## The Westinghouse-3 (W-3 or W3 or W 3) correlation for evaluation of critical heat flux (CHF)

Posted by Syeilendra Pramuditya on September 16, 2009

There are about 500 empirical correlations out there (o yeah the world is HUGE man! :mrgreen:) to predict the critical heat flux (CHF), one of the most widely used correlations is (was?) the Westinghouse-3 (W-3) correlation. For predicting the CHF condition in a non-uniform heat flux channel, we follow these two steps:

- The uniform critical heat flux is computed with the W-3 correlation
- The non-uniform critical heat flux distribution is then obtained by employing the so-called “
*F factor*“.

For uniformly heated channels, the critical heat flux is given by:

Where:

The axially non-uniform heat flux is obtained by applying a corrective F factor to the uniform critical heat flux:

Where:

The correlation is valid in the ranges:

Source: N.E. Todreas and Mujid S. Kazimi, *Nuclear Systems I – Thermal Hydraulic Fundamentals*, Hemisphere Publishing Corporation, New York (1990), page 558.

Useful links:

- Material from MIT [quickview]
- Material from NCSU [quickview]
- Material from Forschungszentrum Karlsruhe [quickview]

A variation of this W-3 correlation is the so-called W-3L correlation, which employs a correction factor to take into account the effect from grid spacer and/or mixing vane.

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## Nesko said

Is x_e local steam quality? How can it be negative? Shouldn’t it vary from 0 to 1. Please, explain.

Syeilendra said..Yes it is. x_e is expressed as:

where

h = enthalpy of the fluid

h_sat,l = saturation specific enthalpy of liquid

h_sat,g = saturation specific enthalpy of vapor

Negative x_e means that the flow is single phase, and its temperature is below the liquid saturation temperature, it is also called “subcooled” condition.

Check the book Nuclear Systems I page 142.

## Nesko said

Thank you for the answer. I have one more question.

There is a numerical example in material from MIT. In Figure 3., the steam quality versus fuel lenght is shown and in this figure, the quality is below -0.15. Shouldn’t W-3 correlation be invalid for qualities below -0.15? Can the correlation be valid for below -.15.

Using the quality expression above, I got enthalphy h= 1485.11 kJ/kg for x_e= -0.15. The temperature at this point is 325 C. With my reasoning, W-3 correlation can only be used above 325 C. Since Westinhouse PWR reactor work below this temperature, my reasoning is probably wrong. Could you, please, check this?

Syeilendra said..Well strictly speaking , yes according to the reference, the correlations is valid only for -0.15<x_e<+0.15. I think the MIT material just wanna show the general trend of the CHF along the heated channel. Generally we are interested in the prediction of CHF only around the local saturation point (which depends on local pressure), that's why the range of validity of CHF empirical correlations is usually not so wide.

Are you sure Westinghouse PWR works below 325 C? where did you find this data? because according to the (old) textbook Nuclear Reactor Analysis (Duderstadt & Hamilton) page 635, the (average) outlet temperature of PWR(W) is 332 C. And this is an average value, but the core also has radial power distribution, so outlet temperatures of some fuel assemblies are higher than 332 (where liquid saturation point at 155 bar is about 344 C), and some are lower. That's why when we do plant-wide safety analysis by using system codes, usually the core is represented by only 2 assemblies, one is 'average' assembly, and the other is 'hot' assembly. So somewhere in the core, local temperature higher than 325 exists, we call the highest one as the 'hot spot', so we care about CHF mainly at this hot spot in the hot assembly.

## Nesko said

Thank you for your help. Nuclear Systems I gives in Table 1-2 (pg. 5) for inlet temperature T= 286C and for average outlet temperature T= 324 C at P= 15.5 MPa. These data seem similar to ones in the numerical example of MIT material. Since average bulk temperature of coolant varies from 286 C to 324 C, W-3 correlation should not be used and was not used for heated channel, I think.

## Nesko said

Hello,

In the material from MIT, the range for heated diameter is from 15 mm to 18 mm. In the book Nuclear Systems I page 559, the range for heated diameter given in British units and it is from 0.2 in to 0.7 in. If we convert this to SI units, it should be 5.08 mm to 17.8 mm. In the book W-3 correlation is given in British units though. Do you know why that range changed because of unit conversion?

Syeilendra said..Hmm.. I think it’s time to check the original paper of the W3 correlation by Dr. Tong

## abhijit said

syelendra, i think you must be using this relationship all over in your research but it is found that w3 correlation is not sufficient in many cases.

Syeilendra said..Thanks for your comment. I used the correlation in my research a couple years ago. I was aware that this correlation is not really accurate, but unfortunately most of the more accurate and well-verified correlations are industrial proprietary of Westinghouse or GE or Areva, so I couldn’t use them. Of course Russian researchers also made good progresses in CHF researches and many correlations have been proposed in open literature, but I decided to just use the W3.

So which correlation do you use?

## saad said

I have doubt in expression of k2 in this formula. the term 3271 is too large as compared to all others. Please tell me weather its right or wrong.

Syeilendra said..The number is correct, as written in the book Nuclear Systems I page 558.

## saad said

syeilendra, while calculating quality will we take the value of enthalpy at that pressure or temperature?

Syeilendra said..You take the value of enthalpy at that temperature.