The Cheng-Todreas Correlations for Bundle and Subchannel Friction Factors

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The Cheng-Todreas Correlations

for Bundle and Subchannel Friction Factors

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CONTENT

CONTENT...........................................................................................................................................3

1. INTRODUCTION........................................................................................................................4

2. THE CORRELATIONS EMPLOYED IN ONE-DIMENSIONAL SYSTEM CODES..............4

2.1. Simplified correlations.........................................................................................................4

2.2. Detailed correlations.............................................................................................................6

3. THE CORRELATIONS EMPLOYED IN SUBCHANNEL ANALYSIS CODES..................11

4. ACCURACY AND RANGES OF APPLICABILITY..............................................................15

5. REFERENCE.............................................................................................................................16

6. APPENDIX................................................................................................................................16

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1. INTRODUCTION

This paper briefly describes the Cheng-Todreas correlations for friction factor. These correlations

are probably the most widely used today, yet the most complicated friction factor model in

existence on literatures.

Friction pressure drop is calculated as follow:

Eq. 1

Cheng-Todreas correlations are used to evaluate that . The correlations are basically can be

used in two types of codes: one-dimensional system (plant-wide) codes, and subchannel analysis

codes.

2. THE CORRELATIONS EMPLOYED IN ONE-DIMENSIONAL SYSTEM CODES

2.1. Simplified correlations

Basically the Cheng-Todreas correlations can be divided into two parts: the simplified one, and the

detailed one. This section presents the simplified one. When the correlations are implemented in a

1D system code, we need to calculate “bundle friction factor”, in contrast to “subchannel friction

factors” we will discuss later.

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When used in a system code, the correlations require the following data as inputs:

Pin pitch

Pin diameter

Wire spacer lead

Bundle-averaged Reynolds number

Calculate flow regime boundaries for our rod bundle by the following formulas:

Laminar-transition boundary:

Eq. 2

Transition-turbulent boundary:

Eq. 3

If the flow in our rod bundle is laminar , calculate the bundle friction factor as follow:

Eq. 4

Eq. 5

If the flow in our rod bundle is turbulent , calculate the bundle friction factor as

follow:

Eq. 6

Eq. 7

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If the flow in our rod bundle is in transition region , calculate friction factor for

both laminar and turbulent regimes by using Eq. 4 to Eq. 7, and then calculate the bundle friction

factor as follow:

Eq. 8

Eq. 9

2.2. Detailed correlations

To use the detailed correlations, we need the following input data:

Pin diameter

Pin pitch

Edge pitch

Wire spacer lead

Wire spacer diameter


Number of interior, edge, and corner subchannels

Some typical subchannel definition and key geometrical parameters for a wire-wrapped LMFBR

assembly are shown as follow:

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Figure 1. Subchannel geometrical definition (courtesy of www.scielo.br)

Calculate the bare rod constants for each subchannel type, both for laminar and turbulent

flow regimes:

Eq. 10

Where is replaced by for edge and corner subchannels. The constants

depend on subchannel type, flow regime and , as shown in the following table:

Table 1. Constants for bare rod bundle

Flow regime Subchannel type

Laminar Interior 26.00 888.2 -3334 62.97 216.9 -190.2

Edge 26.18 554.5 -1480 44.40 256.7 -267.6

Corner 26.98 1636.0 -10050 87.26 38.59 -55.12

Turbulent Interior 0.09378 1.398 -8.664 0.1458 0.03632 -0.03333

Edge 0.09377 0.8732 -3.341 0.1430 0.04199 -0.04428

Corner 0.10040 1.625 -11.850 0.1499 0.006706 -0.009567

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Calculate wire drag and wire sweep constants :

Turbulent region

Interior subchannel:

Eq. 11

Edge subchannel:

Eq. 12

Corner subchannel:

Eq. 13

Laminar region

Eq. 14

Eq. 15

Then calculate the wire-wrapped rod constants, also both for laminar and turbulent

flow regimes:

Eq. 16

Eq. 17

Eq. 18

Calculate flow split parameters for both laminar and turbulent flow regimes:

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Eq. 19

Eq. 20

Eq. 21

Eq. 22

Calculate flow split parameters for transition flow regime:

Eq. 23

Eq. 24

Eq. 25

Calculate Reynolds number of each subchannel type:

Eq. 26

Calculate bundle flow regime boundaries :

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Eq. 27


Eq. 28

Calculate subchannel flow regime boundaries :

Eq. 29

Eq. 30

The flow regime in all subchannels is determined based on bundle-average flow regime:

Condition Flow

regime

Laminar

Transition

Turbulent

Then subchannel friction factors are calculated as follow:


Eq. 31

Edge subchannel:

Eq. 32

Corner subchannel:

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Eq. 33

For transition flow, we must calculate the friction factors for both laminar and turbulent regimes,

and then use the intermittency factor to obtain the transition friction factor:

Eq. 34

Eq. 35

The bundle friction factor is then calculated as follow:

Eq. 36

Eq. 37

In which the formulas to calculate all geometric parameters are described on appendix part at the

end of this paper.

3. THE CORRELATIONS EMPLOYED IN SUBCHANNEL ANALYSIS CODES

When used in a system code, the correlations require the following data as inputs:

Pin pitch

Pin diameter

Wire spacer lead

Wire spacer diameter


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Subchannel Reynolds number

Flow split parameter

Note that subchannel Reynolds number and flow split parameter are obtained from fluid dynamics

solution, and the bundle-averaged Reynolds number is obtained by averaging the Reynolds number

in all subchannels over the entire bundle.

Calculate the bare rod constants for each subchannel type, both for laminar and turbulent

flow regimes:

Eq. 38

Where is replaced by for edge and corner subchannels. The constants

depend on subchannel type, flow regime and , as shown in the following table:

Table 2. Constants for bare rod bundle

Flow regime Subchannel type

Laminar Interior 26.00 888.2 -3334 62.97 216.9 -190.2

Edge 26.18 554.5 -1480 44.40 256.7 -267.6

Corner 26.98 1636.0 -10050 87.26 38.59 -55.12

Turbulent Interior 0.09378 1.398 -8.664 0.1458 0.03632 -0.03333

Edge 0.09377 0.8732 -3.341 0.1430 0.04199 -0.04428

Corner 0.10040 1.625 -11.850 0.1499 0.006706 -0.009567

Calculate wire drag and wire sweep constants :

Turbulent region

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Eq. 39

Edge subchannel:

Eq. 40

Corner subchannel:

Eq. 41

Laminar region

Eq. 42

Eq. 43

Then calculate the wire-wrapped rod constants, also both for laminar and turbulent

flow regimes:

Eq. 44

Eq. 45

Eq. 46

Calculate bundle flow regime boundaries :


Eq. 47

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Eq. 48

Flow split parameter is available from fluid dynamics solution, that is:

Eq. 49

Eq. 50

Then we can directly calculate subchannel flow regime boundaries :

Eq. 51

Eq. 52

Reynolds number in each subchannel is also available from fluid dynamics solution, and then flow

regime in each subchannel type is determined as follow:

Condition Flow

regime

Laminar

Transition

Turbulent

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Then depending flow regime in each subchannel type, calculate subchannel friction factor as

follow:


Eq. 53

Edge subchannel:

Eq. 54

Corner subchannel:

Eq. 55

For transition flow, we must calculate the friction factors for both laminar and turbulent regimes,

and then use the intermittency factor to obtain the transition friction factor:

Eq. 56

Eq. 57

4. ACCURACY AND RANGES OF APPLICABILITY

The correlations can predict the bundle-average friction factor data within at least ±14% with a 92%

confidence interval for turbulent flow and within ±30% for laminar flow and all flow split data

within ±5% in the following ranges:

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(detailed model)

(simplified model)

5. REFERENCE

1. Shih-Kuei Cheng, Neil E. Todreas, Hydrodynamic models and correlations for bare and

wire-wrapped hexagonal rod bundles -- Bundle friction factors, subchannel friction factors

and mixing parameters, Nuclear Engineering and Design, Volume 92, Issue 2, 1 April 1986,

Pages 227-251, ISSN 0029-5493, DOI: 10.1016/0029-5493(86)90249-9. (

http://dx.doi.org/10.1016/0029-5493(86)90249-9 )

6. APPENDIX

Equations for geometrical parameters

Bare rod flow area and wetted perimeter

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http://dx.doi.org/10.1016/0029-5493(86)90249-9


Wire-wrapped flow area and wetted perimeter

Wire projected area

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Equivalent hydraulic diameter

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The Cheng-Todreas Correlations for Bundle and Subchannel Friction Factors

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