What Is the Scramjet Isolator Shock Train Length Calculator?
A scramjet isolator contains a pseudo-shock system that buffers the inlet against intense combustor heat-release backpressure.
How Does the Scramjet Isolator Shock Train Length Calculator Work?
Adverse pressure gradients propagate upstream through the turbulent boundary layer, creating a series of bifurcated oblique and normal shocks.
Scramjet Isolator Shock Train Length Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
rac{S}{H} = rac{1}{sqrt{M_1^2 - 1}} (Re_ heta)^{0.25} left[ 0.5left( rac{P_2}{P_1} - 1
ight) + 1.69left( rac{P_2}{P_1} - 1
ight)^2
ight]
Waltrup and Billig empirical correlation for pseudo-shock train length in constant-area isolator ducts.
How to Use the Scramjet Isolator Shock Train Length Calculator
- Input isolator inlet Mach number, duct height, boundary layer Re_theta, and expected combustion pressure ratio.
Step-by-Step Example Calculation
Mach 6 Hypersonic Vehicle Isolator
Input Values:
inletMach:2.2
ductHeightM:0.06
boundaryLayerReTheta:4500
pressureRatioP2P1:2.8
Worked Steps: Shock train length S = 1.15 m (~19 duct heights), recommended isolator length = 1.50 m.
Understanding Your Result
Displays the shock train length S and recommended safe isolator duct length including a 30% margin against inlet unstart.
Factors That Affect the Result
- Higher combustor pressure rise quadratically lengthens the required shock train.
When Should You Use This Calculator?
- Designing dual-mode scramjet flowpaths, hypersonic cruise missile engines, and reusable launch vehicles.
Assumptions & Limitations
- Applies to rectangular and circular constant-area isolators with turbulent boundary layers.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Empirical Waltrup-Billig formulation with industry standard unstart margins.