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The Ranque-Hilsch vortex tube is a simple device with no moving parts and no mechanical operations. This tube separates the inlet air into two distinctive regions; an outward high temperature region and an inner low-temperature one. A computational study of the vortex tube is presented in this article using the ANSYS Fluent software whose results showed good agreement with the ex-perimental measurements.
The effects of different geometrical parameters such as the tube length to diameter ratio and the cold orifice size on the coefficient of performance of the tube were investigated. The results showed that the coefficient of performance (COP) of the tube is highly affected by the tube length to diameter ratio (*L*/*D*), and this effect varies when operating at different cold mass fractions where the maximum coefficient of performance occur at cold mass fraction of 0.64. The results also showed that the coefficient of performance of the tube is also affected by the cold orifice to tube diameter ratio (*d _{c}*

_{/}

*D*) and that the maximum (COP) at any (

*d*/

_{c}*D*) ratio occurs also at a cold mass fraction of 0.64.

The vortex tube (VT) is a device with a simple geometry without moving mechanical parts [

The VT is used in many applications such as cooling of airborne electronic components, cooling of gas samples, and cooling of soldered parts including spot welding and ultrasonic welding. It is also used in the separation of air into nitrogen and oxygen rich fluid stream [

The results presented in this paper show that the COP of the VT can be enhanced by adjusting the cold orifice to tube diameter ratio ( d c / D ) and the length to the tube diameter ratio while depending on the adjusted cold mass fraction. This opens a new door to research on enhancing the performance of the VT based on the requirements of the application.

An energy separation occurs in the vortex tube between the cold and hot streams which causes the temperature changes between the inlet and exit streams. Many researchers suggested various theories to explain the energy separation inside the vortex tube. For example, Ahlborn [

The effect of friction and turbulence in the VT has always been a major concern of many researchers and was considered by some researchers as the reason for energy separation. For example, using a simple vortex tube model with CFX software and κ-ε turbulence model, Kazantseva et al. [

Some researchers noted the existence of secondary circulations in the vortex tube. They attributed the energy separation to the secondary circulations. For example, Behara et al. [

The performance of the RHVT is affected by geometrical properties such as the length to tube diameter ratio ( L / D ) and cold orifice to tube diameter ratio ( d c / D ). The length to tube diameter ratio L / D is a very important parameter that attracted the interest of many researches s such as [

Kandil and Abdelghany [

The effects of varying d c / D on the performance of the VT was investigated by Maurya and Bhavsar [

Recently, Kandil and Abdelghany [

The results presented in this paper support and build on the research of Kandil and Abdelghany [

An Axisymmetric model of the RHVT was designed and simulated using ANSYS Fluent^{®} software. The model was validated using the experimental measurements of Skye et al. [

Continuity equation in tensor notation:

∂ ρ ¯ ∂ t + ∂ ∂ x j ( ρ ¯ u ¯ j + ρ ′ u ′ j ¯ ) = 0 , j = 1 , 2 , 3 (1)

Momentum equations in tensor notations (all three components):

∂ ∂ t ( ρ ¯ u ¯ i + ρ ′ u ′ i ¯ ) + ∂ ∂ x j ( ρ ¯ u ¯ i u ¯ j + u ¯ i ρ ′ u ′ j ¯ ) = − ∂ p ¯ ∂ x i + ∂ ∂ x j ( τ ¯ i j − u ¯ j ρ ′ u ′ i ¯ − ρ ¯ u ′ i u ′ j ¯ − ρ ′ u ′ i u ′ j ¯ ) (2)

Where

τ ¯ i j = μ [ ( ∂ u ¯ i ∂ x j + ∂ u ¯ j ∂ x i ) − 2 3 δ i j ∂ u ¯ k ∂ x k ] (3)

Energy Equation:

∂ ∂ t ( ρ ¯ H ¯ + ρ ′ H ′ ¯ ) + ∂ ∂ x j ( ρ ¯ u ¯ j H ¯ + ρ ¯ u ′ j ¯ H ′ ¯ + ρ ′ u ′ j ¯ H ¯ + ρ ′ u ′ j H ′ ¯ + u ¯ j ρ ′ H ′ ¯ − k ∂ T ¯ i ∂ x j ) = ∂ ρ ¯ ∂ t + ∂ ∂ x j [ u ¯ i ( − 2 3 μ δ i j ∂ u ¯ k ∂ x k ) + μ u ¯ i ( ∂ u ¯ j ∂ x i + ∂ u ¯ i ∂ x j ) − 2 3 μ δ i j u ′ i ∂ u ′ k ∂ x k ¯ + μ ( u ′ i ∂ u ′ j ∂ x i ¯ + u ′ i ∂ u ′ i ∂ x j ¯ ) ] , i , j , k = 1 , 2 , 3 (4)

Equation of State (ideal gas law)

p = ρ R T (5)

where δ i j is the Kronecker delta function ( δ i j = 1 if i = j and δ i j = 0 if i ≠ j ); τ i j denotes viscous stress tensor; H represents the total enthalpy; T is the static temperature, p is the pressure, ρ is the density and R is the universal gas constant at standard conditions.

The results of the CFD model of the RHVT using the κ-ε Turbulence model showed the best agreement with the experimental results of Skye et al. [

The geometry used in the current CFD model is based on the Exair^{TM} 708 slpm vortex tube used by Skye et al. [

The results of the CFD model of the VT became mesh independent when the number of elements reached 17,000 elements. Due to the complexity and sensitivity of the flow inside the VT, the time step of the solution had to be very small

to allow converge such that the computation time of one simulation ranged from 12 to 48 hours using 8 processors on a 3.64 GHz HP workstation Z800 with 16 GB Ram.

The experimental data from Skye et al. [

The current CFD model was validated by comparing its results with the experimental measurements of Skye et al. [

The results in

The results show that the hot temperature rise increases as the cold mass fraction increases to reach a maximum value of 86.7 K at cold mass fraction of 0.87. Increasing the cold mass fraction further will be impractical due to the very low

Boundary Condition | Type and Parameter of boundary condition |
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Inlet nozzles | Mass flow inlet boundary condition with mass flow rate of 8.35 g/s, total temperature of 294.2 K |

Cold outlet | Pressure outlet |

Hot outlet | Pressure outlet |

Tube wall | No slip boundary conditions with adiabatic wall |

Tube axis | Axisymmetric swirl conditions |

flow rate of air from the hot outlet. The results show also that at very low cold mass fraction, the hot temperature rise decreases till it reaches a minimum value of 11.4 K at cold mass fraction of 0.2099. The results show also that when operating at cold mass fractions from 0.2 to 0.45 the increase in temperature rise is slow while as the cold mass fraction increases, the increase in temperature rise becomes rapid especially at very high cold mass fractions. The comparison shows that the current model has better agreement with the experimental measurements than that of Skye et al. [

The performance of the VT was determined by Kandil and Abdelghany [

The coefficient of performance for the RHVT when it is used as a refrigerator is the cooling power Q ˙ c divided by the input power P . The input power for any refrigeration system is the input to the compressor. But for a RHVT system a compressed air source is used which makes it difficult to define the input power. Fulton [

P = m ˙ i n R m T i n ln ( p i n p c ) (6)

where

Q ˙ c = m ˙ c c p ( T i n − T c ) (7)

where R m is the specific gas constant, p i n is the input pressure and p c is the cold exit pressure

Therefore the COP of the RHVT as a cooler is expressed as

C O P c = γ γ − 1 μ c ( T i n − T c ) T i n ln ( p i n p c ) (8)

The COP for the RHVT when it is used as a heat pump is defined as the heating power Q ˙ h divided by the input power P . The input power used by the system takes the same from as the one used for the cooling RHVT

Therefore, the COP of the RHVT as a heat pump is expressed as

C O P h = γ γ − 1 ( 1 − μ c ) ( T h − T i n ) T i n ln ( p i n p c ) (9)

The total performance of the RHVT can be determined using the summation of the COP as a cooler and as a heat pump which is expressed as:

C O P total = C O P c + C O P h (10)

The performance of the VT in terms of C O P total at different L / D ratios was studied at different values of cold mass fraction. The results in

These results show that the C O P total at different L / D ratios is dependent upon the cold mass fraction, where at low cold mass fraction, as the L / D increases the C O P total increases to reach a maximum value at a critical L / D ratio. Any further increase in the L / D ratio will result in decreasing the C O P total . While as the cold mass fraction increases the difference between the maximum and minimum C O P total is reduced from 0.04 at μ = 0.34 to 0.0086 at μ = 0.5 . Any further increase in the cold mass fraction will change the trend of the curve

between the C O P total and different L / D ratios such that the lowest L / D ratio has the highest C O P total and as the L / D ratio increases the C O P total decreases to reach asymptotic value at critical L / D ratio.

In

Such results don’t follow the same pattern of the results of total temperature of Kandil and Abdelghany [

The cold orifice diameter is an important parameter that affects the performance of the VT. Therefore, several trials were done to optimize the performance of the tube of a diameter of 11.4 mm by varying the cold orifice diameter to pipe diameter ratio, d c / D .

When studying the performance of the RHVT taking into consideration not just the highest temperature drop but also the cold mass fraction, the pressure at the inlet and the pressure at the cold outlet, a new dimensionless parameter had to be defined to combine the effect of all the previously mentioned parameters on the performance of the vortex tube. This dimensionless parameter is the C O P c which was defined by Equation (8).

It is shown in

It is shown in

When studying the performance of the RHVT taking into consideration not just the highest temperature rise but also the hot mass fraction, the pressure at the inlet and the pressure at the cold outlet, a new dimensionless parameter had to be defined to combine the effect of all the previously mentioned parameters on the performance of the vortex tube. This dimensionless parameter is the C O P h which was defined by Equation (9).

It is shown in

mass fraction which is almost the same value of 0.64 in all cases after which any further increase in the cold mass fraction will result in decreasing the C O P h . The highest C O P c of different d c / D ratio cases existed at this exact cold mass fraction as stated in the previous Section 5.2.1. The d c / D ratio of 0.6316 has the highest C O P h of 0.2145 at cold mass fraction of 0.64.

From the previous sections, it was noted that the highest C O P c and C O P h were at a cold mass fraction of 0.64 for all d c / D ratio cases The C O P total was defined in Equation (10) as the summation of the C O P c and C O P h , therefore when studying the performance of the RHVT in terms of the C O P total , the maximum C O P total for all the different d c / D ratio cases should exist at cold mass fraction of 0.64 which is confirmed in

It is noted from the results in Section 5.1 and Section 5.2 that the best performance of the vortex tube in terms of C O P total occurs when operating the vortex tube at a cold mass fraction of 0.64 regardless of the length to tube diameter ratio or the cold orifice to tube diameter ratio.

For Future research, these results can be more investigated in terms of flow analysis using 3D modeling of the RHVT to gain more insights about what actually occurs at the cold mass fraction of 0.64. Building on these results, the flow visualization at different d c / D ratios at this cold mass fraction will also be very beneficial.

The results of the current model are in good agreement with the available experimental measurements. Many geometrical parameters affect the performance of the tube. In this study, the length to tube diameter ratio effect in terms of C O P total was investigated and the results showed that its effect on the performance of the tube is different at different cold mass fractions where the maximum C O P total at any length to tube diameter ratio occurs at cold mass fraction of 0.64.

Also the effect of the cold orifice to tube diameter ratio on C O P c , C O P h and C O P total was investigated and the results showed that all the studied VTs at different d c / D ratios have the maximum C O P c and the maximum C O P h at a cold mass fraction of 0.64. The highest d c / D ratio of 0.6361 has the highest C O P c and C O P h .

It can be concluded that the best performance of the studied vortex tube at any L / D or d c / D ratio occurs at a cold mass fraction of 0.64. Future investigation of the physical properties of the tube at such cold mass fraction and its relation to other operating points of the vortex tube should be considered.

Abdelghany, S.T. and Kandil, H.A. (2018) Effect of Geometrical Parameters on the Coefficient of Performance of the Ranque-Hilsch Vortex Tube. Open Access Library Journal, 5: e4347. https://doi.org/10.4236/oalib.1104347