Unsteady RANS and LES Analyses of Hooper’s Hydraulics ... · Unsteady RANS and LES Analyses of...

The 8th International Topical Meeting on Nuclear Thermal-Hydraulics, Operation and Safety (NUTHOS-8) N8P0218

Shanghai, China, October 10-14, 2010

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Unsteady RANS and LES Analyses of Hooper’s Hydraulics Experiment

in a Tight Lattice Bare Rod-bundle

L. Chandra*1, F. Roelofs, E. M. J. Komen E. Baglietto

Nuclear Research and consultancy Group

Westerduinweg 3, 1755 ZG, Petten, The Netherlands.

Tel:+31 224 56 8152 , Fax:+31 224 56 8490

*E-mail: [email protected]

CD-adapco, New York

60 Broadhollow Rd. Melville,

NY 11747

ABSTRACT

Several experiments have already reported the existence of flow oscillations in a tight

lattice bare rod-bundle. This in-turn results in temperature oscillations, when heat transfer

is also involved. Consequently, assessment of flow oscillations plays an important role in

the design of future innovative reactor systems as proposed by the Generation IV

International Forum. Literature review reveals that such flow oscillations have recently

numerically been analyzed using Unsteady Reynolds Averaged Navier-Stokes (URANS)

and Large Eddy Simulation (LES) techniques.

The objective is to assess URANS and LES turbulence modelling techniques for

application in tight rod bundles to determine:

temperature oscillations arising from flow oscillations in a tight lattice rod bundle

occurrence of flow induced vibrations

To this purpose, as a first step this paper will present URANS and LES analyses of the

hydraulics experiment performed by Hooper in a tight lattice bare rod-bundle (pitch-to-

diameter ratio is 1.107). These simulations are performed using STAR-CCM+. The

numerical analyses reveal the existence of flow oscillation as observed in the experiment.

This is concluded from the analyzed instantaneous velocities at a plane and the time

dependent velocities at a point in the computational domain. As expected, for a given grid

and time step, these results show that the employed LES approach resolves smaller

structures compared to the employed URANS approach. The influence of the flow on the

surface of the rods is assessed by analyzing the wall shear stress magnitude and its power

spectra.

Key words: URANS, LES, flow oscillation, rod-bundle.

1: Current address: Indian Institute of Technology, Rajasthan, India.



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1. INTRODUCTION

Six innovative reactor concepts are considered under Gen IV International Forum, [1].

Usually, in Computational Fluid Dynamics (CFD) analyses of fuel assembly subchannels,

Reynolds Averaged Navier Stokes (RANS) is employed for evaluation of the reactor core

in these systems. The applicability of RANS approaches has already been assessed for

widely spaced rod-bundles, see e.g. [2], [3]. The isotropic first-order two-equation based

k-ε or k-ω models are known to be incapable of capturing the secondary flows and

resulting anisotropy, which are inherent in a rod-bundle. This necessitates the use of

second-order Reynolds Stress Model (RSM) or non-linear anisotropic eddy viscosity

based turbulence models as outlined e.g. by [4], [5], [6], [7].

Well-instrumented and detailed experiments by e.g. [8], [9] and [10] have provided

valuable insight to the flow hydraulics in a rod-bundle. Such experiments benefit from

the fact that the flow hydraulics mainly depends on the flow conditions and is largely

independent of the fluids, see e.g. [11].

The hydraulics experiments by [10] and the thermal-hydraulics experiment by [8] have

revealed the existence of flow oscillations or unsteadiness in a tightly spaced rod-bundle

with pitch-to-diameter ratio (p/d) of 1.1 and 1.06, respectively. The flow oscillations can

cause flow-induced vibration in a rod-bundle. It has been revealed by the thermal-

hydraulics experiment that these flow oscillations result in temperature oscillations.

These temperature oscillations in turn can induce thermal shock or thermal fatigue

damage to the walls of the rods in a bundle. To capture such time-dependent flow

features an Unsteady RANS, a Large Eddy Simulation (LES), or even a Direct Numerical

Simulation (DNS) approach is needed, see e.g. [12], [13].

Keeping the above aspects in mind this paper aims at:

- Assessment of URANS and LES modelling approaches by analyzing Hooper’s

hydraulics experiment as described in [10].

- Analyses of obtained results to compare these two different approaches.

The first section of the paper deals with the analyzed Hooper’s hydraulics experiment

[10], the second section describes the adopted CFD model for URANS and LES analyses,

the third section deals with the obtained results and finally the last section summarizes

and concludes the paper.

2. ANALYZED CASE

To assess the capabilities of URANS and LES approaches, Hooper’s hydraulics

experiment [10] with a tight lattice bare rod-bundle having a p/d of 1.1 is selected. The

cross section of this experimental geometry revealing six bare rods arranged in a square

lattice is shown in Fig. 1. This six-rod cluster is supported by an external frame that

maintains the dimensional accuracy without the need of additional spacer grids. This

experiment is performed with air as a working fluid at a bulk Reynolds number (Rebulk) of



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about 49 000 with an inlet uniform or bulk velocity of 10.3 m/s. The length of the

experimental six-rod cluster is 9.14 m, which is equivalent to 128 hydraulic diameters.

This is expected to be sufficient for obtaining a fully developed flow condition. This

experiment measures time-dependent velocities with hot-wire anemometer probes

positioned at (x,y) = (0, ±0.102m), in a plane that is about 126 hydraulic diameters from

the inlet. These probes are placed in the smallest gap region between the rods. These

measurements reveal the existence of flow oscillations or instabilities in the experiment.

The estimated measurement uncertainty in the axial or main flow velocity component is

about 15 % (see e.g. [14]). The experimental details are summarized in Table 1.

Fig. 1: Cross section of the Hooper’s hydraulic experiment with a tight lattice six-rod

cluster ([10]). The red dotted lines are indicating the selected computational domain.

Table 1. Conditions for Hooper’s hydraulic experiment with pitch-to-diameter of 1.1

Rod-bundle

arrangement

Bulk Reynolds

number

Bulk velocity

(m/s) Measuring plane

Experimental

uncertainty

Square 49 000 10.3

126

hydraulic diameter

from inlet

15 % in the main

flow direction

3. CFD MODEL

The selected region for the URANS and LES analyses of Hooper’s hydraulics experiment

is indicated with red dotted lines in Fig. 1. This modelled geometry is elaborated in Fig.

2. The length of this modelled geometry for CFD analyses is 1.272 m, which is four times

an average wavelength of oscillations as determined by [15]. The selected length

corresponds to about 18 hydraulic diameters. The average wavelength is approximated

from the ratio of bulk velocity 10.3 m/s to an average cycle frequency of flow

oscillations. An average cycle frequency (f) of flow oscillations is obtained from its given

graphical relationship with Rebulk in [10]. Analysis of this relationship provides a value of

f close to 30 Hz for the defined experimental conditions. It is already explained that the



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flow measurements include a certain error, and therefore, it can be expected that a

relationship between Rebulk and f will also contain a certain amount of error. However, no

details in this respect for the considered experiment are available.

Fig. 2: Selected computational domain (left) and generated hexahedral mesh at the cross

section (right) for CFD analyses of Hooper’s hydraulics experiment.

The generated cross-sectional grid for the present analyses is shown in Fig. 2. The wall

near resolution of this grid exhibits an average y+ of the order of 2 for the closest grid

point to the walls. The stretching factor in the boundary layer is about 1.07. In other

words, the selected grid resolves the wall near region at least in the radial direction. In

general, the largest grid-width (=max (∆x, ∆y)) in the cross section as shown in this

figure in terms of wall-units is about 20. Consequently, the generated cross-sectional

mesh follows the recommendations for a suitable grid in nuclear applications involving

heat transfer for Large Eddy Simulations (LES), see e.g. [16]. The maximum grid aspect

ratio of the generated grid is 80. Furthermore, a practical guideline by [17] indicates that

the generated wall-resolved grid is capable of representing the flow structures in the near-

wall region and is suitable for LES. In the bulk region, the grid aspect ratio is about 8.

The grid is having about 80 axial grid points in one average wavelength of the

oscillations and consists of about 8.5 million computational hexahedral volumes. Such a

grid resolution for capturing flow oscillations or unsteadiness restricts the selection of a

larger computational domain. The generated grid is summarized in Table 2. It should be

emphasized that the same grid is used for both URANS and LES simulations. Therefore,

the obtained results allow us a direct comparison between these two approaches based on

the selected numerical schemes and closure models.

Outlet

Inlet

Wall

Outlet

Inlet

Wall

Flow



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Table 2. Generated mesh for URANS and LES analyses of Hooper’s hydraulic

experiment

Computational volumes (million) 8.5

Average y+ (nearest node to the wall) ~ 2

Stretching factor in the boundary layer ~ 1.07

Maximum bulk grid-width in wall-units ~ 20

Maximum grid aspect ratio 80 (~160 wall-units)

Grid aspect ratio in bulk 8

For the URANS and LES analyses, the STAR-CCM+ CFD code is used. The open

boundaries of the modelled geometry are treated as rotationally periodic. These are

indicated by the same types of arrows in Fig. 2. The inlet and outlet are treated as cyclic

and a mass flow rate corresponding to a bulk velocity of 10.3 m/s is applied to sustain the

flow and turbulence in the selected computational domain. The employed computational

set up using a Finite Volume Method (FVM) consists of:

- Implicit unsteady based segregated flow solver in which convection terms are

discretized with a second-order (quadratic upwind for URANS and bounded-

central for LES) scheme in the continuity and momentum equations.

- A stable first-order upwind scheme to discretize the convective terms in the

transport equations of turbulent quantities such as k and ε for URANS analyses.

- k-ε based non-linear quadratic anisotropic eddy-viscosity turbulence model for

URANS analyses.

- The Wall-Adapting Local Eddy-viscosity (WALE) model for LES analyses.

- All y+-wall treatment, which is a hybrid treatment that attempts to emulate the

high-y+ wall treatment for coarse meshes and the low-y+ wall treatment for fine

meshes in both approaches.

- A selected time step of ∆t = 5x10-5

seconds results in a maximum Courant

number of 0.5. This is much smaller than 1/f with f ~30 Hz for the present case i.e.

∆t << 1/f. Note that [18] have employed an even smaller Courant number of

about 0.2 for analyzing [8] experiment.

For details on the employed scheme, turbulence models etc. refer to the STAR-CCM+

User Guide [19]. The discussed computational set-up is summarized in Table 3.



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Table 3. Computational set-up for Hooper’s hydraulics experiment with

STAR-CCM+

Solver

URANS LES

Implicit unsteady

Segregated flow

Turbulence model

k-ε based non-linear anisotropic

quadratic eddy-viscosity model

Wall-Adapting Local Eddy-

viscosity (WALE) model

All y+ wall treatment

Numerical scheme

for convective terms

Continuity, momentum equations:

Second-order upwind scheme

Continuity, momentum equations:

Bounded-central scheme

Turbulence equations: First order

upwind scheme for URANS ---

Time step 5E-5 seconds

Maximum convective

Courant number

0.5

Computed flow

through times 12 22

Inlet – outlet Cyclic: Forced with mass flow rate

Open boundaries Rotationally periodic

4. RESULTS

The URANS and LES computations are carried out for a total time of 1.5s and 2.6s,

respectively. This corresponds to about 12 and 22 flow-through times, respectively, in the

modelled geometry with a bulk velocity of 10.3 m/s. The first 2-3 flow-through times

based results are not considered for the analyses in both approaches.

The URANS and LES analyzed axial velocity fluctuations at a certain point (z = 0.636 m,

x = - 0.102 m) are shown in Fig. 3. This also includes the recorded response of hot-wire

anemometer probes as given in [10]. Following can be inferred from this figure:

- URANS and LES analyzed axial velocity fluctuations are mostly within ± 1.5

m/s. Some of the analyzed values are as high as ± 2m/s. In other words, the

fluctuations are almost 10-14 % of the axial bulk flow velocity of 10.3m/s.

This is not negligible and could cause flow induced vibrations of the six-rod

cluster.

- LES analysis reveals a higher frequency of axial velocity fluctuation in

comparison to URANS analysis. This indicates that wider ranges (or scales) of

flow structures are captured with LES than that of RANS approach, as

expected.

- Experimental measurement reveals that the axial velocity fluctuations are

mostly within ± 1.3 m/s.



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It should be emphasized that the measurement of axial velocity component involves an

error of the order of 15% (see e.g. [14]). In other words, the measured axial velocity

fluctuation can vary within ± 1.5 m/s including the explained experimental error.

Moreover, although it has been outlined that appropriate measures have been taken, it

should be noted that there are always several possible reasons for uncertainties in a CFD

analysis, such as, generated grid, selected domain, turbulence model, boundary

conditions and the selected approaches etc. Even with all these practical aspects of

differences between experimental and computational approaches, it can be safely stated

that the calculated values agree well with the experimentally measured axial velocity

fluctuation. These are summarized in Table 4.

Table 4. Experimental and CFD analyzed axial velocity fluctuations

Axial velocity fluctuations (m/s)

Experimentally

measured

± 1.5

(± 1.3 ± 15%)

URANS and LES

analyzed ± 1.5

Fig. 3: URANS analyzed (top) and Experimentally measured (bottom) axial velocity fluctuations for

the Hooper’s hydraulics experiment.

z = 0.636 m, x = - 0.102 m

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Axial-velocity fluctuation (m/s)- URANS

Axial-velocity fluctuation (m/s)- LES

URANS LES

u: Axial velocity

component (at 126

hydraulic diameter, x =

±.102 m



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A three dimensional perspective of URANS and LES analyzed axial velocity is shown in

Fig. 4. This figure shows:

- A wavy pattern that can be inferred from the regions with different axial

velocities in the analyzed mid-plane. These are indicated by arrows in the

figure. As expected, the velocity is lower in the smallest gap region and higher

in a region close to the open boundaries.

- The presence of smaller flow structures in the LES computed flow field in

comparison to URANS computed flow field. For instance, small plumes of

low velocity are observed at the inlet section in LES and are not visible with

URANS computation.

The presence of smaller flow structures in LES is attributed to smaller values of analyzed

turbulent eddy viscosity in comparison to URANS. In general, analyzed effective

viscosity with LES is lower than that of URANS with the generated grid and employed

computational frame-work.

Fig 4: URANS (left) and LES (right) analyzed axial velocity after about 1s of

computational time.

Power Spectral Densities (PSD) of the URANS and LES analyzed axial velocity

fluctuations at two different measurement points are shown in Fig. 5. The CFD software

STAR-CCM+ is used for computing PSD. The analyzed axial velocity fluctuations over

six and eight flow-through times are employed for this purpose in the adopted URANS

and LES approaches, respectively. These indicate:

- The PSD peaks are observed in the production frequency range of 10-20 Hz

for URANS and in the range of 17-27 Hz for LES analyzed axial velocity

fluctuations. These can be inferred as frequencies associated with the

dominant amplitudes (e.g. ± 1.5 m/s) of axial velocity fluctuations.



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- Based on a graphical relationship between frequency and bulk Reynolds

number ([10]) it can be deduced that an average characteristic frequency of

such large scale structures is about 30 Hz. The LES analyzed results shows a

closer resemblance with the experimental observation than that of URANS

analyzed results.This indicates the presence of large scale structures that

contribute to a higher production of turbulence energy or power in the

indicated frequency ranges.

- It can be observed that the energy of turbulent structures with a frequency,

say, 300 Hz is much smaller in URANS in comparison to LES. This can be

attributed to a higher eddy-viscosity in the URANS approach compared to

LES. This means, smaller scales with such a high frequency in URANS are

not sustainable whereas they still exist in LES. At the same time, energy

contents of turbulent structures with frequency below 100 Hz are comparable

in URANS and LES. In other words, URANS will be useful for applications

where lower frequencies or larger or mean flow structures are relevant.

Fig 5: Power Spectral Density (PSD) analyzed from URANS (left) and LES (right)

analyzed axial velocity fluctuations.

It can be expected that the flow oscillation may even influence the wall shear stress. In

order to determine the influence of flow oscillations on the wall shear stress, its

magnitude is noted over time at a point in the lower wall at the smallest gap between the

rods. The time dependent wall shear stress magnitude (in Pa) is shown in Fig. 6. This

shows that:

- Oscillations exist in wall shear stress magnitude.

- URANS analyzed wall shear stress magnitude has a higher lower limit of 0.2

Pa than that of about 0.1 Pa in LES analyzed wall shear stress magnitude.

- LES analyzed wall shear stress has a higher amplitude of oscillation (varying

between 0.1 to 0.4 Pa) than that of URANS analyzed wall shear stress

(varying between 0.2-0.35 Pa).

It can be emphasized that an oscillating wall shear stress is not desirable in a rod-bundle

as it can challenge the integrity of the reactor core by damaging the fuel rods surface.



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0.1

0.15

0.2

0.25

0.3

0.35

0.4

1.2 1.4 1.6 1.8 2 2.2 2.4

Wall-shear-stress-URANS

Wall-shear-stress-LES

Fig 6: URANS and LES analyzed wall shear stress magnitude (Pa) at a point lower wall in the

smallest gap between the rods, indicated by an arrow in the right figure.

Fig 7: Power Spectral Density (PSD) of URANS (left) and LES (right) analyzed wall

shear stress magnitude

The PSD of URANS and LES analyzed wall shear stress magnitude are shown in Fig. 7.

These are obtained from monitored signals over seven flow-through times. These reveal

distinct peaks in a frequency range of 10-20 Hz for both approaches. In other words, the

signals of wall shear stress magnitude as shown in Fig. 6 have dominant amplitudes in

this frequency range. If this time response of dominant wall shear stress (in this

frequency range) is below a characteristics response time of the material of which the fuel

rods are made, then the material may adjust having enough time to react on the changes

of wall shear stress. In case this time response of dominant wall shear stress (in the

indicated frequency range) is higher than that of a characteristic response time of the

material of which the fuel rods are made, then the material may not be able to react on the

changes of wall shear stress. Otherwise, it can be expected that the material will react to

the changes in wall shear stress and will not be able to adjust to these changes.

It can be noted that dominant frequencies of axial velocity fluctuations and wall shear

stress magnitudes are quite comparable values that indicate a possible relationship

between these quantities. However, at this moment this is purely qualitative. For a

URANS LES

Time (s)

Wall shear stress magnitude (Pa)



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quantitative statement further analyses are needed by recording velocity at a point closest

to the monitor point for wall shear stress magnitude. Such oscillatory wall shear stresses

can damage the fuel rods surface, and therefore, the safety or integrity of such a rod-

bundle need special attention. It can also be expected that such flow oscillations will also

produce temperature oscillations at the fuel rods surface. These can in turn result in

thermal shocks or thermal fatigue damage to the surface.

5. SUMMARY AND CONCLUSIONS

This paper aims at assessment of URANS and LES approaches by analyzing Hooper’s

hydraulic experiment with a tight lattice bare rod-bundle. For this purpose, a CFD model

is constructed comprising of a domain that allows the use of periodicity as a boundary

condition, a grid that is generated following the practical requirements for LES and

resolves the wall-near region, and numerical schemes for both these approaches.

The analyses of URANS and LES computed results reveal the following:

- URANS and LES analyzed axial velocity fluctuations are mostly within ± 1.5

m/s and agree well with the experimentally obtained limits of ± 1.3 m/s ±

15%.

- The axial velocity fluctuations are 10-14 % of the bulk velocity, which is

significant. This could cause flow induced vibration of such a tight lattice rod-

bundle.

- As expected, LES captures a wider range of turbulent structures or scales in

comparison to URANS.

- The frequency range corresponding to the power spectra peaks of LES

analyzed axial velocity fluctuations is closer to the experiment in comparison

to URANS.

- In URANS, the smaller turbulent structures contain much lower energy (or

power) compared to LES. Therefore, such smaller structures in URANS are

not sustained whereas they exist in LES.

- It is expected that URANS will be useful for applications where mean or large

flow structures are relevant.

- Analyses of wall shear stress magnitude at a point in bare rods surface reveal

oscillations. They also contain distinct peaks in their analyzed power spectra.

This indicates a possible relationship between flow oscillations and wall shear

stress magnitude oscillations. Further analyses are needed for a quantitative

assessment.

- Oscillations in wall shear stress at the fuel rods surface are not desirable as

they can cause damage to the fuel rods surface and therefore special attention

to the safety of such a reactor core is necessary.

- Flow oscillations can cause temperature oscillations when heat transfer is

involved. This in turn can cause thermal shocks or thermal fatigue damage to

the surface of fuel rods, depending on the frequencies of dominant amplitudes

of oscillations.

- Flow oscillations and their consequences need special attention in a tight

lattice rod-bundle with spacer grids.



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6. ACKNOWLEDGEMENT

The authors gratefully acknowledges the support from Dutch Ministry of Economic

Affairs and the seventh framework program THINS Project No. FP7-249337 sponsored

by the European Commission.

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