Pool Fire Radiation (Shokri & Beyler)Heat flux to a vertical target at ground level

What this calculates

This is a simplified equation to predict heat flux due to radiation from a circular pool fire at a point on the ground some distance away.

An optional section has also been added that can be used to calculate the equivalent diameter of a square pool fire (at the bottom).

How to use it

First determine whether the pool fire is a circle, or more square. If it is a circle, put the diameter of the pool fire in the yellow cell next to “D”. If the pool fire is a square (or close to square), put the length of the edges in cells yellow cells in the equivalent diameter section, then use the resulting equivalent diameter as your “diameter of pool” in the above portion of the Shokri Beyler Pool Fire calculation.

Enter the distance from the center of the pool to the edge of the target in in the yellow cell next to “L”.

The resulting radiant heat flux from the pool fire to the target will be displayed in the “q” cell.

A check against the validity of the equation (see discussion of L/D) below is provided in the last cell of the top portion. If the distance of the target is very close to the pool edge the heat flux will be under-predicted, this will say “Too close to pool edge”. If the target is too far from the pool edge, the heat flux will be outside the parameters of the testing that developed the equation and it will say “Too far from pool edge”. If it is within the valid range of this equation it will say “OK”.

Variables

q″: Heat flux received by target [kW/m²]
L: Distance from pool center to target edge [m]
D: Diameter of pool fire [m]
A: Area of (square) pool fire — optional [m²]

Equations

$$ q = 15.4 \, \left( rac{L}{D} ight)^{-1.59} \quad [kW/m^2] $$Shokri–Beyler heat flux (SFPE eq. 1)

$$ D_{eq} = \sqrt{ \dfrac{4 \, A}{\pi} } $$Equivalent diameter for a square pool (SFPE eq. 2)

Discussion

This equation assumes that the target is vertical and located at ground level (a person standing on the ground, not a person in the third-floor window of the building next door). The equation is valid for pool fires with diameters from 1 to 50 meters.

The equation is valid for values of L/D between 0.7 and 15. If L/D is less than 0.7 the heat flux to the target will be under-predicted.

Notice that this equation does not require a heat release rate as input.

Worked example

Example 1

A (circular) pool fire has a 3’ diameter. A person is standing 10 feet from the center of the pool. What is the radiant heat flux from the pool fire to the person?

Enter the diameter of 3’ and the distance of 10’. The heat flux to the target is 2.3 kW/m^2. Looking at the last cell in this section we see that this set of data is valid for this equation.

Example 2:

A square-shaped fire has a width of 3’. A person is standing 10 feet from the center of the pool. What is the radiant heat flux from the pool fire to the person?

Enter the width of the square pool in the bottom section, then put the resulting equivalent diameter of 3.39’ into the pool diameter entry in the top section; enter the distance of 10’. The heat flux to the target is 2.8 kW/m^2. We see that this set of data is valid for this equation.

Example 3

A (circular) pool fire has a 3’ diameter. A person is standing 1.6 feet from the center of the pool. What is the radiant heat flux from the pool fire to the person?

Enter the diameter of 3’ and the distance of 10’. The heat flux to the target (cell D13) is ~42 kW/m^2. We see that this set of data is not valid for this equation, because the target is too close to the pool edge. In reality, the heat flux to the target should be higher.

References

SFPE Engineering Guide — Assessing Flame Radiation to External Targets from Pool Fires, Society of Fire Protection Engineers, June 1999. Equations (1) and (2).