VORTEX TUBE REFRIGERATION SYSTEM
THEORY
STEPS: 𝐶𝑜𝑚𝑝𝑟𝑒𝑒𝑠𝑒𝑑 𝑎𝑖𝑟 𝑖𝑛 → 𝑆𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 𝑐𝑟𝑒𝑎𝑡𝑒𝑠 𝑎 𝑣𝑜𝑟𝑡𝑒𝑥(106 𝑟𝑝𝑚) ↓
↓ 𝑇ℎ𝑖𝑠 𝑜𝑢𝑡𝑒𝑟 𝑣𝑜𝑟𝑡𝑒𝑥 𝑔𝑎𝑖𝑛𝑠 ℎ𝑒𝑎𝑡 𝑓𝑟𝑜𝑚 𝑒𝑛𝑒𝑟𝑔𝑦 𝑙𝑜𝑠𝑡 𝑖𝑛 𝑖𝑛𝑛𝑒𝑟𝑒 𝑣𝑜𝑟𝑡𝑒𝑥
𝑆𝑜𝑚𝑒 ℎ𝑜𝑡 𝑒𝑥ℎ𝑎𝑢𝑠𝑡 𝑎𝑖𝑟 𝑖𝑠 𝑣𝑒𝑛𝑡𝑒𝑑 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑎𝑛 𝑎𝑑𝑗𝑢𝑠𝑡𝑎𝑏𝑙𝑒 𝑣𝑎𝑙𝑣𝑒 ↓
↓ 𝑇ℎ𝑖𝑠 𝑖𝑛𝑛𝑒𝑟 𝑣𝑜𝑟𝑡𝑒𝑥 𝑙𝑜𝑠𝑒𝑠 𝑒𝑛𝑒𝑟𝑔𝑦 ← 𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑎𝑖𝑟 𝑓𝑙𝑜𝑤𝑠 𝑏𝑎𝑐𝑘 𝑡𝑜𝑎𝑟𝑑 𝑡ℎ𝑒 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟
𝑇ℎ𝑒 𝑐𝑜𝑜𝑙𝑒𝑑 𝑎𝑖𝑟 𝑝𝑎𝑠𝑠𝑒𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑒 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 → 𝑆𝑢𝑝𝑒𝑟 𝑐𝑜𝑜𝑙𝑒𝑑 𝑎𝑖𝑟 𝑒𝑥𝑖𝑡𝑠 𝑡ℎ𝑒 𝑣𝑜𝑟𝑡𝑒𝑥 𝑡𝑢𝑏𝑒
Vortex tube is a simpler (no moving parts) and non-conventional mechanical device that
produce cooling (separates hotter and cold streams) when compressed air source is readily
available.
TEMPERATURE DROP: 100℉ (or 56℃) below the inlet air temperature.
The compressed air is entered into a swirl chamber which cools the air (adiabatic expansion of
the gas) and the lost heat is transferred into kinetic energy and the chamber which is designed
to swirl the air and produce vortex at high speed which facilitates the tangential entry into hot
side. Some of the hot gas leaves the hot outlet and the rest of the gas turns towards the cold
outlet which have low velocity because it lost heat at the outlet and that means low kinetic
energy and the enthalpy becomes low. The low enthalpy cools the air and leave the colder
outlet.
𝐹𝐼𝐺𝑈𝑅𝐸: 𝑉𝑂𝑅𝑇𝐸𝑋 𝑇𝑈𝐵𝐸
If you observe the above figure at the end of the tube conical nozzle is placed to facilitate the
outer shell of the vortex air escapes and the remaining air turn back to colder side.
To study the vortex tube refrigeration, a long debate is going on between empirical approach
and the approach relies on observations and experimental data.
If we take empirical approach, “The vortex tube effect” is completely explained by Euler turbine
equation that is.,
𝑇−
⃗ ∙𝜔
⃗⃗⃗ ×𝑟̅
𝑣
𝑐𝑝
= 𝑐𝑜𝑛𝑠𝑡
Where is the temperature at stagnation point of a fluid (stagnation temperature)
𝑣 is absolute gas velocity observed from fixed reference frame
𝜔
⃗ is angular velocity of system
𝑟̅ is radial position of rotating gas
𝑐𝑝 is isobaric heat capacity of working fluid
Actually, the turbine equation more focuses on power output and not on turbine cooling which
is of very few applications and due to complexity of the vortex flow, it only shows the aspects of
the effect but not operating principle.
On the other hand, the design based on experimental data. When it comes to experimental
data many factors taken into account like geometrical shape of the vortex tube, turbulence,
acoustic phenomena, pressure fields and air velocities. These all parameters are taken into
account to optimize inlet, outlet components and the main tube variations. It will be more
convincing to explain the operating principle clearly by validating via experimental studies
available in the literature.
𝐹𝐼𝐺𝑈𝑅𝐸: 𝑀𝑜𝑟𝑒 𝑑𝑒𝑡𝑎𝑖𝑙𝑒𝑑 𝑠𝑐ℎ𝑒𝑚𝑎𝑡
To validate our result there are so many researches are done, and one of famous one is
Stephen et al. (1983) expressed his result as:
∆𝑇𝑐
(∆𝑇𝑐 )𝑚𝑎𝑥
= 0.849 + 1.49𝑥𝑐 − 4.505𝑥𝑐2 + 2.427𝑥𝑐3
∆𝑇
Where, (∆𝑇 ) 𝑐
𝑐 𝑚𝑎𝑥
a fraction that tells how much accurate our result is which is always < 1.
𝑥𝑐 is cold flow fraction or cold mass ratio is the ratio of the mass flow rate at the cold outlet 𝑚̇ 𝑐
𝑚̇
to that at the inlet 𝑚𝑖𝑛
̇ , 𝑥𝑐 = 𝑚 ̇ 𝑐 .
𝑖𝑛
∆𝑇
And the optimized value of 𝑥𝑐 is 0.2 which gives (∆𝑇 ) 𝑐
𝑐 𝑚𝑎𝑥
≈ 1.
Some of the theoretical formulas usually encountered in refrigeration analysis in vortex tube:
1. The difference between the total temperatures at the inlet and cold outlet,
∆𝑻𝒄,𝒕𝒐𝒕 = 𝑻𝒊𝒏,𝒕𝒐𝒕 − 𝑻𝒐𝒖𝒕,𝒕𝒐𝒕
2. Temperature efficiency, which compares the actual temperature decrease with that in
the isentropic expansion process,
∆𝑻𝒄,𝒕𝒐𝒕
𝜼𝑻 =
𝜸−𝟏
𝑷𝒄,𝒕𝒐𝒕 𝜸
𝑻𝒊𝒏,𝒕𝒐𝒕 [𝟏 − (𝑷
) ]
𝒊𝒏,𝒕𝒐𝒕
Where, 𝑃𝑐,𝑡𝑜𝑡 and 𝑃𝑖𝑛,𝑡𝑜𝑡 are the stagnation pressure values at the cold outlet and the
inlet, respectively, and 𝛾 is the specific heat ratio of air.
3. Cooling capacity of the cold air,
𝑸̇ 𝒄 = 𝒙𝒄 𝒎̇𝒄𝒑 ∆𝑻𝒄,𝒕𝒐𝒕
Where, 𝑚̇ is the inlet (supplied) mass flow rate of air, and is the specific heat at
constant pressure.
4. Coefficient of performance of the vortex tube as a refrigerator, (Eiamsa-ard and
Promvonge, 2008),
𝒙𝒄 𝒄𝒑 ∆𝑻𝒄,𝒕𝒐𝒕
𝑪𝑶𝑷𝑹 =
𝜸−𝟏
𝑷𝒊𝒏,𝒕𝒐𝒕 𝜸
𝜸
− 𝟏]
𝜸 − 𝟏 𝑹𝑻𝒊𝒏,𝒕𝒐𝒕 [( 𝑷𝒄,𝒕𝒐𝒕 )
References:
https://www.vortec.com/vortex-tubes-video
https://www.sciencedirect.com/science/article/abs/pii/S0140700719303792
https://www.sciencedirect.com/science/article/abs/pii/S0140700710002057
https://www.sciencedirect.com/science/article/pii/S2214157X19305404
Image sources:
https://www.youtube.com/watch?v=Q_y2FvH2DHE
https://en.wikipedia.org/wiki/File:Ranque-Hilsch_Vortex_Tube.svg
https://www.sciencedirect.com/science/article/abs/pii/S0140700719303792