🌊 Turbulent Free Jet & Impingement Force

Compute turbulent submerged free jet expansion, potential core length, Schlichting self-similar velocity profile, ambient fluid entrainment, and dynamic impact thrust on target plates.

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

Fluid Mechanics

📊 Solver Telemetry ● ACTIVE

👁️ Views 42

⚡ Solves 36

💾 Downloads 357 📦 Fortran Code 4.5 KB

📅 Released Aug 2026

⏱️ Latency < 1 ms

🌊 Free Jet Spreading, Potential Core & Target Impingement

Real-time velocity field & target deflection physics

📝 Configuration & Presets

💧 HP Waterjet (400 bar) 🏢 HVAC Air Diffuser 🚒 Fire Deluge Monitor ⚡ Pelton Turbine Vane

📐 Nozzle Geometry & Flow Conditions

Nozzle Diameter D₀ [mm]:

Initial Jet Velocity U₀ [m/s]:

💧 Fluid Properties

Fluid Density ρ [kg/m³]:

Dynamic Viscosity μ [Pa·s]:

🎯 Target Surface & Distance

Distance to Target X [mm]:

Target Geometry:

Key Formulations:
• Potential Core: L_core ≈ 5.5 · D₀
• Axial Decay: u_max(x) / U₀ = 5.8 / (x / D₀)
• Spread Radius: r_1/2(x) = 0.097 · x
• Stagnation Pressure: q_stag = ½ ρ u_max(X)²
• Impact Force: F = ṁ U₀ (flat 90°) or 2 ṁ U₀ (180° Pelton)

📊 Simulation Results

📊 Output Summary
💾 Fortran Source

Normal Impact Reaction Force 25340.89 N Nozzle Thrust F₀ = 13337.31 N

Target Centerline Velocity (u_max) 75.00 m/s u_max/U₀ = 1.000

Stagnation Impact Pressure 2806.88 kPa 28.069 bar

Jet Half-Width Radius (r_1/2) 27.5 mm Entrainment Q(X)/Q₀ = 1.00x

📈 Axial Centerline Velocity Decay u_max(x)

📉 Schlichting Radial Velocity Profile at Target X

=================================================================
 THERMOFLUIDCALC — TURBULENT FREE JET & IMPINGEMENT REPORT
=================================================================
Case Title                 : Hydroelectric Pelton Turbine Jet Impingement
Nozzle Exit Diameter (D0)  : 55.00 mm (5.5000e-2 m)
Initial Jet Velocity (U0)  : 75.00 m/s
Exit Reynolds Number (Re0) : 4.109e+6
Mass Flow Rate (mdot)      : 1.7783e+2 kg/s (10691.23 L/min)
-----------------------------------------------------------------
Potential Core Length      : 302.50 mm (5.5 x D0)
Target Distance (X)        : 250.00 mm (4.5 x D0)
Centerline Velocity at X   : 75.00 m/s (100.0 % of U0)
Jet Half-Width Spread r1/2 : 27.50 mm
Fluid Entrainment Factor   : 1.00 x initial flow
-----------------------------------------------------------------
Stagnation Dynamic Press.  : 2806.88 kPa (28.069 bar)
Nozzle Reaction Thrust F0  : 13337.31 N
Target Impact Force        : 25340.89 N
Target Geometry Selected   : pelton-180
=================================================================

📘 Calculation Methodology & Engineering Theory

Submerged Turbulent Jet Structure

A turbulent jet issuing into a stagnant ambient fluid experiences strong shear-layer mixing, developing three distinct hydrodynamic zones:

Potential Core ($x \le 5.5 D_0$): Wedge-shaped inner core where fluid velocity remains equal to initial exit speed $U_0$.
Transition Zone ($5.5 D_0 < x < 8 D_0$): Core decay and turbulence saturation.
Fully Developed Similarity Zone ($x \ge 8 D_0$): Centerline velocity decays inversely with distance: $$\frac{u_{max}(x)}{U_0} \approx \frac{5.8}{x / D_0}$$

Schlichting Self-Similar Profile

In the similarity region, radial velocity profiles normalized by centerline velocity and half-width $r_{1/2}(x)$ collapse onto a single universal curve:

                    u(x, r) / umax(x) = [1 + 0.414 (r / r1/2)²]−2
                

Impact Force & Momentum Conservation

Applying the control-volume momentum theorem to target impingement:

Flat Plate ($90^\circ$ deflection): $F_N = \dot{m} U_0$.
Inclined Plate ($\theta$): $F_N = \dot{m} U_0 \sin(\theta)$.
Reversing Bucket ($180^\circ$): $F_N = 2 \dot{m} U_0$.

ThermoFluidCalc Engineering Report