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A computational and experimental study of thermal energy separation by swirl

01 Sep 2018-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 124, pp 11-19

AbstractWhen compressed air is introduced into a tube in such a way as to generate a strong axial vortex, an interesting phenomenon is observed wherein the fluid temperature at the vortex core drops below the inlet value, while in the outer part of the vortex, the temperature is higher than at inlet. The most familiar manifestation of this phenomenon is known as the Ranque-Hilsch effect, and several alternative explanations for it have been proposed. In this study, we present an analysis of the heat transfer mechanism underlying this phenomenon, based on consideration of the exact equation governing the conservation of the turbulent heat fluxes. The outcome is a model that explicitly accounts for the dependence of the heat fluxes on the mean rates of strain, and on the gradients of mean pressure. These dependencies, which are absent from conventional closures, are required by the exact equation. To verify the model, an experimental investigation of flow in a swirl chamber was conducted, and the measurements were used to check the model’s performance as obtained by three-dimensional numerical simulations. Comparisons between predictions and measurements demonstrate that the new model yields predictions that are distinctly better than those obtained using conventional closures.

Topics: Vortex (56%), Heat transfer (56%), Thermal energy (51%)

Summary (2 min read)

1. Introduction

  • Vortices that influence the local temperature distribution are frequently encountered in nature and in engineering practice.
  • When flow occurred in a vortex tube with an open outlet, measurements showed that the temperature in the vortex core was lowered, vortex breakdown occurred and pressure fluctuations with descent frequencies.
  • Thus, while the phenomenon is clearly evident when the working fluid is air [8–10], the situation is far less clear when the working fluid is water.
  • From consideration of the equation governing the conservation of energy in a rotating fluid under adiabatic conditions, they derive an expression for the total temperature that shows this quantity to depend on both the axial and angular velocities and hence vary in the radial direction leading to temperature separation.
  • Taken together, these results strongly suggest that the simple model for the turbulent heat flux is not adequate in this case.

2. Analysis and model development

  • The exact equations that govern the conservation of the turbulent heat fluxes in compressible flows are obtained from the Navier-Stokes and energy equations by replacing the instantaneous variables by the sum of mean and fluctuating parts, and by time-averaging after some manipulation.
  • When the mean pressure gradient is finite, the following functional relationship is obtained: uit ¼ f i uiuj; @Ui @xj ; @T @xj ; @P @xj ð3Þ Smith [18] gives the general representation for uit, a first-order tensor, in terms of the first- and second-order tensors in the functional relationship of Eq. (3).
  • When the heat transport is accomplished by fluid particles that are moving along a pressure gradient and work is done, they can maximally change their temperature according to an isentropic change of state.
  • This results in the same value for C5 as the one given above.

3.1. Geometry

  • The outlet from the tube is open and the pressure there is atmospheric.
  • For the flow inside a Ranque-Hilsch tube, the axial flow is bi-directional in the sense that the flows in the central core and the periphery move in opposite directions and thus the swirl number as defined in Eq. (10) would not be an appropriate indicator of the strength of swirl at a given streamwise section.
  • At inlet to the swirl chamber, however, the axial flow is uniformly directed across the entire section and hence the swirl number as defined in Eq. (10) is a meaningful indicator of the strength of swirl at that location.
  • This being the case, the inlet swirl number in the experiments is obtained as SI ¼ 5:30.

3.2. Instrumentation

  • A schematic representation of the test rig used for the present experiments is shown in Fig.
  • From the mass flow element, the flow passed through a plenum chamber followed by a honeycomb flow straightener before entering the swirl chamber via the tangential slots.
  • Temperature TW was measured using ten thermocouples that were placed directly below the surface at different axial positions.
  • The air flow was seeded with small oil droplets with a diameter of about 0:25 lm.
  • Each time an image was captured with a camera orientated perpendicularly to the laser sheet.

4.1. Computational details

  • The computations were performed using the compressible flow form of the Ansys CFX (v. 11sp1) software in which the governing equations are discretized by second-order accurate finite-volume methodology.
  • Implementation of the latter into the computations software was fairly straightforward and was accomplished via user defined subroutines.
  • For comparison, a model with a constant turbulent Prandtl number Prt ¼ 0:9 was also used.
  • This was done to ensure that the computations accurately captured the steep temperature gradients that occurred there.
  • The refinement factor for the thickness of the grid cells from the wall is 1:20.

4.2. Comparisons with measurements

  • The computed and measured cross-stream profiles of the axial component of velocity are compared in Fig.
  • The computed and measured circumferential velocity at four streamwise locations along the vortex chamber are compared in Fig.
  • It is thus the case that the low velocity within the axial backflow in this region was also subject to high experimental uncertainty.
  • Further downstream, the degree of temperature separation is reduced as the swirl weakens and with it the radial gradients of static pressure.
  • The result correlates well with the numerically calculated static temperature distribution.

5. Conclusions

  • The results presented in this paper demonstrate the importance of accounting for the effects of pressure gradients in the prediction of swirl-induced thermal energy separation.
  • An algebraic model for the turbulent heat fluxes was thus developed to explicitly include the pressure-gradient effects.
  • It was found that at the entry region to the chamber, where the swirl effects aremost pronounced, the predictions obtainedwith the newmodel matched quite closely the experimental results to within the estimated accuracy in the latter.
  • It should be noted that the temperature variations in the experiment were not very large and hence the close agreement obtained here does not necessarily mean that the model would be equally successful in predicting the RanqueHilsch regime of parameters where the temperature differences are much larger.
  • The swirl-induced temperature separation was clearly evident with a cold vortex core and a temperature distribution that looks almost like an adiabatic change of state compared to the pressure.

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Title
A computational and experimental study of thermal energy separation by swirl
Permalink
https://escholarship.org/uc/item/7q07f163
Authors
Kobiela, B
Younis, BA
Weigand, B
et al.
Publication Date
2018-09-01
DOI
10.1016/j.ijheatmasstransfer.2018.03.058
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California

A computational and experimental study of thermal energy separation
by swirl
B. Kobiela
a
, B.A. Younis
b,
, B. Weigand
a
, O. Neumann
c
a
Institut für Thermodynamik der Luft- und Raumfahrt, Universität Stuttgart, 70569 Stuttgart, Germany
b
Department of Civil & Environmental Engineering, University of California, Davis, CA 95616, USA
c
Department of Mechanical Engineering, University of Applied Sciences, 24149 Kiel, Germany
article info
Article history:
Received 22 December 2017
Received in revised form 14 March 2018
Accepted 16 March 2018
Available online 21 March 2018
Keywords:
Energy separation by swirl
Turbulent heat fluxes
Ranque-Hilsch effect
abstract
When compressed air is introduced into a tube in such a way as to generate a strong axial vortex, an
interesting phenomenon is observed wherein the fluid temperature at the vortex core drops below the
inlet value, while in the outer part of the vortex, the temperature is higher than at inlet. The most familiar
manifestation of this phenomenon is known as the Ranque-Hilsch effect, and several alternative expla-
nations for it have been proposed. In this study, we present an analysis of the heat transfer mechanism
underlying this phenomenon, based on consideration of the exact equation governing the conservation of
the turbulent heat fluxes . The outcome is a model that explicitly accounts for the dependence of the heat
fluxes on the mean rates of strain, and on the gradients of mean pressure. These dependencies, which are
absent from conventional closures, are required by the exact equation. To verify the model, an experi-
mental investigation of flow in a swirl chamber was conducted, and the measurements were used to
check the model’s performance as obtained by three-dimensional numerical simulations. Comparisons
between predictions and measurements demonstrate that the new model yields predictions that are dis-
tinctly better than those obtained using conventional closures.
Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction
Vortices that influence the local temperature distribution are
frequently encountered in nature and in engineering practice. In
the core of a strong vortex, for example, the static temperature is
significantly lower than the ambient temperature. It is for this rea-
son that water vapour condenses in the funnel of a tornado, and in
the core of the wing tip vortex of an aircraft landing in humid air.
An extreme manifestation of the effect of vortical motion on local
temperature is seen when compressed air is introduced into a cir-
cular tube via tangential inlet slots designed to induce a strong
axial vortex. Measurements show that in the core of the vortex,
the temperature (both static and total) drops to a value lower than
that at inlet, while in the outer part of the vortex, it is higher. The
most familiar manifestation of this phenomenon of ‘‘thermal
energy separation” is the Ranque-Hilsch effect (Fig. 1). Another
manifestation, which is the subject of this study, is the flow in a
swirl chamber where in the absence of a cold-air outlet, the
temperature separation is evident in a substantial decrease of
temperature at the vortex axis relative to the inlet value.
Several alternative explanations of the Ranque-Hilsch effect
have been put forward since the phenomenon was first observed
by Ranque [1] and elaborated on further by Hilsch [2] . A thorough
review of the literature on this subject can be found in Eiamsaard
and Promvonge [3]. Behera et al. [4], for example, assumed that the
mechanism is related to viscous shear that arises due to the strong
radial variation of the circumferential velocity. Kurosaka [5] attrib-
uted the effect to ‘‘acoustic streaming”. When flow occurred in a
vortex tube with an open outlet, measurements showed that the
temperature in the vortex core was lowered, vortex breakdown
occurred and pressure fluctuations with descent frequencies.
When the pressure fluctuations were suppressed by using Helm-
holz resonators, the temperature in the vortex core increased and
the vortex breakdown did not occur. Gutsol [6] assumed that there
is a ‘‘sorting” of fluid particles with different speeds and therefore
energy separation occurred due to centrifugal forces, i.e. faster par-
ticles move radially outwards. Eckert [7] explained the tempera-
ture change by adiabatic compression processes. The uncertainty
regarding the mechanism underlying this phenomenon is not
diminished by recent experimental findings. Thus, while the phe-
nomenon is clearly evident when the working fluid is air [8–10],
the situation is far less clear when the working fluid is water.
Balmer [11], for example, in experiments in water, showed that a
https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.058
0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
Corresponding author.
E-mail address: bayounis@ucdavis.edu (B.A. Younis).
International Journal of Heat and Mass Transfer 124 (2018) 11–19
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ijhmt

temperature separation can still be observed, but the static tem-
perature of the cold water at outlet was higher than that at inlet.
Clearly compressibility effects that will have been absent from
the water experiments will have played a more important role
than hitherto suspected. This is confirmed in the study of Polihro-
nov and Straatman [12] who considered the simplified but related
case of the radial flow of a compressible fluid taking place in a uni-
formly rotating adiabatic duct. From consideration of the equation
governing the conservation of energy in a rotating fluid under adi-
abatic conditions, they derive an expression for the total tempera-
ture that shows this quantity to depend on both the axial and
angular velocities and hence vary in the radial direction leading
to temperature separation. Their analysis highlighted the impor-
tant role of compressibility in the process of temperature separa-
tion since, in its absence, the fluid cannot give away internal
energy and hence cooling cannot take place.
The numerical simulation of flows in which thermal energy sep-
aration as manifested by the Ranque-Hilsch effect has also received
much attention and comprehensive reviews of previous work in
this area can be found in [13,14]. Farouk and Farouk [15] reported
results obtained with Large-Eddy Simulations that showed that,
while the flow field was well predicted, the total temperature sep-
aration at the cold exit underpredicted the measurements. Most
other previous numerical studies of the thermal energy separation
as manifested by the Ranque-Hilsch effect have been based on the
solution of the Reynolds-averaged form of the equations governing
the conservation of mass, momentum and energy [3,4,9]. In this
approach, closure models are needed to approximate the unknown
turbulence correlations that arise from the averaging process.
While a variety of different models were used to obtain the Rey-
nolds stresses, the turbulent heat fluxes were invariably modelled
by using Fick’s law in which the turbulent diffusivity was defined
on the basis of a constant turbulent Prandtl number. The outcomes
were generally the same: the predicted difference in total temper-
ature was always smaller than that observed in experiments.
Moreover, the calculated profile of static temperature exhibited a
maxima on the tube axis and thereafter a decrease towards the
adiabatic tube wall. This is contrary to the measured behaviour
where the static temperature at the tube axis was in fact at min-
ima. Taken together, these results strongly suggest that the simple
model for the turbulent heat flux is not adequate in this case. In the
study of Polihronov and Straatman [12] mentioned earlier, compu-
tations were performed of the flow in a rotating rectangular duct
with adiabatic walls with heated flow introduced at the inlet. Com-
parisons of the temperature drop between inlet and outlet as com-
puted with their theoretical model with results obtained from
solving the conservation equations in three dimensions showed
very close agreement between the two. The authors point out a
number of important differences between the rotating duct flow
considered, and the more complex flow in a vortex tube notably
in the necessity of a hot fluid outlet in the vortex tube flow and
the absence of such an outlet in the rotating duct case. The patterns
of thermal energy transfer, being partly dependent on turbulent
diffusion, wil thus be different in the two cases and hence the need
for further computations to demonstrate the utility of the theoret-
ical model in a vortex tube flow.
In this paper, we put forward an explanation for the thermal
energy separation by swirl based on analysis of the fundamental
equations governing conservation of momentum and thermal
energy in vortical flows. It will be shown that the phenomenon
can be explained from consideration of the thermal energy trans-
port associated with the turbulent heat flux and the turbulent
volume work in a pressure gradient field in a compressible fluid.
A model for the turbulent heat fluxes that can account for these
effects is proposed, and its validity is checked by comparisons with
experimental data obtained in a swirl chamber.
2. Analysis and model development
The exact equations that govern the conservation of the turbu-
lent heat fluxes in compressible flows are obtained from the
Navier-Stokes and energy equations by replacing the instanta-
neous variables by the sum of mean and fluctuating parts, and by
time-averaging after some manipulation. Le Ribault and Friedrich
[16] give the outcome as:
c
p
@
q
u
i
t
@
s
þc
p
@
q
U
j
u
i
t
@x
j
¼
q
c
p
u
j
t
@U
i
@x
j
q
c
p
u
i
u
j
@T
@x
j
c
p
@
@x
j
ð
q
u
i
u
j
t þ ptd
ij
Þþ
s
jk
u
i
@u
k
@x
j
þc
p
t
@
s
ij
@x
j
u
i
@q
j
@x
j
þu
i
@p
@
s
þU
j
u
i
@p
@x
j
þu
i
u
j
@P
@x
j
þu
i
u
j
@p
@x
j
zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{
ð1Þ
where U; T and P are the mean components of velocity, temperature
and pressure, respectively, u; t and p are their fluctuating values, q is
the density, c
p
is the heat capacity at constant pressure,
s
ij
ð¼
l
ð@u
i
=@x
j
þ @u
j
=@x
i
Þ2=3
l
ð@u
k
=@x
k
Þd
ij
Þ is the stress tensor
with
l
being the dynamic viscosity and q
j
ð¼ k@T=@x
j
Þ is Fourier’s
heat-flux vector with k being the molecular diffusivity [16].
While Eq. (1) can be used to obtain the turbulent heat fluxes
after the unknown correlations that appear there have been suit-
ably modeled, it would be more convenient from a practical stand-
point to use this equation to derive an algebraic model that is
simpler to implement in a computational procedure yet one that
contains all the requisite dependencies to represent the effects of
compressibility, turbulence, and the mean rates of strain. In this
regard, attention is drawn to the group of terms that appear on
the last line of Eq. (1). These terms, which originate from expansion
of
u
i
DðP þpÞ=D
s
, represent the contribution to the turbulent scalar
Fig. 1. Schematic view of a Ranque-Hilsch tube.
12 B. Kobiela et al. / International Journal of Heat and Mass Transfer 124 (2018) 11–19

fluxes due to the work done by the pressure field. In formulating
the heat-flux model, it is important to note that the term in that
group that contains the mean pressure gradient does not also con-
tain gradients of temperature or of mean velocity. This suggests
that for the algebraic model to accurately reflect the contributions
made by these terms, it should be formulated in the form:
q
u
i
t ¼ D
T
ij
@T
@x
j
þ D
p
ij
@P
@x
j
ð2Þ
where D
T
ij
is the turbulent diffusivity tensor [17] which is unknown
and in need of approximation, and D
p
ij
is a second-order tensor that
is a function of the Reynolds-stress tensor and the turbulence time
scale but not a function of the velocity or temperature gradients. In
this work, and following usual practice, this time scale is assumed
to be proportional to the ratio k=
i.e. of the turbulence kinetic
energy to its rate of dissipation by viscous action.
Several proposals for modelling D
T
ij
can be found in the litera-
ture. In this study, we adopt the proposal of Younis et al. [19]
who used tensor representation to obtain an explicit expression
for
u
i
t in terms of the vector and tensor quantities suggested by
Eq. (1). When the mean pressure gradient is finite, the following
functional relationship is obtained:
u
i
t ¼ f
i
u
i
u
j
;
@U
i
@x
j
;
@T
@x
j
;
@P
@x
j

ð3Þ
Smith [18] gives the general representation for u
i
t, a first-order
tensor, in terms of the first- and second-order tensors in the func-
tional relationship of Eq. (3). This representation and the assump-
tions underlying its simplification for the case with no pressure
gradients are given in [19] and hence will not be reproduced here.
When the gradients of mean pressure are finite, additional terms
arise. If the terms that involve the products of two second-order
tensors are dropped (which is in keeping with the approximations
of the previous study), the following pressure-gradient related
terms remain:
a
1
@P
@x
i
;
a
2
u
i
u
j
@P
@x
j
;
a
3
@U
i
@x
j
@P
@x
j
;
a
4
@T
@x
j
@P
@x
j
where the as are linear multipliers that are required for dimen-
sional consistency.
It is immediately evident that only one of the terms in this rep-
resentation corresponds in form to the term in the exact equation
(Eq. (1)) that includes the gradients of mean pressure; specifically,
the term that involves the product of the Reynolds stresses and the
mean pressure gradient. The remaining terms either include gradi-
ents of temperature and velocity which are not present in the exact
equation, or, for dimensional consistency, would require the intro-
duction of a dependence on the temperature variance which is also
absent from the exact equation. It is for this reason that it is argued
here that the term involving the Reynolds stresses should alone be
included in the model for
u
i
t. After inclusion of the terms from the
proposal of Younis et al. [19], the complete model now reads:
u
i
t ¼ C
1
k
2
@T
@x
i
þ C
2
k
u
i
u
j
@T
@x
j
C
5
1
q
c
p
u
i
u
j
@P
@x
j

þ C
3
k
3
2
@U
i
@x
j
@T
@x
j
þ C
4
k
2
2
u
i
u
k
@U
j
@x
k
þ u
j
u
k
@U
i
@x
k

@T
@x
j
: ð4Þ
It is worth noting that the additional term, being independent of
the temperature gradients, implies that in an initially isothermal
turbulent flow, such gradients can be generated by the application
of pressure gradients.
The model given by Eq. (4) bears some similarity to an earlier
model that was proposed by Deissler and Perlmutter [20] based
on the theory of turbulent volume work in a pressure gradient.
By utilizing certain empirical analogies with atmospheric pro-
cesses, they proposed that the pressure gradient term should be
included in the model for turbulent fluxes in the form:
u
i
t ¼ k
t
@T
@x
i
1
q
c
p
@P
@x
i

ð5Þ
where k
t
is an eddy diffusivity. Their analytical solutions for the
temperature distribution in a Ranque-Hilsch tube showed a static
temperature distribution corresponding to an adiabatic change of
state over the radial pressure distribution. The minimum value of
static temperature was predicted to occur on the tube axis, in
good agreement with experiments. The model of Eq. (4) can thus
be considered a generalization of the isotropic model of Deissler
and Perlmutter [20] via the presence of
u
i
u
j
that brings about the
consistency with the exact equation for the heat fluxes. The new
model also provides a convincing explanation for the need for the
explicit inclusion of a dependence on the gradients of mean
pressure.
The complete model of Eq. (4) contains a number of coefficients
that need to be determined. Of those, the coefficient of the original
model of Younis et al. [19] that were determined by reference to
results from Direct Numerical Simulations of some fundamental
heated flows remain unchanged, viz. C
1
¼0:0455; C
2
¼ 0:373;
C
3
¼0:00373; C
4
¼0:0235. This is logical, because in the
absence of a strong pressure gradients, the new model should
revert to its original form.
In determining the new coefficient (C
5
), consideration must be
given to the fact that the pressure gradient term must be balanced
by the other terms in the model in such a way as to maintain the
correct asymptotic behavior in conditions of strong pressure
gradients and turbulence. This requirement can be seen when
examining the physical process underlying the heat transfer
processes in these conditions.
Briefly, turbulent eddies transport small amounts of fluid coun-
ter to the local pressure gradient. When moving along the pressure
gradient into an area with higher pressure, these fluid volumes are
compressed and volume work is done leading to rise in fluid tem-
perature. In their final position the temperature is equalized to the
new environment due to heat conduction. In strong turbulence this
mechanism is much stronger than heat conduction and turbulent
heat transport due to the temperature gradient, it results in a tem-
perature distribution that looks like an adiabatic change of state. A
temperature difference that is larger than the one corresponding to
an adiabatic distribution is physically impossible. This has implica-
tions for the value of C
5
. When the temperature distribution is sim-
ilar to an adiabatic change of state compared to the pressure
distribution, the influence of the pressure term, which is in part
determined by C
5
, has to be equal or smaller than the influence
of the terms depending on the component of the temperature gra-
dient, which is parallel to the pressure gradient.
To assess the relative importance of the terms that are functions
of the gradients of temperature and pressure in isolation, we con-
sider the case of flow in the x-direction, with velocity component U
and a pressure gradient @P/@x. To balance the internal heat transfer
due to the pressure gradient, the only relevant gradient of temper-
ature is @T/@x. Under these circumstances, the model of Eq. (4)
reduces to:
0 ¼ C
1
k
2
@T
@x
þ C
2
k
u
2
@T
@x
C
5
1
q
c
p
u
2
@P
@x

þ C
3
k
3
2
@U
@x
@T
@x
þ C
4
k
2
2
u
2
@U
@x
þ u
2
@U
@x

@T
@x
: ð6Þ
It is immediately apparent that the terms u
2
@T=@x and
C
5
1
q
c
p
u
2
@P=@x are very similar in form. Considering the velocity
B. Kobiela et al. / International Journal of Heat and Mass Transfer 124 (2018) 11–19
13

distribution in a vortex in Eq. (6), the terms containing C
3
and C
4
are
much smaller than the term containing C
2
, as the included velocity
gradient @U/@x becomes small (in the geometrical point that is
discussed, the velocity component U is equal to the radial velocity.
This is always almost equal to zero). Moreover, the term containing
C
1
is of minor importance being much smaller than the term
containing C
2
.
When the heat transport is accomplished by fluid particles that
are moving along a pressure gradient and work is done, they can
maximally change their temperature according to an isentropic
change of state. Thus, due to turbulence in a pressure gradient,
the static temperature changes in its limit to a distribution adapt-
ing an adiabatic change of state compared to the pressure distribu-
tion. In this case the turbulent heat flux has to tend to zero, when
neglecting heat conduction and convection. With this assumptions
only the term belonging to the coefficient C
2
is able to balance the
pressure term resulting in the following equilibrium:
0 ¼ C
2
k
u
2
@T
@x
C
5
1
q
c
p
u
2
@P
@x

ð7Þ
@T
@x
¼
C
5
q
c
p
@P
@x
: ð8Þ
Integrating this equation results in
T
T
0
¼
P
P
0

j
1
j
C
5
: ð9Þ
For an ideal gas with C
5
¼ 1 an isentropic change of state is
obtained. The fact that turbulent particles move adiabatically in
radial direction has also been noted by Deissler and Perlmutter [20].
Beside this consideration, the coefficient C
5
has also been deter-
mined out of the comparison of temperature calculations and mea-
surements in the vortex chamber, which are presented in the next
section. This results in the same value for C
5
as the one given
above.
3. Experiments in a swirl chamber
3.1. Geometry
The flow in a swirl chamber provides an ideal manifestation of
thermal energy separation by swirl as the geometry is fairly simple
and the effect can be studied in isolation of other phenomena. In
the present swirl chamber, which is depicted in Fig. 2, air is intro-
duced via two tangential slots into a round tube with diameter
D ¼ 50 mm and length of 1 m. The slots themselves have a length
l ¼ 0:66 D and a width of b ¼ 0:1 D. The outlet from the tube is open
and the pressure there is atmospheric. The tube walls are assumed
to be adiabatic and the inlet temperature was maintained at a con-
stant value of T
E
¼ 300 K.
The strength of swirl is generally quantified by the swirl num-
ber i.e. by the ratio of the flux of tangential momentum I
H
to that
of axial momentum I
x
:
S ¼
I
H
RI
x
¼
R
R
r¼0
q
WU 2
p
r
2
dr
R
R
R
r¼0
q
U
2
2
p
rdr
: ð10Þ
where R is the pipe radius, r is the radial coordinate, U is the axial
component of velocity and W the tangential velocity. For the flow
inside a Ranque-Hilsch tube, the axial flow is bi-directional in the
sense that the flows in the central core and the periphery move in
opposite directions and thus the swirl number as defined in Eq.
(10) would not be an appropriate indicator of the strength of swirl
at a given streamwise section. At inlet to the swirl chamber, how-
ever, the axial flow is uniformly directed across the entire section
and hence the swirl number as defined in Eq. (10) is a meaningful
indicator of the strength of swirl at that location. This being the
case, the inlet swirl number in the experiments is obtained as
S
I
¼ 5:30.
The Reynolds number is defined with the mean axial velocity of
the flow U
0
and the tube diameter
Re
D
¼
U
0
D
m
¼
4
_
m
qp
D
m
: ð11Þ
In the present experiment, the mean axial velocity was
U
0
¼ 6:18 m=s and Re
D
¼ 20; 000.
3.2. Instrumentation
A schematic representation of the test rig used for the present
experiments is shown in Fig. 3. Air entered the test section through
a conical inlet where the mass flow has been measured using a
laminar flow element (TetraTec LMF 50MC02-02-FS). According
to the manufacturer, this mass flow element is accurate to within
0:15% of the actual value in the range 300–2400 l/min. From the
mass flow element, the flow passed through a plenum chamber fol-
lowed by a honeycomb flow straightener before entering the swirl
chamber via the tangential slots. Downstream of the swirl cham-
ber, the flow passed through a 500 mm long tube leading to a sec-
ond plenum. The tube was made out of Plexiglass with a wall
thickness of 20 mm. Thus the outer wall can be considered to be
adiabatic. From there the air was sucked by a vacuum pump. In
the PIV experiments, small oil droplets where injected directly
after the first plenum.
Measurement of temperature was with thermocouples (type K,
Omega 5SCTT-KI-40-2 M) with a manufacturer quoted accuracy of
0:3 K and a response time of 0:02 s at 18 m=s air speed. The voltage
of the thermocouples was measured with an Agilent 34830A ana-
lyzer with external temperature reference. To measure the radial
profile of fluid temperature, the test rig was equipped with a
traversing mechanism that spanned the entire range. The wall
Fig. 2. Geometry of a swirl chamber.
14 B. Kobiela et al. / International Journal of Heat and Mass Transfer 124 (2018) 11–19

Citations
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Abstract: Various methods had been taken for the flow field studies, among them, qualitative visualizations and probe intrusive measurements have a long history and had been adopted since last 50s, while laser non-intrusive measurements and numerical simulations are the emerging methods, especially the former. Nowadays, more and more researchers have realized there are specific and regular flow structures in the strong turbulence of vortex tube, and the flow structures have great significance on understanding the energy separation process and performance. However, there still did not exist a review on the flow structure studies. The aim of this paper is to offer a critical review and discussion on the current studying methods, findings and differences on the flow structures in vortex tube. In addition, future scopes were proposed on the experimentally and theoretically verification of these flow structures and their effects on the energy separation process and performance.

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Abstract: This review will focus on perfect gas models developed to predict the performances of counterflow vortex tubes. It includes empirical and thermodynamics models, models of heat exchangers, models based on a pressure gradient, models based on the momentum transfer with particles spinning inward and models based on unsteady phenomena like the vortex breakdown. A detailed comparison of these models shows that most of them solve the same set of equations but lead to different explanations regarding the flow and heat transfer phenomena within Ranque-Hilsch tubes. The energy balance links the hot and cold flow temperatures for a given cold mass fraction as long as kinetic energy is included in the analysis. Secondly, almost all models consider the radial momentum balance, which reduces to a simple expression linking the pressure gradient and the tangential velocity. Usually, a given velocity profile (forced vortex or Rankine vortex) closes this set of equations. The form of the velocity profile may be dependent on the magnitude of the radial flow. None of the analytical models analyzed in this paper could predict all the geometrical parameters of a vortex tube. Empirical knowledge is still required. However, the pressure difference between the inlet and the cold outlet is a major component. It is related to the pressure drop of the cold air downstream of the vortex tube. To predict the main vortex tube dimensions (diameter and length), the most promising avenue is linked to the occurrence and the good localization of the vortex breakdown inside the tube. This review ends with some future views to improve the predictions of the existing models and the knowledge of the temperature separation phenomenon within vortex tubes.

15 citations


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Abstract: In this study, an investigation of a vortex chamber was carried out to gain a full understanding of the nature of the vortex flow and the cooling capability inside the chamber. The paper discusses the effects on flow and heat transfer rates when the inside surface of the vortex chamber was roughened by adding flow turbulators to its wall. The turbulators took the shape of a rib with a square cross-section, the dimension of which varied between 0.25 mm and 2.00 mm. The paper also presents the results of a comparative investigation of jet impingement and vortex cooling on a concave wall using different parameters, such as the total pressure loss coefficient, Nusselt number and thermal performance factor, to evaluate the cooling effectiveness and flow dynamics. Furthermore, the entropy generation in swirl flow with the roughened wall was assessed over a wide range of Reynolds numbers. The results show that surface roughness considerably influences the velocity distribution, heat transfer patterns and pressure drop in the vortex chamber. The highest thermal performance factor takes place at rib heights of 0.25 mm and 0.50 mm with a low Re number. Further increase in rib height has an adverse impact on thermal performance. At a Reynolds number lower than 50,000, it is highly recommended to use roughened vortex cooling to obtain the best thermal performance.

10 citations


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Abstract: In order to get the internal parameters of a vortex tube, a large-scale vortex tube was designed and an experimental device was built. A five-hole probe and thermocouples were used to obtain the three-dimensional velocities, the static pressure, static temperature and total temperature distributions inside the vortex tube. Four different cold mass fraction conditions (0.2, 0.4, 0.6 and 0.8) were chosen and the impacts on the internal parameters of the vortex tube were discussed. Different from the traditional view, the tangential velocity was considered to be the steady Burgers vortex form. A reverse flow boundary was found, and the location of which was changed at different operation conditions and axial positions. Further, it was found that the lowest static temperature existed near the nozzle outlet, and a new static temperature difference distribution law was firstly proposed experimentally.

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References
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Abstract: Some new developments of explicit algebraic Reynolds stress turbulence models (EARSM) are presented. The new developments include a new near-wall treatment ensuring realizability for the individual stress components, a formulation for compressible flows, and a suggestion for a possible approximation of diffusion terms in the anisotropy transport equation. Recent developments in this area are assessed and collected into a model for both incompressible and compressible three-dimensional wall-bounded turbulent flows. This model represents a solution of the implicit ARSM equations, where the production to dissipation ratio is obtained as a solution to a nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean flow description of the stress anisotropy. The resulting EARSM has been found to be well suited to integration to the wall and all individual Reynolds stresses can be well predicted by introducing wall damping functions derived from the van Driest damping function. The platform for the model consists of the transport equations for the kinetic energy and an auxiliary quantity. The proposed model can be used with any such platform, and examples are shown for two different choices of the auxiliary quantity.

698 citations


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  • ...The unknown Reynolds stresses were obtained using an explicit algebraic Reynolds stress model [21,22] incorporating the modification proposed byWallin and Johansson [23] to account for streamline curvature....

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Abstract: In an earlier paper the author considered the problem of the turbulent diffusion, relative to a fixed origin, of a cloud of marked fluid whose initial position is given. This was found to be determined by the initial shape of the cloud and the statistical properties of the displacement of a single fluid particle. The present paper is concerned with the relative diffusion of the cloud, i.e. with the tendency to change its shape, or, more precisely, with that part of the relative diffusion which is described by the probability that a given vector y can lie with both its ends in marked fluid at time t. This aspect of the relative diffusion is found to be determined by the initial shape of the cloud and the statistical properties of the separation, at time t, of two fluid particles of given initial separation. The statistical functions introduced to describe the relative diffusion are found to be related to Richardson's distance-neighbour function.The relative diffusion of two particles is a more complex problem than diffusion of a single particle about a fixed origin because the relative diffusion depends on the initial separation. The closer the particles are together, the smaller is the range of eddy sizes that contributes to their relative velocity; for the same reason, relative diffusion is an accelerating process, until the particles are very far apart and wander independently. The hypothesis is made that if the initial separation is small enough, the probability distribution of the separation will tend asymptotically to a form independent of the initial separation, before the particles move independently. This hypothesis permits various simple deductions, some of which make use of Kolmogoroff's similarity theory. The important question of the description of the relative diffusion by a differential equation is examined; Richardson has put forward one suggestion, and another, based on a normal distribution of the separation, is made herein.

621 citations


"A computational and experimental st..." refers background in this paper

  • ...where DT ij is the turbulent diffusivity tensor [17] which is unknown and in need of approximation, and Dpij is a second-order tensor that is a function of the Reynolds-stress tensor and the turbulence time scale but not a function of the velocity or temperature gradients....

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Journal ArticleDOI
TL;DR: The design of a vortex tube of good efficiency in which the expansion of a gas in a centrifugal field produces cold is described and the important variables in construction and operation are discussed and data for several tubes under various operating conditions are given.
Abstract: The design of a vortex tube of good efficiency in which the expansion of a gas in a centrifugal field produces cold is described. The important variables in construction and operation are discussed and data for several tubes under various operating conditions are given. Low pressure gas, 2 to 11 atmospheres, enters the tube and two streams of air, one hot and the other cold, emerge at nearly atmospheric pressure. The cold stream may be as much as 68°C below inlet temperatures. Efficiencies and applications are discussed.

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  • ...B. Kobiela a, B.A. Younis b,⇑, B. Weigand a, O. Neumann c a Institut für Thermodynamik der Luft- und Raumfahrt, Universität Stuttgart, 70569 Stuttgart, Germany bDepartment of Civil & Environmental Engineering, University of California, Davis, CA 95616, USA cDepartment of Mechanical Engineering, University of Applied Sciences, 24149 Kiel, Germany a r t i c l e i n f o Article history: Received 22 December 2017 Received in revised form 14 March 2018 Accepted 16 March 2018 Available online 21 March 2018 Keywords: Energy separation by swirl Turbulent heat fluxes Ranque-Hilsch effect a b s t r a c t When compressed air is introduced into a tube in such a way as to generate a strong axial vortex, an interesting phenomenon is observed wherein the fluid temperature at the vortex core drops below the inlet value, while in the outer part of the vortex, the temperature is higher than at inlet....

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  • ...Their analytical solutions for the temperature distribution in a Ranque-Hilsch tube showed a static temperature distribution corresponding to an adiabatic change of state over the radial pressure distribution....

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  • ...For the flow inside a Ranque-Hilsch tube, the axial flow is bi-directional in the sense that the flows in the central core and the periphery move in opposite directions and thus the swirl number as defined in Eq....

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  • ...It should be noted that the temperature variations in the experiment were not very large and hence the close agreement obtained here does not necessarily mean that the model would be equally successful in predicting the RanqueHilsch regime of parameters where the temperature differences are much larger....

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  • ...The most familiar manifestation of this phenomenon of ‘‘thermal energy separation” is the Ranque-Hilsch effect (Fig....

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Journal ArticleDOI
Abstract: The Ranque–Hilsch effect, observed in swirling flow within a single tube, is a spontaneous separation of total temperature, with the colder stream near the tube centreline and the hotter air near its periphery. Despite its simplicity, the mechanism of the Ranque–Hilsch effect has been a matter of long-standing dispute. Here we demonstrate, through analysis and experiment, that the acoustic streaming, induced by orderly disturbances within the swirling flow is, to a substantial degree, a cause of the Ranque–Hilsch effect. The analysis predicts that the streaming induced by the pure tone, a spinning wave corresponding to the first tangential mode, deforms the base Rankine vortex into a forced vortex, resulting in total temperature separation in the radial direction. This is confirmed by experiments, where, in the Ranque–Hilsch tube of uniflow arrangement, we install acoustic suppressors of organ-pipe type, tuned to the discrete frequency of the first tangential mode, attenuate its amplitude, and show that this does indeed reduce the total temperature separation.

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Abstract: The development and preliminary validation of a new k-ω turbulence model based on explicit algebraic Reynolds-stress modeling are presented. This new k-ω model is especially designed for the requirements typical in high-lift aerodynamics. Attention is especially paid to the model behavior at the turbulent/laminar edges, to the model sensitivity to pressure gradients, and to the calibration of the model coefficients for appropriate flow phenomena. The model development is based on both analytical studies and numerical experimenting. The developed model is assessed and validated for a set of realistic flow problems including high-lift airfoil flows.

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Frequently Asked Questions (1)
Q1. What are the contributions in "A computational and experimental study of thermal energy separation by swirl" ?

In this study, the authors present an analysis of the heat transfer mechanism underlying this phenomenon, based on consideration of the exact equation governing the conservation of the turbulent heat fluxes.