Efficiency evaluation of vortex tube cyclone separator

Accepted Manuscript Efficiency evaluation of vortex tube cyclone separator Seyed Ehsan Rafiee, M.M. Sadeghiazad PII: DOI: Reference:

S1359-4311(16)33303-8 http://dx.doi.org/10.1016/j.applthermaleng.2016.11.110 ATE 9521

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

16 April 2016 9 November 2016 14 November 2016

Please cite this article as: S. Ehsan Rafiee, M.M. Sadeghiazad, Efficiency evaluation of vortex tube cyclone separator, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.11.110

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Efficiency evaluation of vortex tube cyclone separator

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Corresponding Author email: [email protected]

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Exclusive producer (Dr. Sadeghiazad) email: [email protected] *

Seyed Ehsan Rafiee , M. M. Sadeghiazad

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Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran

Abstract The aim of the present investigation is analysis on separation phenomenon in a convergent cyclone separator affected by the structural factors including; throttle angle (15-45deg), nondimensional throttle diameter (0.444-0.722), convergence main tube angle (2-12deg), nondimensional convergent length (20-22.22), injector slots number (2-6) and injection pressure (4.5-6.5bar), as well as the numerical optimization of these parameters in terms of the separation efficiency using 3D-CFD methods(RSM). The initial experimental results show that, the separation improves with an increase in the nondimensional throttle diameter up to DRth=0.611, then beyond DRth=0.611, the separation capabilities are decreased. Also, the cyclone equipped with the throttle angle of α=30deg provides43.76% and 50.60% higher separation efficiencies as compared to the basic model. Furthermore, there are the initial optimum values (experiments) for the convergence angle and nondimensional length of main tube as β=10deg and LN=21.66. Also, the separation efficiency improves with an increase in the slot number up to N=4. The comparison between the computed and laboratory outputs presents a favorable agreement with the maximum and minimum relative differences of 6.22% and 0.93%, respectively. In this study,

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the experiments determine the correct ranges for the factors, then, the exact optimum values will be selected by the CFD models.

Keywords: Convergent vortex tube; RSM turbulence model; Separation; Cyclone separator

1. Introduction The cyclone separator or vortex tube (VT) is called Ranque-Hilsch vortex tube in respect of the inventors (Ranque, 1933 [1] and Hilsch, 1947 [2]), also, is a simple, suitable and useful device with simplified structure. When a pressurized gas is injected (through slots) into the main chamber of the VT cyclone separator, the temperature regarding the escaping flow at the central exhaust (at near the vortex chamber or slots area) is lower than the flow incoming from the storage tank. At the same time, the temperature regarding the flow exiting from the circumferential exhaust (at the other side) has higher value than the inlet flow. Fig. 1 describes a schematic representation of a counter-flow VT cyclone separator by air flow division within the main tube. The structure of the VT cyclone separator system can be divided into a number of components such as; a cold end orifice, a vortex-chamber, a number of nozzle slots, a main or hot tube and a control valve. The gas or fluid is pressured by a compressor and is stored in the storage tank. This pressured gas is transported through the pipes and is injected in the main chamber via the slots. The tangential injection of pressured gas creates the strong rotating layers of gas inside the cyclone separator.

Fig. 1 The gas is injected (tangentially) via the nozzle slots, then the entered flow rotates around the central axis of the main tube. Consequently, the gas will be cooled and expanded. Also, after the occurrence of the phenomenon of flow separation inside main tube, the input gas through the nozzle slots is separated into two streams (cold and hot) with large temperature difference. The first output is known as the "cold exhaust" and is located close the nozzle slots. The hot exhaust is designed on the other side of the tube and this output is covered by a valve which controls the hot flow rate. Opening the mentioned valve leads to increase in the rate of hot flow at hot 2

exhaust, consequently, related cold air flow rate is reduced. It should be said that the VT cyclone separator performance is managed with the motion of the control valve. Several scientific works have been done to develop the VT cyclone separator structure and efficiency. Here, we look at a brief review of some of these researches. Dutta et al. [3] tried to apply a CFD model for analyzing the fluid flow in the main tube utilizing the NIST model. Baghdad et al. [4] examined the prediction ability of several numerical models (the k–ω, SST k–ω and k–ɛ). The effect of the main tube bending on the VT cyclone separator efficiency is studied by Valipour and Niazi [5], Bovand et al. [6 and 7], and Rafiee et al. [8]. Dincer [9] tested three different types of the VT cyclone separator (the conventional VT, threefold VT, and six RHVT cascade types) under different pressure injections. Some structural parameters (e.g., the length of the straight main tube, the cold and hot exhausts, the nozzle area ratio, and the inlet slots) have been optimized by Im and Yu [10]. Through laboratory work, Rafiee and Sadeghiazad [11] and Han et al. [12] examined the effects of applying various types of inlet gases (i.e., N2, O2, CO2, R32, R728, R134a, R744, R161, and R22) on the heating and cooling performance of a VT cooling system based on pressure analysis. Thakare and Parekh [13] numerically studied the effect of this operating parameter (different working gases). Mohammadi and Farhadi. [14] tested a cooling VT cyclone separator system to optimize the number and diameter of the nozzles, cold mass ratio, and intake pressure. Some researchers (Rafiee and Sadeghiazad [15]; Shamsoddini and Hossein Nezhad [16]) focused on the effect of number of slots and proved that the straight VT cyclone separator with the higher number of nozzles has greater cooling power compared with the separator with less nozzles. A new type of nozzle, the convergent nozzle, has been tested and optimized by Rafiee and Rahimi [17]. They also demonstrated that if the velocity of the gas entering the chamber increases, then the efficiency of the straight VT cyclone separator can be improved to a certain extent. The separated flow hysteresis phenomenon that occurs during the process of streamlining the gasturbine engine’s axial compressor has been analyzed by Kulyk et al. [18].

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Moreover, the accuracy of different turbulence methods (for predicting the separation phenomenon) has been analyzed by Rafiee and Sadeghiazad [19]. The geometrical optimization techniques are usually applied to increase the energy separation rate and the thermal performance; doing so optimizes the dimensions of the straight VT cyclone separator system, thereby decreasing the operating costs. Various methods, such as the exergy analysis, have been successfully used to optimize the structural parameters of the straight VT cyclone separator (Saidi and Allaf Yazdi [20]; Ouadha et al. [21]; Rafiee and Sadeghiazad [22]). Secchiaroli et al. [23] conducted a computational investigation to study the internal flow in a straight VT cyclone separator, which is used in a jet impingement system. Some numerical methods, such as the Taguchi methods (Pinar et al [24], the neural networks (Korkmaz et al. [25]), and the Rule-based Mamdani-Type Fuzzy (RBMTF) modeling method (Berber et al. [26]), have recently been used to optimize the operating conditions of the straight VT cyclone separator. Rafiee and Sadeghiazad [27] analyzed the effect of radius of rounding off edge on the energy separation procedure in a vortex tube. Saidi and Valipour [28] managed the factors influencing the thermal efficiency of the straight VT cyclone separator into two categories: thermo–physical and structural categories. The influence of the geometrical parameters of the nozzle intakes, such as the internal diameters, has been experimentally investigated by Aydin and Baki [29]. Rafiee et al. [30] evaluated the effect of cooling orifice diameter on flow separation in a convergent cyclone. A special type of VT is the divergent VT, which in some small angles can have better performance than the straight ones (Chang et al. [31]; Rahimi et al. [32]). Meanwhile, Dincer et al. [33] and Agrawal et al. [34] have accomplished complete experimental works on the straight VT cyclone separator with various length to diameter ratios. The secondary circulation in the straight VT cyclone separator has been explained and described by Ahlborn and Gordon [35]. There are many benefits that can be gained from using CFD numerical models. One of these advantages is that the CFD models present a clear and detailed description regarding the thermal distribution and the velocity field inside the straight VT cyclone separator (Akhesmeh et al. [36]; Rafiee and Rahimi [37]; Aljuwayhel et al. [38]; Skye et al. [39]). Two detailed reviews (Subudhi 4

and Sen, [40]; Thakare et al. [41]) have been presented in relation to the contents of the VT cyclone separator. Piralishvili and Polyaev [42] and Alekhin et al. [43] introduced a novel kind of VT, which is a double-circuit VTs wherein an additional inlet is added on the hot throttle valve. Kandil and Abdelghany [44] assessed the effects of some geometrical parameters, such as the L/D, on the straight VT cyclone separator performance. Pourmahmoud et al. [45] reported that the best working fluid to create the maximum cold temperature difference is CO 2. Liu and Liu [46] proposed a three-dimensional (3D) model for predicting and calculating the temperature and velocity distributions, which in turn, are used to describe the energy and the gas separation phenomenon inside the straight VT cyclone separator. Meanwhile, Pourmahmoud et al. [47] reported that the cold temperature difference can be improved using the helical nozzles. The effect of inlet temperature is analyzed by Pourmahmoud et al. [48]. Khazaei et al. [49] found that the size of the hot exhaust does not affect the thermal efficiency of the straight VT cyclone separator, whereas Li et al. [50] demonstrated that the increase of cold flow fraction (or decrease of pressure at injectors) moves the stagnation point to cooling orifice. Rafiee and Sadeghiazad [51] analyzed the influence of control valve angle on flow distribution inside the vortex tube. Gutak [52] utilized a straight VT cyclone separator with high pressure natural gas stream and found that the Joule–Thomson factor has an important effect on the energy distribution. Rafiee et al. [53] performed a numerical work on optimization of working tube radius for a normal vortex tube. Mohammadi and Farhadi [54] analyzed the separation process and the gas fractions inside a straight VT cyclone separator for a hydrocarbon mixture. The hot tube length is optimized (in a numerical study) by Rafiee and Sadeghiazad [55]. Khait et al. [56] employed the RSM turbulence model to introduce a comprehensive CFD model for predicting the flow distribution inside the straight VT cyclone separator. Rafiee and Sadeghiazad [57] optimized the vortex chamber radius based on a three dimensional model. The annular straight VT cyclone separator, in which the hot flow is redirected on the hot tube, has been introduced by Sadi and Farzaneh–Gord [58]. 5

Rafiee and Sadeghiazad [59] optimized (numerically and experimentally) the control valve diameter for a convergent cyclone.

Pourmahmoud et al. [60] optimized the convergence angle of a nozzle to improve the performance of a common VT cyclone. Bej and Sinhamahapatra [61] worked on the hot cascadetype straight VT cyclone separator, in which the hot gas flow exiting the first VT cycle is utilized as the inlet of the second VT cycle. The concept of the nozzle aspect ratio and its effect on the separation phenomenon are studied in an experimental work by Avci [62]. Rafiee and Sadeghiazad [63] considered the impact of control valve shape on energy distribution in a straight cyclone. According to the mentioned scientific works, there are a lot of computational and experimental considerations into optimization of common or Ranque-Hilsch vortex tubes, but, there is no comprehensive work on the efficiency of convergent vortex tubes. In other words, the impacts of the structural factors and the flow separation process in a convergent vortex tube were not analyzed (yet). So, this is a great gap between the vortex tube researches. This subject motivated us to perform a parametric analysis (precise and effective design of throttle diameter, throttle angle, convergence angle, main tube length and a pressure analysis) on the flow treatments in a convergent air separator to cover this scientific gap. In fact, we believe that, an appropriate and precise design of the throttle diameter, the throttle angle, the convergence angle and the main tube length leads to the higher cooling and heating efficiency of convergent air separator. Also, the present research describes a detailed explanation for difference between flow and thermal separation patterns inside the convergent vortex tubes with different geometrical factors. This research presents a fairly accurate three-dimensional numerical model (as well as the experimental tests) which clarifies the difference between the cooling and heating capabilities of the convergent vortex tubes with different throttle diameters, throttle angles, convergence angles and main tube lengths. Also, this paper tries to explain and clarify the effect of increasing

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pressures on the efficiency of the convergent vortex tubes (this subject has not been analyzed yet) based on different convergence angles.

2. Experimental study The detailed structural plot of the convergent VT cyclone separator is shown in Fig. 2. Actually, this laboratory set up is considered to focus on the separation phenomenon of the compressed air as the operational fluid. A steel convergent VT cyclone separator is designed with structural factors as shown in Table 1.

Fig. 2 Table 1 Fig. 3 Also a schematic approach of the experimental set up utilized in the investigation is shown in Fig. 3. The system is designed so that all components have the ability to change, specially the conical valve and the convergent main tube. The changeable design makes the capability to consider the impacts of some structural factors on the convergent VT cyclone separator performance. The room temperature was 21 degrees during the tests. The measuring instruments (with details) are listed in the Table 2.

Table 2 Twelve different hot control valves with different angles and throttle diameters have been manufactured and used in the tests. Two Ø2 mm holes are drilled on the VT cyclone separator axis for adjusting the thermo probes. The distance between each hole and the related exhaust is considered to be 1.25 cm. Before beginning the tests, the hot valve is adjusted in the open situation. In the next stage the tank starts to work. The used pressure (0.45 MPa) in the cycle is supplied by the action of the valve fixed on the inlet of the VT cyclone separator. The pressures and the entering or exiting mass rates are evaluated by the pressure sensors and the rotameters 7

during the tests. Then, each convergent VT cyclone separator with specified parameters is tested. The test processes are repeated several times for each parameter to determine the reliable values for the exhaust temperatures and pressures. The photograph of the control valves used in the tests is shown in Fig.4.

Fig. 4 In this section, the uncertainty and the error evaluations regarding the measurements of the pressure and temperature are discussed. A differential method is presented by Moffat [64] (in 1985) to estimate the maximum temperature and the pressure uncertainties. This method uses two parameters namely the instrument accuracy and the minimum value of the outputs for estimating the errors. We assumed that an especial quantity like g is calculated by some independent variables such as yi, so the value of error for g is estimated by:

g  g



n

( 1

y i 2 ) yi

In the present equation, the terms of y i , y i and

(1)

y i represent the minimum value of the yi

independent parameter, the measuring instruments accuracy and the error of the independent parameter, respectively. The accuracies of the pressure and the temperature are 0.025 bar and 0.2 C respectively. Also the logged accuracies regarding the pressure and the temperature are 0.01 (bar) and 0.1 K. So, we can calculate the maximum errors for the pressure and the temperature as bellow:

T T T 0.2 0.1  ( Thermometer )2  ( Logged )2  ( ) 2  ( ) 2  0.017  1.7 % T Tm Tm 13 13 P P P 0.025 2 0.01 2  ( Sensor )2  ( Logged )2  ( ) ( )  0.024  2.4 % P Pm Pm 1.1 1.1

3. Numerical approach 3. 1. Equations 8

The fluid stream has a compressible pattern with the high rotational specifications, so the RSM turbulence model is applied to solve the nonlinear equations (conservation of momentum, mass and energy equation) of flow streams inside the tested convergent VT cyclone separator. A numerical model (three-dimensional) is developed to predict the fluid treatment inside the convergent VT cyclone separator. This model is employed to create an accurate validation between the experimental and the numerical outputs. This model is executed by a finite volume technique (Fluent 6.3.26) using the steady state conditions. The equations of conservation of mass, momentum and energy (thermal consideration) can be provided as bellow: The continuity equation:

.(  ) 

 0 t

(2)

The fluid flow in the present work is considered to be steady, so the term of

 is assumed to be t

zero. Momentum equation:   xj

(  ui u j )  

p     ui  u j 2     ij   xi  x j    x j  xi 3 

 u k   (  uiu j )    xk    x j 

(3)

Energy equation:      T 1    u j u j  h    ui ( ij ) eff  k eff u  i  xi   xj 2   x j  

k eff  K 

c Pr p

t

(4)

t

The influence of the compressibility is assumed as follow (the utilized air is assumed as the ideal gas):

P  RT

(5)

The Fluent software provides the Reynolds stress model (LRR-IP) [65, 66 and 67] as the most elaborate numerical modeling to simulate the full turbulent rotational flows. The transport equations have been solved together with the equation of dissipation rate to close the Reynoldsaveraged Navier-Stokes relations by RSM "abandoning the isotropic eddy-viscosity assumption". 9

So, seven transport equations are solved in the three-dimensional issues, while, five transport equations are required to be solved in the two dimensional problems. This model has several advantages compared with other models (two-equation or one-equation models). Some of these benefits can be listed as: (a) considering the streamline curvature effect and involving the impact of the sharp changes in the rate of strain and (b) modeling the high rotational and swirl patterns. These great potentials and excellent performances convince the researchers to use this model, in spite of a lot of time to solve the 3D problems by this model. The main transport equations of Reynolds stresses,( u iu j ), can be considered as bellow:      ( u iu j )  ( u k u iu j )   [ u iu j u k  p ( kj u i   ik u j )]  [ u iu j ] t x k x k x k x k Local Time Derivative

C ij Convection

  (u iu k

u j x k

DT ,ij  Turbulent Diffusion

 u j u k

u i u  u j )   ( g i u j   g j u i )  p ( i  ) x k x j x i G ij  Buoyancy Production

Pij Stress Production

2

D L ,ij  Molecular Diffusion

ij  Pr essure Strain

u i u j  2 k (u j u m  ikm  u iu m  jkm )  S user x k x k User-Defined Source Term

 ij  Dissipation

Fij  Production By System Rotation

Where Suser, Fij, ɛij, ϕij, Gij, Pij, DL, ij, DT, ij, Cij and

(6)

 ( u iu j ) are considered as User-Defined t

Source Term, Production By System Rotation, Dissipation, Pressure Strain, Buoyancy Production, Stress Production, Molecular Diffusion, Turbulent Diffusion, Convection and Local Time Derivative, respectively. Here we present the modeling process for D T,ij, Gij, ϕij and εij. 3. 1. 1. Modeling process for the Turbulent Diffusive Transport Daly and Harlow [68] introduced the generalized gradient-diffusion model which can be used for modeling DT,ij. DT ,ij  C s

k u k u l u iu j  ( ) x k  x l

10

(7)

Direct using of this equation leads to numerical instabilities so this equation is simplified as bellow [69]: DT ,ij 

 t u iu j ( ) x k  k x k

(8)

 k is equal to 0.0.82 [69], also t is the turbulent viscosity, then can be calculated as: t  C 

(9)

k2



And C  =0.09. 3. 1. 2. Modeling process for the Pressure-Strain Term (Linear Pressure-Strain Model)

ij or the pressure strain term (equation 6) is modeled as follows (proposed by Gibson and Launder [65], Launder [70,66] and Fu et al. [71]). As the classical approach we have the following decomposition:

ij  ij ,1  ij ,2  ij ,w

(10)

In this equation, ij ,1 is a term regarding the slow pressure-strain (the return-to-isotropy term),

ij ,2 is known as the rapid pressure-strain term, and ij ,w is called (as the last term) the wallreflection term. The slow pressure strain term or ij ,1 can be modeled according the following relation:

ij ,1  C 1



2 [u iu j   ij k ] k 3

(11)

And C1=1.8.

ij ,2 or the rapid pressure-strain term can be defined as bellow: 2 3

ij ,2  C 2 [(Pij  Fij  G ij  C ij )   ij (P  G  C )]

(12)

1 In this equation C2=0.60. Also, C ij , G ij , Fij and Pij are presented in Equation (6), G  G kk 2 P

1 1 Pkk and C  C kk . 2 2 11

ij ,w or the wall-reflection factor refers to the normal stresses redistribution near the walls. It tends to enhance the stresses parallel to the wall, while damping the normal stress perpendicular to the wall:

C k 3/ 2  3 3 ij ,w  C 1 (u k u m n k n m  ij  u iu k n j n k  u j u k n i n k ) l k 2 2 d (13) 3/ 2

C k 3 3 C 2 (km ,2 n k n m  ij  ik ,2 n j n k   jk ,2 ni n k ) l 2 2 d

In equation 13, C 2 =0.3, C 1 =0.5, d can be define as the normal distance to the wall, n k is presented as the x k component of the unit normal to the wall, also C l  C  3/ 4 / k which k is the Von Kármán constant equal to 0.4187 and C  =0.09. 3. 1. 3. Buoyancy effect on turbulence

G ij refers to the production term through the buoyancy effect: G ij  

t Prt

(g i

T T gj ) x j x i

(14)

Prt is assumed as the turbulent Prandtl number for energy (=0.85).  is the coefficient for thermal expansion, and can be defined as:

 

1  ( )  T p

(15)

We have the following equation for G ij using equation (15):

G ij  

t   (g i gj )  Prt x j x i

(16)

3. 1. 4. Modeling process for the turbulent kinetic energy if the turbulent kinetic energy is applied for considering a special term, it can be provided by taking the Reynolds stress tensor trace:

12

1 k  u iu i 2

(17)

In this case, the following relation is considered to model the transport equation for the turbulent kinetic energy (for obtaining boundary conditions regarding the Reynolds stresses).

 k    1 (k )  (  ku i )  [(   t ) ]  (Pii  G ii )   (1  2M t 2 )  S k t x i x j  k x j 2

(18)

In this equation  k =0.82, also S k is assumed as a user defined source term. It should be said that this equation is achievable by contracting equation 6. It should be said that, this equation is similar to the equation applied for k-epsilon model. Equation (18) is solved for the flow domain but the obtained magnitudes for k are applied only for boundary conditions. 3. 1. 5. Modeling process for dissipation rate Here the dissipation tensor (  ij ) will be modeled as follow: 2 3

 ij   ij (  Y M )

(19)

In this equation Y M  2 M 2t is defined as an additional "dilatation dissipation" term which the turbulent Mach number (in equation (19)) can be modeled as:

Mt 

(20)

k a2

Where a   RT is the sound speed. Because we use the ideal gas law in our assumptions, this compressibility modification should be used. Finally, the scalar dissipation rate (  ) is calculated using a transport equation similar to that applied in the standard k-epsilon model.

     1  2 (  )  ( u i )  [(   t ) ]C  1 [Pii  C  3G ii ]  C  2   S  t x i x i   x j 2 k k

(21)

Here C  1 =1.44,   =1 and C  2 =1.92, also, C  3 can be calculated as a function of the direction of local flow relative to the vector of gravitational factor. 3. 1. 6. Modeling process for turbulent viscosity

13

This subsection tries to explain the modeling process for the turbulent viscosity, so, it can be said that this factor is calculated same as the k-epsilon model.

t  C 

k2

(22)



And C  =0.09. 3. 1. 7. Modeling process for convective heat and mass transfer In this case (Reynolds stress model (LRR-IP)), the process of turbulent heat transfer is evaluated applying the concept of Reynolds' analogy to turbulent momentum transfer. So, we have the "modeled" energy equation which is presented as: c p t T    (E )  [u i (  E  p )]  [(k  )  u i ( ij )eff ]  S h t x i x j Prt x j

(23)

Where the total energy is presented by E and ( ij )eff is the tensor of deviatoric stress: ( ij )eff  eff (

u j x i



u i u k 2 )  eff  ij x j 3 x k

(24)

It should be pointed that the viscous heating is evaluated by the term involving ( ij )eff . In this investigation the turbulent Prandtl number is assumed to be equal to 0.85. Turbulent mass transfer is treated similarly, with a turbulent Schmidt number of 0.7. In fact, the RSM is appropriate for precisely predicting complex flow regimes such as: cyclone flows, rotating flow passages, swirling combustor flows, secondary flows and flows involving separation. The flow field in a vortex tube has the most features listed above. So, in this research the RSM is applied for modeling the separation procedure in the convergent vortex tube.

3. 2. Physical simulation 3. 2. 1. Modeling The three dimensional numerical model developed in the numerical section is created on basis of the exact structural parameters of the real case. So, this means that the geometrical factors are completely similar to the laboratory model (Table 1). In the computational simulation and experimental study, the cold diameter of VT cyclone separator is 9 mm as the fixed property. 14

The flow pattern and the rate of energy separation are changed by changing the mentioned parameters (throttle angle, convergence angle of main tube, throttle diameter, length of convergent main tube and slots number), and then these changes appear as some changes in the output temperatures. This research uses a 3D model to provide a clear observation for the process of energy separation inside the convergent VT cyclone separator. The variations in the axial and tangential velocities also the total pressure are presented in comparison form to analyze the flow properties. There are different meshing methods (unstructured and structured); each can be usable to different geometries. The better mesh quality leads to the greater and faster convergence rate. In other words, the correct solving has been achieved faster. It should be said that the accuracy of the results is very important near the outlets, so this issue shows the importance of using the finer mesh grids near the hot and cold outlets (Fig.5 a). A normal VT cyclone separator with the straight main tube is shown in Fig. 5b (compared with the convergent one). In the following, we have the solution with more accuracy using the better mesh quality. Furthermore the CPU time is an important factor in the computational problems. In some problems which the quality of the arrangement of cells is not efficient, the CPU time needed can be relatively increased. The CPU time will usually be proportional to the quality of the mesh grids. In three dimensional modeling, there are 3-dimensional elements, namely; hexahedron, quadrilateral pyramid and tetrahedron. For the same number of elements, the accuracy of solutions has the highest value using the triangular prism and the hexahedral meshes. So, these two types of mesh units have been used in the developed model as seen in Fig. 5c and 5d. The volume around the center line of the VT cyclone separator is arranged by the triangular prism units; consequently the rest volume is made by the hexahedral meshes. So, in this way, both time and accuracy are combined together to produce the reliable results.

Fig. 5 The turbulence intensity of air stream inside a VT cyclone separator is so high, so that the conventional numerical methods have not the ability to solve the equations in this instrument. 15

The URFs (Under-Relaxation Factors) have important roles in the process of computation. It should be said that these factors determine the development path of the calculations. The calculations should be a step by step process. The number of stages is determined by the URFs. In this way, the stability of the solution increases, significantly. In this article, the URF's changes have been proposed to solve the equations of the flow pattern in the convergent VT cyclone separator to be used by other researchers (as seen in Table 3). The First and Second Order Schemes (intermittent) are applied for the pressure discretization, since according to the CFD experiences, these combinations work better than other Schemes for both the swirling flow with high rotational speed (1,000,000 rpm) and the steep pressure variations. It should be said that, the SIMPLE algorithm is added to the computations for the Pressure-Velocity Coupling. The process of the computing continues as far as the calculations are converged. In this research, the convergences have been occurred in the range of 150000 to 210000 iterations. The changes of the values for the URFs are presented in Table 3, step by step.

Table 3 3.2.2. Boundary conditions The simulated domain requires some boundary conditions (Fig. 6). At hot exit (bottom) and the cold exhaust (top) of the CFD domain, the Pressure-Outlet boundary conditions are assumed. On wall of the 3D model, the adiabatic boundary condition is applied (there is no heat transfer between the convergent VT cyclone and ambient air), consequently, the convection effect is neglected. There is a No-slip boundary-condition between the walls of domain and the rotational stream inside the VT cyclone separator. The other boundary conditions are applied as follow: the nozzle slots (injectors) is set as the pressure inlet (Experimental values) with the pressure 0.45 MPa. The temperature of slots surface is adjusted to be 294.2 K (ambient temperature). The operating fluid inside the convergent VT cyclone separator is considered to be air with the ideal gas properties, so   1.4 . The boundary conditions are listed as bellow:

16

(1) Slots of the injectors, the boundaries are considered as the Pressure Inlet, the specified pressure value 4.5 bar, also, the fixed stagnation temperature 294.2 K. (2) Cold and hot exits set as the Pressure-Outlet. (3) Walls around the domain are set to be the Adiabatic Boundary Conditions, also with no slip properties.

Fig. 6 3.3. Grid independence study Before beginning the process of the numerical modeling, calculation or simulation, the grid independence check is very important. According to this fact, four different numbers of the unit cell volumes are examined and the results are presented in Fig. 7 (in comparison form). A convergent VT cyclone separator with a truncated cone throttle valve (for   2 deg, α=30 deg, Dth=4 mm, L

convergent=185mm

and D cold=9 mm as the basic model) was modeled with different

unit cell volumes to guarantee the mesh sensitivity and the grid independence of the numerical outputs. This grid independence study focuses on the predicted tangential velocity on a radius of the convergent vortex tube located at Z/L=0.1 for the domains with 1.12 million, 1.67 million, 2.02 million and 2.35 million (denoted "fine") unit volumes. As seen in Fig. 7, the comparison between the results of four different unit cell volumes or the resolution of the mesh grids proves that the obtained calculation applying 2.02 million units has the competency to be the mesh independent model. This subject represents that the enhancing unit volume number has no necessary change in the accuracy of the results. To decrease the computational time and the cost, we choose 2.02 million unit cell volumes in all our models.

Fig. 7

17

4. Results and discussion To create a clear insight into the effects of throttle angle, throttle diameter, convergence angle of main tube, length of convergent main tube, slots number and injection pressure on the separation capabilities of the convergent VT cyclone separator (resulting from the exhausts), some experiments and numerical simulations as the parametric studies are presented. This research focuses on the use of the convergent VT cyclone separator in various structural conditions, in other words, what different operating conditions or structural parameters can have the sensitive effects on the separation performance of the VT cyclone separator equipped with convergent main tube. So, this research tries to present the optimum values for the mentioned parameters to create the best possible separation capability (for the convergent VT cyclone separator) applying both experiments and CFD methods (RSM). This parametric study involves some terms such as; (a) testing the effects of six different throttle diameters (4-6.5mm), (b) testing the effect of the seven throttle angles (α=30-90 deg) on the performance of the convergent VT cyclone separator, (c) testing the effect of six different convergence angles for the main tube (β= 2- 12 deg), (d) evaluating the effect of the five different lengths for the convergent main tube (L=180- 200 mm) and (e) testing the effect of applying different slots numbers (inside the chamber) on the CVT performance. Also, this study tries to analysis the thermal reactions of the convergent VT cyclone separator against different operating pressures (Pi=0.45, 0.55, 0.65MPa with compressed air). In each part of experimental analysis, the lengths including (throttle diameter and convergent lengths) are nondimensionalized by dividing to the cold orifice diameter as a constant value in all tests. The separation efficiencies of the convergent VT cyclone separator can be represented as Heating and Cooling which are defined as following equations:

Heating 

T Hot T Hot T Inlet   T Isentropic T Inlet T Isentropic

18

T Hot T Inlet T Inlet [1  (

PAtm ) PInlet

(25)  1 

]

Cooling 

TCold T TCold  Inlet  T Isentropic T Inlet T Isentropic

T Inlet T Cold P T Inlet [1  ( Atm ) PInlet

(26)  1 

]

Where PAtm , PInlet , TCold , T Hot and T Isentropic represent the ambient pressure, the injection pressure, the cold exhaust temperature, the hot exhaust temperature and the isentropic temperature drop, respectively The cold flow fraction is an effective parameter in the modeling of the convergent VT cyclone separator efficiency, because this is an output parameter which defines the flow rate of the cold exhaust. This important parameter is obtained by dividing the rate of the cold flow by rate of inlet flow. Equation (27) shows this relation by:



mc mi

(27)

As mentioned before, the cold air flow is managed by the control valve performance. So, this part of the system has an important and direct impact on the energy distribution. Therefore, the optimal design of this part of the system can have a considerable impact on the efficiency of the convergent VT separator system. So, in the first step, we try to optimize this part of the convergent VT cyclone separator.

4. 1. Experimental Results 4. 1. 1. Effect of nondimensional throttle diameter In the preliminary experimental analysis, the effects of nondimensional throttle diameter of the valve ( D Rth 

Dth

DCold ) on the heating and cooling efficiencies of the convergent VT cyclone

separator are investigated, experimentally. Six conical valves with different throttle diameters

Dth are utilized in the experiments with the diameter of Dth  4, 4.5, 5, 5.5, 6 and 6.5mm. In this part a nondimensional parameter (DRth) should be presented based on throttle diameter to establish a correct analysis, so, the throttle diameter values are divided to the cold orifice diameter as a constant value in all tests. So, the effect of throttle diameter is presented based on 19

different (DRth) as a nondimensional diameter (DRth= 0.444, 0.5, 0.555, 0.611, 0.666 and 0.722). The convergence angle of main tube, the throttle angle, length of convergent main tube and slots number for all the convergent VT cyclone separator are adjusted equal for managing a correct comparison. The hot and cold temperature efficiencies are presented in Figs. 8 and 9. This result can be achieve that, the cooling and heating efficiencies (also the related cold and hot thermal drops ΔTc and ΔTh ) have the highest values at D Rth =0.611 (or the related optimum value for the throttle diameter is 5.5 mm). So, the analyzed range of the throttle diameter can be divided into two subsets, the first subrange contains D Rth smaller than 0.611, and the second subrange contains the values larger than 0.611. It can be seen from Figs. 8 and 9 that, for the first subrange, the smaller nondimensional throttle diameters provide the smaller heating and cooling efficiencies (hot and cold temperature drops). Also, the heating and the cooling (flow separation) capabilities increases extremely with an increase in the throttle diameter up to D Rth = 0.611, then beyond D Rth = 0.611, the heating and the cooling capabilities are decreased. The details of the heating and the cooling improvements are presented in Table 4 (This table is taken from Figs. 8 and 9). According to Table 4, the convergent VT cyclone separator equipped with a throttle valve with D Rth = 0.611 provides 30.01 % higher cooling temperature drop (cold temperature difference) and 20.04 % higher heating temperature drop (hot temperature difference) as compared to the basic model ( D Rth = 0.444). So, the convergent VT cyclone separator with nondimensional throttle diameter of 0.611 provides the best separation (both cooling and heating) performance among all the convergent VT designs. Therefore, the conical valve with

D Rth = 0.611 has been selected for performing further investigations for the design of the optimum convergent VT cyclone separator. Also, in this case (convergent VT); the change in the location of optimum cold mass fraction is almost negligible with increasing the nondimensional throttle diameter from 0.444 to 0.722 (Fig. 9). In other words, the location or behavior of the

20

optimum cold mass fraction point is not significantly influenced by the variation of throttle diameter.

. As seen in Fig. 9, the best cooling efficiency is provided by the throttle diameter of D Rth = 0.611. The cooling efficiency of the convergent VT cyclone separator with D Rth = 0.611 is 22.34 % (at cold flow fraction of 0.27), which is 5.16 % higher than the efficiency of basic model (

D Rth = 0.444). For greater and smaller diameters than D Rth = 0.611 the efficiency allays.

Fig. 8 Fig. 9 Table 4 In this stage, the mean squared error (MSE) is measured that is, the difference between the estimator value and what is measured. The MSE (equation 28) is a risk function, corresponding to the expected value of the squared error or quadratic loss. MSE 

1 n ˆ (Y i Y i )2  i 1 n

(28)

Here, Yˆ is defined as a vector of n predictions. Also, Y can be considered as the vector of the measured magnitudes corresponding to inputs to the function which produced the predictions. A polynomial regression equation is considered to predict the new values for the temperature points on the charts. Table 5 presents the results of the MSE calculations for D Rth = 0.611 based on Fig. 8, step by step. According to Table 5, the mean squared error (MSE) is 0.053 which shows the difference between the estimator (polynomial regression equation) and the experimental measurements. This value indicates that the polynomial regression equation has a considerable accuracy to predict the hot exit temperatures (in the case of D Rth = 0.611). Table 6 illustrates the polynomial regression equations and the MSE values for all temperature variations based on different nondimensional throttle diameters. Table 6 is managed according to the results of Figs. 8 21

and 9. As seen in Table 6, the maximum MSE for the heating and cooling efficiencies are 0.21 and 0.307, respectively. These values (Tables 5 and 6) show the interesting capability of the equations to predict the reliable values for the exhaust efficiencies.

Table 5 Table 6 4. 1. 2. Effect of throttle angle (α) Seven control valves with the various throttle angles are used in this part of the experimental analysis (with the throttle angle of   15, 20, 25, 30, 35, 40 and 45 deg ). It should be said that the nondimensional throttle diameter is considered equal to 0.611 as a fixed parameter (optimum value from the previous section). It should be said that, the impact of the throttle angle of control valve on the separation efficiency for a convergent VT cyclone separator has not been analyzed yet (the impact of the conical valve angle on the straight cyclone separator performance is analyzed by Rafiee and Sadeghiazad [51]). This section presents an optimization procedure for designing of a control valve based on changing the throttle angle. As seen in Figs. 10 and 11, the variations of heating and cooling efficiencies are plotted for different throttle angles. It should be said that, as the throttle angle improves from 15 to 30, the cooling efficiency (also heating) increases, and beyond α=30 deg, the flow separation quality (cold and hot drops) decreases sharply. The heating ability has the highest magnitude in the range of α= 25 to 35 deg. In this range, the throttle angle effect on the heating capability is almost negligible. According to Fig. 10, when the throttle angle is equal or less than 20 deg, the heating efficiency changes softly, but when the throttle angle is larger than 20 deg, the heating efficiency changes very fast. Applying the convergent VT cyclone separator with the throttle angle of 30 deg leads to 11.8 K (50.60%) higher hot temperature drop at cold flow ratio of 0.75, as compared to α= 20 deg, which is very impressive. As another result, the intensity of variation of the heating efficiency (as compared to the basic model) is different in different ranges of cold flow ratio, so that, the improvement of hot temperature drop (from the basic model α= 15 deg and the optimum model α= 30 deg) 22

decreases continuously with decreasing the cold mass fraction and reaches the minimum value (28.61 %) at cold flow ratio of 0.15. According to Fig. 11, the best cooling separation capacity can be taken when the cold flow ratio is in range of 0.3 and 0.5. This means that, unlike the nondimensional throttle diameter, the position of the best cold flow ratio can be affected with the throttle angle variation.

Fig. 10 Fig. 11 The improvements in the separation capabilities are presented in Table 7 using different throttle angles (20 to 45 deg), as compared to   15 deg or the basic model (this table is taken from Figs. 10 and 11). According to Table 7 and equations 25 and 26, the convergent VT cyclone separator equipped with a throttle valve with  = 30 deg provides 43.76 % higher cold temperature drop and 50.60 % higher hot temperature drop as compared to the basic model (   15 deg and D Rth = 0.611). So, the convergent VT cyclone separator with the throttle angle of 30 deg provides the best separation (both cooling and heating) performance among all the convergent VT cyclone separators. Therefore, the conical valve with the throttle angle of 30 deg and the nondimensional throttle diameter of 0.611 is selected to perform further investigations for designing of the optimum convergent VT cyclone separator.

Table 7 Table 8 presents the polynomial regression equations and the MSE values for all temperature variations based on different throttle angles. Table 8 is managed according to the results of Figs. 10 and 11. As seen in Table 8, the maximum MSE for the hot and cold temperature differences are 1.04 and 0.414, respectively. These values prove that the predictor can estimate the temperature values for all cases with different throttle angles, precisely.

Table 8 4. 1. 3. Effects of convergence main tube angle, injection pressure and nondimensional length of convergent main tube 23

This section deals with the impacts of the convergence angle, the injection pressure and the nondimensional length of convergent hot tube (LN= Lconvergent/DCold) on heating efficiency and the cooling capability of the convergent VT cyclone separator. Six convergent main tubes with different convergence angles (   2, 4, 6, 8, 10 and 12deg ) and five convergent main tubes with different nondimensional lengths (LN= 20, 20.55, 21.11, 21.66 and 22.22) are used in these setups. The flow or energy separation phenomenon takes place inside the main tube for all kinds of VTs including straight, convergent and divergent. So, any change in the shape or structural parameters of this part leads to important and severe variation in the pattern of energy distribution and the flow separation inside the cyclone separator. On basis of the previous experimental results (previous sections), the optimum values for the throttle angle and nondimensional diameter are selected (DRth = 0.611 and α=30 deg). Under these conditions, the effects of nondimensional length and convergence angle of the main tube on the cooling and heating capacities are studied.

Fig. 12 Fig. 13 Figs. 12 and 13 show that when the flow fraction increases over the special range of flow fraction (0.15 to 0.5-0.8 for the heating effectiveness and 0.15 to 0.38-0.57 for the cooling ability), the heating and cooling efficiencies (hot and cold temperature differences) improve slowly (for each convergence angle), then as the flow fraction gets further growth, the heating and cooling efficiencies (the hot and cold temperature variations) decrease. With regard to the effect of convergence angle, this becomes obvious that the best angle is equal to 10 deg to achieve the best thermal results. The results show that the cooling and heating abilities of the system will increase by 7.45 and 5.76 percent at the optimum flow fraction (respectively) as a result of increase in the convergence angle from 8 to 10 deg. Meanwhile, figures 12 and 13 indicate that the thermal (heating and cooling) efficiencies of the VT decreases with further increase in the convergence angle from 10 to 12. The amount of the reduction is equal to 5.71% 24

for cooling and 4.90% for heating at the optimum flow fraction. In fact, both cooling and heating capacities improve sharply with enhance in the convergence angle from 2 to 10deg. So, the convergence angle of the main tube is found to be an important parameter for a higher cooling efficiency with an optimum value of 10 deg. These improvements in the cooling and heating separation capacities are pointed in Table 9. Furthermore, it can be said that, the optimum cold flow fraction will be strongly affected with the convergence main tube angle changing (as seen in Figs. 12 and 13). This means that in the case of the cooling efficiency, with changing the convergence angle from 2 to 12 deg, the optimum flow fraction varies from 0.38 to 0.61, also in the case of the heating efficiency the optimum flow fraction varies from 0.74 to 0.52.

Table 9 Table 9 shows that with optimizing and employing the appropriate convergent main tube with the optimized convergence angle, the cooling capacity and heating ability elevate around 29.76 and 20.54% reflectively. Table 10 presents the polynomial regression equations and the MSE values for all temperature variations based on different convergence angles. Table 10 is managed according to the results of Figs. 12 and 13. As seen in Table 10, the maximum MSE for the heating and cooling efficiencies are 1.2 and 0.966, respectively. These values prove that the predictor can estimate the temperature values for all cases with different convergence angles, precisely.

Table 10 According to the charts and tables, we will have the best performance using the convergence angle of 10 deg. The thermal separations are expected to be greatly reduced by increasing the convergence angle greater than 12 deg. The convergence angle of 10 deg provides the highest cryogenic performance between other convergent main tubes at flow fraction of 0.57 with performance value of 41.68 %. Also, for greater and smaller convergence angles, the efficiency allays. So that, if we increase the convergence angle of the device and get to 12 deg, the overall 25

efficiency is reduced from 41.68% to 39.30%. And if the convergence angle is reduced from 10 to 8 degrees the efficiency is reduced from 41.68% to 38.78% again.

As the results of this section, the convergence angle of the main tube imposes some extreme fluctuations in the separation process inside the convergent VT cyclone separator. In this part, to evaluate the impact of the injection pressure (CVTs with different convergence angles) on the cooling performance, three different values of injection pressure (4.5, 5.5 and 6.5 bar) are applied on the convergent VT cyclone separator for each convergence angle in the range of  =2 to 10deg, and the results are shown in Fig. 14. As the first result, the higher injection pressure leads to higher cold temperature difference, so the increasing injection pressure at the injectors is a favor factor which causes a better energy separation inside the convergent VT cyclone separator and greatly increases the convergent VT cyclone separator performance. As the second result, the improvement of the cooling efficiency (with increasing pressure) has the maximum value at the minimum convergence angle (  =2 deg) and the minimum value at the maximum convergence angle (  =10 deg). The cooling efficiency improves more seriously with an increase in the injection pressure upto 5.5 bar and beyond 5.5 bar the increase in the cooling efficiency is nominal for small convergence angles  = 2, 4 and 6 deg. Also, for   8 deg, the increase in the cooling efficiency (with increasing injection pressure) is almost negligible. According to Fig. 14, when the injection pressure is improved from 4.5-6.5 bar for convergence angle of 2 deg, the cooling performance is increased by 12.10%, and, this improvement is equal to 3.91% for the convergence angle of 10 deg. This issue reflects this fact that the increase in the pressure is not economical to achieve the higher separation performance for large convergence angles.

Fig. 14 So far we have considered three structural parameters (throttle angle, nondimensional throttle diameter of control valve and convergence angle of main tube) to analysis the thermal 26

performance of the convergent VT cyclone separator. Up to this point, the optimum values for these parameters which lead to the best separation efficiency can be listed as;   10 deg,   30 deg and D Rth  0.611 . In this stage, we try to explain the impact of nondimensional length of the convergent main tube on separation process inside the convergent VT cyclone separator. For this reason, five convergent main tubes with convergence angle of   10 deg and different nondimensional lengths (LN= 20, 20.55, 21.11, 21.66 and 22.22) are manufactured and applied in the tests, also the previous optimum parameters are constant (   30 deg and D Rth  0.611 ). The cooling and heating efficiencies for the convergent VT cyclone separator equipped with different convergent man tubes with different nondimensional lengths are presented in Figs. 15 and 16. As seen in these Figs, three zones can be considered in the charts, the first zone for low cold flow ratio values (  0.45), the middle zone for medium values (0.45  cold mass fraction  0.8) and the third zone for the large values (0.8  cold mass fraction). a) Zone 1: For both graphs, it can be observed that as the nondimensional length (LN=LConvergent/DCold) of convergent main tube increases from 20 to 22.22, the cooling and heating efficiencies decrease, excepting the heating efficiency for the nondimensional convergent length of 22.22, which lies between 21.11 and 21.66. Also, as the cold mass fraction decreases, the difference between the heating and cooling efficiencies increases and reaches the maximum value at minimum cold mass fraction. As nondimensional length decreases, the cooling and heating capabilities increase by up to 19.75 and 10.26 percent, respectively. As a conclusion, when the convergent VT cyclone separator is used for the low cold flow rates, it is better to use a convergent model with the less nondimensional length as compared to other models. b) Middle Zone: Figs. 15 and 16 show that we have an optimum value regarding the nondimensional length which provides the maximum cooling and heating efficiencies. It can be observed that, the thermal capability (cooling and heating efficiencies or cold and hot temperature drops) improves with an increase in nondimensional convergent length of main tube 27

upto LN= 21.66, then beyond LN= 21.66, the improvement of the thermal efficiency is stopped; this means that, the thermal ability decreases. It can be seen that for a fixed geometry (   10 deg,   30 deg and D Rth  0.611 ), the convergent VT cyclone separator with LN= 21.66 provides 10.13 and 6.72 % higher cooling and heating efficiencies than the model with LN= 20 (the minimum length), respectively. Also, the cooling ability and the heating efficiency are 12.67 % and 8.87 % higher for LN= 21.66 as compared to LN= 22.22 (the maximum length) also, 9.79 % and 3.76 % as compared to LN= 20.55 (the basic model). c) Zone 3: We can observe that the pattern of the thermal improvements in this zone is similar to that explained in Zone 1. This denoted that as the nondimensional length of the convergent main tube is reduced, the separation efficiency (both cold and hot) improves. So, for smaller lengths, the energy or flow separation phenomenon becomes stronger leading to the higher hot and cold temperature drops (heating and cooling efficiencies). Therefore, the convergent main tube with convergence angle of 10 deg and the nondimensional length of 21.66 is selected for performing further investigations.

Fig. 15 Fig. 16 Table 11 presents the polynomial regression equations and the MSE values for all temperature variations based on different main tube lengths (based on Figs. 15 and 16). As seen in Table 11, the maximum MSE for the heating and cooling efficiencies are 0.704 and 1.87, respectively.

Table 11 4. 1. 4. The slots number effect In the case of straight VT cyclone separator, Rafiee and Rahimi [17] stated that the cooling efficiency improves by 45.7 percent (11.9°C) as the number of nozzle slots improves from 2-6. In other words, the cooling efficiency enhances continuously, with an increase in nozzles number. So, it can be said that the nozzles number has very impressive effect on the cooling performance of the VT cyclone separator with straight main tube. Fig. 17 shows the variation of 28

cooling efficiency of the optimum convergent VT cyclone separator with cold mass fraction for different nozzles (slots) numbers. Unlike the conclusion provided by Rafiee and Rahimi [17] (in the case of straight VT cyclone separator), this research proves that the convergent VT cyclone separator has a different reaction against the increasing slot number. The cooling efficiency improves sharply with an increase in the slots number up to N= 4 (the basic model has 4 slots), then beyond N= 4, the cooling efficiency decreases (nominal). It can be seen that the cooling efficiency has the lowest values at the minimum slots number N=2. As the slot number is increased from 2 to 4, the cold temperature difference increases by 21.12%. The physical reason can be explained in this way; when the slots number is increased from 2 to 4, the turbulence kinetic energy improves, and then beyond 4 slots, it becomes constant (approximately). This is on basis of the fact that the pressure and the velocity drops increase as the increasing number of slots in the range of 2 to 4, consequently this event is seen with an enhance in the cold temperature drop. According to the statements, it can be concluded that, by increasing the slots number, the level of turbulence improves in the convergent VT cyclone separator, which leads to an improve in cooling efficiency (cold temperature drop). Overall, the optimum values for mentioned structural parameters (nondimensional throttle diameter, throttle angle, convergence angle of main tube, the nondimensional length of convergent man tube and number of slots) can be presented as Table 12.

Fig. 17 Table 12 According to Table 12, it can be pointed that the throttle angle has the maximum effect on the cooling performance by 43.76%, also, the influence of the nondimensional throttle diameter of the valve is the second highest by 30.01%. The last effect belongs to the nondimensional length of the convergent main tube by 9.79 %. An investigation has been conducted on a similar VT cyclone equipped with straight or common hot tube by Stephan et al. [72]. Their results show that the ratio of cold temperature difference to

29

the maximum temperature difference illustrates a special fraction which varies only with the cold flow fraction as bellow:

T c  f ( ) T c ,max

(29)

According to Fig. 18, the Stephan's theory is confirmed for the slots numbers. As seen in Fig. 18, this can be said that variation of number of slots does not vary the balance of the pressure patterns, so the optimum cold flow fraction is not changed. The similarity relation for the slots number can be reported as bellow:

y  4.582x 2  4.029x  0.1 The Equation (30) (reported from Fig. 18), indicates that the ratio of

(30)

T c for the convergent T c ,max

VT cyclone separators is independent of the slots number, and can be reported as only one variable parameter namely cold flow fraction.

Fig. 18 The results by Stephan et al. [72], Farzaneh-Gord and Sadi [73] and Hilsch [2] are employed to verify the similarity equation for the present convergent VT cyclone separator. The variation of

T c with the cold flow fraction is presented for four different works in Fig. 19. The results T c ,max of

T c for different researches are showing the same trend but with different optimum cold T c ,max

mass fractions (red lines). The red lines determine the point of the optimum cold flow fraction for each VT cyclone separator. This difference refers to the dissimilarity of the pressure balance inside the used VT cyclone separators. The structural parameters of the VT cyclone separators in other researches (which are compared to our convergent VT cyclone separator) are presented in Table 13.

Table 13 Fig. 19 30

4. 2. Numerical Results 4. 2. 1. Validation In the following, the three dimensional numerical results are validated through a comparison with the experimental outputs. In this way, to compare the predicted data, the computed outputs are considered against the laboratory results gained in the experimental section. Fig. 20, Table 14 and 15 demonstrate the comparison result between the temperature results of the real model (with six throttle valve diameters) and the three dimensional computing which was considered as same as the geometrical and the operating conditions of the real case. Fig. 20 shows the thermal efficiencies for the cold and hot exhausts of convergent vortex tube cyclone system equipped with four nozzle slots, an injection temperature of 294.2 K and the pressure of 0.45 MPa. The comparison between the computed and the laboratory outputs presents a favorable consent even though some disagreements exist at some temperature points. The average and the maximum disagreements between the experimental quantities and the predicted values of the cooling efficiency are 2.57% and 6.22%, reflectively. Also, the average and maximum values regarding the disagreements between the simulated data and experimental values for heating efficiency are 1.97 % and 2.56 %. These validations depict that the simulations can present the successful and reliable predictions regarding the laboratory sets. The quantified and detailed presentation of the disagreements regarding the cooling efficiency at cold flow ratio of 0.27 (optimum cold flow fraction for cooling efficiency) is described in Table 14. According to Table 14, the cooling efficiency values confirm the experimental measurements with 0.97–6.22% disagreement. As the result of Table 15, this can be concluded that, the results of heating efficiency agree very well with the experimental results including a deviation in the range of 0.93–2.56 %. The disagreement between the laboratory values and CFD data is due to some assumptions (in this

31

case, the walls of convergent VT cyclone separator are the adiabatic surfaces) which are considered in the simulations.

Fig. 20 Table 14 Table 15 4. 2. 2. Contours Because of the main objective of this investigation (study on the correlation between the flow separation and the energy pattern with different geometrical parameters) this is very important to describe some relevant factors within the convergent VT cyclone separator. The total temperature variations (contours) throughout the convergent VT cyclone separator are presented in Fig. 21. This is clearly certifiable that the total temperature of the region close the walls has the higher value compared to the central region. This temperature difference is very clear at the entrance of the chamber (near the cold orifice) in comparison with other longitudinal areas. The volume of the cold core is constantly growing from bottom to top of Fig. 21 (based on the cold exhaust temperature using different nondimensional throttle diameters). In fact, the use of different values of nondimensional throttle diameter causes an obvious variation in the volume of cold core. So, the volume of the cold core belongs to DRth= 0.611 (Fig. 21 b) is the coldest core and has the highest volume in comparison with other control valves. The next control valve is DRth=0.666 which has the second place in the cold core volume list. In other words, DRth=0.666 is located into the second place in the highest cold volume and the lowest temperature rankings. The last position belongs to the control valve with D Rth=0.444. According to these results, this can be said that Fig. 21 confirms the results of Figs. 8 and 9 (experimental approach), completely.

Fig. 21 In order to explain a clear understanding of the procedures happening inside the convergent VT cyclone separator, this section tries to analyze the flow pattern for these special cases involving 32

the injection pressure equal to 0.45 MPa and the cold flow fraction equal to 0.27, which, corresponded to the laboratory operating conditions. Fig. 22 describes the stream line structures within the developed convergent VT cyclone separators simulated by the RSM turbulence model. These patterns are shown on the longitudinal section of convergent VT separators equipped with three different valves (with different nondimensional throttle diameters). All the models emphasize on the creation of some recirculation areas named vortices near the chamber (cold exit) and near the control valve, which have different sizes and properties. It should be noted that, the larger size of the vortices leads to the higher level of mixing between the central cold core and the peripheral layers, so the separation capability of the convergent VT cyclone separator decreases with increasing size of the vortices. As seen in Fig. 22 (a), that's why the convergent VT cyclone separator equipped with the valve with DRth=0.444 has the lowest cooling efficiency. In this way, the flow inside this convergent VT cyclone separator has the highest amount or level of turbulence (turbulent viscosity Fig. 23). The convergent VT cyclone separator with the throttle diameter of DRth=0.444 has two longitudinal vortices, while the rest of VT cyclone separators have three longitudinal vortices. This is because of the better aerodynamic shape of the valve of DRth=0.444 which causes the fluid moves easily inside the main tube. Also Fig. 22 (a) shows the effect of level of turbulence on the location of the stagnation point. It can be pointed that distance between the stagnation point and the control valve can be limited by the amount or level of the turbulence. As said before, the convergent VT cyclone separator with DRth=0.444 has two vortices and the VT cyclone separators with DRth=0.611 and 0.666 have three vortices. According to Fig. 22 (a), it can be concluded that the development of third vortex has a very important role in enhancement of the system performance by moving the stagnation point towards the control valve position. So that, the stagnation point gets closer to the valve with third vortex growth. Fig. 22 (b) demonstrates the process of stagnation point transfer along the main tube by the third vortex. The third vortex in the convergent VT cyclone separator with DRth=0.611 is more developed as compared to the convergent VT cyclone separator with DRth=0.666, as a result, the stagnation point is closer to 33

the valve in DRth=0.611. So, the convergent VT cyclone separator with DRth=0.611 has the smallest distance between the stagnation point and the hot valve as well as the highest cooling ability. On the other hand, the largest distance between that point and the valve belongs to the convergent VT cyclone separator with DRth=0.444 which has the lowest separation efficiency. It can be obvious from the explanations above that the cooling capability can moves to the maximum value by decreasing the distance between the stagnation point and the control valve as much as possible. Two top cases having the smallest distances between the stagnation point and the valve are the convergent VT cyclone separator with DRth=0.611 and 0.666 (because of third vortex). These results confirm the Nimbalkar and Muller [74] statements. They stated that if there is an improve in the cooling performance (or decrease in the cold ratio), the mentioned stagnation point goes towards the control valve. Consequently, the convergent VT cyclone separator with DRth=0.611 has the best separation process and thermal performance among all simulated VT cyclone separators.

Fig. 22 Fig. 23 In highly rotating and fully turbulent flow pattern within the domain of the convergent VT cyclone separator, the turbulent viscosity can be assumed as the dominant factor in comparison with the molecular viscosity [13], so the turbulent viscosity can play an effective role to illustrate and explain the amount of turbulence during the thermal separation process. Fig. 23 describes the turbulent viscosity contours inside the convergent VTs with different nondimensional throttle diameters. As said before, the separation process quality was lower for the larger turbulent viscosities. The turbulent viscosity decreased by 26.64 % with an increase in the nondimensional throttle diameter from 0.444 to 0.611. also the turbulent viscosity at DRth=0.666 is 9.98 % higher than DRth=0.611. Consequently, for the convergent VT cyclone separators, the smaller level of

34

turbulent viscosity provides relatively the higher separation process quality or the smaller vortices near the chamber.

Fig. 24 The change of the rotational velocity for different convergent VT cyclone separators equipped with different control valves (with different nondimensional throttle diameters) is shown in Fig. 24(a). This figure is presented for different streamwise sections (Z/L=0.7 and 0.1) along the main tube. Fig. 24(a) indicates that the rotational or the tangential velocity (along the radius) varies greatly with different nondimensional throttle diameters. The maximum value of the tangential velocity is changed with the streamwise section and has a downward trend along the length of the hot tube. Table 16 explains the maximum total pressures, axial and tangential velocities at Z/L=0.1 and 0.7 based on different nondimensional throttle diameters. As seen in Table 16, the largest possible rotational speeds are occurred at the entrance of main tube (or Z/L=0.1), then drop to lower values as the gas expansion along the tube.

Table 16 As mentioned previously, the convergent VT cyclone separator with DRth=0.611 exhibits the highest rate of the energy separation, also, according to the results of Fig. 24(b) the highest value of the maximum tangential velocity drop belongs to this convergent VT cyclone separator. So, this result can be picked up that the higher tangential velocity drop leads to the higher cooling and separation efficiency. This issue reflects the fact that the high tangential velocity drop and the high cooling efficiency are the results of the efficient expansion of the gas inside the chamber. Consequently, the VT cyclone separators with DRth=0.444 and 0.722 have the minimum rotational velocity drops as well as the lowest cooling capabilities. Fig. 25(a) presents the axial velocity variations on the radial lines at different axial sections. As seen in Fig. 25(a), the axial velocity values consist of some positive and negative speed values in each axial section. It can be said that, the cross section area has been assumed as a velocity domain in which the velocity of the flow changes from a maximum positive value to a minimum negative magnitude. 35

This issue shows that there is a reversal pattern for the axial velocity. So, a gas return process occurs for all the flows inside the VT cyclone separator. The difference between the cold core and the flow field pressure produces a drag force which is affecting continuously on the fluid particles moving towards the control valve. The expansion process occurs from the outer to the core layers when the fluid particles cannot resist against the drag force then their velocities reach zero. During the process (expansion), the particle temperature decreases sharply and the fluid particle redirects to the central cold region. The pressure difference acting on the particles creates an accelerating movement which increases the axial velocity towards the cold exit.

As

mentioned above, the convergent VT cyclone separator with DRth=0.611 produces the highest cooling and separation capability, also, according to the results of Fig. 25(a) and Table 16, the highest value of axial speed belongs to this convergent VT cyclone separator (87.46 m.s-1 at Z/L=0.1 and 49.22 m.s-1 at Z/L=0.7). Also, according to Fig. 25(b) and Table 16, the highest possible pressure values are occurred at the entrance of main tube (at Z/L=0.1) then drops to the lower values as the gas expansion along the tube. As mentioned before, the convergent VT cyclone separator with DRth=0.611 exhibits the highest rate of the energy separation, also, according to the results of Fig. 25(b and c) and Table 16, the highest values of the total pressure in the sectional locations (exactly in Z/L=0.1, and approximately in Z/L=0.7) and the internal pressure drop belong to this convergent VT cyclone separator. So, this result can be picked up that the higher values of total pressure and maximum pressure drop lead to the higher cooling and separation efficiencies.

Fig. 25

4. 2. 3. CFD optimization In section 4. 1. 1. (Effect of nondimensional throttle diameter), six experimental setups are managed to determined the optimum value of nondimensional throttle diameter (0.444 to 0.722). As said before (in section 4. 1. 1), the convergent vortex tube with DRth=0.611 has the highest cooling and heating abilities. This is obviously observable that there is limited opportunity to determine the 36

optimum parameters in the experimental studies. It should be said that the experimental measurements are very necessary and useful to create a correct vision on the initial range of the optimization process. The experimental tests proved that we have an optimum value regarding the nondimensional throttle diameter in range of 0.5- 0.666. In this part, the simulated 3D CFD case is tested for determining the optimal model based on different nondimensional throttle diameters. These CFD optimization studies are based on the first experimental optimization (section 4. 1. 1). As seen in Fig. 26a, twenty one 3D CFD models are created (including the CFD models in the validation part) based on the variation of nondimensional throttle diameter value (between 0.5 to 0.722). The outputs of these CFD models show some amassing results. These models (based on the determined range by experimental tests) prove that we have another optimum magnitude for the nondimensional throttle diameter in the range of 0.611- 0.666. This model is a convergent vortex tube with DRth=0.633 which produces the cooling efficiency equal to 22.75% (cooling temperature drop equal to 23.29K, and 0.72K more than the basic optimum model (DRth=0.611)). After this stage, the CFD optimization will be continued using DRth=0.633. The throttle angle was considered in the range of 15 deg to 45 deg in the experimental tests. So, this range is applied to perform the CFD optimization for the throttle angle, but the difference (compared to experimental tests) is that the nondimensional throttle diameter is equal to DRth=0.633 based on the CFD optimization. Thirteen 3D CFD models are created for the optimization process in this stage. As depicted in Fig. 26b, results show that the convergent vortex tube with throttle angle of 32.5 deg and nondimensional throttle diameter of 0.633 (CFD optimization) provides the best cooling efficiency by 33.33% (or by 34.12 K which is 2.86 K higher than the cooling ability of optimized value created by the convergent VT equipped with the throttle angle of 30 deg and nondimensional throttle diameter of DRth=0.611 (comparison is between two CFD values)). In step three, this section tries to present a 3D CFD optimization for the convergence angle. So, eleven 3D CFD models are created in the convergence angle range of 2 to 12 deg. As seen in Fig. 26c, these CFD models help us to detect the exact optimum value for the convergence angle. Previously, the experimental results (section 4.1.3) presented the optimum convergent vortex tube with the convergence angle of 10 deg 37

which located between 8 deg and 12 deg. However, the CFD optimization modified the experimental results and presented the convergence angle of 9 deg as the optimum model. Finally, sixteen CFD model are developed to optimize the nondimensional main tube length (LConvergent/DCold between 20.55 and 22.22, on basis of the initial laboratory data). The initial experimental results depicted that the convergent VT with the nondimensional main tube length of 21.66 is the best convergent vortex tube for cooling purposes. However, the CFD models can provide more accurate results about the exact optimum model. The CFD optimization results show that the convergent VT equipped with the nondimensional main tube length of 21.55 has the best cryogenic treatment equal to 46.89% (or 48.01K, this value is a numerical data, generally the experimental values are higher than CFD predicted results also this value is 1.3K higher than the best model provided by the experimental tests (LN=21.66)). As an important result, it can be said that, the experimental tests are very important to determine the correct range for the parametric optimizations, but, using the precise numerical models is necessary and very important to elect the exact optimum models. So, in this study the exact optimum model is the convergent vortex tube with D Rth=0.633, α=32.5 deg, β=9 deg and LN=LConvergent/DCold=21.55, using the parameter ranges obtained in the experimental tests. This optimum model is selected after six experimental tests and sixty two CFD simulations. After this CFD optimization, the obtained optimum model was manufactured with the exact optimum geometrical factors. This convergent vortex tube provide the cooling efficiency equal to 50.53% (numerical value from the CFD optimization=46.99%). While, the cooling efficiency was equal to 45.72% when (only) the experimental tests were used for the structural optimization. In this way, the optimum model (obtained by CFD optimization) enhances the cooling efficiency of the convergent VT separator by 29.80% and 3.62% compared to the basic experimental model and the initial experimental optimum model, respectively. The optimum model is selected after 23 laboratory tests in the experimental section. This model is a convergent vortex tube with DRth=0.611, α=30 deg, β=10 deg and LN=21.66. While, the exact optimum model (DRth=0.633, α=32.5 deg, β=9 deg and LN=LConvergent/DCold=21.55) is selected after 6 experimental tests (initial tests on Dth) and sixty two CFD simulations. 38

Fig. 26

4. 2. 4. The effect of inlet pressure and Reynolds number on cooling efficiency of the optimum model In this section the impact of inlet pressure (at nozzle) and the related Reynolds numbers on related cooling effectiveness of the optimum model is investigated (DRth=0.633, α=32.5 deg, β=9 deg and LN=LConvergent/DCold=21.55) using 3D CFD models. In the case of experimental process, this is very difficult to evaluate and measure the velocity in vortex tubes because the pitot tube blocks a considerable area inside the vortex tube. So, the accurate CFD methods are very useful to detect the velocity magnitudes in the VTs. If the pressure is improved at the inlet of nozzles, the mass flow rate is increased in nozzle channel. Re 

(32)

vL



Equation (32) presents the relation for Reynolds number in a rectangular channel (in this case is the nozzle channel). In this equation v is the velocity of flow in the channel, L is the hydraulic diameter of the channel (=1.83 mm) and  is the kinematic viscosity for air equal to 1.4 ×10 -5 m2/s (the temperature of inlet air is equal to 294.2 K). Table 17 shows the effect of injection pressure and related Reynolds numbers on the cooling efficiency regarding the optimum convergent VT (CFD results). As seen in Table 17, if the injection pressure is improved in the range of 0.45 MPa to 0.8 MPa, the related velocity in the channel is increased in the range of 205.21 m/s-343.77 m/s, so, the related Reynolds number is enhanced from 26823.87 (0.45MPa) to 44935.6 (0.8MPa). As seen in Fig. 27, when the nondimensional injection pressure (PInlet/PHot) is increased 0.35 (from 0.45 to 0.8), the cooling efficiency is improved 10.56%. It should be said that this increase in the cooling efficiency is a considerable value due to the increased nondimensional pressure.

Table 17 Fig. 27 39

5. Conclusions In this investigation, the laboratory tests and the CFD modeling of the convergent VT cyclone separator with different geometrical and operational parameters (including; nondimensional throttle diameter, throttle angle, convergence angle of tube, nondimensional length of convergent tube, injection slots number and the operational pressure) have been performed and the impact of these factors on the separation process has been investigated. The efficiency distributions obtained from the CFD analysis show good agreement with the laboratory results. This investigation explains the results of a series of laboratory tests and three-dimensional numerical predictions focusing on the optimization of the mentioned parameters to understand what values of these parameters lead to the best separation, cooling and heating efficiencies. Also, the internal flow structure and the details of the separation phenomenon have been analyzed which are affected by these parameters. There are some summarized conclusions as below: 1) The separation process improves extremely with an increase in the throttle diameter up to

D Rth = 0.611, then beyond D Rth = 0.611, the heating and the cooling capabilities are decreased. The convergent VT cyclone separator equipped with a throttle valve with D Rth = 0.611 provides 30.01 % higher cooling efficiency and 20.04 % higher heating efficiency as compared to the basic model ( D Rth = 0.444). 2) When the throttle angle is equal or less than 20 deg, the heating efficiency changes softly, but when the throttle angle is larger than 20 deg, the heating efficiency changes very fast. Applying the convergent VT cyclone separator with the throttle angle of 30 deg leads to 50.60% higher heating performance at the cold flow ratio of 0.75, as compared to α= 15 deg. Also, the convergent VT cyclone separator equipped with a throttle valve with  = 30 deg provides 43.76 % higher cooling efficiency and 50.60 % higher heating efficiency as compared to the basic model (   15 deg and D Rth = 0.611). 3) The results show that the cooling and heating abilities of the system will increase by 7.45 and 5.76 percent at the optimum flow fraction (respectively) as a result of increase in the 40

convergence angle from 8 to 10 deg. Also, the separation efficiency of the system decreases with further increase in the convergence angle from 10 to 12. The amount of the reduction is equal to 5.71% for the cooling and 4.90% for the heating at the optimum flow fraction. So, the convergence angle of the main tube is found to be an important parameter for a higher cooling efficiency with the optimum value of 10 deg. 4) In the case of injection pressure, as the first conclusion, the higher injection pressure leads to a higher cooling efficiency. As the second, the improvement of the cold temperature difference (with increasing pressure) has the largest value at the minimum convergence angle (  =2 deg) and the minimum value at the maximum convergence angle (  =10 deg). Also, for   8 deg, the increase in the cooling efficiency with increasing injection pressure is almost negligible. 5) In the case of nondimensional length of convergent main tube, three zones can be considered in the charts, the first zone for the low flow fraction values (  0.45), middle zone belongs the medium values (0.45  cold mass fraction  0.8) and the third zone for the large values (0.8  cold mass fraction). For flow fraction  0.45, it can be observed that as the nondimensional length of convergent main tube increases from 20-22.22, the cooling and heating efficiencies decreases, excepting the heating efficiency for the nondimensional convergent length of 22.22, which lies between 21.11 and 21.66. For 0.45  cold mass fraction  0.8, we have an optimum value for the nondimensional main tube length which provides the maximum heating and cooling efficiencies (21.66). For 0.8  flow ratios fraction, the pattern of the thermal enhances is similar to that explained in the first Zone. 6) The cooling efficiency improves sharply with an increase in the slots number up to N= 4, then beyond N=4, the cooling efficiency decreases (nominal). It can be seen that the cooling efficiency has the lowest values at minimum slots number N=2. As slots number is increased from 2 to 4, the cooling efficiency increases by 21.12%.

41

7) The results indicate that the ratio of

T c for the convergent VT cyclone separators is T c ,max

independent of the slots number, and can be reported as only one variable parameter namely the cold flow fraction. 8) The average and the maximum disagreements between the experimental quantities and the predicted values of the cooling efficiency are 2.57% and 6.22%, respectively. Also, the average and the maximum values regarding the disagreements between the experimental data and the predicted values for the heating efficiency are 1.97 % and 2.56 %. These validations depict that the simulations can present the successful and reliable predictions regarding the laboratory sets. 9) The third vortex in the convergent VT cyclone separator with D Rth = 0.611 is more developed as compared to the convergent VT cyclone separator with D Rth = 0.666, as a result, the stagnation point is closer to the valve in D Rth = 0.611. So, the convergent VT cyclone separator with D Rth = 0.611 has the smallest distance between the stagnation point and the hot valve as well as the highest cooling efficiency. On the other hand, the largest distance between that point and the valve belongs to the convergent VT cyclone separator with D Rth = 0.444 which has the lowest cooling efficiency. 10) For the convergent VT cyclone separators, the smaller level of turbulent viscosity provides relatively the higher separation process quality or the smaller vortices near the chamber.

11) The highest values of maximum tangential velocity and total pressure drops belong to D Rth = 0.611. So, this result can be picked up that the higher maximum tangential velocities and pressure drops lead to the higher cooling and separation efficiencies. 12) It can be said that, the experimental tests are very important to determine the correct range for the parametric optimizations, but, using the precise numerical models is necessary and very important to elect the exact optimum models. The optimum model is selected after 23 laboratory tests in the experimental section. This model is a convergent vortex tube with D Rth = 0.611, α=30 42

deg, β=10 deg and LN=21.66. While, the exact optimum model ( D Rth = 0.633, α=32.5 deg, β=9 deg and LN=21.55) is selected after 6 experimental tests (initial tests on D Rth) and sixty two CFD simulations.

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47

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[56] A.V. Khait, A.S. Noskov, A.V. Lovtsov, V.N. Alekhin. Semi-empirical turbulence model for numerical simulation of swirled compressible flows observed in Ranque–Hilsch vortex tube . International Journal of Refrigeration, Volume 48, December 2014, Pages 132-141. [57] Rafiee S. E, Sadeghiazad, M. M., 2016, “Three-dimensional CFD simulation of fluid flow inside a vortex tube on basis of an experimental model- The optimization of vortex chamber radius,” International Journal of Heat and Technology, 34(2), 236-244. [58] Meisam Sadi, Mahmood Farzaneh-Gord. Introduction of Annular Vortex Tube and experimental comparison with Ranque–Hilsch Vortex Tube .International Journal of Refrigeration, Volume 46, October 2014, Pages 142-151. [59] Rafiee S. E, Sadeghiazad, M. M., 2016, “Experimental and 3D-CFD study on optimization of control valve diameter for a convergent vortex tube,” Frontiers in Heat and Mass Transfer, 7, 1, 1-15. [60] Pourmahmoud, N., Hassanzadeh, A., Rafiee, S. E., Rahimi, M., 2012, “Three-dimensional numerical investigation of effect of convergent nozzles on the energy separation in a vortex tube,” International Journal of Heat and Technology, 30(2), 133-140 [61] Nilotpala Bej, K.P. Sinhamahapatra. Exergy analysis of a hot cascade type Ranque-Hilsch vortex tube using turbulence model . International Journal of Refrigeration, Volume 45, September 2014, Pages 13-24. [62] Mete Avci. The effects of nozzle aspect ratio and nozzle number on the performance of the Ranque–Hilsch vortex tube. Applied Thermal Engineering, Volume 50, Issue 1, 10 January 2013, Pages 302-308. [63] Rafiee, S. E., Sadeghiazad, M. M., 2017, “Experimental and 3D CFD investigation on heat transfer and energy separation inside a counter flow vortex tube using different shapes of hot control valves,” Applied Thermal Engineering, 110, 648-664. [64] Moffat, R.J. "Using Uncertainty Analysis in the Planning of an Experiment", Trans. ASME, J. Fluids Eng., 107, pp.173-178 (1985).

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[65] M. M. Gibson and B. E. Launder. Ground E_ects on Pressure Fluctuations in the Atmospheric Boundary Layer. J. Fluid Mech., 86:491{511, 1978. [66] B. E. Launder. Second-Moment Closure: Present... and Future? Inter. J. Heat Fluid Flow, 10(4):282{300, 1989. [67] B. E. Launder, G. J. Reece, and W. Rodi. Progress in the Development of a Reynolds-Stress Turbulence Closure. J. Fluid Mech., 68(3):537{566, April 1975. [68] B. J. Daly and F. H. Harlow. Transport Equations in Turbulence. Phys. Fluids, 13:2634{2649, 1970. [69] F. S. Lien and M. A. Leschziner. Assessment of Turbulent Transport Models Including Non-Linear RNG Eddy-Viscosity Formulation and Second-Moment Closure. Computers and Fluids, 23(8):983{1004, 1994. [70] B. E. Launder. Second-Moment Closure and Its Use in Modeling Turbulent In- dustrial Flows. International Journal for Numerical Methods in Fluids, 9:963{985, 1989. [71] S. Fu, B. E. Launder, and M. A. Leschziner. Modeling Strongly Swirling Recirculating Jet Flow with Reynolds-Stress Transport Closures. In Sixth Symposium on Turbulent Shear Flows, Toulouse, France, 1987. [72] Stephan K, Lin S, Durst M, Seher F, Huang D. An investigation of energy separation in a vortex tube. Int J Heat Mass Transf 1983; 26(3):341-8 [73] Mahmood Farzaneh-Gord, Meisam Sadi, Improving vortex tube performance based on vortex generator design, Energy, Volume 72, 1 August 2014, Pages 492–500, [74] Nimbalkar SU, Muller MR. An experimental investigation of the optimum geometry for the cold

end

orifice

of

a

vortex

tube.

Appl

http://dx.doi.org/10.1016/ j.applthermaleng.2008.03.032.

50

Therm

Eng

2009;29(2e3):509-14.

Captions (Figs)

Fig. 1: Schematic diagram of a VT cyclone separator with flow directions Fig. 2: A schematic drawing of the convergent VT cyclone separator with geometrical parameters Fig. 3: Schematic drawing of the experimental setup. Fig. 4: The photograph of control valves with different throttle diameters (in comparison form) used in the tests Fig. 5: Schematic demonstration of the mesh domain and the shape of the unit volumes, (a) Convergent VT cyclone separator, (b) Straight cyclone separator, (c) Control valve position, (d) Nozzle injector's position Fig. 6: Boundary conditions required for the simulation Fig.7: Grid independence study based on the swirl velocity as a function of dimensionless radial distance Fig. 8: The effects of nondimensional throttle diameter of the valve (DRth) on the heating performance of the convergent VT cyclone separator Fig. 9: The effects of the nondimensional throttle diameter of the valve (DRth) on the cooling performance of the convergent VT cyclone separator Fig. 10: The effects of the throttle angle (α) on heating performance of the convergent VT cyclone separator

51

Fig. 11: The effects of the throttle angle (α) on cooling performance of the convergent VT cyclone separator Fig. 12: The effects of convergence angle of the main tube (β) on the heating efficiency of the convergent VT cyclone separator Fig. 13: The effects of convergence angle of the main tube (β) on the cooling efficiency of the convergent VT cyclone separator Fig. 14: The pressure effect on the cooling efficiency of convergent VT cyclone separators with different convergence angles. Fig. 15: Variation of heating efficiency with cold mass fraction for various nondimensional lengths Fig. 16: Variation of cooling efficiency with cold mass fraction for various nondimensional lengths Fig. 17: Impact of number of slots on cooling efficiency as a function of cold mass fraction for the optimum model (β=10 deg, α=30 deg, DRth =0.611 and LN=21.66) Fig.18: Effects of slots number on non-dimensional cold temperature drop as a function of cold flow fraction Fig. 19: Verification of the similarity relation for the present work, the similarity relation for different works are compared against each other (with different optimum cold mass fractions) Fig. 20: Validation of the laboratory results and the outputs gained by the numerical modeling Fig. 21: The local contours of temperature distribution for convergent VT cyclone separators with different nondimensional throttle diameters; (a) 3D contours, (b) Longitudinal displacement of the cold core and the cross section contours Fig. 22: a) Structural plot of streamlines, vortices, location of stagnation point and the shrinking of vortices for three convergent VT cyclone separators with different nondimensional throttle diameters, b) Direction of stream lines around the third auxiliary vortex near the valve (DRth=0.611) Fig. 23: Contour plot of turbulent viscosity for longitudinal sections in comparison form 52

Fig. 24: (a) The radial plot for swirl (tangential) velocity, the swirl velocity varies with dimensionless radial distances and different nondimensional throttle diameters for different Z/L, Z/L=0.1, Z/L=0.7. (b) Tangential velocity drop (m/s) for convergent VT cyclone separators with different nondimensional throttle diameters Fig. 25: (a) The radial plot for axial velocity, the axial velocity varies with dimensionless radial distances and different nondimensional throttle diameters at Z/L=0.1 and Z/L=0.7, (b) The radial plot for total pressure (Z/L=0.1 and Z/L=0.7), (c) Maximum total pressure drop for convergent VT cyclone separators with different nondimensional throttle diameters Fig. 26: a) CFD results of numerical optimization for nondimensional throttle diameter between 0.5 and 0.722 in comparison with the experimental results. b) CFD results of numerical optimization for throttle angle between 15 deg and 45 deg, c) CFD results of numerical optimization for convergence angle between 2 deg and 12 deg. d) CFD results of numerical optimization for nondimensional main tube length between 20.55 to 22.22. Fig. 27: The effect of nondimensional inlet pressure on cooling efficiency of the optimum model (DRth=0.633, α=32.5 deg, β=9 deg and LN=LConvergent/DCold=21.55)

Captions (Table)

Table 1 Structural parameters Table 2 Measuring instruments Table 3 Under-relaxation factors used for computations Table 4 Cooling and heating improvements of the convergent VT cyclone separator with different values of DRth as compared to DRth= 0.444 (the basic model) Table 5 MSE calculations for DRth=0.611 in the case of heating efficiency Table 6 MSE evaluations for different nondimensional throttle diameters

53

Table 7 Cooling and heating improvements of the convergent VT cyclone separator with different values of throttle angle α as compared to α= 15 deg and DRth=0.611 (the basic model) Table 8: MSE evaluations for different throttle angles Table 9 Cooling and heating improvements of the convergent VT cyclone separator with different values of convergence angle β as compared to β= 2deg, α= 30 deg, and DRth=0.611 (the basic model) Table 10 MSE evaluations for different convergence angles Table 11 MSE evaluations for different nondimensional lengths Table 12 Details of the experimental optimization (as compared to the default model) Table 13 The VT cyclone separators applied by other researchers compared to the present work Table 14 The disagreements between laboratory and measured results for cooling efficiency at the optimal cold flow ratio Table 15 The disagreement between the laboratory and measured results for heating efficiency at the optimal cold flow ratio Table 16 The maximum values of total pressure, tangential and axial velocities at Z/L=0.1 and Z/L=0.7 Table 17 Effects of the nondimensional inlet pressures and the related Reynolds numbers on cooling performance of convergent vortex tube (CFD results)

54

Fig. 1

Fig. 2

55

Fig. 3

Fig. 4

56

Fig. 5

Fig. 6

57

Swirl Velocity (m/s)

300

2.35 million cells 2.02 million cells

250

1.67 million cells

200

1.12 million cells

150 100 50

0 0

0.2

0.4

0.6

0.8

1

Dimensionless Radial Distance (r/R) Fig. 7

23

β=2 deg P=4.5 bar α=15 deg

21 19

η Heating %

DRth=0.444

DRth=0.5 DRth=0.555 DRth=0.611

17

DRth=0.666

15

DRth=0.722 Poly. (DRth=0.444)

13

Poly. (DRth=0.5)

11

Poly. (DRth=0.555)

9

Poly. (DRth=0.611)

7

Poly. (DRth=0.666) Poly. (DRth=0.722)

5 0

0.2

0.4

0.6

Cold Mass Fraction Fig. 8

58

0.8

1

25

DRth= 0.444 The optimum cold flow ratio position

23

η Cooling %

21

β=2 deg α=15 deg P= 4.5 bar

DRth=0.5 DRth=0.555

19

DRth=0.611

17

DRth=0.666

15

DRth=0.722

13

Poly. (DRth= 0.444)

11

Poly. (DRth=0.5)

9

Poly. (DRth=0.555)

7

Poly. (DRth=0.611)

5

Poly. (DRth=0.666)

0

0.2

0.4

0.6

0.8

1

Poly. (DRth=0.722)

Cold Mass Fraction Fig. 9

α= 15 deg

36

DRth=0.611 β=2 deg P=4.5 bar

31

α= 20 deg α= 25 deg α= 30 deg

α= 35 deg

η Heating%

26

α= 40 deg α= 45 deg

21

Poly. (α= 15 deg)

Poly. (α= 20 deg)

16

Poly. (α= 25 deg) Poly. (α= 30 deg)

11

Poly. (α= 35 deg) Poly. (α= 40 deg)

6 0

0.2

0.4

0.6

Cold Mass Fraction Fig. 10

59

0.8

1

Poly. (α= 45 deg)

Movement of optimum colf flow fraction location

28

η Cooling%

α= 15 deg

DRth=0.611 β=2 deg P=4.5 bar

33

α= 20 deg α= 25 deg α= 30 deg α= 35 deg α= 40 deg

23

α= 45 deg Poly. (α= 15 deg) Poly. (α= 20 deg)

18

Poly. (α= 25 deg) Poly. (α= 30 deg)

13

Poly. (α= 35 deg) Poly. (α= 40 deg) Poly. (α= 45 deg)

8 0

0.2

0.4

0.6

0.8

1

Cold Mass Fraction Fig. 11

β= 4 deg

DRth=0.611 α=30 deg P=4.5 bar

40 35

η Heating%

β= 2 deg

Movement of location of optimum cold flow ratio

45

β= 6 deg β= 8 deg β= 10 deg

β= 12 deg

30

Poly. (β= 2 deg)

25

Poly. (β= 4 deg) Poly. (β= 6 deg)

20

Poly. (β= 8 deg)

15

Poly. (β= 10 deg)

10

Poly. (β= 12 deg)

0

0.2

0.4 0.6 Cold Mass Fraction Fig. 12

60

0.8

1

DRth=0.611 α=30 deg P=4.5 bar

43

η Cooling%

38

Movement of location of optimum cold flow ratio

β= 2 deg β= 4 deg β= 6 deg

β= 8 deg

33

β= 10 deg β= 12 deg

28

Poly. (β= 2 deg)

23

Poly. (β= 4 deg)

Poly. (β= 6 deg)

18

Poly. (β= 8 deg) Poly. (β= 10 deg)

13

0

0.2

0.4 0.6 Cold Mass Fraction Fig. 13

61

0.8

1

Poly. (β= 12 deg)

45

45

DRth=0.611 α=30 deg β=2 deg

40

η Cooling %

η Cooling %

40

35 30 P= 4.5 bar

25 P= 5.5 bar

20

DRth=0.611 α=30 deg β=4 deg

35 30 P= 4.5 bar

25

P= 5.5 bar

20

P= 6.5 bar

15

P= 6.5 bar

15

0

0.2

0.4

0.6

0.8

1

0

0.2

Cold Mass Fraction

0.8

1

50

50

η Cooling %

40 35 P= 4.5 bar

30

DRth=0.611 α=30 deg β=8 deg

45

DRth=0.611 α=30 deg β=6 deg

45

40 35 P= 4.5 bar 30 P= 5.5 bar

P= 5.5 bar

25

25

P= 6.5 bar

P= 6.5 bar 20

20 0

0.2

0.4 0.6 Cold Mass Fraction

0.8

1

0

0.2

0.4 0.6 Cold Mass Fraction

55

DRth=0.611 α=30 deg β=10 deg

50

η Cooling %

η Cooling %

0.4 0.6 Cold Mass Fraction

45

40 35

P= 4.5 bar P= 5.5 bar P= 6.5 bar

30

25 20 0

0.2

0.4 0.6 Cold Mass Fraction

Fig. 14

62

0.8

1

0.8

1

45 Middle Zone

LN= 20.55

41

β=10 deg α=30 deg P= 4.5 bar DRth=0.611

39

Zone 3

LN=21.66

η Heating%

43

LN= 20

LN=21.11

Zone 1

37

LN=22.22

35

Poly. (LN= 20.55)

33

Poly. (LN= 20)

31

Poly. (LN=21.11)

Poly. (LN=21.66)

29

Poly. (LN=22.22)

27 0

0.2

0.4

0.6

0.8

1

Cold Mass Fraction Fig. 15

β=10 deg α=30 deg P= 4.5 bar DRth=0.611

48

η Cooling %

43

Middle Zone

LN=20.55 LN=20 LN=21.11

Zone 3

LN=21.66

38

LN=22.22 Poly. (LN=20.55)

33

Poly. (LN=20)

Zone 1

Poly. (LN=21.11)

28

Poly. (LN=21.66) Poly. (LN=22.22)

23 0

0.2

0.4

0.6

Cold Mass Fraction Fig. 16

63

0.8

1

55

N=4

50

N=2

β=10 deg α=30 deg P= 4.5 bar DRth=0.611 LN=21.66

N=3

45

N=6

40 35 30 25 20 0

0.2

0.4

0.6

0.8

Cold Mass Fraction Fig. 17

1.05 0.95

ΔTc/ΔTc,Max

η Cooling %

60

0.85

N=2 N=3 N=4 N=6

0.75 0.65 0.55 0.45 0.1

0.3

0.5

0.7

Cold Mass Fraction

Fig.18

64

0.9

1

1.2 1.1 1

ΔTc/ΔTc,Max

0.9 0.8 0.7 0.6

Prasent Work

0.5

Hilsch [2]

0.4

Stephan et al. [72]

0.3

Farzaneh-Gord et al. [73]

0.2

0

0.2

0.4

0.6

Cold Mass Fraction Fig. 19

65

0.8

1

23

25

η Heating Exp η Heating 3D CFD η Cooling Exp η Cooling 3D CFD

21 19

21 19

17

15

η%

η%

η Heating Exp η Heating 3D CFD η Cooling Exp η Cooling 3D CFD

23

13

17 15

13

11

11

DRth=0.444 β=2 deg α=15 deg

9 7

DRth=0.5 β=2 deg α=15 deg

9 7

5

5 0

0.2

0.4

0.6

0.8

1

0

0.2

Cold Mass Fraction

26

η Heating Exp

24

η Heating 3D CFD

0.6

0.8

1

0.8

1

Cold Mass Fraction

DRth=0.611 β=2 deg α=15 deg

25

η Cooling Exp

22

0.4

η Cooling 3D CFD

20

18

η%

η%

20

16 14

DRth=0.555 β=2 deg α=15 deg

12

10

15

η Heating Exp η Heating 3D CFD

10

η Cooling Exp

8 0

0.2

0.4

0.6

0.8

η Cooling 3D CFD

1

5

Cold Mass Fraction

0

η Heating Exp

24

η Cooling Exp

20

η Cooling 3D CFD

20

η Heating 3D CFD

22

η Cooling Exp

η Cooling 3D CFD

η %

η%

18 18 16

16 14 12

14

DRth=0.666 β=2 deg α=15 deg

12 10

0.4 0.6 Cold Mass Fraction

η Heating Exp

24

η Heating 3D CFD

22

0.2

DRth=0.722 β=2 deg α=15 deg

10 8 6

8

0

0.2

0.4

0.6

0.8

0

1

0.2

0.4

0.6

Cold Mass Fraction

Cold Mass Fraction

Fig. 20

66

0.8

1

DRth=0.666

DRth=0.611

DRth=0.444 (a)

67

(b) Fig. 21

68

(a)

(b) Fig. 22

69

DRth=0.444

DRth=0.611

DRth=0.666 Fig. 23

70

(a)

(b) Fig. 24

71

(a)

(b)

(c) Fig. 25

72

η Cooling %

25 24 23 22 21 20 19 18 17 16 15

maximum cold temperature difference at optimum cold mass fraction Optimum Model Using Experimental Optimization

Experimental Values CFD Validation Data CFD Optimization Data

Optimum Model Using CFD Optimization

0

1 0.444

2 0.5

30.555

40.611

50.666

6 0.722

Nondimensional Throttle Diameter (DRth=Dth/Dc)

η Cooling %

(a) 40 38 36 34 32 30 28 26 24 22 20

The optimum model based on experimental optimization (DRth=0.611) The optimum model based on CFD optimization (DRth= 0.633)

Experimental Values with DRth=0.611 CFD Validation Data With DRth=0.611 CFD Optimization Data With DRth=0.633

0

1 15 30

2 20 40

3 25 50

4 30 60

5 35 70

Throttle Angle (α) deg

(b)

73

6 40 80

7 45

8

7

48 The Optimized Model Using CFd Optimization

46

Initial Experimental Values

η Cooling %

44

42

Numerical Results Based On 3D CFD Optimization

40

38 36

34 32

The Optimized Model Using Experimental Optimization

30 21

0

42

63

84

5 10

6 12

7

Convergence Angle β (deg)

(c) 48 Initial Experimental Values

η Cooling %

47

46

Numerical Results Based On 3D CFD Optimization

45

44 43

42 41 40 0

1 20.55

2 21.11

3 21.66

4 22.22

Nondimensional Length (Lconvergent/Dc)

(d) Fig. 26

74

5

30 CFD Results

η Cooling %

28 26 24 22 20 18 16 0.4

0.5 0.6 0.7 0.8 Nondimensional Inlet Pressure (Pressure Inlet /(P Hot)) Fig. 27

75

Table 1 Length of convergent main tube

180,185,190,195,200 mm

Diameter of cold exhaust

9 mm

slots number

2, 3, 4, 6

The shape of control valve

Truncated cone

Nozzle section

2×1.7

Angle of throttle valve

15, 20, 25, 30, 35, 40 and 45 deg

Convergence angle

2, 4, 6, 8, 10 and 12 deg

Throttle diameter

4, 4.5, 5, 5.5, 6 and 6.5 mm

Table 2 Instrument

Accuracy

Pressure sensor BD 26.600G (0 to 1.4 MPa)

≤1%

Rotameter (DK800S-6)

±1%

Thermometer PT 100

±0.2 C°

Humidity sensor 10-95(% R.H.)

3%

76

Table 3 Default

Step

URF

1

2

3

4

5

6

7

8

9

10

11

Energy

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.95

1

Turbulent

0.8

0.1

0.1

0.2

0.2

0.3

0.4

0.5

0.5

0.6

0.7

0.8

Body Force

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.95

1

Reynolds Stresses

0.5

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.45

0.5

0.5

Density

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.95

1

Turbulent Viscosity

1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.95

1

Turbulent Kinetic

0.8

0.1

0.1

0.2

0.2

0.3

0.4

0.5

0.5

0.6

0.7

0.8

Momentum

0.7

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.4

0.5

0.6

0.7

Pressure

0.3

0.1

0.1

0.3

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.3

Dissipation Rate

Energy

Table 4

D Rth  0.5

D Rth  0.555

D Rth  0.611

D Rth  0.666

D Rth  0.722mm

11.31

23.82

30.01

19.32

9.55

6.45

15.44

20.04

12.50

6.97

Cooling improvement [%] Heating improvement [%]

77

Table 5

 Heating

= -21.21x3 + 17.43x2 +

DRth=0.611 15.78x + 9.402 Cold Mass

 Heating Heating

  -

(   )2

Fraction 0.13 0.19 0.28 0.32 0.43 0.48 0.55 0.60 0.66 0.73 0.76 0.81 0.87 0.91 0.93 0.96

11.60 13.12 14.64 15.81 17.74 18.94 19.81 20.57 20.98 21.74 22.16 22.71 22.71 22.50 22.18

11.79 12.91 14.73 15.61 17.85 18.79 19.82 20.61 21.34 21.98 22.18 22.36 22.35 22.19 22.03

0.19 -0.21 0.09 -0.2 0.11 -0.15 0.01 0.04 0.36 0.24 0.02 -0.35 -0.36 -0.31 -0.15

0.0361 0.0441 0.0081 0.04 0.0121 0.0225 0.0001 0.0016 0.1296 0.0576 0.0004 0.1225 0.1296 0.0961 0.0225

21.74

21.80

0.06

0.0036 0.847

SUM mean squared error (MSE) = (T h T h )2 /16

78

0.0530

Table 6 DRth

Polynomial regression equation

MSE (Cold)

MSE (Hot)

0.119

0.134

0.081

0.159

0.307

0.21

0.282

0.053

0.0852

0.0911

0.147

0.0973

 h = -54.33x3 + 75.50x2 - 14.12x + 9.228 0.444

c =47x3 – 93.92x2 + 43.93x + 10.35  h = -30.53x3 + 31.68x2 + 10.10x +6.803

0.5

c = 42.85x – 87.18x + 39.04x + 13.47 3

2

 h = -19.06x3 + 17.48x2 + 14.00x +8.232 0.555

c = 28.18x3 - 66.26x2 + 29.59x + 16.85

 h = -21.21x3 + 17.43x2 + 15.78x + 9.402 0.611

c = 14.63x – 40.33x + 17.49x + 19.22 3

2

 h = -30.36x3 + 39.38x2 + 0.848x +10.57 0.666

c = 40.50x – 78.36x + 32.37x + 16.06 3

2

 h = -28.02x3 + 38.55x2 - 0.49x + 9.695 0.722

c = 33.94x3 – 65.53x2 + 24.98x + 15.50

Table 7

  20 deg

  25 deg

  30 deg

  35 deg

13.37

28.98

43.76

33.44

18.40

9.18

21.42

44.53

50.60

46.08

27.66

14.75

  40 deg   45 deg

Cooling improvement [%] Heating improvement [%] 79

Table 8

 (deg)

Polynomial regression equation

MSE (Cold)

MSE (Hot)

0.282

0.053

0.414

0.817

0.174

0.502

0.144

0.593

0.239

1.04

0.263

0.493

0.135

0.331

 h = -21.21x3 + 17.43x2 + 15.78x + 9.402 15

c = 14.63x – 40.33x + 17.49x + 19.22 3

2

 h = -71.56x3 + 101.7x2 - 19.39x + 13.29 20

c = 42.34x3 – 94.72x2 + 45.93x + 18.16  h =-96.58x3 + 117.9x2 - 11.15x + 14.36

25

c = 66.37x – 142.9x + 73.74x + 17.05 3

2

 h = -69.97x3 + 65.86x2 + 18.17x + 11.85 30

c =70.77x3 – 163.8x2 + 91.06x + 16.94  h = -125.6x3 + 156.0x2 - 25.74x + 15.76

35

c = 31.99x – 104.0x + 60.97x + 19.45 3

2

 h = -147.1x3 + 167.1x2 - 24.1x + 12.91 40

c = 76.59x - 182.0x + 105.1x + 7.855 3

2

 h = -55.27x3 + 40.53x2 + 24.46x + 7.279 45

c = 86.28x – 196.3x + 121.0x + 1.724 3

2

Table 9

Cooling improvement [%]

  4deg

  6deg

  8deg

  10deg

  12deg

4.5

13.13

20.74

29.76

22.35

3.2

8.25

13.97

20.54

14.62

Heating improvement [%]

80

Table 10

 (deg)

Polynomial regression equation

MSE (Cold)

MSE (Hot)

0.144

0.593

0.418

0.559

0.338

0.577

0.325

1.2

0.966

0.531

0.028

0.311

 h = -69.97x3 + 65.86x2 + 18.17x + 11.85 2

c =70.77x – 163.8x + 91.06x + 16.94 3

2

 h = -115.7x3 + 134.9x2 – 17.78x + 20.28 4

c = 30.08x – 97.99x + 61.33x + 22.48 3

2

 h = -61.56x3 + 51.06x2 + 17.04x + 20.39 6

c = 63.67x3 – 146.1x2 + 82.16x + 22.36  h = -69.19x3 + 37.64x2 + 35.94x + 17.28

8

c = 28.81x3 – 117.2x2 + 88.23x + 19.62  h = -83.68x3 + 69.72x2 + 11.42x + 26.05

10

c = -9.384x – 56.23x + 61.81x + 24.69 3

2

 h = 27.97x3 – 157.9x2 + 145.3x + 1.055 12

c = -159.0x3 + 201.1x2 – 66.4x + 40.85

81

Table 11 LN

Polynomial regression equation

MSE (Cold)

MSE (Hot)

0.162

0.158

0.966

0.531

1.86

0.704

1.87

0.562

1.04

0.165

 h = -71.18x3 + 61.96x2 + 8.627x + 27.64 20

c = -19.45x – 22.69x + 38.19x + 30.11 3

2

 h = -83.68x3 + 69.72x2 + 11.42x + 26.05 20.55

c = -9.384x – 56.23x + 61.81x + 24.69 3

2

 h = -119.6x3 + 114.0x2 - 0.462x + 25.91 21.11

c = -56.72x - 10.49x + 60.67x + 20.94 3

2

 h = -187.6x3 + 202x2 – 29.7x + 27.07 21.66

c = -111x3 + 26.97x2 + 70.89x + 14.87

 h = -18.17x3 – 41.40x2 + 69.73x + 15.71 22.22

c = -5.292x – 98.16x + 110.1x + 9.4 3

2

Table 12 Value of parameters

Nondimensional throttle angle throttle

(deg)

diameter

convergence

Nondimensional

slots

angle of main

length of

(nozzle)

tube(deg)

convergent man

number

tube Minimum

0.444

15

2

20

2

Default

0.444

15

2

20.55

4

Optimum

0.611

30

10

21.66

4

Maximum

0.722

45

12

22.22

6

Improvement of

30.01

43.76

29.76

9.79

0

cooling performance (%)

82

Table 13 Cold Exit Main Tube Slots Diameter

Shape

Nondimensional Shape

Number

Length

Control Valve

(mm) Present Work

9

Convergent 4

21.66

Truncated

Hilsch [2]

2.6

Straight

1

115.38

cone

Stephan et al. [72]

6.5

Straight

1

54.15

cone

Farzaneh-Gord and Sadi. 7.76-12.28 Straight

6

12.26-7.75

N/A

[73]

Table 14

Nondimensional Throttle

Cooling efficiency Cooling efficiency (Ex)

Diameter

Disagreement (%) (Num)

D Rth = 0.444

17.18

16.11

6.22

D Rth = 0.5

19.13

18.52

3.18

D Rth = 0.555

21.27

20.73

2.53

D Rth = 0.611

22.34

22.05

1.29

D Rth = 0.666

20.50

20.30

0.97

D Rth = 0.722

18.82

18.58

1.27

83

of

Table 15 Nondimensional

Heating

Heating efficiency

Throttle Diameter

efficiency (Ex)

(Num)

D Rth = 0.444

18.92

18.47

2.37

D Rth = 0.5

20.13

19.66

2.33

D Rth = 0.555

21.83

21.38

2.06

D Rth = 0.611

22.71

22.34

1.62

D Rth = 0.666

21.28

21.08

0.93

D Rth = 0.722

20.24

19.72

2.56

Disagreement (%)

Table 16 Z/L=0.1

Z/L=0.7

Tangential

Axial

Total pressure

Tangential velocity

Axial velocity

Total pressure

velocity (m/s)

velocity (m/s)

(kPa)

(m/s)

(m/s)

(kPa)

0.444

305.395

84.29

247.002

176.80

39.14

100.309

0.5

291.105

71.61

280.528

156.00

43.79

118.351

0.555

283.326

79.22

308.404

128.00

46.89

134.33

0.611

277.448

87.46

338.488

109.60

49.22

130.206

0.666

287.839

75.42

293.477

141.60

45.73

125.567

0.722

293.082

70.35

268.793

171.20

41.08

111.134

DRth

84

Table 17 Reynolds

Cooling

P Inlet (MPa)

0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62

Reynolds P Inlet (MPa)

Number

Performance

26823.87

48.01

26937.53

48.45

27273.68

48.83

27514.44

49.12

27797.3

49.51

28517.4

49.87

29073.62

50.18

29821.04

50.46

30520.04

50.77

31062.6

Cooling Performance Number

0.63

36408.76

52.80

37091.62

52.85

37805.52

52.88

38535.56

52.94

39111.63

52.97

39821.83

52.95

40262.57

52.91

41086.96

52.89

0.71

41375.02

52.81

51.03

0.72

41913.85

52.83

31774.02

51.29

0.73

42210.58

52.81

32507.78

51.56

0.74

42470.08

52.85

33003.16

51.73

0.75

42857.43

52.66

33563.11

52.1

0.76

43242.3

52.72

34100.7

52.33

0.77

43757.55

52.78

34755.12

52.44

0.78

44228.09

52.79

35324.88

52.65

0.79

44694.94

52.71

35991.6

52.71

0.8

44935.6

52.69

0.64 0.65 0.66 0.67 0.68 0.69 0.70

85

Highlights



Comprehensive study on the effects of five structural parameters on CVTs performance



Study on the effect of injection pressure on CVTs performance



Experimental and CFD optimization of the structural parameters.



Introducing an accurate 3D-CFD model to predict a correct separation procedure



Numerical visualization of separation phenomenon.

86