What Is the Rankine-Hugoniot Reactive Shock Jump Conditions Calculator?
The Rankine-Hugoniot equations govern conservation across discontinuous shock and deflagration fronts.
How Does the Rankine-Hugoniot Reactive Shock Jump Conditions Calculator Work?
Mass, momentum, and energy balances determine downstream state variables given the pressure ratio.
Rankine-Hugoniot Reactive Shock Jump Conditions Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
\frac{\rho_2}{\rho_1} = \frac{\frac{\gamma + 1}{\gamma - 1}\frac{P_2}{P_1} + 1}{\frac{P_2}{P_1} + \frac{\gamma + 1}{\gamma - 1} - \frac{2 q \rho_1 (\gamma - 1)}{P_1 (\gamma + 1)}}
Reactive Rankine-Hugoniot density ratio relation with exothermic heat addition.
How to Use the Rankine-Hugoniot Reactive Shock Jump Conditions Calculator
- Input initial pressure, density, target pressure ratio, gamma, and heat release.
Step-by-Step Example Calculation
Reactive Shock Front
Input Values:
initialPressurePa:101325
initialDensityKgPerM3:1.2
pressureRatioP2OverP1:15
specificHeatRatioGamma:1.4
heatReleaseQJPerKg:100000
Worked Steps: Evaluates shocked downstream density ratio ~4.26 and downstream pressure ~1.52 MPa.
Understanding Your Result
Gives final pressure, downstream density, and gas temperature increase ratio.
Factors That Affect the Result
- Higher pressure ratios compress gas toward the asymptotic limit (gamma+1)/(gamma-1).
When Should You Use This Calculator?
- Explosion safety, supersonic combustors, and hypervelocity impact shock analysis.
Assumptions & Limitations
- Ideal gas law with constant specific heat ratio gamma across the discontinuity.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard gas dynamics formulation verified in high-energy physics literature.