Impinging Jet Heat Transfer Model

[Er9y714]

Impinging Jet Heat Transfer Model is intended to overcome the not-well resolved velocity area, including below ceiling, above fire. Although this is more significant for heat transfer to the boundaries (e.g. walls), it is also relevant for the sprinklers.

I have looked at the validation experiments but I have not found many examples in which sprinkler is directly located above the fire. However, in specific cases this may be interesting for the sprinkler activation time.

Has this feature been considered as a setting option for sprinkler setups as well? Or was it ignored for sprinkler applications?

Thanks.

[mcgratta]

The special heat transfer coefficient for an impinging jet is a relatively new feature, and we have not gone back to look at the older validation cases involving sprinklers. It may be difficult to assess the effect of the boundary condition for these large-scale warehouse experiments. It might be better to look at a simple test case and do a sensitivity study.

[Er9y714]

Interesting take. I had not thought about the effect of the ceiling wall on the sprinkler. I had initially thought of the velocity component on the link temperature (or heat detector) equation in the impingement zone where velocity is near zero.

Maybe it is easier to start with looking at the velocity at the impinging zone in varying D*/dx ratios. Then I can compare them with Alpert's ceiling jet velocity. I will report back.

[johodges]

My expectation would be that a sprinkler near the ceiling would have a higher heat transfer coefficient than the ceiling due to the smaller length scale. However, I have not done analysis to back that up. We do not typically look at the sprinkler directly above the fire in fire protection design as the fire between sprinklers is usually more hazardous. But this is an interesting question.

There are a few convection correlations that have been targeted to a fire impinging on a ceiling, for example this one by Cooper. These targeted correlations usually calculate Reynolds number based on the separation distance from the base of the fire to the ceiling. It would be interesting to see how well these agree with the convection to a sprinkler.

[1] L.Y. Cooper, Heat Transfer From a Buoyant Plume to an Unconfined Ceiling, Journal of Heat Transfer 104 (1982) 446–451. https://doi.org/10.1115/1.3245113.

[mcgratta]

I think we need to think of a fire plume meandering to and fro across the ceiling such that the velocity near the center point and/or the sprinkler itself is not going to be zero. That is why it might be hard to isolate the effect of the heat transfer correlation or the velocity near the sprinkler.

[Er9y714]

Regarding @mcgratta's meandering flame concern, @johodges, do you remember such a fluctuation in Wasson cases during "Convective Heat Transfer from Impinging Flames" study? Would it be a suitable setup?

[johodges]

A few thoughts while you are looking at this. The Wasson experiments had a wire mesh around the system to try and reduce the ambient laboratory effects. However, we found that introducing a slight wind bias in the model better agreed with the experimental measurements when modeling these cases. From what I have seen in experiments it is quite difficult to have a perfectly symmetric plume.

This is particularly challenging when you are looking at heat fluxes at the stagnation point, because you are assuming that the measurement was achieved at the stagnation point. The data on which Alpert's ceiling jet correlations were developed were collected in a pressure vessel in part to minimize these effects [2]. These experiments also intentionally used a nonluminous fuel and gold plated heat flux gauges to minimize the radiation effects. It is unclear how similar a higher radiative fraction fuel may affect the relationship, although correlations typically assume it is negligible and are based on solely the convective heat release rate. It is also unclear to me whether there is systematic bias in the heat flux measurements in this study. The authors used Gardon gauges which have known issues with convection measurements [3]. Alpert has a more recent study where he discusses the interaction of water droplets with the plume [4]. I have not reviewed this in detail, but it may be useful for your analysis.

Unfortunately, I do not think any of those references are going to address Kevin's point on the intermittence of the flame. You may be able to gather insights in this direction by looking at the intermittence of the flame and puffing frequency. There has been a lot of work in that area by several research groups which are summarized well in Drysdale's textbook [5]. There may be some data out there on RMS variability in temperature and velocity in these studies looking at intermittence which could help answer Kevin's question.

[2] R.L. Alpert, Convective Heat Transfer in the Impingement Region of a Buoyant Plume, Journal of Heat Transfer 109 (1987) 120–124. https://doi.org/10.1115/1.3248031.
[3] E21 Committee, Test Method for Measuring Heat Flux Using a Copper-Constantan Circular Foil, Heat-Flux Transducer, (2020). https://doi.org/10.1520/E0511-07R20.
[4] R.L. Alpert, The Fire-Induced Ceiling-Jet Revisited, (2011). The Science of Suppression, Proceedings of Fireseat (2011): 1-21.
[5] D. Drysdale, Diffusion Flames and Fire Plumes, in: An Introduction to Fire Dynamics, 3rd ed., Wiley, 2011.

[Er9y714]

I have run the wasson_test1_12mm validation case to look at velocities under the ceiling without any change on the inputs.
Below is a slice file of velocity below ceiling (adjacent cell). (120 second averaged)
The plot is velocity of the devices under the ceiling. (steady-state transient averaged)

The lowest velocity at the center is much higher than I assumed (might be due to fine resolution). The low velocity area is limited to less than 20 cm radius.
I also overlapped Alpert's velocity correlation. (Q=50 kW, H= 0.975 m)