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ExergyanalysisofahotcascadetypeRanque-Hilschvortextubeusingturbulencemodel

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Exergy analysis of a hot cascade type Ranque-Hilsch vortex tube using turbulence model

Nilotpala Bej*, K.P. Sinhamahapatra

Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur 721302, India

a r t i c l e i n f o

Article history:

Received 3 October 2013

Received in revised form

17 April 2014

Accepted 25 May 2014

Available online 5 June 2014

Keywords:

Hot cascade type RHVT

Exergy analysis

Second law efficiency

* Corresponding author. Tel.: þ91 993368474E-mail addresses: nilotpala2002@gmail.co

http://dx.doi.org/10.1016/j.ijrefrig.2014.05.0200140-7007/© 2014 Elsevier Ltd and IIR. All rig

a b s t r a c t

Ranque-Hilsch vortex tube (RHVT) is a simple device capable of splitting a compressed inlet

gas stream into a cold and a hot outlet stream without any external source of energy

supply. In hot cascade type RHVT the hot gas stream emerging out of the first stage vortex

tube is supplied to the inlet of second stage vortex tube and thus producing higher heating

effect. This paper presents results of a series of numerical simulation carried out using

standard keε turbulence model focusing on exergy analysis on second stage of RHVT for

different cold fractions. The results obtained from numerical simulations compare favor-

ably with available experimental measurements, which demonstrate successful use of

turbulence model for a cascade type RHVT.

© 2014 Elsevier Ltd and IIR. All rights reserved.

Analyse exerg�etique d'un tube �a vortex de type Ranque-Hilsch�a cascade chaude utilisant un mod�ele turbulent

Mots cl�es : Tube �a vortex de Ranque-Hilsch de type �a cascade chaude ; Analyse exerg�etique ; Efficacit�e en vertu du second principe

1. Introduction

In a Ranque-Hilsch Vortex Tube (RHVT) the compressed gas is

injected into the tube through multiple nozzles oriented

tangentially, which produces strong swirl motion. The swirl

motion splits the incoming stream into two low pressure

streams, one part hotter and the other part colder than the

inlet flow. Being a mechanical device without any moving

part, it bears low manufacture and maintenance cost. The

industrial applications include wide range of cooling

0.m, nilotpala2002@yahoo

hts reserved.

processes such as separating gas mixtures, liquefying gases,

purifying and dehydrating two phase mixtures, welding,

brazing, solidifying polymers and controlling air climate etc.

(Skye et al., 2006); (Xue et al., 2010).

The effect of temperature separation produced due to the

vortex motion of fluid in a simple hollow cylindrical body was

first observedbyRanque (1933). He explained thephenomenon

of temperature separation bymeans of adiabatic expansion of

fluid near the central axis and adiabatic compression of pe-

ripheral flow. Later Hilsch (1947) postulated the effect of radial

gradient of tangential velocity between the gas layers as the

.co.in (N. Bej).

Nomenclature

A vortex tube cross sectional area (m2)

Ai nozzle cross sectional area (m2)

Cp specific heat at constant pressure (J kg�1 K�1)

D diameter of the vortex tube main body (m)

d diameter of cold exit (m)

E exergy (W)

g gravitational acceleration (m s�2)

H enthalpy (J kg�1)

L length of vortex tube (m)

l length of the cold exit (m)

ls equivalent slot width (m)

m_ mass flow rate (kg s�1)

p pressure (Pa)

R gas constant (J kg�1 K�1)

T temperature (K)

v velocity (m s�1)

vn inlet radial velocity (m s�1)

z height difference between the hot exit and inlet (m)

Greek symbols

x cold fraction

h exergy efficiency

Subscripts

c cold exit

h hot exit

i inlet

KN kinetic

PH physical

PT potential

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 414

cause of energy transfer from inner layer to outer layer, thus

producing hot layer of fluid near the periphery and cold fluid

near the central axis. Subsequently, many researchersworked

experimentally and numerically to optimize the flow field and

energy separation taking place inside the vortex tube.

Different factors considered influential in the temperature

separation are pressure gradient, viscosity, turbulence, flow

structure in the tube and acoustic streaming. Flow structure in

the vortex tube has been explained by the concept of multi-

circulation, re-circulation and stagnation point. (Arbuzov

et al., 1997; Behera et al., 2008; Colgate and Buchler, 2000;

Kazantseva et al., 2005) explained the energy separation due

to the structure of the flow in the vortex tube; sudden expan-

sion occurs when the compressed air is injected into the tube

and the temperature of the air flow in the core drops in the

process of expansion. Some other studies suggested that

generation of a forced vortex is the main reason for the exis-

tence of a radial pressure gradient. The pressure gradient

generated due to the forced vortex results temperature rise

near the periphery and temperature drop at the core due to

compression in the peripheral region and expansion in the

core region. The forced vortex and its effect on the velocity

distribution were investigated by (Aljuwayhel et al., 2005;

Behera et al., 2008, 2005; Eiamsa-ard and Promvonge, 2007;

Faroukand Farouk, 2007; Fr€ohlingsdorf andUnger, 1999). (Saidi

andValipour, 2003) performed a series of experiments to study

the effects of geometrical and thermophysical parameters on

the performance of vortex tube for length-to-diameter ratio (L/

D) ranging from 10 to 76. Optimum value of L/D ratio for effi-

ciency was found to lie in the range of 20e55.5. Similarly, op-

timum values for other geometrical parameters that include

dimensionless cold air orifice diameter, number of nozzles etc

were also investigated in this work. (Behera et al., 2005) per-

formed experimental and numerical studies on temperature

separation in a vortex tube to optimize various parameters

such as nozzle profile and number of nozzles, cold end orifice

diameter, length-to-diameter ratio (L/D) etc. The analysis

shows that the flow has forced vortex and free vortex com-

ponents up to stagnation point and temperature difference

betweenhot and cold gas flowcan bemaximized by increasing

the length-to-diameter ratio of vortex tube such that stagna-

tion point is farthest from the nozzle inlet but within the tube.

(Nimbalkar and Muller, 2009) performed a series of experi-

ments with various geometries of cold end orifice. The results

demonstrate that the maximum value of energy separation

was always reachable at 60% cold fraction irrespective of the

orifice diameter and inlet pressure. (Valipour and Niazi, 2011)

carried out experimentalwork in a curvedRHVT refrigerator to

study the effect of uniform curvature of main tube on vortex

tube performance. The study demonstrated that the curvature

in the main tube has different effects on the performance of

the vortex tube depending on inlet pressure and cold mass

ratio. It was also found that the maximum cold temperature

difference is achieved in straight vortex tube whereas

maximum refrigeration capacity is achieved in curved tube.

(Im and Yu, 2012) performed an experimental study to deter-

mine the effect of the nozzle area ratio and inlet pressure for

tube length-to-diameter ratio of 14. The study shows that

variation of the cold exit orifice diameter significantly in-

fluences the energy separation between two exits.

(Farouk and Farouk, 2007) studied the temperature sepa-

ration process using large eddy simulation (LES) technique

and modeled the RHVT used by (Skye et al., 2006). (Secchiaroli

et al., 2009) also performed large eddy simulation (LES) of the

flow in a three-dimensional model of RHVT used in jet

impingement operation. (Eiamsa-ard and Promvonge, 2007)

simulated vortex tube flow using Reynolds-Averaged

NaviereStokes (RANS) equations with algebraic stress

model (ASM) closure. The results predicted by ASM and LES

showed better qualitative agreement with experimental

measurement, but both the methods are computationally too

expensive than the lower order turbulence models such as

two-equations eddy viscosity models. Later (Dutta et al.,

2010) conducted a comparison study in a two-dimensional

axisymmetric domain as used by (Behera et al., 2005) to

predict the temperature separation using four different tur-

bulence models and found that standard keε turbulence

model, amongst all RANS based two-equations turbulence

models, demonstrate best agreement with the experimen-

tally obtained temperature separation. Identical observation

was also made by (Skye et al., 2006). Thus, the present study

on exergy analysis of hot cascade type RHVT has been carried

out using RANS equations with standard keε turbulence

model.

Fig. 1 e Computational geometry of individual RHVT.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 4 15

The literature shows abandon use of single RHVT in cool-

ing processes and numerous experimental and numerical

studies are reported. However, either numerical or experi-

mental studies on cascaded vortex tube are scarcely reported

in the literature. To the best of author's knowledge, the pre-

sent work is the first computational effort to evaluate the

performance of hot gas exhausted from a cascade type RHVT.

In this regard, numerical simulations carried out for the

compressed hot air flowing through the cascaded RHVT, with

emphasis on the second RHVT, are presented. The utilization

of hot exit gas by the method of cascading offers a wide range

of benefits in the process of heating. In exergy analysis losses

are measured in terms of exergy destruction, which provides

direct measurement of thermodynamic inefficiencies. Exergy

is the work potential of energy in a given environment. (Saidi

and Allaf Yazdi, 1999) studied the effect of inlet pressure on

temperature difference in the vortex tube and discussed the

advantages of exergy analysis. They also listed equations for

calculating rate of entropy generation and total irreversibility.

(Cao et al., 2002) performed experimental study for exergy

analysis associated with a new hybrid refrigeration cycle of

the mixed-refrigerant auto-cascade J-T cycle. The total exergy

efficiency achieved in the new hybrid refrigeration cycle is

78.9% better than the auto-cascade J-T cycle. (Rosen and

Dincer, 2004) studied the effect of dead state variation on

energy and exergy analysis of thermal systems and showed

that the variation does not affect the energy and exergy values

significantly. (Kırmacı, 2009) carried out exergy analysis on

vortex tube for two different gases (air and oxygen) using

different inlet pressures and different nozzle numbers. Usage

of exergy concepts in evaluating the performance of energy

systems are increasing now-a-days due to its clear indication

of loss at various locations which is more informative than

energy analysis (Casasa et al., 2010).

Fig. 2 e Schematic representation of ho

The method of cascading ensures more efficient energy

utilization. (Dincer et al., 2010) conducted experiments to

study the exergy of a counter flow RHVT and found exergy

efficiency basically depend upon inlet total pressure, cold

fraction and inlet velocity. Later (Dincer et al., 2011) performed

additional experiments to study the exergy of a hot cascade

type RHVT and compared the results obtained for hot cascade

type RHVT against classical RHVT. It is observed that the hot

cascade type RHVT is more efficient than the classical one.

(Dincer, 2011) conducted further experimental work to study

the exergy of threefold type and six cascade type RHVT for two

different values of inlet total pressure. On the ground of the

above observations, a numerical method using RANS equa-

tions with standard keε turbulence model has been employed

to perform exergy analysis of a hot cascade type RHVT.

Extensive comparison of the numerical prediction and

experimental data aremade to establish that the CFDmodel is

reliable enough in predicting the exergy and can be used for

optimization or other purposes with confidence.

2. Hot cascade type RHVT model descriptionand geometrical domain

Although the RHVT is a very simple device, its geometry has a

strong influence in the fluid dynamics and associated tem-

perature separation. A very small cold orifice would produce

higher back pressure leading to low temperature separation,

whereas a very large cold orifice would tend to draw air

directly from the inlet and yield weaker tangential velocities

near the inlet region resulting in low temperature separation.

Similarly, a very small inlet nozzle would give rise to consid-

erable pressure drop in the nozzle itself, leading to low

tangential velocities and hence low temperature separation. A

t cascade type RHVT arrangement.

Fig. 3 e Variation of cold fraction and enthalpy fraction as a

function of grid size.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 416

very large inlet nozzle would fail to establish proper vortex

flow resulting again in low diffusion of kinetic energy and

therefore low temperature separation (Eiamsa-ard and

Promvonge, 2008). In case of axisymmetric flow model, a

circumferential slot is used as the inlet instead of the nozzle

(or nozzles). The equivalent width of the slot, ls, is calculated

from the conservation of mass with the relation given as

(Eiamsa-ard and Promvonge, 2007)

ls ¼_mi

pDrvn(1)

where ls,D and vn are the equivalent slotwidth, the vortex tube

diameter and the inlet radial velocity, respectively. Sincemass

Fig. 4 e Comparison of swirl velocity profiles for grid size of

15 £ 103 and 13 £ 105.

flow rate is not given in (Dincer et al., 2011) a simplified and

modified computational model of the RHVT has been created

as shown in Fig. 1. Twocounter flowRHVTsare used in cascade

as shown in Fig. 2. The software packageGambit 2.4.6 has been

used to generate structured Cartesian mesh with near wall

refinement.Agriddependency study is carriedout over a range

of 5000 to 25,000 cells to eliminate the errors due to coarseness

of grids. Cold fraction (¼mc/mi) and enthalpy fraction (¼Hc/Hi)

obtained from the simulations on different grid sizes when

Pi¼ 730kPa, Ph¼ 440kPaandPc¼100kPaarepresented inFig. 3.

It is observed that there is no significant difference in results

beyond the grid size of 15,000. A very fine mesh with high

resolution near the wall consisting of 13�105 cells is also used

to assess the effect of near wall resolution. Fig. 4 presents a

comparisonof the swirl velocity profiles obtained from the fine

mesh (more than 13�105 cells) and the mesh with 15000 cells.

The comparison clearly shows that the gain in accuracy is

insignificant though the grid resolution is significantly higher.

The gross performance parameters such as cold fraction,

enthalpy fraction, temperature separation and others at

specified inlet and outlet conditions also do not exhibit any

variation. The fine mesh computation however increases the

computational cost considerably. Therefore, in this paper,

simulations are carried out with grid size of 15,000.

3. Numerical model description andboundary conditions

As the hot exit of the first RHVT is connected to the inlet of the

second RHVT, the properties of hot fluid emerging out of the

first RHVT are used as inlet boundary condition for the second

vortex tube. The numerical simulation has been carried out

for the second RHVTwhen cold fraction (x) of the first RHVT is

0.5. The remaining boundary conditions applied are as fol-

lows. Conditions at all the solid walls are set as adiabatic and

no slip. Total pressure at the inlet of first RHVT is fixed at

730 kPa (abs). The static pressure at the cold exit of both tubes

is set at 100 kPa (abs). Zero temperature gradient is applied at

both the hot and cold exits of both vortex tubes. Hot exit

pressure is varied to get different values of cold fractions. The

cold fraction value of 0.5 at the first vortex tube is obtained

when the first hot exit pressure is 440 kPa (abs).

The flow inside an RHVT deals with the dynamic behavior

of a highly swirling, compressible turbulent flow. Moreover,

strong temperature gradients arise in a vortex tube predomi-

nantly in the axial direction. Thus the dynamic problem is

strongly coupled with the thermal problem. As a consequence

of the relevance of the thermal gradients and of the flow

compressibility, the continuity and Reynolds-averaged

NaviereStokes equations are computed in association with

the energy equation and the gas equation of state as given in

Equations (2)e(7). A first order turbulence closure model,

namely the standard keεmodel, has been used in this study to

model the turbulence. Assuming steady state condition in the

vortex tube, the governing equations are given as follows

(Fluent User's Guide, release 6.3.26, Ansys Inc. USA, 2006).

v

vxiðruiÞ ¼ 0 (2)

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 4 17

v

vxj

�ruiuj

�¼�vpvxi

þ v

vxj

�m

�vui

vujþvuj

vxi�23dijvuk

vxk

��þ v

vxj

��ru'

iu'j

�(3)

v

vxi½uiðrEþ pÞ� ¼ v

vxj

�keff

vTvxj

þ ui

�tij�eff

�(4)

where the stress tensor (tij)eff is given by

�tij�eff

¼ tviscous þ tt ¼ meff

�vuj

vxiþ vui

vxj

�� 23meff

vuk

vxkdij (5)

keff, meff represent effective thermal conductivity and effective

viscosity respectively and are defined as meff ¼ m þ mt and

keff ¼ k þ kt.

Reynolds stresses tt ¼ �ru'iu

'j are calculated by the

following relation

�ru'iu

'j ¼ mt

�vui

vxjþ vuj

vxi

�� 23dij

�rk� mt

vuk

vxk

�(6)

Equations (2)e(4) are supplemented with the equation of

state

p ¼ rRT (7)

In steady-state keε model the turbulent kinetic energy and

dissipation are calculated as given in Equations (8) and (9)

respectively

v

vxiðrkuiÞ ¼ v

vxj

��mþ mt

sk

�vkvxj

�þ Pk þ Pb � rε� YM þ Sk (8)

v

vxiðrεuiÞ ¼ v

vxj

��mþ mt

sε

�vε

vxj

�þ C1ε

ε

kðPk þ C3εPbÞ � C2εr

ε2

kþ S

ε(9)

where turbulent viscosity, mt is given by

mt ¼ rCm

k2

ε

(10)

The production of turbulent kinetic energy k is given by,

Pk ¼ mtS2 (11)

where S is themodulus of themean rate of strain tensor and is

defined as

S≡ffiffiffiffiffiffiffiffiffiffiffiffiffi2SijSij

q(12)

Effect of buoyancy Pb is given as

Pb ¼ bgimt

Prt

vTvxi

(13)

where Prt is the turbulent Prandtl number and gi is the

component of the gravitational acceleration vector. The co-

efficient of thermal expansion is defined as

b ¼ �1r

�vr

vT

�p

(14)

YM represents the contribution of the fluctuating dilatation

in compressible turbulence to the overall dissipation rate and

is given by

YM ¼ 2rεM2t (15)

where

Mt ¼ffiffiffiffiffiffiffiffiffik

gRT

s(16)

Sk and Sεare appropriate source terms in the respective

equations.

The model constants are

Prt ¼ 0:85;C1ε ¼ 1:44;C2ε ¼ 1:92;C3ε ¼ �0:33;Cm ¼ 0:09; sk

¼ 1:0; sε¼ 1:3

The predicted flow solution is applied to carry out exergy

analysis of the RHVT. Exergy analysis of a vortex-tube pro-

vides better understanding of the system than the conven-

tional energy analysis since in an exergy analysis, effects of

irreversibility or exergy destruction caused by the internal

dissipative effects like viscosity, turbulence, thermal irre-

versibility due to heat transfer, thermal separation and pres-

sure drop losses are considered. On the contrary, a

conventional energy analysis of a vortex tube considers only

energy balance and cooling or heating effect of the vortex tube

(Saidi and Allaf Yazdi, 1999).

The physical exergy EPH, kinetic exergy EKN, potential

exergy EPT, total hot exergy, total cold exergy, total lost exergy

and exergy efficiency are calculated using Equations (17) and

(23) (Dincer et al., 2011). As no chemical process occurs dur-

ing temperature separation, the chemical exergy is not taken

into consideration.

EPH ¼ _m

�CpðT� T0Þ � T0

�Cpln

TT0

� RlnPP0

��(17)

where _m is the mass flow rate, Cp is the specific heat at con-

stant pressure, R is the gas constant for ideal air, T and P are

temperature and pressure at any instant.T0 and P0 are refer-

ence ambient temperature and pressure with To ¼ 293.15 K

and Po ¼ 100 kPa.

EKN ¼ _mv2

2(18)

EPT ¼ _mgz (19)

The total inlet exergy calculated at the inlet of first RHVT is

given by

SEi ¼ Ei;PH þ Ei;KN (20)

The total hot exergy and cold exergy calculated for the hot

exit and cold exit of the second RHVT are given as

SEh ¼ Eh;PH þ Eh;KN þ Eh;PT (21)

SEc ¼ Ec;PH þ Ec;KN (22)

The total lost exergy is given as

SElost ¼ SEi � ðSEh þ SEcÞ (23)

Second law efficiency or exergy efficiency is used as a

guideline for the evaluation of an actual device. This is defined

as

Fig. 7 e Comparison of exergy efficiency of a single RHVT.Fig. 5 e Comparison of total temperature separation in a

single RHVT.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 418

hII ¼minimum exergy intake to perform the given taskactual exergy intake to perform the same task

Thus, exergy efficiency calculated for the hot exit of the

cascaded RHVT is given by

hII;h ¼ SEh

SEið1�zÞ (24)

This efficiency expresses the operation of the actual device

relative to what is theoretically possible with the same inlet

and exit states as in actual device.

4. Results and discussion

Numerical simulations of compressible turbulent flow dis-

cussed so far are performed using the commercial CFD

Fig. 6 e Comparison of total lost exergy in a single RHVT.

package FLUENT™ 6.3.26 (Fluent User's Guide, release 6.3.26,

Ansys Inc. USA, 2006). The numerical results for a cascaded

RHVT are compared and validated against (Dincer et al., 2011)

as to the authors knowledge that is the only experimental

work conducting exergy analysis of hot cascade RHVT avail-

able in literature. However, to assess and evaluate the adopted

numerical model computed results for two different configu-

rations of single RHVT are compared with experimental re-

sults available in literature, namely (Behera et al., 2005) and

(Im and Yu, 2012). Total temperature separation for the two

configurations is shown in Fig. 5. In one case L/D ¼ 20, Ai/

A ¼ 0.07 and the corresponding numerical results are

compared with those due to (Behera et al., 2005). For the sec-

ond case L/D ¼ 14, Ai/A ¼ 0.14 and the results are validated

against (Im and Yu, 2012). In both cases the numerical results

Fig. 8 e Total inlet exergy in second stage RHVT as function

of cold fraction.

Fig. 9 e Total hot exergy in second stage RHVT as a

function of cold fraction.

Fig. 11 e Total lost exergy in second stage RHVT as a

function of cold fraction.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 4 19

show good agreement with the corresponding experiment.

Figs. 6 and 7 present comparison of total lost exergy and

exergy efficiency in a single RHVT obtained from present nu-

merical solution with the experimental results (Dincer et al.,

2011). The computed parameters match well with their

experimental counterpart. The comparisons suggest that the

RANS standard k-ε model is reliable enough for further ap-

plications including analysis of cascade RHVT.

The total inlet exergy for the hot cascade RHVT calculated

using the data obtained from CFD simulation and due to

experimental investigation by (Dincer et al., 2011) is shown in

Fig. 8. Since the inlet boundary conditions for the second

RHVT are maintained at a constant total pressure of 440 kPa

when the cold fraction for first RHVT is 0.5, a constant value of

total exergy of 1855.85 W is found at the inlet. As observed

Fig. 10 e Total cold exergy in second stage RHVT as a

function of cold fraction.

from Fig. 7 themaximumdeviation in predicting the total inlet

exergy by CFDmodel is only 2.3%. This difference is attributed

to the assumption of an axisymmetric computational model

instead of a 4-nozzles three-dimensional geometry.

Comparison of total hot exergy predicted by the CFDmodel

with experimental data, as a function of cold fraction (x) is

shown in Fig. 9. Total hot exergy decreases as the cold fraction

increases. The highest value of total hot exergy of 602.2 W is

observed for cold fraction of 0.24 and the value drops to

136.8 W for x ¼ 0.72. Maximum difference between the

experimental and computed values (22.9 W) is found at

x ¼ 0.62. The difference in results is significantly small for x in

the range of 0.24e0.52. As cold fraction decreases, hot gas

mass flow rate increases which stimulates energy separation

due to vigorous momentum transfer.

Fig. 12 e Exergy efficiency in second stage RHVT as a

function of cold fraction.

Table 1 e Deviation in CFD results from experimentaldata (%).

x DEinlet DElost DEefficiency

0.24 2.3 1.5 1.8

0.34 2.3 1.6 0.5

0.42 2.3 2.1 0.5

0.52 2.3 1.2 1.4

0.62 2.3 4.4 5.4

0.72 2.3 2.8 1.1

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 420

Comparison of total cold exergy Ec obtained from numeri-

cal simulation and experimental data is shown in Fig. 10. The

numerical model shows excellent agreement until x ¼ 0.52,

but consistently underpredicts by a small amount of about

20 W for higher values of cold fraction. However, the trend

agrees well. Cold exergy is a function of mass flow rate and

pressure drop. As increase in cold mass flow rate occurs in

conjunctionwith an increase pressure drop, the vortex driving

momentum transfer at the cold end improves. This results in

an increase in cold exergy. In numerical simulation, the

highest cold exergy is observed to be 832.26 W at x ¼ 0.72.

Total lost exergy is the difference of total inlet exergy and

total outlet exergy. Comparison of total lost exergy is shown in

Fig. 11. The method of cascading helps in reducing total lost

exergy and hence results in more efficient energy utilization.

The numerical result gives maximum total lost exergy of

1197.9W at x¼ 0.24 and drops to 897.9W as x reaches 0.72. The

difference between experimental data and computed predic-

tion are practically negligible.

Hot exergy efficiency calculated using Eq. (24) as a function

of cold fraction is given in Fig. 12. Turbulencemodel provides a

very good qualitative as well as quantitative agreement with

the experimental results. At x ¼ 0.24 hot exergy efficiency is

42.69% and it drops to 28.26% as x reaches 0.72. Though total

temperature separation increases with increasing cold frac-

tion, themass flow rate at hot exit reduces. Lowmass flow rate

at hot exit results in reduced values of kinetic and physical

exergy. Consequently, hot exergy efficiency decreases with

increase in cold fraction.

Quantitative deviations in inlet exergy, lost exergy and

exergy efficiency of CFD predictions from experimental data

as a function of cold fraction are summarized in Table 1. The

discrepancies are expressed in percentage. It is observed that

cold fraction in the range of 0.34e0.52 demonstrates best

agreement with the experimental results.

Fig. 13 illustrates the streamlines in second stage of RHVT

for a cold fraction of 0.52. In order to identify the source of

internal energy transfer between the inlet gas and the gas

leaving the hot and cold exit, the vortex tube is divided into

three regions: hot flow region, cold flow region, and

Fig. 13 e Streamlines contours in s

recirculating region (the flow that perpetually circulates near

the inlet nozzle). Forced vortex flow is observed near the

central axis and free vortex near the periphery of the tube. No

secondary circulation of flow is found which confirms

improved temperature separation between cold end and hot

end.

Fig. 14 shows total temperature distribution in the vortex

tube predicted by the numerical model for the cold fraction

value of 0.52. The phenomenon of temperature separation

along the axial and radial direction is clearly observed in this

figure.

Static temperature profiles are shown in Fig. 15. Large

quantitative difference is found between the locations near

the inlet (x/L ¼ 0.23) and two other sections (x/L ¼ 0.58 and x/

L ¼ 0.94) for same cold fraction. The difference can be attrib-

uted to the boundary conditions imposed at the inlet. At each

station large gradients in temperature is observed near the

wall. However, while the profile near the inlet shows tem-

perature gradient all along the radius, the profiles that are far

away from the inlet show nearly uniform temperature except

very close to the wall. Moreover, the static temperature pro-

files show decrease in radial temperature gradient on moving

towards the hot exit.

Radial distribution of axial velocity at three different sta-

tions is shown in Fig. 16. The phenomenon of flow reversal in

the vortex tube is clearly revealed in this figure. Very fast drop

in axial velocity is observed towards the axial core region. This

suggests a significantly high level of turbulencewhich leads to

stronger mixing in the flow.

The swirl velocity profiles presented in Fig. 17 show nearly

linear variations away from the wall region. The profiles are

very similar to rigid body rotation except at the station near

the inlet at x/L ¼ 0.23 where the swirl velocity is strongly

influenced by the inlet conditions. As a result of the no-slip

condition at the wall, maximum swirl velocity occurs near

the wall of the tube at all sections.

Static pressure profiles for different values of cold fraction

at three sections are shown in Fig. 18. Pressure drop of hot exit

gas varies from 72.56 kPa to 59.38 kPa as cold fraction in-

creases from 0.24 to 0.72. Maximum radial pressure drop oc-

curs near the inlet resulting in vortex generation in the

chamber, which helps inmomentum transfer from the axis to

the wall of the tube. Resulting reduced radial pressure drop

due to increase in cold fraction indicates generation of weaker

vortex at higher cold fraction. Thus, static temperature pro-

files confirm that hot exergy decreases with increase in cold

fraction.

Radial distributions of turbulent viscosity obtained from

CFD solution at three different sections of the vortex tube are

shown in Fig. 19. Similar kind of qualitative trend is observed

at all sections except at x/L ¼ 0.23 (near the inlet), where the

econd stage RHVT at x ¼ 0.52.

Fig. 15 e Radial distribution of static temperature in second stage RHVT at the sections x/L ¼ 0.23, 0.58 and 0.94.

Fig. 16 e Radial distribution of axial velocity in second stage RHVT at the sections x/L ¼ 0.23, 0.58 and 0.94.

Fig. 14 e Total temperature contours in second stage RHVT at x ¼ 0.52.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 4 21

Fig. 17 e Radial distribution of swirl velocity in second stage RHVT at the sections x/L ¼ 0.23, 0.58 and 0.94.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 422

turbulent viscosity is substantially large due to inlet condi-

tions. Due to the influence of inflow large turbulent eddies

formnear the inlet and further away as the disturbance due to

inlet reduces the energy-carrying eddies approach a smoother

distribution. This results in substantially reduced level of

turbulent viscosity but with increased uniformity in its

distribution.

5. Conclusions

Exergy analysis of a hot cascade type Ranque-Hilsch vortex

tube is carried out using standard keε turbulence model and

the results are validated against the experimentally measured

data due to (Dincer et al., 2011). Exergy analysis of the hot

Fig. 18 e Radial distribution of static pressure in second

cascade type RHVT helps in predicting the quality of available

energy as the pressure and temperature approach that of the

surroundings. The conclusions drawn from this study are

� The loss of exergy is more when heat loss due to irrevers-

ibility occurs at a higher temperature. The rate of irre-

versibility decreases as the temperature of the gas

decreases. The numerical simulations show that the hot

exit temperature increases with increase in cold fraction.

Therefore, the exergy destruction at hot exit is more when

cold fraction is high. This results in decrease of total hot

exergy with increase in cold fraction.

� Quality of available energy or exergy at the hot exit as well

as at cold exit is highly affected by mass flow rate, exit

temperature and pressure drop. The combined effect of the

stage RHVT at the sections x/L ¼ 0.23, 0.58 and 0.94.

Fig. 19 e Radial distribution of turbulent viscosity in second stage RHVT at the sections x/L ¼ 0.23, 0.58 and 0.94.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 3e2 4 23

three parameters shows hot exit gas performs better at low

cold fraction whereas cold exit gas is more efficient at

higher cold fraction. The highest value of exergy obtained

at hot and cold exit are 602.25 W and 832.26 W for x ¼ 0.24

and 0.72 respectively for same inlet conditions.

�Exergy efficiency decreases with increase in cold fraction.

The hot gas at lower cold fraction has the capacity of doing

more work than the hot gas at high cold fraction under

same environmental conditions. The highest exergy effi-

ciency of 42.69% is noted for x ¼ 0.24 and it differs from the

experimentally determined data by only 1.8%.

� Second law efficiency always provides a mean of assigning

a quality index to energy. Quantity of energy loss and the

temperature at which it occurs together defines exergy

efficiency for a particular process. In hot cascade type

RHVT, hot gas exergy efficiency variation shows that the

degradation is more for energy loss at higher cold fraction

than that at lower cold fraction.

� Nosecondarycirculation is found in the secondstageRHVT.

This confirms that geometry of the RHVT is optimally

designed for exergy. Formation of secondary circulation

could be treated as performance degrading mechanism in

vortex tubes. The degradation could be due to transfer of

colder fluid elementsnear the cold exit through the swirling

secondary loop to thewarmer flow region causing decrease

in the hot end temperature and transfer of warmer flow

elements back to the cold exit zone causing increase in cold

exit temperature (Behera et al., 2005).

� Static temperature profile and turbulent viscosity profile

confirms radial expansion of air from the wall to axis and

enhanced turbulent mixing.

� Cascading offers more efficient energy utilization and

produces larger total temperature separation compared to

a classical single RHVT.

� The model predictions compare favorably with experi-

mental data. Hence, it can be confidently used to further

investigate the performance of multiple vortex tubes used

in different combinations. Investigating the performance

of such cascaded RHVT numerically is far less time

consuming than conducting experimental investigation.

Thus, as a matter of fact, this model is useful as a time

saving and of course cost saving tool for designingmultiple

combination of vortex tubes.

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