Brief description

A De Laval nozzle (or convergent-divergent nozzle) is a tube pinched in the middle, resembling an hourglass. It accelerates a hot, pressurized gas passing through it to supersonic speeds, converting thermal and pressure energy into directional kinetic energy.

Use / Function

• Steam Turbines: Directing high-velocity steam jets onto turbine blades to maximize mechanical energy output.
• Rocket Propulsion: Accelerating exhaust gases to high supersonic velocities to generate forward thrust.
• Supersonic Ejectors and Jet Pumps: Creating strong suction or high vacuum levels in chemical and industrial processes.
• Scale: Small laboratory ejectors to massive industrial rocket nozzles.

Operating principle

The nozzle operates by exploiting the thermodynamic and gas dynamic properties of compressible fluids transitioning from subsonic to supersonic flow.

1. Convergent Section: Subsonic gas enters the wide inlet. As the cross-sectional area decreases toward the throat, the gas speeds up while its pressure and temperature decrease.
2. Throat: At the narrowest point (the throat), if the pressure ratio is sufficient, the gas reaches Sonic Velocity (Mach 1).
3. Divergent Section: Past the throat, as the cross-sectional area expands, compressible supersonic gas continues to accelerate rather than slow down, reaching supersonic speeds (Mach > 1).
4. Energy Conversion: Thermal and pressure energy from the high-pressure reservoir are converted efficiently into kinetic exhaust energy.

How to create it

1. Calculate Dimensions: Determine the throat area and exit area ratio based on the available inlet pressure and target pressure ratio.
2. Machining the Internal Profile: Turn a cylinder of brass, bronze, or heat-resistant steel on a lathe, boring a smooth converging cone (around 20° total angle) down to the exact calculated throat diameter.
3. Boring the Divergent Cone: Machine a gradually expanding exit cone (typically 10° to 12° total angle) from the throat to the exit bell to avoid flow separation and shock losses.
4. Polishing: Smooth and mirror-polish the inner walls using fine abrasives to eliminate surface roughness that causes turbulence or internal shockwaves.
5. Mounting: Thread or flange the wide inlet onto a high-pressure gas chamber or steam boiler.

Materials needed

• Essential materials:
  • Steel or Stainless Steel: High strength and thermal tolerance for steam or combustion gas nozzles.
  • Brass or Copper: High thermal conductivity and easy machinability for low-temperature or compressed air testing nozzles.
• Tools:
  • Lathe or Screw-Cutting Lathe: For precise internal conical boring and turning.
  • Calipers or Vernier Caliper: For verifying throat and exit diameters.
• Possible substitutes:
  • Dense hardwood or epoxy resin: Acceptable for cold-gas or low-pressure demonstrations.

Variants and improvements

• Conical Nozzle: Simple straight-walled cone design; easy to manufacture but slightly less efficient due to radial gas divergence at the exit.
• Bell Nozzle (Parabolic): Curved contour that redirects gas parallel to the centerline, shortening length and maximizing axial thrust.
• Aerospike Nozzle: Altitude-compensating nozzle that maintains high efficiency across varying atmospheric pressures.

Limits and risks

• Over-expansion and Under-expansion: Operating at ambient pressures off design specifications causes efficiency losses and internal shockwaves.
• Thermal Stress and Erosion: High-temperature gas flow can melt or erode the narrow throat area, destroying nozzle geometry.
• Pressure Requirement: Supersonic flow requires a critical pressure ratio (inlet pressure roughly double ambient pressure); otherwise, the gas remains subsonic throughout.