๐ Supersonic de Laval Nozzle & Shock Sizer
Size converging-diverging de Laval nozzles, identifying normal shock location inside diverging section, choked mass flow rate, exit Mach, and rocket thrust.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Cfd
๐ Solver Telemetry
โ ACTIVE
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30
โก Solves
26
๐พ Downloads
452
๐ฆ Fortran Code
4.4 KB
๐
Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ Supersonic de Laval Nozzle, Throat Choking (M = 1.0) & Normal Shock Position
Real-time visual simulation of converging-diverging geometry, sonic throat, moving normal shock & exhaust plume๐ Configuration & Presets
๐ Rocket Engine Sea-Level (30 bar)
๐จ Wind Tunnel Nozzle (6 bar)
โก Internal Normal Shock Wave
๐ Space Vacuum (Ae/At = 15)
de Laval Nozzle Formulations:
โข Area-Mach Relation: A/A* = (1/M) [ (2 + (ฮณโ1)Mยฒ) / (ฮณ+1) ](ฮณ+1)/2(ฮณโ1)
โข Choked Mass Flow: แน = [ Pโ At / โTโ ] ยท โ(ฮณ/R) ยท [ 2/(ฮณ+1) ](ฮณ+1)/2(ฮณโ1)
โข Thrust Force: F = แน Ve + (Pe โ Pb) Ae [N]
โข Thrust Coeff: CF = F / (Pโ At)
โข Area-Mach Relation: A/A* = (1/M) [ (2 + (ฮณโ1)Mยฒ) / (ฮณ+1) ](ฮณ+1)/2(ฮณโ1)
โข Choked Mass Flow: แน = [ Pโ At / โTโ ] ยท โ(ฮณ/R) ยท [ 2/(ฮณ+1) ](ฮณ+1)/2(ฮณโ1)
โข Thrust Force: F = แน Ve + (Pe โ Pb) Ae [N]
โข Thrust Coeff: CF = F / (Pโ At)
๐ Supersonic Nozzle Results
Configure inputs and click Compute to view results.
๐ Calculation Methodology & de Laval Rocket Standards
Isentropic Area-Mach Relation
Flow reaches Mach 1 at the minimum throat area. Diverging geometry allows supersonic acceleration governed by:
A/A* = (1/M) [ (2 + (ฮณโ1)Mยฒ) / (ฮณ+1) ](ฮณ+1)/2(ฮณโ1)
Back Pressure Shock Regimes
When back pressure $P_b > P_{design}$, a normal shock wave moves upstream into the diverging cone to adapt pressure, causing boundary layer separation and thrust loss.
Key Engineering Assumptions
- 1D isentropic core flow with normal shock discontinuity.
- Calorically perfect gas with constant $\gamma$ and $R$.
- Choked throat condition ($P_0 / P_b > 1.89$).