Ranque-Hilsch Vortex Tube in 2D: Energy Separation Cross-Section

Inlet Conditions

Inlet pressure 6.0 bar

Inlet temperature 20 °C

Hot-End Control Valve

Cold fraction μ 0.30

Live Readouts

Cold outlet T

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Hot outlet T

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Cold-side ΔT

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Hot-side ΔT

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Total temperature separation (hot − cold)

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How it works

Compressed air enters tangentially near one end of a plain cylindrical tube through a nozzle, spinning up into a fast vortex with no moving parts. Because the device is axisymmetric, its whole mechanism lives in one radial cross-section — which is exactly what the top panel shows edge-on: the outer layer of the vortex spirals down the tube toward an adjustable conical valve at the far ("hot") end, while turbulent shear transfers rotational kinetic energy from the inner layers outward. The inner core loses energy, cools, reverses axial direction, and flows back up the tube's centre to exit through a small orifice at the near ("cold") end.

The valve position sets the cold mass fraction μ = ṁ_cold/ṁ_in. Closing it forces more flow out the cold orifice (μ↑); opening it sends more out the hot end (μ↓). Drag left/right on the lower graph to sweep μ directly.

Ideal isentropic expansion drop:
  ΔT_s = T_in · [1 − (P_in/P_atm)^(−(γ−1)/γ)],  γ = 1.4 (air)

Cold-side temperature drop (empirical vortex-tube
efficiency correlation, peaks near μ ≈ 0.3):
  η_c(μ) = η_max·(μ/μ_p)·exp(1 − μ/μ_p)
  T_cold = T_in − η_c(μ)·ΔT_s

Hot-side temperature (first-law energy balance,
adiabatic, no external work — exact, not empirical):
  μ·T_cold + (1−μ)·T_hot = T_in
  T_hot = (T_in − μ·T_cold) / (1 − μ)

Inlet pressure — sets the isentropic drop ΔT_s available to work with; higher pressure ratio means a bigger possible split.
Cold fraction μ (valve) — the single strongest lever: the cold stream cools most around μ≈0.3, while the hot stream keeps heating further as μ→0 because less mass carries the same rejected energy.
Inlet temperature — both outlet temperatures shift with it, since the separation is a fraction of the inlet's absolute temperature.
Real devices reach 40–60 °C splits from compressed shop air and are used for spot-cooling machining tools, cabinet cooling and gas sampling where a compact, moving-part-free cooler is worth the poor thermodynamic efficiency (~10–15% of a Carnot device).

Cold reversed core Hot outer vortex

drag graph ↔ to set μ