Enter the thermal diffusivity and a characteristic reaction rate into the calculator to estimate the flame speed using a simplified scaling relationship.

Flame Speed Calculator

Enter any 2 values to calculate the missing variable





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Flame Speed Formula

This page uses a simplified scaling estimate (order-of-magnitude) for flame speed based on thermal diffusion and a characteristic chemical time scale:

S_f \approx \sqrt{\alpha \cdot R}

Variables:

  • Sf is the (estimated) flame speed
  • α is the thermal diffusivity (m²/s)
  • R is an effective reaction rate (1/s), often treated as the inverse of a characteristic chemical time scale (τc ≈ 1/R)

To estimate the flame speed, multiply the thermal diffusivity by the effective reaction rate and take the square root.

What is Flame Speed?

Flame speed is the rate at which a flame front propagates through a combustible gas mixture. It is a critical parameter in combustion processes, influencing the efficiency and stability of combustion systems. Flame speed depends on various factors, including the type of fuel, the mixture ratio, temperature, pressure, and the presence of diluents or inhibitors. Understanding flame speed is essential for designing and optimizing combustion systems, such as engines, burners, and industrial furnaces, to ensure safe and efficient operation.

How to Calculate Flame Speed?

The following steps outline how to estimate the Flame Speed using the simplified relationship shown above.

  1. First, determine the thermal diffusivity (α).
  2. Next, determine an effective reaction rate (R) (often approximated as 1/τc).
  3. Finally, estimate the Flame Speed using the formula (Sf ≈ √(α · R)).
  4. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Thermal Diffusivity (α) = 0.0001 m²/s

Reaction Rate (R) = 10 1/s

Estimated Flame Speed (Sf) ≈ √(0.0001 × 10) = √(0.001) ≈ 0.0316 m/s