Using Detect3D's Inverse Square Law Calculator

Open the Tutorial 4.d3d from the Detect3D Tutorials.zip (22MB) before continuing.

 

What is the power of the 1ft x 1ft pool fire?

The difficulty in using this method is knowing what the Power 1 value should be. In the past, it had been common practice that the 1ft x 1ft n-heptane fire used for testing detectors resulted in a 10kW radiant heat output (RHO). However there is little documentation to support this value. In more recent years, with the increased awareness and popularity of F&G mapping, the value has come into question, with many supporting values closer to 40kW:

  • BP’s GP 30-85 (2009 version) references their older standard using a 10kW size but then states “...other sources say this (1ft x 1ft n-heptane fire) should be 40kW” 1 It should also be noted that this note from an older version of BP's GP (pre 2009) mentions use of a 70kW RHO value for the FM3260 test data but does not give any other reference to this value.

  • “When using the inverse square law, 37.5kW to 40kW may be used as the basis for the 1ft2 n-heptane fire used to test flame detector FOVs”2,3

 

However, it is up to the user to determine which value is best for their project for the Power 1 value.

 

Using the Inverse Square Tool, Detect3D can calculate the corresponding FOV ranges for varying fire powers. Three values are needed as inputs:

  • Range - the maximum range of the detector, this is generally the value from the manufacturer

  • Power 1 - the RHO value of the fire used when determining the Range 1 distance

  • Power 2 - the RHO value of the fire which you want the analysis performed

Inverse Square Law Tool

The below steps will go over using the Inverse Square Law Calculators, direct method, to determine the FOV Multiplier value needed for a 100kW fire when there is data for a 40kW fire. The Heskestad Method is described at the bottom of this page.

  1.  From the Project Menu, select the Inverse Square Law Tool

  2. The below window should appear. Set the Method as Direct for both Fire 1 and Fire 2.

     

    Detect3D_Fire_and_Gas_Mapping_Inverse_Square_Law_Tool_Flame_Detection

    Tutorial 7 - Figure 5 - Inverse Square Law Calculator Window

     

  3. Enter a value of "40kW" as the Power of Fire 1. This is the estimated power of the fire used when determining the maximum range of the detector.

  4. Set the Power of Fire 2 to "100kW". Notice that the FOV Multiplier Value changes to 1.58 and will remain the same regardless of the distance entered in the Range textbox of Fire 1. This is because of the inverse square law relationship where the ratio of the powers (P1 and P2 below) will remain the same regardless of the squared ranges (D1 and D2).

     

    Tutorial 7 - Figure 6 - Equation of the relationship between the two power values and two detector distances

     

  5. Enter a value of "30 meters" as the Range for Fire 1 and see that the Fire 2 Range value is then calculated as 47.43 meters and doesn't change the FOV Multiplier value.

  6. The calculated FOV Multiplier can then be applied to an already defined risk grade in the project. Select Grade A and click the button to set the FOV Multiplier for Grade A as 1.58.

  7. In the Project Items Tab select Grade A to open the properties panel, and check to ensure that the new value was entered, shown below.

     

    Tutorial 7 - Figure 7 - Grade A properties showing the updated FOV multiplier

     

  8. Change the Name of the risk grade to "Grade A - 100kW" and click off the panel to verify the entered text.

     

     

Repeat Steps 1 to 7 to calculate the FOV Multiplier for a 10kW fire when the Power of Fire 1 is 40kW. Apply this value to Grade B and change the name accordingly.

 

Your window should be similar to the below.

 

Tutorial 7 - Figure 7 - Renamed Grade A and Grade B with FOV Multipliers added

 

 

Continue to the next section to view the updated coverage results.

 

Heskestad Method

With version 2.61 of Detect3D an additional option was provided for determing power of fires - the Heskestad Method. With this method, rather than entering power value, a flame width and flame height may be entered for a power value to be calculated. The underlining equation of the Heskestad correlation is below, where L is the flame length, D is the flame diameter and Qdot the heat release rate. 

 

The below shows and example of the Inverse Square Law Calculator using the Heskestad method for determining the power of Fire 1. Either method can be selected for Fire 1 and Fire 2. 

 

 

Footnotes:

  1. BP GP30-85 (2009) Appendix C.3

  2. SFPE Handbook, section 2

  3. Cozzani  V.,  Tugnoli  A.,  Bonvicini  S.,  Salzano  E.,  2013,  9  -Threshold-Based  Approach,  189-207,  2013, Domino Effects in the Process Industries, Eds. Reniers G., Cozzani V., Elsevier, Waltham, MA, USA

  4. Mariotti (2014) paper which references Cozzani (2013) https://www.aidic.it/cet/14/36/048.pdf