LARGE EDDY SIMULATION OF MIXING IN THE OUTLET PLENUM...

1 Copyright © 2004 by ASME

Proceedings of ICONE-12 : 12th International Conference on Nuclear Engineering

April 25-29, 2004 Arlington, Virginia (Washington, D.C.), USA

ICONE12-49446

LARGE EDDY SIMULATION OF MIXING IN THE OUTLET PLENUM OF A HIGH TEMPERATURE REACTOR. A BENCHMARK EXERCISE

Jan-patrice Simoneau

Ph. +33 4 72 74 73 75 Fax : +33 4 72 74 73 25

e-mail : [email protected] Framatome-Novatome

10, rue Juliette Récamier F69456 LYON cedex06 – France

Julien Champigny

Ph. +33 4 72 74 76 73 Fax : +33 4 72 74 73 25

e-mail : [email protected] Framatome-Novatome

10, rue Juliette Récamier F69456 LYON cedex06 - France

ABSTRACT

This paper is related to the validation of the CFD codes in

the frame of High Temperature Reactor studies. A code to code benchmark involving complex unsteady flows in the outlet plenum is proposed and the Large Eddy Simulation technique is retained. The paper presents the benchmark conditions, the results obtained by the Star-cd software used in Framatome-ANP and the comparison with the Trio-U code (from CEA) and the literature. It presents the advantages of such fine unsteady calculations and mainly highlights the coherence between both analyses.

INTRODUCTION

As the numerical simulations in fluid dynamics (CFD)

develop, the confidence in the corresponding codes must be ensured. The best validation procedure involves experimental tests, generally costly. Another way to increase the confidence in our CFD codes and also in our modeling practices is to perform code to code benchmarks.

Preliminarily, this paper shows why and how this process is set up in the frame of High Temperature Reactors (HTR) studies, through a benchmark on mixing in the outlet plenum of an HTR. The results of the Framatome-ANP contribution are then presented, and compared with those obtained with the Trio-U code by the CEA (ref. [9] and [10]).

PRESENTATION OF THE BENCHMARK

Choice of the configuration

In high temperature reactors (HTR) based on prismatic blocks concept, the helium coolant flow is made of a main flow crossing the fuel blocks, and of secondary flows : helium crossing gaps between blocks and helium flowing around control rods. Those flows, at different temperatures, merge together in an outlet plenum : The hottest helium (issued from fuel blocks) is injected in the plenum by the means of hollow columns. The highly turbulent mixing in this area involves mainly high velocity jets in a cross flow coupled with wakes behind supporting columns.

The knowledge of helium and graphite thermal hydraulic behavior in this plenum is of great importance since this area is at high temperature and supports the whole core. The potential risks to be examined further are an insufficient mixing (hot streaks) and subsequent temperature fluctuations and vibrations induced by wakes.

Moreover, wake flows are known to be better predicted by unsteady calculations. The computational needed is therefore a fine unsteady turbulent modeling.


Choice of the numerical method The numerical method proposed is the Large Eddy

Simulation technique (ref. [1], [2] and [5]). Although it needs to set up a large CFD model and a noticeable effort in computation resources, this method brings some informations not reachable by other means :

• Frequencies of the turbulent fluctuations of the velocity

• Amplitude of temperature fluctuations • Time history of temperature

Secondly, the mean fields of temperature and velocity (obtained by averaging the time history fields) are expected to be more accurate (especially in cases of flows around tubes). The conjugate heat transfer in solid parts (graphite) is also modeled since one of the objectives of such studies is to obtain the thermal field in the supporting columns.

Objectives of the code to code benchmark The 2 codes involved in this benchmark are :

• Star-cd used in Framatome-ANP for several years and developed by the Imperial College of London and Computational Dynamics (ref. [7])

• Trio-U used and developed by the French Atomic Energy Agency (CEA) (ref. [3])

The objectives are to compare : • The set up of the model (grid needed, …) • The results themselves

The comparison has to be processed on velocities and temperatures in both averaged and instant values. Each of the two studies and the comparison itself will increment the set of best practices in CFD.

The Trio-U results are presented in references [9] and [10], this paper will present the methodology and the results of the Framatome-ANP contribution, and a comparison between the two analyses of the benchmark.

MODEL

Geometry The High Temperature Reactor considered in this

comparison exercise is of prismatic blocks type. Figure 1 presents a short view of the reactor vessel. The outlet plenum is located at the bottom of the graphite core which it supports. Figure 2 shows a section plot of the plenum, the following components are seen :

• full graphite blocks (periphery), • (full) columns supporting the major part of

reflector blocks,

• hollow columns supporting the active core blocks (fuel blocks + axial reflectors)

The main flow crossing the fuel blocks is driven towards the hollow columns and discharged in the outlet plenum. The gap flow enters the outlet plenum from its upper surface (distributed flow from gaps between blocks).

Since the helium exit is a pipe connected to the side of the outlet plenum, the flow is mainly characterized by a cross flow is a tube bundle with local injections.

The complexity of the geometry, especially of the hollow columns, coupled with a simulation technique needing refined meshes does not allow modeling the entire outlet plenum. Only a significant part of the outlet plenum is retained (see figure 3), this part is chosen near the exit where the cross flow is maximum. It represent 6 rows of columns (full and hollow), it contains also graphite blocks. A symmetry plane is assumed although a rigorous Large Eddy Simulation requires not to consider it.

Software

The general-purpose code Star-cd for fluid mechanics and thermics (ref. [7]) is used. The main characteristics of this software are listed below :

• 3 dimensional code, • Finite volume formulation, • Unstructured grid capabilities including advanced

features : local refinement, non-conformant grids with arbitrary interfaces. Meshes are mainly hexahedrons and prisms.

• Matrices inverted by bi-conjugate gradient method with preconditioning or algebraic multigrid.

• PISO algorithm for pressure linked equations (the pressure solver is semi-implicit : pressure fields are corrected at every iteration in order to achieve both momentum and continuity balances) (ref. 6),

• Numerical schemes up to third order. The Navier-Stokes and energy equations are solved in primary variables (velocity, pressure and temperature). For this specific study, computations are run in transient regime. The turbulence is taken into account as described below. The Trio-u code is presented in references [9] and [10], the main differences with the Star-cd code (for this benchmark) are :

• Explicit time marching procedure, • Structured grid with identical cubic meshes.

The Large Eddy Simulation model

In a turbulent flow, one can observe all-sized eddies, so that this flow can be represented by a continuous spectrum of eddies ranging from great structures (order of magnitude of the


domain) to the smallest eddies (of the Kolmogorov scale order). An explicit calculation of all the eddies is not reachable in a 3D configuration and the Large Eddy Simulation so proposes to compute the large eddies until the discretization mesh size, while the other ones (subgrid scale eddies) are appropriately modeled. The subgrid scale model here used is the selective structure function model (ref. [4], [5]) with adaptations. In the structure function model, a "box" filter is used to split each flow variable into a large scale part (solved via Navier-Stokes and energy equations) and a subgrid part. The subgrid contribution is proportional to the spatial correlation of the velocity between two points (called structure function) and introduced in the Navier-Stokes and energy equations via an additional turbulent viscosity νt. The selective feature is that this viscosity is applied only if the flow is "sufficiently" 3D, i.e. if the angle between vorticity vector at the considered point and the averaged vorticity vector of the neighboring points is large enough. Note that the magnitude of this viscosity is much lower than the turbulent viscosity calculated by a k-ε model. In case of discretization of the viscous sublayer, the turbulent viscosity is set to zero in the viscous sublayer, the thickness of this sublayer is evaluated by y+ < 3. Where the grid includes local refinement, the mesh size variation is severe, hence, the calculation of the turbulent viscosity νt leads to high non physical values. Specific studies (see ref. [11] for details) lead to consider a threshold for the value of νt. The threshold is νt / ν < 15 and was found to get a correct behavior of the subgrid model. In the present grid (see below), the viscous sublayer is not specifically discretized.

Mesh The Star-cd solver accepts non hexahedral finite volumes

and non structured grids. It also allows non conformant grids with local refinement and arbitrary interfaces.

Both solid and fluid parts are modeled since the heat transfers between helium and solid are calculated. Figure 3 presents the mesh of the solid part, showing the 10 full columns and 7 hollow columns. Those hollow columns have several openings (on 7 altitudes) used to inject the hottest helium in the cross flow (see figure 4). On this figure the solid meshes are in blue and fluid ones in red. The top view of the mesh on figure 5 shows the refinement around the hollow columns, and the larges meshes (in yellow) used to represent the blocks of graphite in which only the thermal conduction in calculated. The grid is not fine enough to meet the academic requirements of Large Eddy Simulations, but the objective is to assess the behavior of Star-cd code on industrial models. The grid size has therefore been dimensioned from this point of view.

Boundary conditions

The boundary conditions are considered as uniform and constant :

• The cross velocity (horizontal) is prescribed at the necks of the first row of columns,

• The velocity is prescribed at the top of the hollow columns (vertical),

• An arbitrary temperature difference of 25°C is set between the two flows,

• A symmetry condition is used for the mid plane of the plenum,

• The outlet is characterized by zero gradients on all variables.

At the solid / fluid interfaces, a heat transfer coefficient is

used. Its value is obtained from a standard correlation of forced convection in gases. This permits a correct treatment of the heat transfer even in the regions where the mesh is less refined, and the viscous sublayer does not need a specific discretization.

Numerical considerations Velocities are found at levels which implies low mach

numbers (fluid is helium), hence the Navier-Stokes equations are solved in incompressible formulation. The numerical schemes are of second order in space :

• MARS scheme for velocities (MARS is a second order scheme filtered to avoid instabilities) (ref. [7]),

• Central differencing for density, • Self filtered second order scheme for temperature. The time step, prescribed by the user, is set to 2 10-4s (first

order discretization).

RESULTS AND ANALYSIS The computation times presented below show that this

kind of simulation must be only employed in specific configurations where explicit time dependant solutions are needed.

Physical time (s) CPU time (days)

0.45 5 (The workstation is a SUN "Sunblade 1000" with a

750 Mhz CPU, monoprocessor, 64 bits) Among the 0.31 s calculated, the first 0.11 s part

corresponds to the establishement of the flow. Hence, a range of 0.2 s is used for post-processing. The initial condition at t = 0 s was obtained from a standard k-ε steady solution.


This post-processing, on which the comparison between the codes Star-cd and Trio-U will be based is made of :

• Instant temperature and velocity fields, • Instant temperature and velocity signal at some

specific points, • Frequency spectra, • Average temperature and velocity profiles.

Instant values of velocity Figure 6 presents the time history of the velocity

magnitude for the point (noted #16) located at the centre of the neck between 2 columns, and in front of the 4th column opening (1st openings are in upper part, 7th ones in lower part). The wake effect behind columns implies very unstable flows with high fluctuations. Figures 9 and 10 present a zoom of the velocity pattern between columns and show the interaction between the main cross flow and the injected flow. The main cross flow produces wakes which impact downstream columns. Moreover, the helium coming from interior of hollow columns is injected in this cross flow, it implies a reduction of the free section and produces accelerations. This competition between injected flow and cross flow increases the intensity of the instabilities. The difference between figures 9 and 10 (same section plot but a different times) illustrates the instabilities.

The cross flow has a sufficient strength to penetrate into the columns by the openings, located upstream. This penetration is more important in the bottom part of the plenum. On figure 11 are shown the instant velocity vectors in a vertical section crossing to hollow columns. This picture points out the mixing induced by the injection of the hot helium and highlights that the uniform velocity profile prescribed at inlet is arbitrary and the results are not usable for the first row of columns.

The amplitude of the fluctuations is compared through the RMS (root mean square) value of the velocity fluctuations : the table below gives the comparison between Star-cd and Trio-u (from ref. [9]). Three points are considered in the wake of a hollow column and at 3 altitudes (2nd opening, 4th opening and 6th opening) :

Star-cd Trio-U (*) 2nd opening 9 5-7.5 4th opening 16 ~12 6th opening 10 8-10

(*) the values are obtained from a contour plot. This table shows that the 2 calculations are coherent. The frequency analysis is discussed together with the

temperature fluctuations frequencies.

Averaged values of velocity Averaging is performed from the different times stored

along the 0.2 s of physical time. Figure 12 presents the averaged field of velocities on a vertical section. It shows similar behaviors for the openings located on the same vertical line.

One should be more confident in a velocity field obtained from averaging instant fields than from a steady computation. Figure 8 presents for the v component of the velocity, the comparison of the LES (averaged field) and the k-ε simulation : the differences are noticeable in the wakes of the columns.

Figure 17 and 18 presents the contour plot of averaged velocity magnitude in a horizontal section (2nd opening level) for both Star-cd and Trio-u analyses. The scales are quasi identical. Some differences in the neck between columns occur due to the rough modeling of the columns by Trio-U using structured grid with cubic meshes. The general behavior is nevertheless similar.

Instant values of temperature The thermal instant fields are illustrated by the time history

of temperature at 3 points located near a column of the third row (figure 7) :

• Centre of an upper opening (2nd), upstream side (point 48),

• Centre of a lower opening (6th), upstream side (point 54),

• Centre of neck between this column and its neighbor (point 4).

The major fluctuation amplitudes occur at the neck between columns and reach 76% of the total temperature difference.

Figures 13 and 14 show instant temperature fields at the

same time for 3 horizontal sections : lower part and upper part (zoom on figure 15). Severe gradients occur. Those gradients are maximum in the upper part and decrease from top to bottom of the plenum. They are due to the entrance of colder helium by the openings located upstream side. This effect could be reduced by displaying those openings not in front of neck between columns.

Despite of high local gradients, the mixing obtained by the injection of hot helium is good. This mixing occurs immediately near the column and sometimes in the hole of the column itself (bottom parts). The jets exiting the column are quickly driven by the high velocity instabilities, which leads to mixing.

The comparison with Trio-U is performed on RMS values, at 2 locations : downstream the central column of the second row at the altitude of the 2nd opening and at the altitude of the 6th opening. The following table presents the RMS values obtained for both analyses and their coherence :


star-cd trio-u (*) 2nd opening 1.

2.6 0.9

1. to 2.5

6th opening 0.7 1.2 0.7

≤ 0.75

(*) values obtained from contour plots

Averaged values of temperature Figures 19, 20 and 21 present the time averaged fields of

temperature (3 horizontal sections at the levels of the 2nd, 4th and 6th openings) (Star-cd plots on left hand side of the figures). They show principally the gradients affecting the graphite structures (since temperature fluctuations do not penetrate). Such thermal field may be directly used for mechanical assessments. Those figures confirm also the good mixing obtained by the multiple injections.

The comparison with the Trio-U plots (right hand side of the figures) shows that the agreement is good.

Frequencies Figures 22, 23 and 24 presents the plot of the spectrum of

velocity fluctuations for 3 points located downstream a hollow column, at 3 different altitudes (2nd opening, 4th opening, 6th opening). The frequencies corresponding to the temperature fluctuations at the same points are plotted on figures 25, 26 and 27.

A first peak appears within the range [75-100] Hz. It corresponds to the wake effect behind columns : the corresponding Strouhal number is found to be about 0.23 – 0.30, which is coherent with the literature (0.27 for a cylinder, ref. [8]). On some plots, a secondary peak appears, roughly around 250 Hz, it corresponds to the jets exiting the hollow columns through the openings : the corresponding Strouhal number is found at 0.13, value also coherent with the literature (0.13 for flow in a rectangular section, ref [8]).

Another way to get a main frequency from a signal is the "zero cross method" (see ref. [9] and [11]), the following table gives the values obtained for the previously defined locations, for both Star-cd and Trio-U computations :

Star-cd Trio-U (*) 2nd opening 180 156-194 4th opening 190 140-266 6th opening 161 304-548 (**)

(*) : the values of Trio-u are those of 2 points neighboring the Star-cd values

(**) : according to ref. [9], the lowest frequencies (around 100-200Hz) characterize well developed fluctuations whereas higher frequencies characterize erratic behaviors, the high values for this location are therefore not completely representative of the structure of the flow.

According to those 2 remarks, the agreement can be

considered as good. A preliminary remark is that those frequencies are too high

to penetrate into the graphite structures. This is obviously seen by the calculation of the conduction in the solid parts. The physical time of the computation (0.2 s) does not allow to catch correctly frequencies lower than 50 Hz (i.e. 10 periods), but the turbulence generated in the plenum, where the velocities are high, would not imply low frequencies.

Nevertheless, other phenomena may induce temperature fluctuations at lower frequencies (loop excitations, other instabilities), and introduce thermal fluctuations in the graphite. The present study is therefore not sufficient to answer this point, and specific studies must assess those low frequencies.

Synthesis The first conclusion is that both analyses are coherent and

a general agreement between results is obtained. Moreover, this general agreement (more or less precise) is obtained on averaged fields, amplitude of fluctuations and frequencies. The difference may be explained by the following items :

• The geometrical description is different and less accurate with the structured grid used by Trio-u,

• The mesh size and shape are uniform and perfectly cubic in Trio-u, and variable for Star-cd,

• The discretization scheme and time marching procedure are different.

A lack in the comparison is that the subgrid scale model remains almost the same for both analyses (they are based on structure function model).

CONCLUSION The quality and confidence in computational fluid

dynamics requires both good modeling practices and code validation. Code to code benchmarks are often used to improve them. In the frame of High Temperature Reactors studies, a complex configuration has been chosen, it involves highly turbulent flows in a complicated geometry and requires a computation of Large Eddy Simulation type.

The results of the Star-cd computation performed by Framatome-ANP presented here highlights some advantages of the Large Eddy Simulation : instant fields of velocity and temperature produce more informations than classical steady computations and are expected to give better assessments of mean fields in the particular configuration of wakes behind columns. Such calculations are also expected to provide


informations for flow induced vibrations in the columns bundle and for the efficiency of the mixing between helium flows (hot streaks production).

The code to code comparison between the Star-cd and Trio–u softwares shows a general agreement on averaged fields of velocity and temperature, on amplitudes of fluctuations and on their frequencies. Moreover, a first validation is obtained by comparing positively the major frequency peaks of velocity fluctuations with literature results.

Another important and positive point is that the comparison was concerning the CFD codes themselves but was also including the modeling practices.

This work which is a first and rather general approach, can be improved by extending the comparison (other codes, literature), and then by focusing on specific physical behaviors (hot streaks, vibrations induced, …). Finally, the best practice guidelines in CFD and the confidence in codes will be incremented from those benchmarks.

NOMENCLATURE HTR : High Temperature Reactor LES : : Large Eddy Simulation νt : turbulent viscosity ν : molecular (kinematic) viscosity y+ : adimensional distance to the wall k : turbulent kinetic energy ε : rate of dissipation of k

REFERENCES

1. G. Grötzbach, M. Wörner. "Direct numerical and large eddy simulations in nuclear applications". International Journal of Heat and Fluid Flow, 20 (1999), 222-240.

2. JP. Simoneau, H. Noé, B Menant. "Large Eddy Simulation of Sodium Flow in a Tee Junction - Comparison of temperature fluctuations with experiments". Proceedings of ICONE-5 conference, paper #2145. Nice, May 1997.

3. D. Grand, JP. Magnaud, JR. Pages, M. Villand. "Three dimensional computations of thermal-hydraulic phenomena in reactor vessels". Advances in mathematics, computations and reactor physics, Pittsburgh, April 28 - may 1st, 1991.

4. M. Lesieur, O. Métais. "New trends in large-eddy simulations of turbulence". Annu. Rev; Fluid. Mech., 28, 1996.

5. J-P. Simoneau, H. Noé, B. Menant. "Large eddy simulation of mixing between hot and cold sodium flows, comparison with experiments". Proceedings of the 7th Nuclear Reactor Thermalhydraulics conference (Nureth 7), Sept. 1995, Saratoga Springs, NY, USA.

6. Issa R I, Ahmadi Befui B, Beshay K and Gosman A D , "Solution of the implicit discretised reacting flow equations by operator splitting" J. Comp Phys., 93, pp 388-410, 1991.

7. Star-cd software, version 3.15, Computational Dynamics ltd, London, 2001.

8. F. Boulot, Y Cavaille, R-J Gibert, J-C Guilloud, J-C Jouannet, D. Milan, M. Sagner, M. Wegner, "Vibrations de structures dans un écoulement sous l’effet du détachement tourbillonnaire de sillage", Société hydrotechnique de France, Paris,

9. N. Tauveron, Analysis of thermal fluctuations in the lower plenum of an high temperature gas reactor. Proceeedings of the 10th International Topical Meeting on Nuclear Reactor ThermalHydraulics (NURETH-10), Seoul, Korea, October 5-9, 2003.

10. N. Tauveron, "Thermal fluctuations in the lower plenum of an high temperature reactor", J. Nuclear Engineering and Design (accepted), 2003.

11. J.P. Simoneau, "Simulation of attenuation of thermal fluctuations near a plate impinged by jets", Proceedings of ICONE-9 conference, paper #9651, April 8-12, 2001, Nice, France.


Figure 2 – Lower plenum and zone modeled

Figure 1 – Reactor core and helium flow

Outlet plenum

Figure 3 – Model (solid meshes) and inlets (Star-cd)

Figure 4 – details of hollow column modeling (Star-cd)

Fluctuations de vitesse

0

20

40

60

80

100

120

0,10985 0,15985 0,20985 0,25985 0,30985

Temps (s)

Vite

sse

(m/s

)

point 16

Figure 6 – Instant velocity record (Star-cd)

Figure 5 – mesh refinement (Star-cd)

SOLID

FLUID

Instant velocity (m/s) (point 16)

Time (s)


Figure 8 – Comparison LES averaged / k-epsilon

(component v of velocity) (Star-cd)

Temperature fluctuations

850

855

860

865

870

875

0,10985 0,15985 0,20985 0,25985 0,30985

time (s)

Tem

pera

ture

(°C

)

point 48 point 4 point 54

Figure 7 - Instant temperature record (Star-cd)

Figure 9 – Instant velocity field t= 0.13 s (Star-cd)

Figure 10 – Instant velocity field t= 0.28 s (Star-cd)

Figure 11 – instant velocity field – vertical section (Star-cd) Figure 12 – Averaged velocity field – vertical section (Star-cd)

Instant temperature (°C)


Figure 13 – instant temperature – horizontal section (mid height of plenum) (Star-cd)

Figure 14 – instant temperature – horizontal section

(lower part of plenum) (Star-cd)

Figure 16 – averaged temperature – vertical section (Star-cd)

Figure 15 –instant temperature – zoom on hollow columns (Star-cd)

Figure 17 - Averaged velocity field – horizontal section (Star-cd)

Figure 18 – averaged velocity field – idem as fig. 17

Trio-U result (ref. [9], [10])


Figure 19 – Comparison of averaged temperature – horizontal section – upper part (opening 2 level)

Figure 20 – Comparison of averaged temperature – horizontal section – mid height (opening 4 level)

Figure 21 – Comparison of averaged temperature – horizontal section – mid height (opening 6 level)

Trio-U Star-cd

Star-cd Trio-U

Star-cd

Trio-U


Spectre fréquentiel des fluctuations de vitesse

10 100 1000 10000Fréquence (Hz)

point 16

Figure 22 – Velocity spectrum (lower part – opening 4)


10 100 1000 10000Fréquence (Hz)

Série3



10 100 1000 10000Fréquence (Hz)

Série3


Spectre fréquentiel des fluctuations de température du fluide

0,00E+00

5,00E-02

1,00E-01

1,50E-01

2,00E-01

2,50E-01

10 100 1000 10000Fréquence (Hz)

16

Figure 25 – Temperature spectrum (lower part – opening 4)


00,050,1

0,150,2

0,250,3

0,350,4

0,45

10 100 1000 10000Fréquence (Hz)

5



0

0,1

0,2

0,3

0,4

0,5

0,6

10 100 1000 10000Fréquence (Hz)

10


Frequency spectrum of velocity fluctuations Frequency spectrum of velocity fluctuations

Frequency spectrum of velocity fluctuations Frequency spectrum of temperature fluctuations

Frequency spectrum of temperature fluctuations

Frequency spectrum of temperature fluctuations

Frequency (Hz) Frequency (Hz)

Frequency (Hz)

Frequency (Hz)

Frequency (Hz) Frequency (Hz)

LARGE EDDY SIMULATION OF MIXING IN THE OUTLET PLENUM...

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