🚀 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.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

Supersonic de Laval Nozzle & Shock Sizer

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📊 Solver Telemetry ● ACTIVE

👁️ Views 30

⚡ Solves 26

💾 Downloads 452 📦 Fortran Code 4.4 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

🚀 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 plume

📝 Configuration & Presets

🚀 Rocket Engine Sea-Level (30 bar) 💨 Wind Tunnel Nozzle (6 bar) ⚡ Internal Normal Shock Wave 🌌 Space Vacuum (Ae/At = 15)

📐 Nozzle Geometry

Throat Diameter D_t [mm]:

Exit Area Ratio A_e / A_t:

Diverging Section Length [mm]:

Specific Heat Ratio γ: Air: 1.40, Rocket Gas: 1.20–1.30

🚀 Stagnation & Ambient Pressures

Chamber Total Pressure P₀ [bar]:

Chamber Total Temp T₀ [K]:

Ambient Back Pressure P_b [bar]: Sea level: 1.013 bar, Vacuum: ~0.01 bar

de Laval Nozzle Formulations:
• Area-Mach Relation: A/A* = (1/M) [ (2 + (γ−1)M²) / (γ+1) ]^{(γ+1)/2(γ−1)}
• Choked Mass Flow: ṁ = [ P₀ A_t / √T₀ ] · √(γ/R) · [ 2/(γ+1) ]^{(γ+1)/2(γ−1)}
• Thrust Force: F = ṁ V_e + (P_e − P_b) A_e [N]
• Thrust Coeff: C_F = F / (P₀ A_t)

📊 Supersonic Nozzle Results

📊 Output Summary
💾 Fortran Source

Thrust Force & Flow Regime

F = 12,287 N (C_F = 1.449)

Regime: Under-Expanded (Exit Expansion Waves)

M_e,des = 2.51

Design Exit Mach (M_e) 2.510 Design P_e = 1.645 bar

Choked Mass Flow Rate (ṁ) 7.765 kg/s Sonic throat condition

Normal Shock Position At Exit / Outside In diverging cone

Throat & Exit Area 28.3 cm² A_e = 90.5 cm²

📈 Design Mach Number M(x) along Diverging Length (%)

📉 Design Static Pressure P(x) [bar] vs Length (%)

=================================================================
 THERMOFLUIDCALC — SUPERSONIC DE LAVAL NOZZLE REPORT
=================================================================
Case Title                 : Liquid Rocket Engine Sea-Level Static Hot Firing
Nozzle Geometry            : Throat Dt = 60.00 mm, Area Ratio Ae/At = 3.20, Length = 220.0 mm
Operating Pressures        : Chamber P0 = 30.00 bar, Back Pb = 1.013 bar, T0 = 1800.0 K
-----------------------------------------------------------------
NOZZLE FLOW REGIME         : Under-Expanded (Exit Expansion Waves)
Design Exit Mach (Me)      : 2.5098
Design Exit Pressure (Pe)  : 1.6445 bar
Choked Mass Flow Rate      : 7.7655 kg/s
Thrust Force & Coeff CF    : 12287.0 N (CF = 1.4485)
Critical Limit Pressures   : P_crit1 = 29.349 bar, P_crit2 = 11.327 bar
=================================================================

📘 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 + (γ−1)M²) / (γ+1) ](γ+1)/2(γ−1)
                

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 ($P_0 / P_b > 1.89$).

ThermoFluidCalc Engineering Report