Static pressure and wall shear stress distributions in air flow in a seven wire-wrapped rod bundle

Static Pressure and Wall Shear Stress Distributions in Air Flow in a Seven Wire-Wrapped Rod Bundle

Elói Fernandez y Fernandez

Departamento de Engenharia Mecânica. Pontifícia Universidade Católica do Rio de Janeiro

Pedro Carajilescov

Departamento de Engenharia Mecânica. Universidade Federal Fluminense, Niterói, RJ

[e-mail]

An experimental investigation is performed in a turbulent flow in a seven wire-wrapped rod bundle, mounted in an open air facility. Static pressure distributions are measured on central and peripheral rods. By using a Preston tube, the wall shear stress profiles are experimentally obtained along the perimeter of the rods. The geometric parameters of the test section are P/D=1.20 and H/D=15. The measuring section is located at L/D=40 from the air inlet. It is observed that the dimensionless static pressure and wall shear stress profiles are nearly independent of the Reynolds number and strongly dependent of the wire-spacer position, with abrupt variations of the parameters in the neighborhood of the wires.

Keywords: Wall shear stress. Static pressure distribution. Rod bundles. Nuclear reactors.

Introduction

Current LMFBR (Liquid Metal Fast Breeder Reactors) fuel elements consist of wire-wrapped rod bundles. The rods are arranged in a triangular array, housed in hexagonal ducts, with the coolant flowing along them. The core design of such reactors requires a detailed representation of the rods and duct temperature distributions under any operational conditions.

It is important to predict localized hot spots generated by the wire wrap and gap spacing, and therefore it is necessary to study the characteristics of local heat and momentum transfer in turbulent fluid flow in wire wrapped rod bundles.

Most of the previous works analyze the thermalhydraulic behavior of the fuel elements in a subchannel basis (see, for example, Rowe (1973), Khan et al. (1975), Wheeler et al. (1976) and Fernandez (1984)), obtaining average values of the design parameters over the subchannels. Braz Filho (1991) presents a very complete revision of the existing subchannel methods. This type of approach, however, is inadequate to describe local peaks of temperature and pressure, which affect the coolant conditions. The occurrence of a low pressure region, near the wire, might lead to local film boiling, degrading the heat transfer coefficient, resulting in a local hot spot. Beside this, a core positive reactivity insertion might also occur. Since, for LMFBR reactors, the major thermalhydraulic limits are the clad and fuel temperatures (see Todreas and Kazimi (1990)), those effects have to be avoided. An effort to analyze the flow conditions in a distributed parameter basis has been carried out by Chuang et al (1983). They developed the FATHOM-360 and FATHOM-360S computer codes for two-dimensional flow analysis in a specified subchannel. In their technique, the bulk velocities and temperatures were previously established by a lumped parameter subchannel analysis. This procedure has also been followed by Shimizu (1983).

The application of this hybrid technique requires:correlations for the eddy momentum and heat diffusivity that take into account the strong convective coolant mixing process induced by the wire wrap;prior knowledge about the location of the hot spot in order to avoid costly calculations at all axial planes;extensive tests to the developed codes with comparisons of the predicted results with local experimental data.

Experimental data for the velocity field can be found in several previous works (see, for example, Roidt et al. (1976), Roidt et al. (1980), Chen et al. (1974), Lafay et al. (1975)). Also, Lafay et al. (1975), Arwikar and Fenech (1979) and Fernandez and Carajilescov (1979) measured the static pressure distributions on the surface of the rods. To our knowledge, no experimental data for the wall shear stress distribution, in wire-wrapped rod bundles have been published.

The purpose of the present work is to present experimental results for local static pressure and wall shear stress distributions in turbulent air flow. The main ideas are to provide some insight about the fine structure of the flow in the subchannels and to furnish local data of the fundamental flow parameters. These data can be used for comparison with the predicted results given by the distributed parameter codes.

Experimental Apparatus

The measurements were performed in an open loop with air as the flowing fluid. Figure 1 shows a general view of the apparatus. The flow rate was measured by a calibrated Pitot tube mounted in the feeding tube and it was controlled by a throttling valve located adjacent to the fan.

The test section consists of a bundle assembly with 7 wire-wrapped rods. Flow perturbations due to the instrumentation were reduced by taking rods with diameter of 50 mm. The full length of the test section is 2300 mm. The bundle characteristic parameters are: P/D=1.20 (pitch to diameter ratio) and H/D=15 (wire lead to diameter ratio).

The static pressure profiles at wall of the hexagonal duct were obtained by 9 pressure taps uniformly distributed on one side of the housing as shown in Figure 2. The hole diameter is 0.8 mm.

To measure the static pressure and the wall shear stress distributions on the surface of the rods, a static pressure take and a Preston tube were installed on a portion of one of the rods, as presented in Figure 3. Such section can rotate independently of the remaining part of the rod and of the wire. This procedure allows continuous angular measurements of the parameters. The static pressure take has a diameter of 0.8 mm. The outside diameter of the Preston tube is 0.42 mm and the internal diameter is 0.20mm. The measuring station is located at L/D=40 from the entrance section. From axial pressure drop measurements, the flow was observed to be fully developed at that stage.

The Preston tube was calibrate with a TSI calibrator, model 1125 OR and the experimental data were reduced using the results given by Patel (1965).

The angular wire position is given by the angle a, defined in Figure 2, and its effect on the measured profiles was experimentally observed by rotating simultaneously the seven rods of the same amount.

Experimental Results

The static pressure distributions on the wall of the hexagonal duct were measured for a varying in steps of 60o and for Reynolds numbers, Re, between 26000 and 48000. For the central rod, the static pressure and the wall shear stress profiles were obtained for a varying in steps of 30o, while for the peripheral rod, it was considered a varying in steps of 60o. In these cases, it was taken, Re=33000 and 77000.

The values of the static pressures were written in dimensionless form given by

(1)

where is the average static pressure at the measuring station and is the average air velocity of the flow.

The shear stress readings were non-dimensionalized dividing them by the average value of the wall shear stress, to,avg, obtained from the friction factors previously measured in pressure drop measurements.

Static pressure distribution on duct wall

Figures 4 and 5 show the static pressure distributions measured along the duct wall for different values of a, for Re=33000 and 77000. For side A in Figure 4, the wire is in the gap between the rods of the measuring face and is leaving the edge subchannel. It can be observed that the wires induce a low pressure zone in their wake region. For side D, the wire is also blocking the gap between the rods but, in this case, it is entering the edge subchannel, directing the flow against the wall and creating a high pressure zone.

Analogous behavior can be observed for sides C and F.

When the wire is in the edge subchannel, as for side B, the static pressure has a very low value near the left side of the wall, which is the wake region of the wire of the left rod. In this case, the wire is almost blocking the gap between the wall and the rod.

Similar results can be observed in Figure 5.

These measurements are in qualitative agreement with the result of Lafay et al (1975), obtained for 19 wire-wrapped rod bundle.

For all the cases, it can be observed that the effect of Re on the dimensionless static pressure, p*, is quite small.

Static pressure distribution at the surface of the rods

Measurements of the static pressure distributions are presented in Figures 6 and 7, for the central rod, and in Figures 8 and 9, for the peripheral one.

In the cases shown in Figures 6 and 8, the surface of the rod is in contact with the wire of a neighboring rod. Maximum and minimum static pressures are observed on both sides of that spacer. In such configurations, that wire represents an obstacle to the flow, reducing its velocity and increasing locally the static pressure. Behind the wire, a wake region is created, reducing the static pressure. The lowest peak occurs at the peripheral rod. This situation can also be observed in Figure 10, for different values of the angle a, when contact occurs.

When the described contact is absent, the static pressure profiles do not show abrupt variations, as can be seen in Figures 7 and 9. Additional results of this situations is presented in Figure 11, for different values of the angle a. Figures 6 and 8 show that the static pressure distributions at the surface of the central and peripheral rods, for a=0o, are similar to each other in the qualitative sense and they agree with the result of Arwikar and Fenech (1979).

Also, in this case, the data did not reveal any appreciable effect of Reynolds number.

Wall shear stress distributions

The complex structure of the three-dimensional flow field, in the subchannels, yields large variations on the wall shear stress profiles, as shown in Figures 12 through ¹⁵.

Below the wire, the streamlines seem to gather, following the wire and generating a high wall shear stress due to local flow acceleration. By flow visualization, Lafay et al (1975) observed that, at certain positions, the flow spills over the wire. This would generate a local increase in the axial velocity of the flow, leading to the appearance of peaks on the wall shear stress. This effect is confirmed by the present measurements, not only for the peripheral rods, as visualized by Lafay et al, but also for the interior rods.

Qualitatively, it was observed that the wall shear stress varies from 23% to 180% of its average value.

Reynolds number does not play an important role on the non-dimensional wall shear stress distribution. This observation is in contrast with those of Trupp and Azad (1975), for bare rod bundles. In bare rod bundles, the wall shear stress distribution is affected by the secondary flow induced by turbulence, which is a function of Reynolds number. In the present case, turbulence induced secondary flows are negligible when compared to the strong transversal flow forced by the wire wrap.

Conclusions

The effects of the wire-wrap on the static pressure and on the wall shear stress have been experimentally analyzed for a 7 wire-wrapped rod bundle. The main results are:

• The static pressure profiles on the hexagonal duct wall and on the surface of the rods reveal the existence of a sharp pressure variation across the wire. As expected, the minimum static pressure occurs in the wake region of the wires.

• The static pressure profiles on the central and peripheral rods are quite similar in qualitative sense.

• The lowest pressure peak was observed at the surface of the peripheral rod, behind the wire that belongs to the neighboring peripheral rod.

• A change in Reynolds number has no appreciable effect on these non-dimensional static pressure profiles.

• Local wall shear stress peaks seem to agree with Lafay's observation that some of the flow spills over the wire.

• Large variations, between 243% and 180%, occur on the wall shear stress. So, similar variations are expected on the local friction factor.

• The negligible effect of the Reynolds number on the wall shear stress reveals that the transverse crossflow generated by the wire-wrap overshadows any effect of secondary flows eventually induced by turbulence.

• Considering the apparatus, the instrumentation and the operational procedure, the experimental errors were determined to be 5% for the static pressure measurements and 12% for the wall shear stress. The angular positional error was estimated to be 1.50.

• As a final remark, it is worth to remind that the present results were obtained for P/D=1.20 and H/D=15. Comparisons with different values of these parameters can be performed only in a qualitative basis, since their influence in the static pressure and wall shear stress distributions was not analyzed.

Manuscript received: May 1999. Technical Editor: Angela Ourívio Niekele.

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Publication Dates

• Publication in this collection
  15 Dec 2000
• Date of issue
  2000

History

• Received
  May 1999