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ExergyanalysisofahotcascadetypeRanque-Hilschvortextubeusingturbulencemodel
ARTICLEinINTERNATIONALJOURNALOFREFRIGERATION·SEPTEMBER2014
ImpactFactor:2.24·DOI:10.1016/j.ijrefrig.2014.05.020
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NilotpalaBej
IITKharagpur
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K.P.Sinhamahapatra
IITKharagpur
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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
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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: [email protected]
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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