International Journal of Heat and Fluid Flow 73 (2018) 174–187
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International Journal of Heat and Fluid Flow
journal homepage: www.elsevier.com/locate/ijhff
Flow and heat transfer measurements in swirl tubes with one and multiple
tangential inlet jets for internal gas turbine blade cooling
T
⁎
Christoph Bieggera, , Yu Raob, Bernhard Weiganda
a
b
Institute of Aerospace Thermodynamics (ITLR), University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
School of Mechanical Engineering, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240, China
A R T I C LE I N FO
A B S T R A C T
Keywords:
Swirling flow
PIV
Swirl tube
Heat transfer
Gas turbine cooling
In this paper, we present a detailed experimental and numerical study of the flow phenomena and the heat
transfer in swirl tubes with one and multiple tangential inlet jets. Such tangential jets induce a highly 3D swirling
flow and an enhanced turbulence in the tube, increasing the convective heat transfer. Thus, a swirl tube is
considered as an effective cooling method for technical applications with high thermal loaded components like
gas turbine blades.
The flow field, the heat transfer and the pressure loss are examined in a swirl tube with three different inlet jet
configurations with one (MI1), three (MI3) or five (MI5) tangential inlet jets in axial direction. For this purpose,
we measured the flow field via stereo-PIV (Particle Image Velocimetry) and the heat transfer by applying a
transient technique using thermochromic liquid crystals for several Reynolds numbers. The numerical simulations are performed via Detached Eddy Simulation.
The PIV results reveal a complex axial velocity changing after each inlet due to the additional mass flow. Two
main structures occur in the swirl tube with five inlet jets: a vortex in the tube center in a wave-like form and
large spiral vortices around the tube axis especially near the inlet jets. In the inlet region(s) the highest heat
transfer occurs and decreases continuously until the next inlet or towards the tube outlet for the swirl tube with
one inlet. The swirl tubes with multiple inlets show lower maximum heat transfer rates compared to the swirl
tube with only one inlet due to lower inlet jet velocities. However, the heat transfer distribution is more
homogeneous over the entire tube length at a much lower pressure loss. The homogeneous heat transfer can be
explained by two mechanisms. At the inlets, the tangential jets impinge onto the concave wall and cause an
enhanced convective heat transfer correlating with large spiral vortices. Secondly, the axial velocity becomes
stronger further downstream after each inlet jet and causes an enhanced heat transfer between the inlet jets.
The thermal performance parameter for all investigated swirl tube configurations is in the same order of
magnitude. Thus, all swirl tube configurations are suitable for cooling. If one is interested in a maximum heat
transfer paid by a high pressure loss, the swirl tube with one inlet is the best choice. If a lower but more
homogeneous heat transfer with a low pressure loss is desired, one should choose the swirl tube with multiple
inlets.
1. Introduction
Major development goals for gas turbines used for propulsion and
power generation are to increase the thermal efficiency, which can be
achieved by operating the gas turbines at increasingly higher pressures
and temperatures. These conditions result in temperatures well above
the melting temperature of the blade material, which requires the development of more efficient internal turbine blade cooling strategies
(Han et al., 2012). Currently different cooling techniques are investigated like rib turbulators, pin fins, jet impingement, swirl tubes
⁎
and dimples (Ligrani et al., 2003; Weigand et al., 2011). Here swirl
cooling tubes and dimples show a promising cooling performance as
they promote a high turbulent mixing in the near wall region and
provide high heat transfer enhancement capabilities.
A swirl tube consists of a tube with one or more tangential inlet jets,
as shown in Fig. 1, which induce a strong swirling flow circumferentially, enhancing the turbulent mixing near the wall and therefore improves the wall heat transfer significantly. Due to the complex swirling
flow coupled with high turbulence, the understanding of the flow and
heat transfer characteristics in a swirl cooling system remains a
Corresponding author.
E-mail address: christoph.biegger@gmail.com (C. Biegger).
https://doi.org/10.1016/j.ijheatfluidflow.2018.07.011
Received 17 February 2018; Received in revised form 27 July 2018; Accepted 30 July 2018
Available online 28 August 2018
0142-727X/ © 2018 Elsevier Inc. All rights reserved.
International Journal of Heat and Fluid Flow 73 (2018) 174–187
C. Biegger et al.
Δ
η
Θ
ν
ρ
τ
ω
Ωij
Nomenclature
c, cp
d͠
d
D
f
h
k
L
ṁ
Nu
Pr
r, ϕ, z
Re
p
q
Sij
t
T
Uz
u, Ui
x, y, z
Γ
heat capacity, J kg−1 K−1
DES limiter
wall distance, m
tube diameter, m
friction factor, = Δp /(1/2 ρUz 2) D / L
heat transfer coefficient, W m−2 K−1
thermal conductivity, W m−1 K−1
length, m
mass flow rate, kg s−1
Nusselt number, = h D / k
Prandtl number
cylindrical coordinates
Reynolds number, = Uz D / ν
pressure, N m−2
dynamic pressure, N m−2
strain rate, s−1
time, s
temperature, K
bulk velocity (axial), m s−1
velocity, m s−1
cartesian coordinates
thermal diffusivity, m2 s−1
grid spacing, m
Kolmogorov length scale, m
dimensionless temperature
kinematic viscosity, m2 s−1
density, kg m−3
shear stress, N m−2
vorticity, s−1
rotation rate, s−1
Indices
()+
()
⟨()⟩
0
f
in
r
ref
t
w
z
ϕ
dimensionless
filtered
averaged
initial
fluid
inlet
radial
reference
turbulent
wall
axial
circumferential
remarkably enhanced heat transfer rates. Khalatov et al. (2000) investigated the heat transfer and pressure loss in a three-pass serpentine
cyclone cooling system. They concluded that the cyclone cooling configuration demonstrated a great potential to reach high heat transfer
rates in the cooling passages, which was found to be superior compared
to rib turbulators. Ling et al. (2006) experimentally studied the heat
transfer characteristics of a swirl tube with two tangential inlet jets by
using transient liquid crystal thermography with the same swirl tube
geometry than Hedlund and Ligrani (2000). Winter and Schiffer (2009)
showed that the swirl stabilizes the flow in the cyclone cooling channel,
and the system rotation may not have appreciable effects on the flow
and heat transfer in the tube.
Recently, Biegger and Weigand (2015) and Biegger et al. (2015)
studied the heat transfer and flow structure in a swirl tube with tangential inlet jets at the beginning of the tube by using transient liquid
crystal thermography and PIV measurements for the experiments and
by conducting Detached Eddy Simulations (DES). They showed that the
circumferential velocity has strong gradients in the near-wall region
and the helical vortices with enhanced turbulent mixing are mostly
responsible for the high heat transfer in the swirl tube. Different outlet
boundaries (like a straight outlet, a tangential outlet and a 180° bend
outlet) had no severe influences on the flow field or the heat transfer in
the swirl tube. This is an important result, because it shows that the
challenging subject.
Kreith and Margolis (1959) first proposed that swirling flow induced
in tubes can enhance surface heat transfer rates relative to unswirled
flows in a heat exchanger application. Recently, a large number of other
researchers employed tangential wall jets to induce large-scale swirling
flows to enhance the heat transfer rates for gas turbine blade internal
cooling. Glezer et al. (1996, 1997, 1998) studied three different configurations based on a swirling flow generated by tangential wall jets
for gas turbine blade leading edge internal cooling. The swirl cooling
configuration developed in the study demonstrated superior heat
transfer rates in comparison with rib turbulated cooling as well as jet
impingement cooling. They also showed that system rotation has only a
little effect on the heat transfer. Qian et al. (1997) indicated that the
swirling flow can drastically increase heat transfer rates by about 20%
higher than those generated by impingement cooling. More importantly, swirl cooling produces a more uniform heat transfer distribution on the surface than jet impingement cooling.
Later, Ligrani et al. (1998) and Hedlund and Ligrani (2000) experimentally investigated the flow and heat transfer characteristics in a
swirl chamber with two tangential inlet jets displaced axially along the
tube. They used the inlet temperature as reference temperature for the
heat transfer coefficient and showed that the large-scale swirling and
Goertler vortex pairs in the swirl chamber are responsible for the
Fig. 1. (a) Tangential jet induced swirling flow in a tube (Ligrani et al., 2003), and (b) swirl cooling for gas turbine blade (Biegger and Weigand, 2015).
175
International Journal of Heat and Fluid Flow 73 (2018) 174–187
C. Biegger et al.
investigated swirl cooling configurations can later been integrated e.g.
in a multi-pass cooling scheme for a gas turbine blade. Bruschewski
et al. (2016) investigated another novel ring orifice outlet for cyclone
(swirl) cooling, and found that the ring orifice can obviously change the
flow patterns and improve the heat transfer in cyclone cooling.
In contrast to the above-mentioned swirl cooling investigations with
one tangential flow inlet, one can also introduce the cooling flow by
multiple tangential inlets distributed at different axial locations along
the swirl tube. Rao et al. (2016) shows a comparative study on the heat
transfer and pressure loss in swirl tubes with two different jet configurations: (1) one tangential inlet jet at the beginning of the tube, and
(2) five tangential inlet jets distributed equidistantly along the tube
length. In the swirl tube with one jet, the swirling flow effect decays
quite fast, therefore the heat transfer decreases along the tube length
rapidly. This results in a non-uniform heat transfer distribution in the
swirl tube. However, in the swirl tube with five inlet jets, since the jet
flow is distributed along the tube length, a lower but more uniform heat
transfer distribution and a much lower pressure loss across the tube
length can be achieved. Therefore, a swirl cooling tube with multiple
tangential inlet jets shows promising characteristics of providing an
enhanced heat transfer with a more uniform heat transfer distribution.
Swirl cooling is a robust cooling method and is straightforward to
manufacture due to its simplicity. Thus, it is well applicable as a cooling
device for high thermal load components such as turbine blades.
In the present paper, further comparative experimental and numerical studies have been done for the swirl tubes with different multiple inlet jet configurations, i.e. three inlet jets and five inlet jets. The
aim of the study is to explore the influence of the inlet jet number along
the swirl tube length on the swirling flow and heat transfer performance. Detailed flow and heat transfer characteristics in the swirl
cooling tubes with different inlet jet numbers have been measured by
using the transient liquid crystal thermography and Particle Image
Velocimetry (PIV) technique. Additionally, three-dimensional numerical computations based on Detached Eddy Simulation were performed
to show more details of the flow structure and heat transfer patterns in
swirl tubes with multiple inlets.
fitting block to maintain the cylindrical tube cross-section. Finally, the
air exits through an outlet tube into a plenum connected to the vacuum
pump. The entire model is transparent and is manufactured out of
Perspex because of its low thermal conductivity for the heat transfer
experiments and to provide an optical access for the heat transfer and
flow measurements.
The dimensions of the multiple inlet swirl tube and the positions of
the temperature and pressure probes are shown in Fig. 3. The tube
diameter is D = 50 mm with a length of L/ D = 20 . Eight thermocouples (TC) are positioned through capillary tubes equidistantly in
axial direction, which measure the fluid temperature in the tube center.
At the same axial coordinates, pressure taps are installed to measure the
static pressure along the tube wall. Additionally, one thermocouple is
placed in each tangential inlet channel to measure the jet inlet temperature.
The investigated Reynolds numbers Re = Uz D / ν are based on the
tube diameter D, the axial bulk velocity Uz at the tube outlet and the
kinematic viscosity ν. The PIV measurements are conducted at
Re = 10, 000 for the one, three and five inlet(s) case. The heat transfer
coefficients are measured for a Reynolds number range from 10, 000 to
40, 000 for MI1 and MI3, respectively, and for a range from 10, 000 to
80, 000 for MI5.
For the characterization of the swirl strength in a flow one can use
the swirl number defined as the ratio of the angular momentum to the
axial momentum. If we assume a complete transformation of the angular to the axial momentum (or velocity components) one obtains the
maximum possible swirl strength. This can be estimated by the relation
of the tangential and axial cross-sections. Here, the inlet channel has
the dimensions of 33.3 mm × 8.5 mm. So, the area ratios between the
tube cross-section and the inlet channel area for the one inlet case (MI1)
is 6.94, for the three inlets case (MI3) it is 4.17 and for the swirl tube
with five tangential inlets (MI5) it results in 1.39. So, theses configurations are characterized by a high, medium and low swirl strength,
respectively.
2. Experimental setup
The optical PIV method is used to measure the instantaneous flow
field in the swirl tube with multiple tangential inlets. Therefore, the
flow is seeded with light scattering particles with a mean diameter less
than 1 μm. A laser light sheet illuminates the particles with two laser
pulses within a short time difference (10 μs − 50 μs ). The scattered light
showing the particle distribution is recorded onto two consecutive
frames of a CCD camera. For small interrogation windows the velocity
vector can be calculated from the particle shift between both frames by
cross-correlation methods and the time period Δt. For stereo-PIV (2D3C) two cameras are used to obtain all three velocity components in a
2D plane.
For the here performed measurements a PIV system from LaVision
with a New Wave Research double-pulse Nd: YAG laser with a wavelength of 532 nm (green) is used. The camera angle to the direction
2.1. Stereo particle image velocimetry (PIV)
The experimental apparatus used for the flow and heat transfer
measurements is schematically shown in Fig. 2. The flow is sucked
through a vacuum pump connected to the outlet tube and is situated far
away downstream. The air enters a laminar flow element from Tetra
Tec Instruments (LFE 50MC2-2F) to determine the mass flow rate
through the measuring section. Then, the flow can be either heated via
an electrical mesh heater for the heat transfer experiments or seeded
with tracer particles for PIV flow measurements. The following plenum
is directly attached to the swirl tube and enables to supply up to five
tangential inlets to the measurement section. The orange arrows in
Fig. 2 highlight the air flow path through the tangential inlets into the
swirl tube. Each inlet section can be closed separately by a curved
Fig. 2. Experimental rig and measuring section for the multiple inlet swirl tubes.
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International Journal of Heat and Fluid Flow 73 (2018) 174–187
C. Biegger et al.
Fig. 3. Multiple inlet swirl tube geometry and thermocouple (TC) position (Biegger, 2017).
a semi-infinite wall (Carslaw and Jaeger, 1959) yields
perpendicular to the tube axis is set to ± 30° recommended by Raffel
et al. (2007). The measurement section for one measurement contains
the tube diameter in height (50 mm) and a length of around 100 mm, so
at least ten experiments are needed to capture the entire swirl tube. For
each PIV measurement 2000 images are recorded, processed and ensemble averaged using the software DaVis 8 from LaVision. The accuracy of the sample size is validated with a statistical analysis varying
the number of ensemble averages. The maximum scatter for 1000 ensemble averages for the axial velocity is below 2% and for the circumferential velocity below 1%. The reader is referred to Biegger et al.
(2013) for more details about the statistical analysis and the PIV setup.
Θ=
We measured the heat transfer coefficient in the swirl tube using the
well-established transient technique using thermochromic liquid crystals (TLC), see, for example, Ireland and Jones (2000) and Poser et al.
(2007). The heat transfer coefficient h can be calculated from the time
evolution of the wall temperature. We use the Nusselt number to express the dimensionless heat transfer based on the temperature gradient
at the wall, the tube diameter D and the driving temperature difference
between wall and fluid temperature:
∂T
− ∂n D
w
Tw − Tf
=
hD
k
(2)
Here, h is the local heat transfer coefficient and ρwcwkw are the wall
material properties density, specific heat capacity and thermal conductivity. The swirl tube model is made of Perspex with a wall thickness
of 25 mm, which very well satisfies the assumption of a semi-infinite
wall due to a low thermal conductivity (Vogel and Weigand, 2001).
Additionally, the curved surface is taken into account considering an
analytical expression given by Buttsworth and Jones (1997) for transient heat transfer experiments.
Fig. 4 shows the experimental TLC setup with the CMOS camera,
two lamps and the cross-section of the plenum with the attached swirl
tube. The jet inlet temperature is measured in the plenum and in each
tangential inflow channel with a fast response thermocouple type K
with a wire diameter of 0.08 mm (Omega 5SC-TT-KI-40) and a temporal
sample rate of 10 Hz. The inner surface of the tube is sprayed with
narrowband TLCs (SPN/R38C1W by Hallcrest Ltd.) and a black coating
for a defined contrast. A typical liquid crystal color play is displayed in
Fig. 5, which starts from unchanged (black due to the background) to
red, yellow, green and blue. After analyzing the camera viewing angle
influence on this highly curved surface, we concluded that it has no
significant effect for this particular experiment. Thus, for post-processing the data are averaged in circumferential direction. More information about the liquid crystal technique and the here used experimental setup can be found in Biegger and Weigand (2015) and Rao
et al. (2016).
2.2. Thermochromic liquid crystal (TLC) technique
Nu =
Tw − T0
h2 t ⎞
⎛ h t ⎞
= 1 − exp ⎛⎜
⎟ erfc
⎜ ρ c k ⎟
Tf − T0
ρ
c
k
w
w
w
⎝
⎠
⎝ w w w⎠
(1)
Here, k is the thermal conductivity of the fluid and Tw and Tf are the
wall and fluid temperature. Regarding the fluid or reference temperature, one can either use the inlet jet temperature or the local bulk
temperature which will be discussed in detail in the result Section 4.2.
For the transient TLC technique, the calibrated liquid crystals are
sprayed onto the inner tube surface, which change their color at a
specific temperature and hence indicating the wall temperature. Before
the experiment begins, the measuring section has a uniform initial
temperature. The measurement starts with a sudden temperature rise
and heated fluid is exposed to the test section. The liquid crystal color
play is recorded on video and the time to reach a specific temperature
(color) can be determined. With the initial temperature T0, the fluid
temperature Tf and the time t to reach the TLC temperature at the wall
Tw, the local heat transfer coefficient can be calculated by an analytical
solution of the 1D transient heat conduction problem. With a convective boundary condition, the solution of the 1D Fourier equation for
2.3. Measurement uncertainty
The measurement uncertainties are calculated by means of the rootmean-square method described by Moffat (1990) based on a 95%
confidence level. The uncertainties of the measurement quantities are
summarized in Table 1. The production tolerance of the Perspex tube is
± 1.0% and the calibrated laminar flow element has an uncertainty of
the mass flow rate of ± 0.33%. With it, the uncertainty of the Reynolds number results in ± 1.07%. Scanivalve Corp. DSA pressure
modules are used to measure the static pressure at the tube wall with an
accuracy of ± 0.2% of the full scale (2500 Pa). The uncertainty of the
dimensionless temperature Θ (see Eq. 2) is ± 1.0% depending on the
Fig. 4. TLC measurement setup with thermocouple and pressure tap positions.
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C. Biegger et al.
RANS:
LES:
Table 1
Experimental parameters, their typical range in the experiments and the measurement uncertainty.
Typical range
D
ṁ
Re
p
Θ
ρwcwkw
0.05 m
0.007 − 0.028 kg / s
10, 000 − 80, 000
170 − 2500 Pa
0.5 − 0.7
1190 kg/m3, 1470 J/(kg K), 0.19 W/
(m K)
3 − 90 s
t
h
15 − 500 W /(m2 K )
(8)
3.1. Computational domain and boundary conditions
±
±
±
±
±
±
The DES simulations are performed with the open-source finitevolume code OpenFOAM version 2.2.1 (Jasak et al., 2007). We used the
Pressure-Implicit Split-Operator (PISO) algorithm as pressure corrector
for the momentum equations. For the pressure corrector we used the
PCG (Preconditioned Conjugate Gradient) solver in combination with
the GAMG (Generalized geometric-Algebraic Multi Grid) preconditioner. We applied a second-order backward differencing scheme for
the time discretization and a second-order accurate central differences
scheme to approximate the viscous and convective fluxes.
The numerical setup for the MI5 swirl tube simulations is chosen in
accordance with the experimental setup. The computational domain
consists of five inflow boundary sections, the swirl tube (as the evaluation section), an outlet tube and a plenum. The computational grid
for the MI5 configurations is a hexahedral O-grid with 9 and 12 million
cells for the investigated Reynolds numbers of 10,000 and 50,000, respectively. A cross-section of the swirl tube mesh and a detailed view of
the wall resolution is shown in Fig. 6. The wall is resolved to provide a
dimensionless wall distance of y1+ < 1.5 for the first cell near the wall.
Here y+ = (y u τ )/ ν with the friction velocity u τ = τw / ρ . We used the
Kolmogorov length scale as a reference scale, which can be approximated by η = D Re−3/4 with the diameter D as the characteristic length
(Pope, 2000). The time step is automatically adjusted with a Courant
number limit of 0.9 mostly in the inlet part. The simulation is run for
3Δtdomain (= L/ Uz is the domain flow time), before starting averaging
over 15Δtdomain. More details about the mesh, the Kolmogorov length
scale η and the wall and center cell sizes are listed in Table 2.
The wall boundaries are set with a no-slip condition. A turbulent
velocity profile is mapped onto the inflow boundary section. A uniform
inlet temperature is given of Tin = 333 K and the wall temperature is set
constant to Twall = 293 K . At the outlet, a fixed pressure value is set and
zero gradient boundary conditions are applied for all other variables
(Biegger and Weigand, 2016).
The inflow conditions for each tangential inlet are obtained from a
preliminary RANS simulation for the entire domain with an additional
inlet plenum (Rao et al., 2016). A DES simulation of the entire swirl
tube together with the plenum would be too time-consuming. The mass
flow distribution and the respective velocity through each inlet are
1.0%
0.33%
1.07%
0.2%
1.0%
0.8%, ± 0.7%, ± 5.3%
± 3.33%
± 8.0% − 13.0%
3. Numerical setup
For a DES simulation, we have to consider the RANS and LES governing equations, which are based on the Reynolds decomposition and
the filtering concept, respectively. The time averaged (RANS) and filtered (LES) equations show a structural similarity and read for the time
averaged velocity ⟨U⟩ and the filtered velocity U :
LES:
∂T
LES
+ Uj ∇T = ∇ (Γeff
∇T ).
∂t
(7)
Measurement uncertainty
thermocouple accuracy ( ± 0.16 K) and the narrowband TLC indication temperature ( ± 0.1 K). The heat transfer coefficient is time and
space dependent due to the transient experiment with an uncertainty
between ± 8.0% − 13.0% considering the uncertainty of the Perspex wall
material properties ρwcwkw and the sample rate Δt. In the regions of the
tangential inlets and therefore very high heat transfer the highest uncertainty occurs due to a faster TLC color change and hence a higher
relative time error Δt/t.
RANS:
RANS
+ Uj ∇ T = ∇ (Γeff
∇ T )
Here, Γeff is the effective thermal diffusivity and includes the molecular diffusivity Γ = ν / Pr and the turbulent diffusivity Γt = νt / Prt assuming a constant turbulent Prandtl number with Prt = 0.4 suggested
for LES (Fröhlich, 2006).
Fig. 5. Liquid crystal color play for the MI5 swirl tube.
Parameter
∂T
∂t
∂ Ui
1
+ ∇ ( Ui Uj ) = − ∇ p + ∇ (ν∇ Ui ) − ∇τijRANS
ρ
∂t
∂Ui
1
+ ∇ (Ui Uj ) = − ∇p + ∇ (ν∇Ui ) − ∇τijLES .
∂t
ρ
(3)
(4)
Here, p is the pressure and ν the kinematic viscosity. The turbulent
stresses on the right-hand side are modeled using the eddy viscosity
concept with a turbulent viscosity νt and the strain rate tensor Sij:
τij = νt ∇Sij
(5)
Spalart and Allmaras (1994) proposed to model the turbulent viscosity νt = ν͠ fv1 by a single transport equation:
2
Dν͠
͠ ͠ + 1 [∇ ((ν + ν͠ ) ∇ν͠ ) + cb2 (∇ν͠ )2] − c w1 f ⎛ ν͠ ⎞ .
= cb1 Sν
w
͠
Dt
σ
⎝d ⎠
(6)
Here, the variables σ, cb1, cb2 and cw1 are model constants. The last
term is a destruction term for the modified viscosity ν͠ , which depends
on the DES limiter d͠ = min(d, CDES Δ) . Here, d is the distance to the
nearest wall, CDES a constant and Δ the grid spacing. In the present
simulations, we used the maximum cell size of all directions as the grid
spacing: Δ = max(Δx, Δy, Δz) . Thus, the DES limiter switches between
RANS near the wall and LES in the free stream region, so that the
Spalart-Allmaras model act as a turbulence-viscosity model where
d ≪ Δ and as a subgrid-scale model where d ≫ Δ.
The energy equation for the time averaged temperature T and the
filtered temperature T reads
Fig. 6. Cross-section of the swirl tube mesh showing the hexahedral O-grid and
a detailed view of the wall resolution.
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C. Biegger et al.
the configuration with five tangential inlet jets in Fig. 8, here five different flow regions occur. After the first inlet at the beginning of the
tube, recirculation areas are evident, whereas further downstream the
enhanced mass flow is responsible for an axial flow towards the tube
outlet. This axial flow becomes stronger with an increasing number of
inlets, first in the center of the tube and after the fifth inlet also in the
outer region of the tube, analogous to the three inlets configuration.
Comparing the experimental and the numerical flow field of the
axial velocity for the MI5 configuration in Fig. 8, a good agreement can
be seen for the entire tube. In front of each inlet, a recirculation zone
near the opposite wall is evident, which shrinks the cross-sectional area
for the upstream flow and accelerates it in the tube center as already
discussed. Therefore, the DES simulation is capable to predicting such a
complex flow field with five tangential jets with a good accuracy.
Table 2
Details about the MI5 swirl tube mesh in terms of number of cells, Kolmogorov
length scale η and used wall and center cell sizes.
η [m]
Δyw [m]
(Δx, Δy, Δz)c [m]
9 · 106
5·10−5
3·10−5
(9.4, 7.9, 11.0)·10−4
12 · 106
1.5·10−5
2.5·10−5
(7.5, 6.8, 10.4)·10−4
Mesh
Cells
Re = 10, 000
Re = 50, 000
summarized in Table 3. The mass flow rate through the first two inlets
is almost the same, but for the following three inlets the mass flow rate
increases due to an increasing relative pressure difference over the
subsequent inlets. Comparing the first and the last inlet, 30% more mass
flow goes through the fifth inlet.
The numerical setup has been validated simulating a turbulent
channel flow with constant but different wall temperatures and compared to DNS data from Iida and Kasagi (2001). The velocities and
temperature profiles as well as the fluctuations showed a good agreement (Biegger et al., 2015). The numerical swirl tube results have also
been compared with own experimental data (Biegger and Weigand,
2015; Biegger and Weigand, 2014) in previous publications (Biegger
et al., 2015; Biegger and Weigand, 2016), which also showed a good
agreement especially for the flow field.
4.1.2. Circumferential velocity
The measured non-dimensional circumferential velocity Uϕ/ Uz for
the swirl tube with one tangential inlet at Re = 10, 000 is shown in
Fig. 9. Additionally, the circumferential velocity for the configurations
with three and five tangential inlet jets in combination with the numerical results for the MI5 configuration is presented in Fig. 10. Again,
a black rectangle indicates the tangential inlets and the contour legend
for the one inlet case and the multiple inlet cases are different for a
clearer presentation. The symbols besides the legend show the velocity
direction into (red) or out (blue) of the paper.
At the beginning of the swirl tube with one inlet in Fig. 9, the circumferential velocity is clearly the largest velocity component with
Uϕ, max / Uz = ± 6 and thus three times larger than the related axial velocity component with Uz, max / Uz = 2. Near the tangential inlet the circumferential velocity has its maximum value and decreases continuously towards the tube outlet due to friction and dissipation.
The circumferential velocity for the MI3 configuration is shown in
Fig. 10. From the contour color it is evident that the absolute velocity
value is almost constant over the entire tube. The additional tangential
inlet jets in axial direction induce additional swirl and keep the circumferential velocity of around Uϕ, max / Uz = ± 2 on a constant level. The
same can be seen for the MI5 configuration. The overall circumferential
velocity component of around Uϕ, max / Uz = ± 1.5 is almost constant over
the entire tube and obviously lower than for the MI3 swirl tube. For
both configurations, the vortex core is not directly in the tube center,
but scatters around the center in a wave-like form also visible for the
MI1 swirl tube. This is due to the unsymmetrical tangential inlet jets
from one side of the tube.
The comparison of the experimental and the numerical results in
Fig. 10 shows that the DES slightly overestimates the circumferential
velocity by maximum 20% compared to the experiments, especially in
the first inlet section. This might be due to an overestimated tangential
inlet velocity distribution from the preliminary RANS simulation.
However, the overall circumferential velocity distribution shows a
good agreement and the simulation can provide a more detailed view
into the occurring flow structures. The wave-like form in the vortex
core becomes clearer and a larger circumferential velocity component
near the wall on the other side of the inlet is evident. This enhanced
impinging swirl flow might be responsible for the high heat transfer in
the inlet jet regions, which will be shown later in the heat transfer
section.
4. Results and discussion
4.1. Flow field
In this section, the flow field for the different multiple inlet swirl
tubes is discussed in detail. First, the axial and circumferential velocity
components are presented followed by the vorticity. The velocities are
scaled by the axial bulk velocity Uz at the tube outlet.
4.1.1. Axial velocity
The measured non-dimensional axial velocity Uz / Uz is shown in
Fig. 7 for the swirl tube with one tangential inlet at Re = 10, 000 . The
axial velocity for the swirl tube with three and five inlets is shown in
Fig. 8 together with numerical results for the five inlets configuration
for comparison. The contour legend from the one inlet and the multiple
inlet swirl tubes differ for a clearer display. Black rectangles indicate
the respective inlet sections.
The axial velocity for the one inlet configuration in Fig. 7 shows a
strong axial flow in the near wall region and an axial backflow in the
tube center also known as vortex breakdown. The swirling flow is
strong enough that the backflow occurs across the entire tube length.
The magnitude of the backflow even increases towards the tube outlet,
whereas the axial velocity in the outer region slightly decreases due to
wall friction. The axial backflow in the tube center is characterized by a
standing wave, which is caused by an unsymmetrical flow field due to
one tangential inlet.
The axial flow structure for the multiple inlet configurations in
Fig. 8 is completely different and changes after each inlet jet due to the
additional mass flow entering the tube. Depending on the number of
inlet jets, the swirl tube can be divided into three or five different
sections, respectively, highlighted with black dashed lines in Fig. 8. The
first section shows several alternating recirculation areas indicated by a
dark blue color and a black contour line representing zero velocity. The
unsymmetrical inlet jet causes these recirculation areas. In front of each
subsequent inlet, a recirculation zone occurs near the opposite wall
(blue zones) and thus reduces the cross-sectional area of the tube. Due
to this reduction, the flow from the upstream section is accelerated in
the tube center. In the second section for MI3, the axial flow is characterized by a maximum axial velocity in the tube center and no axial
backflow occurs anymore. In the last and third region of the MI3 configuration, the largest axial velocity component appears in the outer
region accompanied with a low velocity in the tube center. Considering
Table 3
Mass flow and inlet velocity distribution of the MI5 swirl tube simulations.
179
Inlet number
1
2
3
4
5
m˙ i / m˙ total
Uin [m/ s] (Re = 10, 000)
Uin [m/ s] (Re = 50, 000)
18.0%
4.03
20.14
17.8%
3.97
19.87
19.2%
4.30
21.48
21.3%
4.78
23.89
23.7%
5.30
26.49
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Fig. 7. Measured non-dimensional axial velocity in the swirl tube with one tangential inlet at Re = 10, 000 .
inlets, one can see dominant vortex structures. This indicates that these
vortex structures are spread over the tube circumference.
For a more detailed insight in the occurring vortices, the Q-criterion
defined as Q = 1/2 (Ωij2 − Sij2 ) is presented in Fig. 13 for the swirl tube
with five inlet jets. Here, Sij and Ωij are the symmetric and antisymmetric velocity gradient tensors. Occurring vortices are visualized with
isosurfaces of Q > 0, where the rotation dominates the shear rate. The
Q-criterion reveals two main structures in the swirl tube that are already indicated by the vorticity contour. First, a vortex in the tube
center in a wave-like form. Second, large spiral vortices around the tube
axis especially near the inlet jets (Biegger, 2017). The strong tangential
momentum induced by the jets causes these turbulent structures,
which, in turn, cause the enhanced heat transfer in the inlet regions as
shown later.
4.1.3. Vorticity
The rotation of a fluid can be described by its vorticity and is defined in the general vector form as ω = ∇ × U . Here, ∇ is the nabla
operator and U is the velocity vector. The measured non-dimensional
vorticity in circumferential direction ωϕ D / Uz (ωϕ = ∂Ur / ∂z − ∂Uz / ∂r ) is
presented in Fig. 11 for the swirl tube with one tangential inlet and in
Fig. 12 for the MI3 and MI5 swirl tube configurations. The contour
legend for the multiple inlet cases is again adjusted for a clearer presentation.
For the configuration with one inlet jet in Fig. 11, a large positive
and negative vorticity stripe on each half of the tube is evident indicating a dominant vortex system. At the beginning of the tube near
the inlet, the vortex system occurs in the outer part of the tube and
shrinks to the core moving further downstream towards the tube outlet.
This process is driven because high velocity fluid moves closer to the
axis and the fluid in the outer tube is slowed down due to friction.
Moreover, this vortex structure describes a wave-like form analogous to
the axial flow as shown in Fig. 7 due to the unsymmetrical inlet jet.
The vorticity becomes more complex for the swirl tube configurations with multiple inlet jets as shown in Fig. 12. In the tube center,
periodically changing positive and negative vorticity areas are evident
over the entire tube. Near the inlet jets and on the opposite side of the
4.2. Heat transfer
In the following, the experimentally and numerically obtained heat
transfer results for the swirl tubes with multiple inlet jets will be presented. First, a reasonable reference temperature will be discussed in
detail followed by an exemplary DES wall heat flux contour for the MI5
swirl tube. Then, the measured circumferentially averaged Nusselt
Fig. 8. Measured non-dimensional axial velocity in the MI3 and MI5 swirl tube. The bottom Fig. shows DES results with five tangential inlets at Re = 10, 000 .
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Fig. 9. Measured non-dimensional circumferential velocity in the swirl tube with one tangential inlet at Re = 10, 000 .
Fig. 10. Measured non-dimensional circumferential velocity in the MI3 and MI5 swirl tube. The bottom Fig. shows DES results with five tangential inlets at
Re = 10, 000 .
Fig. 11. Measured non-dimensional vorticity in the swirl tube with one tangential inlet at Re = 10, 000 .
numbers for the configurations with one, three and five inlet jets are
presented for the Reynolds number 10, 000. Finally, a comparison between the experimentally and the numerically obtained heat transfer is
shown.
In previous publications on single inlet swirl tubes (Biegger and
Weigand, 2015; Biegger et al., 2015; Biegger and Weigand, 2014), we
used the local adiabatic wall temperature as a reference temperature
based on a calculation from the local temperature in the center of the
tube. Due to the complexity of the flow field in swirl tubes with
multiple inlet jets the local adiabatic wall temperature is difficult to
measure and with it the choice of a reference temperature. To determine a reasonable reference temperature for the heat transfer coefficient, the mean temperature field in the swirl tube with five inlet jets
obtained from a numerical simulation is shown in Fig. 14. The wall
temperature is constant at Twall = 293K and the fluid inlet temperature
is set to Tin = 333K . The range of the legend has been adjusted from
303K to 333K for a clearer temperature contour.
Near the inlets, fluid with the jet inlet temperature impinges on the
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Fig. 12. Measured non-dimensional vorticity in the MI3 and MI5 swirl tube at Re = 10, 000 .
Fig. 13. DES vortex structure in the MI5 swirl tube for Re = 10, 000 , isosurfaces of Q = 1, color represents axial velocity according to the legend in Fig. 8 (Biegger,
2017).
Fig. 14. Numerically predicted mean temperatures in the swirl tube with five tangential inlets at Re = 10, 000 with Tin = 333K and Twall = 293K .
and because of the here used different reference temperature this differs
to the previously published thermal performances in Biegger and
Weigand (2015). However, this approach allows to compare the swirl
curved tube wall and is therefore responsible for the high heat transfer
in these regions. For the sections between the inlets, this temperature
cannot serve as a reference temperature in the Nusselt number, because
it is too high and thus would underestimate the local heat transfer
coefficient. On the other hand, the local bulk temperature in the tube
would be too low at the inlets due to the lower temperature in the tube
core indicated by the (light) blue regions and would overestimate the
heat transfer in the inlet regions. Therefore, we use the jet inlet temperature Tj as a conservative reference fluid temperature Tf for the
evaluation of the heat transfer coefficients according to Eq. 1. This also
guarantees a reasonable comparison between the different swirl tube
configurations with multiple inlets investigated here and with other
studies e.g. by Ligrani et al. (1998) and Hedlund and Ligrani (2000).
However, it should be noted that the highest uncertainty occurs for
the swirl tube with only one inlet jet since the temperature difference
increases further downstream. The effect of the two different reference
temperatures (the jet inlet temperature and the local bulk temperature)
on the Nusselt number is exemplarily shown for the swirl tube with one
inlet jet in Fig. 15. As already explained, the Nusselt number based on
the inlet temperature underestimates the heat transfer especially further downstream. In the inlet region, the Nusselt number uncertainty is
around 5%, whereas it increases to 130% further downstream to the
outlet. The Nusselt number in the swirl tube with one inlet based on the
local fluid temperature shows the largest uncertainty at the inlet with
around 18% and decreases to 5% at end of the tube.
This will affect the thermal performance presented in Section 4.4
Fig. 15. Comparison of the measured Nusselt numbers for the swirl tube with
one inlet jet based on the inlet temperature and the local fluid temperature in
the tube as reference temperature.
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Reynolds number of 10, 000 (a) and 50, 000 (b). The vertical lines
indicate the axial position of the tangential inlet jets. The Nusselt
number comparison between experiment and simulation shows a good
agreement for such a complex flow in a multiple inlet jet swirl tube for
both a low and a high Reynolds number. Between the first and the
second jet, slight deviations can be seen for both Reynolds numbers.
This might be due to an overestimated tangential inlet velocity distribution for the first jet and therefore overestimated circumferential
velocity in this region as already discussed in Section 4.1. However, this
comparison confirms that the DES is capable to predicting the heat
transfer for a multiple inlet swirl tube very well (Biegger, 2017).
The globally averaged Nusselt numbers for the three investigated
configurations are listed in Table 4. Additionally, the normalized Nusselt numbers are given as well based on the Dittus–Boelter correlation
(Dittus and Boelter, 1930) for the heat transfer in a fully developed
axial tube flow (Nu 0 = 0.023 Re 0.8 Pr 0.3 ). For each swirl tube inlet configuration, the Nusselt number enhancement compared to an axial tube
flow Nu / Nu 0 is almost constant over the investigated Reynolds number
range. It has to be mentioned that the mass flow rate and consequently
the Reynolds number increase along the tube length due to the additional inlet jets. This makes a comparison of the normalized heat
transfer difficult as the Dittus-Boelter correlation is based on a constant
Reynolds number. Secondly, the Dittus–Boelter correlation is based on
the mean bulk temperature and is therefore only of limited informative
value and just given for completeness.
tube with one inlet with the ones with multiple inlets.
The numerically obtained wall heat flux in the swirl tube with five
inlet jets for Re = 10, 000 is shown in Fig. 16. One can clearly see the
enhanced heat flux originated from each inlet jet. Between the inlets,
the wall heat flux continuously decreases until the next inlet jet. At the
last inlet the highest wall heat flux occurs due to the increasing mass
flow rate and therefore highest inlet jet velocity compared to the upstream inlets. An overview of the respective inlet jet velocities has already been given in Table 3.
The measured circumferentially averaged Nusselt numbers based on
the jet inlet temperatures for all investigated multiple inlet configurations and Re = 10, 000 is shown in Fig. 17. For one tangential jet, the
highest heat transfer occurs in the inlet jet region. Here, the maximum
Nusselt number reaches a value of around 400. Further downstream
from the inlet jet, the heat transfer decreases continuously. For the
multiple inlet swirl tube configurations MI3 and MI5, an increased heat
transfer is observed for each inlet jet. Between the tangential inlet jets
the Nusselt numbers decrease until the next inlet as already seen in the
wall heat flux contours. The maximum Nusselt number is around 150
for the three inlets configuration and around 100 for the five inlets
configuration. It is evident that the maximum Nusselt number for the
multiple inlet jets is lower than for the swirl tube with only one inlet jet
(Nu = 400 ), however due to the additional tangential jets and re-enhanced swirl strength the heat transfer distribution is more homogeneous over the entire tube length.
Additionally, the current heat transfer results are compared to heat
transfer data of a swirl tube configuration with two inlets by Hedlund
and Ligrani (2000). Their investigated swirl tube has a total length of
x / r0 = 15, which relates in the current axial coordinate system to
z / D = 7.5. So in terms of geometry and tangential inlets, the swirl tube
with five inlets is the configuration, which relates best to the one in
Hedlund and Ligrani (2000) in the passage until z / D = 7.5. The Reynolds number of 10,000 in the current study lies in between the Reynolds number of 6,100 and 12,150 by Hedlund and Ligrani (2000).
Comparing the Nusselt numbers, one can see that both are in a similar
range and the maximum is just around 100. In the current investigation,
the Nusselt number for the MI5 swirl tube is slightly below 100, which
means the swirl tube by Hedlund and Ligrani (2000) performs slightly
better. Overall, the swirl tube performances of both studies are comparable.
It can be concluded that two major mechanisms are responsible for
the more homogenous heat transfer in the MI5 swirl tube. At the inlets,
the tangential jets impinge on the concave wall, cause an enhanced
turbulence and consequently an enhanced convective heat transfer.
This can be also seen in the large spiral vortices at the inlets in Fig. 13,
which become stronger for the inlets further downstream due to a
higher inlet mass flow rate. Additionally, with an increasing number of
inlets and therefore increasing local mass flow rate in the swirl tube due
to the downstream inlets, the axial velocity becomes stronger as shown
in Fig. 8 and causes an enhanced heat transfer between the inlet jets.
This results in a more homogeneous heat transfer distribution over the
entire tube (Biegger, 2017).
Fig. 18 shows a comparison between the experimentally and the
numerically obtained heat transfer for the MI5 swirl tube and a
4.3. Pressure loss
The measured pressure loss for the three multiple inlet swirl tubes
and Re = 10, 000 is presented in Fig. 19(a) and a more detailed plot for
the MI3 and MI5 configuration is shown in Fig. 19(b). The pressure loss
over the tube is normalized with the dynamic pressure q = 1/2ρU z2 .
The overall pressure loss for one inlet jet is much higher compared to
the one for the multiple inlet jets configurations. Near the inlet jet at the
beginning of the MI1 swirl tube, the largest pressure loss occurs due to
the largest circumferential velocity and decreases continuously along
the tube length. For the MI3 configuration shown in Fig. 19(b), the
pressure decreases after the first inlet jet, is then slightly enhanced at
the second inlet jet and again decreases at the last jet. For the five inlet
swirl tube, the pressure drop at the beginning of the tube is quite low
due to a low mass flow rate. With an increasing mass flow further
downstream, the pressure difference between each measurement position increases as well.
The measured friction factors over the tube length are listed in
Table 5. The values are normalized by the friction factors for an axial
tube flow ( f0 = 0.3164 Re−0.25 by Blasius (Schlichting and Gersten
(2000)). It is evident that the friction factor increases with increasing
Reynolds number. The highest pressure loss occurs for only one inlet jet
and is between 49 and 66 times higher compared to an axial tube flow
depending on the Reynolds number. With an increasing number of
tangential inlet jets, the friction factor enhancement drastically decreases to around 10% for MI3 and 7.5% for MI5. This is due to lower
inlet jet velocities compared to the MI1 swirl tube configuration.
Secondly, the measured friction factor enhancement over the tube
Fig. 16. DES wall heat flux in the MI5 swirl tube at Re = 10, 000 (Biegger, 2017).
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Fig. 17. Measured Nusselt numbers based on the jet inlet temperatures for all investigated multiple inlet configurations and Re = 10, 000 (a) and swirl tube Nusselt
number results with two inlets by Hedlund and Ligrani (2000) (b).
including the pressure drop over the tangential inlets is listed in
Table 5. For this evaluation, the static pressure in the tube is measured
against the pressure in the plenum. It is evident that the inlet jets cause
a large pressure loss. For the swirl tube configuration with one and
three inlets, the pressure loss over the inlets is the significant part and is
around 2 to 3 times the pressure drop over the tube. This is due to the
large inlet jet velocity. For the swirl tube with five inlets the pressure
drop over the tube and over the inlets is in the same order of magnitude.
This means the friction factor enhancement over the tube including
inlets is around twice the one over the tube.
4.4. Thermal performance
For a comparison with other cooling methods and a rating of the
different configurations, the thermal performance of the investigated
multiple inlet swirl tubes will be analyzed. The thermal performance
parameter (Nu / Nu 0)/(f / f0 )1/3 is the ratio between the heat transfer enhancement and the friction factor increase.
Fig.
20
shows
the
thermal
performance
parameters
(Nu / Nu 0)/(f / f0 )1/3 for all experimentally investigated configurations.
One can see that the thermal performance for all configurations and all
Reynolds numbers are in the same order of magnitude. This means that
all swirl tube configurations are suitable for effective cooling. It
strongly depends on the usage. If one is interested in a maximum heat
transfer paid by a high pressure loss, the swirl tube with one inlet would
be the best choice. If a lower but more homogeneous heat transfer with
a low pressure loss is desired, one should choose the swirl tube with five
inlets.
It should be mentioned again that the here presented Nusselt
numbers are based on the inlet jet temperature and are normalized with
the Dittus-Boelter equation. The jet inlet temperature is higher than the
local fluid temperature, and therefore causes a lower heat transfer and
thermal performance, respectively. For completeness, the experimentally obtained thermal performance parameters (Nu / Nu 0)/(f / f0 )1/3 are
listed in Table 6 for all investigated configurations and Reynolds
numbers.
Fig. 18. Comparison of Nusselt numbers from experiments and DES for the MI5
swirl tube (Biegger, 2017).
Table 4
Measured globally averaged Nusselt numbers Nu and normalized Nu / Nu 0 by
the Dittus–Boelter correlation.
Re
Nu
Nu / Nu 0
10, 000
20, 000
30, 000
40, 000
MI1
MI3
MI5
96.1
46.7
42.3
162.6
81.0
68.7
255.0
121.6
97.3
327.0
153.0
119.4
MI1
MI3
MI5
2.89
1.48
1.28
2.83
1.47
1.23
3.13
1.50
1.23
3.31
1.55
1.17
4.5. Heat transfer, pressure loss and thermal performance in the first inlet
passage
Another possibility to compare the three investigated multiple inlet
swirl tube configurations is an analysis of the first inlet passage. The
second inlet enters at z / D = 4.0 into the tube. However, the incoming
flow already affects a small upstream region and thus, the first inlet
passage is evaluated until z / D = 3.4 . In this first passage, the evaluated
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Fig. 19. Measured normalized pressure loss for all investigated multiple inlet configurations and Re = 10, 000 (Biegger, 2017).
axial tube flow in the first inlet passage. The heat transfer for the MI1
configuration shows the highest values followed by the MI3 and the
MI5 swirl tube. The globally averaged Nusselt number in Fig. 21(b)
shows a heat transfer enhancement between four and seven times the
one in axial tube flow for the three investigated swirl tube configurations.
The thermal performance parameters in the first inlet passage until
z / D = 3.4 is shown in Fig. 22 for comparison of the three investigated
swirl tube configuration. The grey symbols indicate the friction factor
enhancement including the inlet jet pressure loss. The highest thermal
performance in the first inlet passage shows the MI5 swirl tube configuration. Here, the lowest friction factor enhancement occurs. The
MI3 and MI1 swirl tube show a similar thermal performance. However,
the swirl tube with one inlet has the highest pressure loss in the first
passage.
Fig. 23 shows a comparison of relative performances (heat transfer
enhancement over friction factor enhancement) of several heat transfer
enhancement techniques summarized by Ligrani et al. (2003). The results for the multiple inlet swirl tubes in the first inlet passage are added
to this chart for a detailed comparison. The heat transfer to friction
factor ratio of the swirl tube with five tangential inlet jets is in the same
range than previous published swirl chamber investigations. The swirl
tube with three inlet jets shows a high heat transfer performance.
However, this is paid by a high friction factor penalty. This overall
comparison shows the high heat transfer potential of swirl cooling devices such as swirl tubes.
Table 5
Measured friction factor enhancement f/f0 over the tube and including inlets.
Re
10, 000
20, 000
30, 000
40, 000
f/f0 (tube)
MI1
MI3
MI5
48.95
5.14
3.59
54.93
5.43
4.35
61.42
6.52
4.71
66.12
6.74
4.84
f/f0 (tube + inlets)
MI1
MI3
MI5
152.81
16.78
6.46
173.74
19.13
7.81
195.84
23.27
8.62
214.85
27.74
8.87
Fig. 20. Thermal performance parameters (Nu / Nu 0 )/(f / f0 )1/3 over the Reynolds
number Re for all experimentally investigated multiple inlet configurations
(Biegger, 2017).
5. Conclusions
The flow phenomena, the heat transfer and the pressure loss characteristics in swirl tubes with multiple tangential inlet jets were experimentally and numerically studied in detail. Particle Image
Velocimetry has been used to measure the flow field and the transient
liquid crystal technique to determine the heat transfer. The numerical
simulations have been performed by using Detached Eddy Simulation
for a more detailed insight. The following conclusions can be drawn:
Table 6
Thermal performance parameter (Nu / Nu 0 )/(f / f0 )1/3 (experiments).
Re
(Nu / Nu 0)/(f / f0 )1/3
MI1
MI3
MI5
10, 000
20, 000
30, 000
40, 000
0.79
0.86
0.83
0.75
0.84
0.76
0.79
0.81
0.73
0.82
0.82
0.69
(1) The investigation revealed a complex axial velocity changing after
each inlet due to the additional mass flow added by the multiple
inlet jets. Besides, the circumferential velocity is almost constant
since the swirling flow is re-enhanced with each inlet jet, respectively. The numerical results revealed two main structures in the
swirl tube with five inlet jets. First, a vortex in the tube center in a
wave-like form. Second, large spiral vortices around the tube axis
especially near the inlet jets.
(2) The highest heat transfer in swirl tubes occurs in the inlet region(s)
and decreases continuously until the next inlet or towards the tube
Reynolds number Re1st is based on equal parameters as the mass flow
rate is constant for all three swirl tube configurations. This Reynolds
number in the first inlet passage is also used to calculate the Nusselt
number based on the Dittus–Boelter correlation (Dittus and Boelter,
1930) for an axial tube flow Nu0, 1st and the friction factor correlation
for an axial tube flow f0, 1st according to Blasius (Schlichting and
Gersten, 2000).
Fig. 21 shows the Nusselt number enhancement to the one in an
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Fig. 21. Measured Nusselt numbers in the first inlet passage until z / D = 3.4 at Re1st = 11, 250 (a) and globally averaged Nusselt numbers over the Reynolds number
(b) based on the jet inlet temperatures for all investigated multiple inlet configurations.
Fig. 22. Thermal performance parameters (Nu1st / Nu 0,1st )/(f1st / f0,1st )1/3 in the first inlet passage until z / D = 3.4 as a function of the Reynolds number Re1st (a) and as a
function of the friction factor enhancement f1st/f0, 1st (b) for all experimentally investigated multiple inlet configurations. The grey symbols indicate the friction factor
enhancement including the inlet jet pressure loss.
Fig. 23. Comparison of relative performances of different heat transfer enhancement techniques by Ligrani et al. (2003) together with the current work (1st inlet
passage of the multiple inlet swirl tubes).
(3) It can be concluded that two major mechanisms are responsible for
the homogenous heat transfer in the MI5 swirl tube. At the inlets,
the tangential jets impinge on the concave wall, cause an enhanced
turbulence and consequently an enhanced convective heat transfer.
This can also be seen in large spiral vortices at the inlets, which
become stronger for the inlets further downstream due to a higher
inlet mass flow rate. Additionally, with an increasing number of
outlet for the swirl tube with only one inlet jet. For the swirl tubes
with multiple inlets, the maximum heat transfer is lower than for
the swirl tube with one inlet because of the lower inlet jet velocities.
However, the heat transfer distribution is more homogeneous over
the entire tube length at a much lower pressure loss than with only
one inlet due to the additional tangential jets, and thus enhanced
swirl strength.
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C. Biegger et al.
inlets and therefore increasing local mass flow rate in the swirl
tube, the axial velocity becomes stronger and causes an enhanced
heat transfer between the inlet jets. This results in a more homogeneous heat transfer distribution over the entire tube.
(4) For all investigated swirl tube configurations, the thermal performance parameter is in the same order of magnitude. This means
that all swirl tube configurations are suitable for effective cooling. It
strongly depends on the usage. If one is interested in a maximum
heat transfer paid by a high pressure loss, the swirl tube with one
inlet would be the best choice. If a lower but more homogeneous
heat transfer with a low pressure loss is desired, one should choose
the swirl tube with five inlets.
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Acknowledgements
The authors would like to acknowledge the funding of this project
by the Deutsche Forschungsgemeinschaft (DFG). For his research stay in
Germany, the author Dr. Yu Rao would like to thank the support from
the DAAD-K.C. Wong Fellowship and the National Natural Science
Foundation of China (51676119).
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