditioned Conjugated Gradient method: The problem of solving a system is converted to the problem of minimizing a residual; then, at each iteration, a more accurate solution is obtained following the criterion of the conjugated gradient. A technique of preconditioning is applied in order to convergence more rapidly.

P1 -NC/P1-bulle

Ux ∆x

+

1 Uy ∆y

+

(3)

1  1 1 1  2ν  2 + + 2 2  ∆x ∆y ∆z  

(4)

where ν is a generic diffusivity. At each iteration those two parameters are calculated, and the maximum time step to be used for the next iteration is calculated as:

1

1 ∆t diff

   1  + ∆t conv 

Convection

Muscl

Facsec

1.0

Turbulence

LES Sous_maille_smago

Wall function

a) Standard logarithmic/

PREPARATION OF THE NONSTRUCTURED MESH GRID FOR ROCOM

The external parts: • One cold leg part including the ECC injection line for simulating the stratified flow. • Four inlet nozzles, with their axes oriented by two directions forming an angle of 45°; each nozzle comprises a cylindrical segment and a conical segment, • Four orifices of the outlet nozzles • The vessel wall – cylindrical part: it bounds externally the downcomer, and is connected to the outlet and inlet nozzles; below the nozzle region exists a downcomer extension. • The vessel wall – spherical part: it bounds externally the lower plenum. • The cover plate: it is the upper boundary of the downcomer.

Fourier Criteria

  ∆t stab = fac sec ⋅    

Euler explicite

The investigated phenomena are occurring inside the reactor vessel except for the core region, which in first approximation has not a direct feedback on the hydraulics and on the passive scalar concentration field in the downcomer and the lower plenum. Only the fluid domain, from the inlet nozzles until the core support plate, has been modeled and discretised. The geometrical items bounding the calculation domain are listed below:

Courant Friedrich Levy Criteria ∆tdiff =

Time scheme

6.

Uz ∆z

P1 -bulle

b) no slip

The pressure solver is used in combination with explicit time marching schemes. The explicit Euler method has been used to perform all simulations presented here. The following stability conditions must be satisfied in the case of three-dimensional convective/diffusive problems. In fact, both the convection and diffusion terms of a transport equation determine a stability condition, which is expressed as follows: ∆t conv =

Pressure

(5)

The internals: • The barrel: it is the internal boundary of the downcomer. • The core support plate: it is welded to the barrel and, from a hydraulic viewpoint, it connects the

Facsec is a “safety factor” which varies between 0 and 1. It is empirically adjusted in order to account for instabilities that can originate when using a convection scheme more than first-order accurate. Table 2 shows

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•

lower plenum to the core region by its 193 holes, and then it represents the “end” of the domain. The perforated drum: it is placed in the lower plenum.

The ratio between the total area of the holes, and the area of the cylindrical surface results to be 0.208: this value has been used as the superficial porosity for the perforated drum. Part of the water coming from the downcomer enters the drum holes, thus moving toward the radial direction and encountering some singular head losses, and the other part bypass the drum and enters directly the core support plate. The pressure drop through the perforated drum was modeled with additional momentum sources.

Three different mesh sizes were used (Table 3). Using a Laplace smoothing algorithm has optimized the meshing. Table 3

Mean features of the unstructured mesh grids prepared for the ROCOM geometry

Mesh grid Coarse Medium Fine

Minimum cell size

Mesh size

35 mm

~340 000 cells

17.5 mm

~1.150 000 cells

15 mm

~1.730 000 cells

8.

BOUNDARY CONDITIONS

ECCS

7.

THE PERFORATED DRUM

CL 1

Fig. 8 Flow domain with inlet boundary conditions Fig. 7

Solid walls bound the fluid domain; an outlet boundary was put above the core inlet. Three inlet boundaries were set at the reactor inlet nozzles. The cold leg CL1 including the ECC injection line was modeled in detail (Fig. 8). Inlet Boundary conditions were put at the ECC line and at the area after the bend of the cold leg. At the outlet, a free outflow condition with a constant pressure was used. For the solid walls, standard wall functions were applied for both momentum and temperature transport equation. The initial velocity field was set to 5% of the nominal flow (9.25 m3 /h) in Loop CL1 and Zero in the three other loops. The initial scalar field was set to 1 in the whole flow domain. Note, that in this case the mixing scalar is an inverted version of the in eq. (1) defined mixing scalar Θ. All qualitative pictures (chapter 9.2) will be plotted with the inverted mixing scalar. All quantitative results (chapter 9.3) will be in the definition of Θ according eq. (1). The inlet boundary conditions for the momentum equation require constant and uniform velocities in

Lower Plenum including the perorated drum

The perforated drum is placed in the lower plenum of the Konvoi reactor in order to stabilize the flow field at the core inlet. As shown in Fig. 7, the perforated drum is a cylindrical tube with the following dimension: • • •

External diameter = 0.580 m Thickness = 0.008 m Length = 0.191 m

There are 420 holes, whose diameter is 0.015 m, uniformly distributed over the cylindrical surface. There are also other small details that have been neglected, since they are not expected to sensitively affect the flow. Since the characteristic dimensions of the perforated drum and its holes is comparable to the cell size of the realized mesh grids (even t he finest one), the holes have not been modeled; the drum has been defined as a porous sub-domain.

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order to simulate the one loop operation. The velocities in the idle loops were defined as zero, as there was no back flow in the cold legs 2-4 measured. The ECC injection last 10 s. A uniform velocity profile was also defined at the injection line during this period. It was defined zero in the rest of the time (Fig. 9). The tracer injection was simulated by the help of a scalar field, which was defined to be 1 in the Loop 1 and 0 at the ECC injection line (Fig. 10).

chloride, enhancing the conductivity. Generating density differences by high salt concentrations is not possible, because the measurement system is very sensitive and would be saturated at high salt concentrations. Fig. 11 shows the time evolution of the tracer concentration measured at the two downcomer sensors in an unwrapped view.

Mass flow rate / m^3/h

10 8 ECC injection line

6

Cold leg CL1 4 2 0 0

Fig. 9

2

4

6

8

10

t/s

12

14

16

18

20

Mass flow rate over time (Cold Leg 1, ECC Injection)

1

Mixing Scalar / -

0,8 Tracer ECC Injection Line

0,6 0,4 0,2 0 0

2

4

6

8

10

t/s

12

14

16

18

20

Fig. 11 Time dependent Tracer distributions at the Upper and Lower Downcomer Sensor

Fig. 10 Tracer distribution over time at ECC Injection Line

The downwards-directed red arrow indicates the position of the loop with the running pump, in that case delivering 5% of the nominal flow rate. The density difference between the injected ECC water and the primary loop coolant is 10 %. At the upper downcomer sensor, the ECC water (injected in the experiment from t = 5 to t = 15 s) appears directly below the inlet nozzle. At the beginning the covered area is bigger below the inlet nozzle, because the momentum driven flow field is still present after this the density difference partly suppresses the propagation of the ECC water in circumferential direction. The ECC water falls down in an almost straight streamline and reaches the lower downcomer sensor directly below the affected inlet nozzle. Only later, coolant containing ECC water appears at the opposite side of the downcomer. The maximum concentration values observed at the two downcomer sensors are 39 % and 13.5 % from

The Boussinesq approximation (6) was used. The density difference was 10%, the temperature difference 1 K (dimensionless form), as a result of (6) the temperature expansion coefficient becomes β=0.1.

ρ = 1 − β (T − T0 ) ρ0 9.

(6)

RESULTS

9.1 EXPERIMENTAL FINDINGS Due to the fact that the test facility cannot be heated up, the necessary density differences were simulated by adding sugar (glucose) to the water that is injected into the cold leg. To observe the mixing of the ECC water, this water was again labeled by small amounts of sodium

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the initial concentration in the ECC water tank (Fig 12). At the Core inlet the maximum concentration values (5 .5%) are found also in the sector below the inlet nozzle of loop CL1. Only later also at the opposite part of the core inlet ECC water occurs. Later the tracer covers the whole core inlet plane more or less homogeneously.

The first part of the transient calculation was dedicated to an established flow field in the cold leg and downcomer of ROCOM. A sensitivity study was made to check, after which time a constant flow field is reached. During this period the ECC injection line was closed. The imposed flow in cold leg CL1 creates a momentum controlled flow entering the downcomer. It is divided into two jets flowing in a downwardsdirected helix around the core barrel. After the onset of the injection, the flow in the cold leg is changing its shape due to the buoyancy effects. The cold water from the ECC injection line first hits the opposite wall of cold leg CL1 caused by the injection momentum (Fig. 13). Later it is partly mixing with the ambient loop inventory, but mainly propagating towards the reactor inlet at the bottom of the cold leg. During the period of injection and after finishing the injection the ECC water is transported towards the reactor inlet also by the help of the cold leg flow.

Fig. 12 Stratified flow at the reactor inlet, plum of tracer at the downcomer sensors (22 sec) 9.2 QUALI TATIVE ANALYSIS Sensitivity studies were made to find the proper mesh size of the problem. It was found, that a mesh size starting from 1.7 million control volumina was given reasonable results. In order to check the influence of the wall law in the LES turbulence model one calculation was done with the standard logarithmic wall function and one with the “no slip” condition. It was found, that the wall law has a noticeable influence on the results of the calculations, since the logarithmic wall function is creating artificial turbulence near the wall in a flow, which characterized by the transition region between a laminar and a turbulent flow regime. Fig. 14 Tracer distribution in the downcomer (20 s) Due to the density difference between the ECC water and the ambient coolant, the established momentum controlled flow is changing in the downcomer. At the beginning also in the calculations the covered area of the ECC water is bigger below the inlet nozzle, because the momentum driven flow field is still present (Fig. 14). Afterwards a clearly density dominated flow is established. The ECC water creates a plum downward the downcomer (Fig. 15). In the calculation this plum is not stable, it fluctuates by reaching half the downcomer. During this propagation downwards the downcomer the ECC water is well mixed with the ambient coolant. When the plum reaches the lower plenum, it swaps to the opposite side of the injection

Fig. 13 Tracer distribution in the cold leg (7.3 s) zoomed mixing scalar Θ (0.8-1.0)

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loop again into the downcomer region. The lower plenum is constantly filled with the already well-mixed ECC water.

0.5 Azimuthal Position: 22.5°

Mixing Scalar / -

0.4

Trio_U no slip

0.3 0.2 0.1 0 0

5

10

15

20

25

t/s

Fig. 16 Time dependent tracer distribution at the upper downcomer sensor (local position below CL1) 0.4 0.35

CL-1

Mixing Scalar / -

0.3

Fig. 15 Tracer distribution in the downcomer (23 s) zoomed mixing scalar Θ (0.8-1.0)

CL-4

0.25

CL-3

CL-2

Time=20 sec Trio_U no slip

0.2 0.15 0.1 0.05 0 0

9.3 QUANTITATIVE ANALYSIS

Fig. 17

To make a quantitative analysis of the calculated values and for comparison with the measured data 32 circumferential sensor positions in the middle of the upper downcomer sensor plane were selected. The mixing scalar Θ in the calculation (amb ient coolant Θ = 1, ECC water ΘECC = 0) was inverted for comparison. A position in the region below the inlet nozzle CL1 was selected (Fig. 16). Additionally, the azimuthal positions in the circumferential direction of the unwrapped downcomer were taken for comparison (Fig.17). In the figures the Trio_U calculation with the finest mesh and no slip wall condition are plotted against the experiment values. In the position 22.5° (Fig. 16) the mixing scalar Θ is not reaching the values of the experiment (maximum Θ local = 0.32). In the calculation, the ECC water, which is earlier flowing downwards the downcomer than in the experiment, is later not present anymore as in the experiment. The difference to the experimental values at the maximum is ∆Θlocal = 0.02. The diagram of the azimuthal distribution of the mixing scalar Θ shown at 20 s in Fig. 17 clearly describes the creation of a plum falling downwards the downcomer below the inlet nozzle of cold leg CL1. The shape of the perturbation is almost identical.

45

90

135 180 225 Azimuthal Position /°

270

315

360

Tracer distribution in the unwrapped downcomer (20 s)

10. SUMMARY For the validation of the Trio_U code an experiment with constant flow rate in one loop (magnitude of natural circulation) and 10% density difference between ECC and loop water was taken. For this study a LES approach was used for mesh sizes between 300000 – 2 million control volumes. As a result in the experiment as well as in the calculation the ECC water only partly mixes with ambient loop inventory in the cold leg. A stratified flow is developing during the injection. In the downcomer a momentum driven flow field is still present at the beginning, after this the ECC water propagates downwards the downcomer below CL1. Trio_U calculations show a good qualitative agreement with the experiment, while at local positions some differences in the concentration field occur. The obtained results can be used for further studies of the core behavior using coupled thermo - hydraulicneutron- kinetic code systems.

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REFERENCES [1]

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