Experimental analysis of pressure drop and flow redistribution in axial flows in rod bundles

Experimental Analysis of Pressure Drop and Flow Redistribution in Axial Flows in Rod Bundles

Carlos Bastos Franco

RT. Centro Tecnológico da Marinha em São Paulo

[e-mail]

Pedro Carajilescov

Universidade Federal Fluminense. Departamento de Engenharia Mecânica 21410-240 Niterói. RJ. Brasil

[e-mail]

Fuel elements of PWR type nuclear reactors consist of rod bundles, arranged in a square array, and held by spacer grids. The coolant flows, mainly, axially along the rods. Although such elements are laterally open, experiments are performed in closed type test sections, originating the appearance of subchannels with different geometries. In the present work, utilizing a test section of two bundles of 4x4 pins each, experiments were performed to determine the friction and the grid drag coefficients for the different subchannels and to observe the effect of the grids in the crossflow, in cases of inlet flow maldistribution.

Keywords: Flow redistribution, friction factor, spacer grids, PWR type reactor

Introduction

Generally, fuel elements of nuclear reactor cores consist of rod bundles, arranged in square or triangular arrays, with the coolant flowing axially along the rods. In the case of PWR (Pressurized Water Reactors) type reactors, adopted by the Brazilian Nuclear Program, the array is square, with open lattice, with the rods held by grid type spacers.

The thermalhydraulic analyses of nuclear reactors require the precise knowledge of the local thermal and hydraulic conditions of the flow in various operational situations. For this purpose, several computer codes were developed. Among them, it can be mentioned the COBRA codes (Rowe, 1971; Stewart et al, 1977), generally adopted for design purposes, and the THINC codes (Chelemer et al, 1967), property of Westinghouse. The utilization of those codes, nevertheless, require, as input, correlations for the friction factors, as well as for the grid drag coefficients for localized pressure drop due to the presence of grid type spacers that held the fuel rods. Considering that PWR fuel elements are laterally open, the friction factor correlations should refer to the subchannel formed by four rods, with the coolant flowing axially parallel to them. However, pressure drop experiments are performed in closed test sections, originating the appearance of subchannels with different geometries, as shown in Fig. 1. In order to obtain correlations for the friction factor and for grid drag coefficient, it is necessary to determine the flow redistribution among the several subchannels.

Further more, although those codes yield satisfactory results simulating large cores, their application, for small cores, with severe inlet flow maldistribution or with the presence of localized flow blockage, should be validated by comparison with experimental data. For large cores, with approximately cossenoidal axial power distribution, the inlet flow maldistribution will not affect sensibly the value and local of occurrence of the MDNBR (Minimum Departure from Nucleate Boiling Ratio), which represents the main thermalhydraulic design limit (Tong, 1967), despite an imprecise prediction of the crossflow near the entrance. For such situation, the MDNBR will occur in the above half of the rod length where the coolant flow will be, already, mainly axial and well distributed among the subchannels. This picture changes drastically for small cores, with power peaks in the lower half of the rods, in the presence of strong coolant crossflow. Experimental data, for this situation, are practically unavailable in the literature.

In the present work, experiments were performed to determine the flow redistribution among the subchannels and the friction factors were obtained for different types of subchannels. Two test section configurations were utilized, with different sets of interior and edge subchannels (the corner subchannels were considered together with the edge subchannel). For both configurations, pressure drop measurements were performed with and without the presence of grid type spacers.

Also, utilizing a laser anemometer, the axial velocity field was measured for several situations of inlet flow, with and without the grids, aiming to provide experimental data for validation of computer codes for thermalhydraulic analyses.

Theoretical Considerations

Consider two configurations of the test section, with different numbers of interior and edge subchannels, with and without the presence of grid type spacers:

(a) Flow redistribution factor. For a steady state flow, the continuity equation can be written in the form:

where r is the fluid density, A represents the flow area and V is the velocity. The subscripts "ST", "i" and "" refer to whole test section, to interior and edge subchannel sets, respectively.

This equation can be rewritten as follow:

where a _i represents the fraction of the flow area occupied by interior subchannels.

Applying this equation for two configurations with different fractions of the flow area occupied by interior subchannels and rearranging, the flow redistribution factor, for the interior subchannel, is given by:

where .

Analogous expression can be written for the flow redistribution factor for the edge subchannel.

(b) Bundle friction factor. For turbulent flow along the bundle rods of a given test section, without grids, the friction factor can be correlated in the form:

where Re_j is the Reynolds number for the considered geometry j.

For the two configurations, submitted to the same total pressure drop and applying the Darcy law, it yields:

where Dh_j represents the hydraulic diameter of the configuration.

For the whole test section, the correlation coefficients can be determined through the experimental data obtained by the measured flow pressure drop. However, in the cases of the interior and edge subchannels, the correlation coefficients, given by equation (4), are independent of the configuration. So, through equation (5), it is obtained:

These ratios are, then, plugged into equation (3) in order to determine the flow redistribution factor, for flows without the presence of grids.

Regarding the correlation coefficient for the friction factor, for type j subchannel, imposing the same pressure drop for the subchannel and for the whole test section, follows:

(c) Drag coefficient due to grid type spacers. Through pressure drop experimental measurements, for both configurations of the test section, with the presence of the grids, and subtracting the pressure drop due to friction, the grid drag coefficient is determined in the form:

For the same grid pressure drop, in both configurations, the velocity ratio, K_ST, is given by:

Imposing this same relation for the interior subchannel and considering the grid drag coefficient as independent of the configuration, the velocity ratio for both configuration, near the grid, K_i, will be equal to unity. The same occurs for the edge subchannel. Applying these velocity ratios in equation (3), the flow redistribution factor, near the grids, are determined.

Finally, considering that the interior subchannel is submitted to the same pressure drop of the whole test section, the coefficient for the grid drag correlation is obtained in the form:

The subscript "g" indicates the value of the specific velocity in the proximity of the grids.

Similar expression applies to the edge subchannel.

Experimental Apparatus

The pressure drop measurements were conducted in a test section composed by two bundles with 4x4 rods each, initially without any barrier separating the two bundles. After that, a barrier is placed longitudinally between the bundles, changing the fraction of area occupied by the interior and edge subchannels. These situations are shown in Fig. 2.

In the present analysis, the fraction of area occupied by the corner subchannels is very small. So, that area was added to the fraction of area occupied by the edge subchannels.

The experiments are performed with the rods being held by two grids, localized at the ends of the bundles, and, then, they are repeated with six grid distributed along the length of the rods, with the positions given in Fig. 3.

The geometrical data of the test section are presented in Table 1.

With these parameters, the fractions of area occupied by the interior subchannels, a _i, are 0.5885 and 0.4990, without and with a barrier between the bundles, respectively.

The position of the pressure taps, distributed in the test section as shown in Figs. 2 and 3, are presented in Table 2. The measurements were performed utilizing pressurized manometers, allowing reading of water column up to 2000 mm.

The experiments were performed in a closed hydraulic loop, with water flow rate up to 10 Kg/s. This loop is shown schematically in Fig. 4.

As can be observed, each 4x4 bundle has an independent inlet of water, allowing them to operate with different inlet flow rates.

The velocity fields, for the configuration without barrier between the bundles, with and without grid type spacers, was measured by a DANTEC laser anemometer Model LDA-07, with a He-Ne laser, Model 127, fabricated by Spectra Physics, operating in the back propagation mode. The system has also a mechanism that allows movement of the measuring volume along the three axes, as show schematically in Fig. 5.

Further details of this work can be found in Franco (1992).

Results

Figures 6 and 7 present the results of the pressure drop coefficients for the whole test section and for both considered configurations, for Reynolds numbers, Re, up to 30000. In these figures, it was utilized only the readings performed between the measuring levels 3 and 7, presented in Table 4. So, for the cases involving the presence of grids, the correlated pressure drop coefficients take into account only the grids placed between these two levels. From the figures, it can be observed a slight discontinuity for Reynolds numbers below 6000, due the transition in the flow regime. Gunn and Darling (1963) show that the transition range for flows in non-circular ducts are, in general, wide and difficult to reproduce, provoking large dispersion of experimental data. So, the experimental data were correlated only for Re above 6000, in order to assure turbulent flow regime in all subchannels.

From these results, the grid drag coefficients are obtained as:

(a) Setup without grids. Applying the obtained expressions, the velocity ratios between the two configurations are:

In this case, the flow redistribution factors are:

and the friction factors, for interior and edge subchannels, are:

(b) Setup with grids. In this case, for the same pressure drop due to the grids, in both configurations, the observed velocity ratios are given by:

From these values, follow the flow redistribution factors in the proximity of the grids:

Finally, the grid drag coefficients are given by:

From the flow redistribution results, it is worth to observe the differences between the redistribution factors along the bundle and near the grids. These differences can be attributed to the occurrence of crossflow, with fluid flowing from the interior channels to edge channels downstream the grids and returning upstream them. So, the flow cannot be considered strictly one-dimensional. Imposing the same redistribution factor, along the bundle and near the grids, can introduce large errors in the friction factors and in the grid drag coefficients for the interior subchannels, typical of PWR reactors.

The uncertainties in the friction factor coefficients were determined to be between 7% and 12%. For the grid drag coefficients, the uncertainties were between 10% and 17%.

The flow velocity distributions, in the transversal section of the test section, for several axial positions, were measured in steady state regime and adiabatic flow, for the configurations with and without grids. It was considered three main conditions: (a) bundles with same flow rate (50/50), characterizing a balanced flow condition at the inlet; (b) flow rate of a bundle twice of the flow rate of the other (33/67); and (c) flow rate of a bundle equal to zero (0/100). The measurements were performed for Re in the range between 9400 and 28200.

Case 1: Balanced flow (50/50).Figures 8 and 9 present the flow velocity profiles, in a non-dimensional form, for two axial positions, with and without grids. The experimental data refer to measurements performed along the lines Y₁, Y₂ and Y₃, as shown in Fig.5.

Since the bundles are mounted over inlet nozzles, it can be observed, through these figures, a jet flow effect, at the bundle entrance, due to their presence. Nonetheless, it was also observed that this effect tends to disappear after approximately 40 test section hydraulic diameter. In the case of absence of grids, after the disappearance of the jet effect, it appears a slight peak in the velocity field. This effect is associated to the fact that the subchannels, in the intermediate region between the two bundles, have an area that is slightly larger than that of similar subchannels, since the distance between the rods are slightly larger to accommodate the barrier, whenever it is utilized. This fact, however, does not affect sensibly the results.

Yet, it can be observed that, for both cases, away from the walls, the ratio between the local and the average velocities remains around 1.1, which confirms the result given by Eq. (12).

In a non-dimensional form, it was observed that the Reynolds numbers do not affect the flow velocity profiles in a sensible way.

Case 2: Unbalanced flow - 33/67.Figure 10 presents the transversal distribution of the velocity for several axial levels. Observe that the presence of the grids tends to provoke faster flow velocity redistribution.

Considering the bundle average flow rates given by integration of the experimental results over the flow area, Fig. 11 shows its evolution along the test section length.

As can be seen, with the grids, the two parallel flows will gather together faster than without them. In fact, the presence of the grids provokes a larger static pressure difference between the two bundles, which will induce larger crossflow between them, as shown by Franco and Carajilescov (1993).

Case 3: Unbalanced flow - 0/100. Figures 12 and 13 present the results obtained for this case. Qualitatively, the results for this case are similar to the previous case. Quantitatively, however, this extreme case of unbalancing tends to yield more intense crossflow due to larger pressure differences between the two bundles.

Also, due to the inlet flow blocking of one of the bundles, it was observed the appearance of a strong flow recirculation, in the entrance region, not reported in this work. This recirculation, associated to velocity profile induced by the inlet nozzles, yields negative average flow rates, in the blocked bundle, and non-dimensional average flow rates above 2, in the other bundle, as can be inferred from Fig. 12, for values of z/L < 0.18. The presence of the grids tends to reduce the length of recirculation region.

Final Remarks

In the present work, the flow redistribution factors between the test section subchannels, along the bundle length and near the spacers, were obtained. It was also obtained the friction factors and grid drag coefficients for interior subchannels, typical of the open PWR fuel elements, as function of Reynolds numbers. Those coefficients are recommended for utilization in subchannel analysis codes, which represent the universally adopted design tools for thermalhydraulic analyses.

Beside this, this paper presents experimental results for the flow redistribution between the two rod bundles, showing the grid effect in this phenomenon, which is quite insensible to the flow Reynolds numbers. These results represent a very useful information to validate thermalhydraulic analysis codes for the design of reactors with strong core transversal flows.

Acknowledgements

The authors would like to thank the support from CTM/SP - Centro Tecnológico da Marinha em São Paulo, of Ministério da Marinha, and from MCT - Ministério de Ciência e Tecnologia, Brasil.

Manuscript received: August 1999. Technical Editor: Angela Ourívio Nieckele.

• Chelemer, H. et al., 1967, "Subchannel thermal analysis of rod bundle core", Report WCAP-7015, Rev. 1.
• Franco, C.B., 1992, "Determinação experimental da redistribuição axial do escoamento em feixes de varetas com forte componente transversal", Tese de Mestrado, IPEN/USP.
• Franco, C.B. e Carajilescov, P.,1993, "Análise experimental da redistribuição do escoamento em feixes de varetas", Anais do XII Congr.Bras.Eng. Mecânica - COBEM 93, Vol. II, Brasília (Dez.93), pp. 1121-1124.
• Gunn, D.J. and Darling, C.W.W.,1963, "Fluid flow and energy losses in non-circular conduits", Trans.Inst.Chem.Engrs., V.41, pp.163-173.
• Rowe, D.S., 1971, "COBRA-III: A digital computer program for steady state and transient thermal-hydraulic analysis of rod bundle fuel elements", Report BNWL-B-82, Battelle.
• Stewart, C.W. et al., 1977, "COBRA-IV: The model and the method", Report BNWL-2214, Battelle.
• Tong, L.S., 1967, "Heat transfer in water-cooled nuclear reactors", Nuclear Eng.Design, V.6, pp.301-318.

Publication Dates

• Publication in this collection
  04 Oct 2001
• Date of issue
  2000

History

• Received
  Aug 1999