What Is the Chapman-Jouguet Detonation Velocity Calculator?
The Chapman-Jouguet condition defines the self-sustaining velocity of supersonic detonation waves.
How Does the Chapman-Jouguet Detonation Velocity Calculator Work?
Combustion is driven by a leading shock wave that adiabatically compresses reactants to autoignition.
Chapman-Jouguet Detonation Velocity Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
D_{CJ} = c_1 \left[ \sqrt{1 + \frac{(\gamma^2 - 1)q}{\gamma R T_1}} + \sqrt{\frac{(\gamma^2 - 1)q}{\gamma R T_1}} \right], \quad \frac{P_{CJ}}{P_1} = \frac{1 + \gamma M_{CJ}^2}{\gamma + 1}
Chapman-Jouguet detonation velocity and peak CJ overpressure condition.
How to Use the Chapman-Jouguet Detonation Velocity Calculator
- Input heat of reaction, initial temperature, gamma, and gas constant.
Step-by-Step Example Calculation
Hydrogen-Oxygen Stoichiometric Detonation
Input Values:
heatOfReactionQJPerKg:3500000
initialTemperatureK:298.15
specificHeatRatioGamma:1.3
gasConstantR:287
Worked Steps: Predicts CJ detonation speed ~2.2 km/s and peak overpressure ratio ~18:1.
Understanding Your Result
Provides CJ detonation velocity in km/s, Mach number, and overpressure ratio.
Factors That Affect the Result
- Higher heat of reaction q increases detonation velocity with a square-root dependency.
When Should You Use This Calculator?
- Rotating detonation engines (RDE), pulsed detonation engines (PDE), and explosion safety.
Assumptions & Limitations
- Assumes 1D steady planar detonation with complete instantaneous heat release.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard classical formulation matching Rankine-Hugoniot Rayleigh line tangency.