Ranque-Hilsch Vortex Tube

How a vortex tube works

Picture a straight metal tube about the size of a fat pen. Near one end, compressed air is blown in not straight down the bore but sideways, through one or more tiny tangential nozzles aimed along the inner wall. The air has nowhere to go but to spin, and because the bore is small and the inlet pressure is high, it spins astonishingly fast — a forced vortex that can exceed a million RPM at the wall in a small tube.

That spinning column does something strange: it sorts itself into two coaxial streams. The outer layer, hugging the wall, drifts toward the far end of the tube. There it meets a cone-shaped valve that blocks the center but leaves an annular gap at the rim, so the outer air escapes around the edge — and it comes out hot. The cone also reflects the central part of the flow back on itself. That reflected core spins back through the middle of the outer vortex, all the way to the inlet end, and exits through a small central hole called the cold orifice — and it comes out cold.

The genius is in the layout. The cold orifice sits right next to the inlet but on the tube's axis; the hot valve sits at the far end on the rim. So the device has exactly three openings — one inlet, one cold outlet, one hot outlet — and not a single moving part except the cone you screw in and out to tune it.

Why does the core get colder while the rim gets hotter? The inner core rotates almost as a solid body (a forced vortex, so its angular velocity is roughly uniform across the radius) and sits at lower static pressure than the faster-moving outer fluid. As the flow develops, the inner core gives up energy to the outer layer through pressure-volume work and turbulent shear at the boundary between the two streams — heat and kinetic energy are pumped radially outward. The periphery accumulates that energy and warms; the core, robbed of it, cools. This is energy separation, and it is the entire point of the device.

The thermodynamics of energy separation

Nothing here violates the second law. The compressed-air supply already carries a large amount of available work (exergy) because it sits far above atmospheric pressure. The tube simply redistributes the energy of one moderate-temperature stream into two streams — one hotter, one colder than the inlet — while total energy is conserved. An energy balance on the whole tube, treating it as adiabatic and steady, is just:

Mass:    ṁ_in = ṁ_cold + ṁ_hot
Energy:  ṁ_in·h_in = ṁ_cold·h_cold + ṁ_hot·h_hot

Cold fraction:   μ_c = ṁ_cold / ṁ_in        (0 < μ_c < 1)

With h ≈ c_p·T for an ideal gas, the energy balance becomes:
   T_in = μ_c·T_cold + (1 − μ_c)·T_hot

Rearranged to relate the two temperature splits:
   μ_c·(T_in − T_cold) = (1 − μ_c)·(T_hot − T_in)
   μ_c·ΔT_cold        = (1 − μ_c)·ΔT_hot

That last line is the lever rule of the vortex tube: the cold stream's temperature drop, weighted by its mass fraction, exactly equals the hot stream's temperature rise weighted by its mass fraction. If you bleed off only a thin cold stream (small μ_c), it can be very cold; if you take a fat cold stream (large μ_c), it can only be a little cold, because the same total energy is shared more thinly.

Where does the cold actually come from, physically? Treat the cold stream as if it nearly underwent an adiabatic expansion from the inlet pressure p_in down to the cold-outlet pressure (near atmospheric). The ideal isentropic drop sets the ceiling:

Ideal isentropic temperature ratio across the expansion:
   T_cold,ideal / T_in = (p_cold / p_in)^((γ−1)/γ)

For air, γ = 1.4, so (γ−1)/γ = 0.286.
From 6.9 bar (abs, ~7 bar) down to ~1 bar:
   T_cold,ideal / T_in = (1/7)^0.286 = 0.573
   T_in = 293 K (20 °C)  →  T_cold,ideal ≈ 168 K ≈ −105 °C  (perfect-expansion ceiling)

Real tubes reach only ~30–60% of that ideal drop, so a real cold
end is around −18 to −40 °C, not −105 °C. The isentropic
efficiency of the energy-separation process is what falls short.

The gap between the −105 °C ideal and the −40 °C real number is exactly the irreversibility: turbulence, friction, and incomplete separation dump entropy back as heat. That is also why the device is so power-hungry — most of the exergy in the compressed air is destroyed inside the swirl rather than turned into useful cold.

Cold fraction: the one knob you turn

A vortex tube has a single adjustment — the conical valve at the hot end — and it sets the cold fraction μ_c. This one knob trades temperature against flow:

Hot-end valve	Cold fraction μ_c	Cold-air behaviour	Best for
Nearly closed	0.6 to 0.8	High flow, modest drop (e.g. +5 to −5 °C)	Total cooling power (BTU/hr)
Mid	~0.5	Balanced flow and drop	General-purpose spot cooling
Wide open	0.2 to 0.4	Thin flow, large drop (e.g. −40 °C)	Coldest possible air

Two design points get quoted constantly. Maximum temperature drop occurs near μ_c ≈ 0.3 — close the cold stream down to a trickle and it gets as cold as the tube can manage. Maximum refrigeration capacity, the most total heat removed per hour, occurs near μ_c ≈ 0.6 to 0.7 — a bigger cold stream at a smaller drop carries more enthalpy out per unit time. The actual cooling power delivered is:

Q_cold = ṁ_cold · c_p · (T_in − T_cold)
       = μ_c · ṁ_in · c_p · ΔT_cold

c_p,air ≈ 1.005 kJ/(kg·K)

Example: ṁ_in = 0.0142 kg/s (~25 scfm),  μ_c = 0.6,  ΔT_cold = 15 °C
   Q_cold = 0.6 × 0.0142 × 1005 × 15 ≈ 128 W ≈ 438 BTU/hr

Worked example: cooling a CNC cutting tool

A machinist is dry-cutting titanium and wants chilled air at the tool tip instead of flood coolant. The shop air is 6.9 bar (100 psi) at 20 °C. They fit a mid-size vortex tube rated at 25 scfm and tune it for cooling capacity (μ_c ≈ 0.6).

Inlet:   p_in = 6.9 bar (g) ≈ 7.9 bar (abs),  T_in = 293 K
Air use: 25 scfm  →  ṁ_in ≈ 0.0142 kg/s
Setting: μ_c = 0.6,  measured cold drop ΔT_cold = 15 °C  →  T_cold = +5 °C

Cold flow:    ṁ_cold = 0.6 × 0.0142 = 0.0085 kg/s
Hot flow:     ṁ_hot  = 0.4 × 0.0142 = 0.0057 kg/s
Lever rule:   ΔT_hot = μ_c/(1−μ_c) × ΔT_cold = (0.6/0.4) × 15 = 22.5 °C
              →  T_hot = 20 + 22.5 = 42.5 °C  (verify: 0.6·15 = 0.4·22.5 ✓)

Cold capacity: Q_cold = 0.0085 × 1005 × 15 ≈ 128 W (≈ 438 BTU/hr)

Compressor cost: delivering 25 scfm at 100 psi needs roughly
  5 to 6 kW at the compressor (≈ 0.2 kW per scfm rule of thumb).
COP = Q_cold / W_compressor ≈ 128 W / 5500 W ≈ 0.023 at this setting
  (closer to 0.1–0.2 when tuned for a smaller, colder cold stream).

The lesson is stark: 5 kW of compressor power buys about 130 W of cooling. Nobody would build a building's air conditioning this way. But the tube costs about US$80, weighs 200 g, fits on the spindle, never needs maintenance, and turns on the instant the air valve opens — which is exactly what a one-off dry-cutting job wants.

Geometry that matters: nozzles, L/D, and the cold orifice

Four geometric choices dominate vortex-tube performance, and getting them right matters more than tube length alone:

• Tangential inlet nozzles. The swirl is everything, so the inlet must inject air tangentially, not radially. Modern commercial tubes use a multi-nozzle generator (often 4 to 8 small tangential slots cut into a ring) so the air enters as a clean, high-speed sheet against the wall. A single off-center hole works but separates less efficiently.
• Length-to-diameter ratio (L/D). The streams need axial room to exchange energy before the core turns around at the cone. Performance climbs with L/D up to roughly 30 to 50, then plateaus. Below about L/D = 20 the separation is incomplete and the cold drop collapses; far above 50, wall friction just bleeds the swirl with no extra benefit.
• Cold orifice diameter. The central hole the cold stream escapes through is usually about half the tube bore (d_cold ≈ 0.5·D). Too small and it chokes the cold flow; too large and the outer hot vortex short-circuits straight out the cold side, wrecking separation.
• Hot-end cone valve. The adjustable cone is the only control. Screwing it in throttles the hot exit (raising μ_c); backing it out opens the hot exit (lowering μ_c). Its taper and seat finish set how smoothly the core reverses.

Materials are usually brass or stainless steel for the body, since the only loads are pressure and thermal cycling, and the hot end sits at 60 to 120 °C continuously. There is no fatigue-critical part, no seal that rubs, and no bearing — the absence of moving parts is what makes the device essentially immortal.

Vortex tube vs other compact cooling methods

	Vortex tube	Vapor-compression	Thermoelectric (Peltier)	Compressed-air expansion (turbo)
Moving parts	None	Compressor, valves, fan	None (needs fan)	Turbine bearings
Refrigerant	None (air)	R-134a, R-410A, CO₂, etc.	None	None (air)
COP	0.1 to 0.3	2 to 4	0.4 to 0.7	0.5 to 1.5
Lowest practical temp	≈ −40 °C	≈ −40 °C and below	ΔT ≈ 60 °C per stage	Cryogenic with staging
Cooling power range	~10 W to ~3 kW	100 W to MW	~1 W to ~200 W	kW to MW
Response time	Instant (open valve)	Seconds to minutes	Seconds	Seconds
Maintenance	Essentially none	Regular	Fan only	Bearing service
Best home	Spot cooling, hazardous areas	Buildings, fridges, vehicles	Electronics, sensors, coolers	Aircraft ECS, gas processing

The pattern is clear: the vortex tube wins only on simplicity, ruggedness, and instant spot cooling — never on efficiency. If you already pipe compressed air around a factory floor, a US$80 tube buys you a maintenance-free cold jet wherever you need one; if you need efficient bulk cooling, anything else on this table beats it.

Where vortex tubes are actually used

• Machine-tool spot cooling. The flagship use. A vortex tube clamped near a cutting tool or a CNC spindle delivers a focused jet of −5 to −20 °C air, cooling the tool and blowing chips clear — no oily mist, no coolant to dispose of. Sold by Exair, Nex Flow, ITW Vortec, and others for exactly this.
• Electronics-enclosure cooling. Sealed control cabinets in hot, dusty, or washdown environments get a small "cabinet cooler" — a vortex tube feeding cold air inside while the hot stream vents outside. Because there is no fan pulling in contaminated air, the NEMA/IP seal stays intact. Common on food-plant and outdoor industrial panels.
• CCTV and instrument housings. Cameras and sensors sitting in furnaces, foundries, or solar exposure use vortex coolers to hold internals below their ratings with nothing inside the housing that can fail.
• Cooling protective garments and welding. Personal "cold air vests" tap a shop-air line through a small vortex tube to cool a worker in a hot environment; some welding helmets and abrasive-blast hoods do the same.
• Hazardous and explosive areas. Because it is purely pneumatic with no electrical parts, a vortex cooler is intrinsically safe — it can cool a panel in a Class I Div 1 zone where an electric cooler would need expensive explosion-proof certification.
• Set-point soldering, gas chromatography, and lab spot-chilling. Anywhere a small, instantly-available, electrically-quiet cold jet beats the bulk and cost of a refrigeration loop.

Common misconceptions and pitfalls

• "It violates the second law / it's free cooling." No. The cold comes entirely from the work already spent compressing the air upstream. Account for the compressor and the COP is a dismal 0.1 to 0.3. The tube only looks like magic because the energy bill is paid somewhere else.
• "Longer always means colder." Only up to L/D ≈ 30 to 50. Past that, friction eats the swirl with no benefit. Nozzle design and cold-orifice sizing matter as much as length.
• "Crank the pressure for unlimited cold." Cold drop does rise with supply pressure, but with diminishing returns, and the cold flow can choke. Most commercial tubes are rated at 100 psi; going to 250 psi gains a few more degrees, not a doubling.
• "It dries the air for you." It doesn't, and wet inlet air bites back: the cold orifice can frost or ice up as the −20 °C core freezes out moisture, throttling the flow. Feed it clean, dry, filtered air — a coalescing filter and dryer upstream are standard practice.
• "Bigger cold fraction is always better." A high μ_c gives more total cooling but a small temperature drop; a low μ_c gives a very cold but tiny stream. There is no single best setting — you tune the cone for either coldest air or most cooling, never both at once.
• "Any tube and a hole will do." Without true tangential injection you get weak swirl and almost no separation. The tangential nozzle geometry, not just "spinning air," is what makes a Ranque-Hilsch tube work.