Conference on Modelling Fluid Flow (CMFF’09)
The 14th International Conference on Fluid Flow Technologies
Budapest, Hungary, September 9-12, 2009
LES OF THE TRANSITIONAL FLOW IN A MINIATURE CENTRIFUGAL
PUMP
Máté Márton LOHÁSZ1, László NAGY2, Hendrik WURM3
1
Corresponding Author. Department of Fluid Mechanics, Budapest University of Technology and Economics. Bertalan Lajos u. 4 – 6,
H-1111 Budapest, Hungary. Tel.: +36 1 463 1560, Fax: +36 1 463 3464, E-mail: [email protected]
2
Department of Fluid Mechanics, Budapest University of Technology and Economics. E-mail: [email protected]
3
ARTEC Research and Technology Center, WILO SE, Nortkirchenstr. 100, 44263 Dortmund, Germany. http://www.wilo.com. E-mail:
[email protected]
ABSTRACT
WILO SE has developed a decentralised pump
system called GENIAX in order to change from
offer driven heating systems to demand driven
systems [1]. For this, each heating radiator is
equipped with a small centrifugal pump in place of
a thermostat. Instead of the traditional heating
systems, which work with throttle control, the
GENIAX System uses control of every pump.
Therefore the energy saving of the GENIAX
System achieves up to 20%.
The Reynolds number in these pumps is
atypically low compared to common centrifugal
pumps. Therefore, transitional flow occurs inside
the pump.
To investigate the transitional pump flow and
the capability of LES on these flow, LES
calculations have been carried out.
Keywords: LES, centrifugal pump, transitional
flow
NOMENCLATURE
h
∆
[m]
[m]
centrifugal pump instead of a thermostat (Figures 12). Depending on the heat demand, the rotational
speed of the particular radiator pump is controlled.
This means this is not an offer driven heating
system anymore but a demand driven heating
system without throttle losses.
Figure 1. GENIAX System –Decentralised Pump
System
mesh size
length size
1. INTRODUCTION
The traditional heating system is equipped with
one centrally arranged circulator pump. The
disadvantage of this traditional arrangement is the
throttling with the thermostat, which is necessary
for the heat adjustment, and respectively, heat
control. The throttling implies major losses.
Furthermore this throttling control means an offer
driven heating system.
For energy saving reasons, WILO SE has
developed a decentralised pump system called
GENIAX. Decentralised pump system means that
each heating radiator is equipped with a small
Figure 2. Miniature Centrifugal Pump of the
GENIAX System instead of a thermostat
The GENIAX system has further advantages
regarding comfort, warm-up time, hydraulic
balancing, etc.
The Reynolds number in the miniature
GENIAX pumps is atypically low compared to
common centrifugal pumps. Therefore transitional
flow occurs inside the pump.
To investigate this pump flow and the
capability of Large-Eddy Simulation (LES) on this
flow, LES calculations were carried out.
We were especially interested how the general
purpose code ANSYS-Fluent can be used for the
simulation of the low Reynolds number pump.
Although, it is known that basic LES test cases can
be computed using the finite volume code with
sufficient accuracy [2], it is not trivial that the
requirements of a pump LES can be fulfilled at
acceptable cost. The most challenging part of the
simulation is the presence of sliding interfaces. The
mainstream of the interface research activity is the
stationary
interface
problem.
A
detailed
investigation of stationary interface can be found in
the literature [3].
A further aim of the investigation is to use the
detailed result of the LES for understanding main
turbulence mechanisms, which can be later used in
pump development.
2. MINIATURE PUMP
The miniature pump investigated in the present
paper is a version of the development phase. In that
pump, an elbow is placed upstream of the impeller,
providing a flow without tangential velocity. The
impeller is placed in a volute designed to be optimal
at a specific (design) condition (Reynolds number at
the inlet pipe is 2829). The presented investigation
is focused on this working condition. The flow
domain inside the pump is shown in Figures 3-4.
The pump installed in the heating system
consists of the following parts described in
streamwise direction: a) inlet pipe, b) the confuser,
c) elbow, d) impeller, e) volute, f) diffuser, g)
downstream pipe (Figures 3-4).
also appears, which also needs to be modelled. It
also has to be remarked that the resulting equation
is usually solved numerically using a spatial
discretisation. The discretisation together with the
mesh size (h) provides a length scale which can
accurately be resolved. This scale for second order
scheme (used in general purpose codes) is about 4h
[4]. However in practice the length scale of the
filtering is selected to be ∆=h, which means that the
resolution of the smallest resolved scales is strongly
contaminated by the discretisation error. In the case
this discretisation error has a dissipative nature the
error of the scheme can be used as a model of the
sub-grid
scale
motions. Other important
consequence is that cell size variation is directly
linked to filter size variation and is a source of
commutation error.
3.1. Sub-Grid Scale Modelling
Attention in the selection of the sub-grid scale
(SGS) modelling is needed when modelling
laminar-turbulent transition, since laminar flows
contains much fewer spatial scales and need much
fewer scales to be modelled. A commonly used
technique is the dynamic approach [5] applied to
the Smagorinsky (eddy viscosity) model, where the
model coefficient is determined as being dependent
on the flow and so is able to reduce SGS
contribution in laminar regions of the flow.
Dynamic models have been found to be able to
model transitional processes [6, 7]. In the present
work the implementation by [8] was used.
3.2. Computational Domain
As mentioned in the introduction, the pump is
working in a pipe system. The complete simulation
of this working condition would require the
simulation of the incoming pipe and a part of the
downstream pipe as well.
3. LES CALCULATIONS
The LES approach is in between the Reynolds
Averaged Navier Stokes (RANS) simulation, where
the turbulent motions are modelled and the
equations are solved only for the mean quantities,
and the Direct Numerical Simulation (DNS), which
solves the Navier Stokes (NS) equations of fluid
motion directly with appropriate spatial and
temporal resolution. The describing equations of
LES are traditionally developed by applying a
spatial filtering operator of a given length scale (∆)
on the NS equations [4]. These equations are
unclosed since the effect of the unresolved scales
(historically called sub-grid scales) needs to be
represented. If there is a significant spatial variation
in the filtering length scale, a commutation term
Figure 3. The inlet part of the pump.
In order to reduce the computational cost of the
simulation, it was decided to do a detailed
simulation only of the elbow, the impeller and
volute together with the diffuser. To provide
accurate inlet boundary condition at the elbow, the
confuser was also meshed and included in a
precursor RANS simulation (Figure 3).
The domain in the direction of the impeller
shaft was also truncated at approximately one blade
width distance from the hub. The domain used for
the LES can be seen in Figure 4.
The Courant number for most of the cells is
below 0.5 and values above 1 have a very low
probability. The y+ values characterising the
resolution of the wall boundary layer are below 2.
This later value enables the proper resolution of the
boundary layer.
Figure 6. A-posteriori mesh properties.
3.4. Numerical Parameters
Figure 4. The computational domain.
3.3. Mesh
A block structured mesh was created for the
complete domain, in order to have high quality cells
and to have control over the boundary layer meshes.
The blades were meshed using C-H strategy. The
interface between the stationary and rotating parts
was located first: cylindrical cross-section at the end
of the elbow, upstream in the impeller and second: a
circular cylinder at the inner radius of the volute.
The cell number used for the LES is 6080710.
The mesh of the impeller is depicted in Figure 5.
In the present investigation of an industrial
configuration the general purpose finite volume
code ANSYS Fluent 6.3 was selected because of its
wide use in the industry, it has the required features
implemented, and the Department of Fluid
Mechanics already has experience in its use for LES
[9, 10, 11].
The temporal discretisation used the implicit two
level second order method using iterative SIMPLE
method for pressure-velocity coupling. The
equations are treated as pressure based, which is
appropriate for incompressible flows. The surface
fluxes in the momentum equation were interpolated
using the Bounded Central Differencing Scheme
[8]. The pressure was interpolated using a second
order upwind method. The gradients were
calculated using the cell-based method. The slope
of the gradient is limited by means of the standard
limiter of using the minmod function.
3.5. Boundary Conditions
A “velocity inlet” boundary condition was used
as inlet condition at approximately half streamwise
location of the elbow by setting a steady velocity
profile evaluated from a preliminary RANS (using
SST model) simulation. Non-slip condition was
applied at all the walls, prescribing the actual
velocity of the wall. At the shaft, a symmetry
boundary condition was used to represent the
neglected part. At the outlet, the pressure was
prescribed using the “outlet vent” boundary
condition by also incorporating a pressure loss
coefficient of 30 to avoid reverse flow.
3.6. Interface behaviour
Figure 5. The mesh on the impeller.
The two important a-posteriori properties
characterising the mesh are provided in the form of
histogram in Figure 6 (in percent).
The effect of the sliding interface needed to be
investigated in detail for LES, since the dramatic
change in the cell (filter) size and the numerical
interpolation involved represent a challenge. The
upstream interface was investigated by carrying out
a straight pipe simulation having the same bulk
Reynolds number and the same mesh interface at
half streamwise distance as the one used in the
pump simulation. As reference, the same physical
pipe was simulated but the mesh structure of the
upstream part of the pipe has been used for the
complete length. For both case the same temporal
evolution of a turbulent velocity profile was
prescribed as an inlet boundary condition. The cross
section integrated turbulent kinetic energy was
registered at the outlet of the pipe and it was found
that the resultant error of the interface is about 7%.
3.7. Phase Averaging
The analysis of the turbulence simulation in
turbomachinery needs special treatment since
beside the turbulent fluctuations the blade passing
frequency represents a natural period of the flow.
The geometrical position of the impeller can be
defined as a phase of the averaging. For the
presently investigated impeller geometry the phase
is the angle between one (out of six) blade of the
impeller and a geometrical feature of the volute (for
example the tongue) and varies between 0˚ - 60˚.
The phase was discretised to six 10˚ wide angular
intervals, i.e. phase values correspond to an average
of the 10˚ intervals.
The averaged values presented in the paper
correspond to an averaging time of 8 impeller
rotation.
Figure 7. Three successive approximate
streamwise-pitchwise surfaces (1st, 2nd, 3rd)
4.2. Phase-Resolved Pressure
An example for phase averaging is provided in
this section. In Figure 8, the pressure contours
together with the sectional streamlines are shown on
the 2nd approximate streamwise-pitchwise surface.
4. RESULTS
4.1. Approximate Streamwise-Pitchwise
Surfaces
For postprocessing of the 3D flowfield, it
appears to be beneficial to create surfaces
approximating a constant spanwise position
representing,
streamwise,
pitchwise
flow
(streamwise-pitchwise surfaces). The surfaces are
rotationally symmetric, as shown in Figure 7.
Figure 8. The static pressure contours and the
sectional streamlines on the 2nd approximate
streamwise-pitchwise surface. A zoom is shown
for the six successive phases (1st -6th).
The six phases are show only for the side located
oppositely to the tongue of the volute. The pressure
minima located on the suction side of the leading
edge vary with the phase of the impeller
corresponding to a possible vortex shedding, which
will be discussed later again.
4.3. Average Flow Topology
Representation of wall streamlines is an important
tool to investigate the topology of the phase
averaged flow-field [9].
In this section, these lines are shown with the
corresponding
extracted
separation
and
reattachment lines. First, the complete impeller is
shown for the first phase in Figure 9.
The flow is impinging approximately at the
geometrical centroid of the hub with a swirl
corresponding to the rotation of the impeller. The
stream-lines approach the blades at the inlet angle
corresponding to an appropriate design. The flow is
separated from the hub upstream of the leading
edge, forming a horseshoe vortex structure. On the
leading edge of the blade the stagnation line is
almost straight, as it can be seen from the extracted
reattachment line and the corresponding low shear
stress. The shear stress is increasing and than
decreasing on the round leading edge of the blade
on both sides. At the change in the curvature on the
suction side the separates and than reattaches at
some blade width depending on which blade is
considered. These reattachment lines are divided to
three parts by the two streamwise elongated
bifurcation lines. The bifurcation line closer to the
hub is of separation type and is related to the corner
vortex at the junction of the hub and the suction
side of the blade. Its corresponding reattachment
line is also visible on the hub.
The reattachment on the the suction side is related
to the stream-wise vortex attached to the tip of the
blade. The flow on the pressure side of the tip
separates creating strong recirculation on the tip of
the blade, with high shear stress associated. The
flow on the hub also has a stream-wise separation
line approximately at half distance between the
successive blades.
The secondary flow in the blade passages is
further visualised by sectional streamlines at
constant radius surfaces in Figure 11. Because of
the thick tip clearance, the flow in the gap is
remarkable and has a strong influence on the blade
passage flow as well.
4.4. Transitional Behaviour
Figure 9. The shear stress contours, the wall
streamlines (black, thin lines with arrows) and
the extracted bifurcation lines (white:
separation, yellow: reattachment) on the
impeller (1st phase). A zoom is shown for the six
successive phases (1st -6th).
Since the pump works at low Reynolds number,
laminar to turbulent transition plays an important
role. For this reason, special attention is paid to
post-process the result from this viewpoint. Since
spatial transition occurs in streamwise evolution of
the flow, the analysis starts with investigation of the
flow in the elbow in Figure 10. It can be seen that
the flow remains practically laminar until it reaches
the impeller. The transition happens because of the
separations [12, 13] as it can be seen at the inner
radius of the elbow. The transition creating the
highest amount of turbulent kinetic energy (TKE) is
visible on the three other visualised plane sections
in the curvature at the junction of the elbow and the
impeller. The transition can dedicated to the
separation, but also influenced by the sliding
interfaces (located in the middle of the TKE peak).
Further investigation would be required to clarify
this issue.
Figure 10. Turbulent kinetic energy contours in
the X=0 and the Y=0 planes for the 1st phase.
In Figure 11, further evolution of the flow can be
investigated. It can be seen that the junction of the
pressure side to the hub is almost laminar. The
highest TKE is on the casing wall at the tip side of
the impeller, convected to this location from the
previously mentioned separation-induced transition.
Another important source of turbulence is the tip
vortex of the blades, as it can be seen from the high
TKE regions downstream of this location.
Figure 11. Turbulent kinetic energy contours
together with sectional streamlines at three
cylinders of constant radius using perspective
view (1st phase).
Further insight is gained by visualising the shear
stress fluctuations on the walls of the impeller in
Figure 12. High fluctuations can be seen at half of
the leading edge closer to the tip, on the tip vortex,
and in the vortex at the junction of the suction side
and the tip.
Figure 12. Turbulent shear stress fluctuation
square contours, the wall streamlines and the
extracted bifurcation lines on the impeller (1st
phase).
4.5. Coherent Structure Evolution
For better understanding of the turbulence
detected in the impeller, animation was created
from the flow around one selected blade by making
use of vortex detection. In the animations the
evolution of the coherent structures was
investigated by using Q criteria [14] for vortex
detection. In Figure 13, a snapshot of the animation
can be seen.
Figure 13. Snapshot of the animation visualising
the evolution of the coherent structures.
The vortices are associated to the created
turbulence described in the previous section. The
vortices corresponding to separation at the impeller
inlet are very dense in the figures. The vortices at
the tip are roller-shaped, and are perpendicular to
the mean flow direction, presumably due to KelvinHelmholtz instability. Also a source of vortices can
be seen in the separation zone on the suction side of
the leading edge, again rollers and their streamwise
distortion can be recognised.
5. SUMMARY
A miniature pump designed by WILO SE to be
incorporated in the GENIAX system was
investigated by Large-Eddy Simulation technique.
The main purpose of the investigation was to see
the feasibility of the pump simulation using a
general purpose code, and gain knowledge about
the properties of the flow. It was found that the
simulation is feasible but computationally quite
expensive; the highest uncertainties are associated
to the treatment of the sliding interfaces since they
can contaminate the result by generation of spurious
turbulence. On the other hand, it has been
experienced that the detailed inside can be obtain in
to the pump flow by using face averaging technique
based on impeller position. The losses due to
turbulence can be easily located.
ACKNOWLEDGEMENTS
This work has been supported by the Hungarian
National Fund for Science and Research under
contract No. OTKA K63704.
This research has been supported by WILO SE
REFERENCES
[1] Kettner, T., Oppermann, J., 2009, “Das
Dezentrale Pumpensystem”, VDI-Jahrbuch
Bautechnik.
[2] Vanella, M., Piomelli, U.; Balaras, E., 2008,
„Effect of grid discontinuities on large-eddy
simulation statistics and flow fields”, Journal of
Turbulence, Vol. 9, No. 32, pp.1-23.
[3] Piomelli, U., Kang, S., Ham, F., Iaccariona, G.,
2006, "Effect of discontinuous Filter width in
large-eddy simulations of plane channel flow",
Center for Turbulence Research, Proceedings
of the Summer Program 2006, pp. 151-163.
[4] Geurts, B. J., 2004, "Elements of Direct and
Large-Eddy Simulation", R. T. Edwards, Inc.
[5] Germano, M., Piomelli, U., Moin, P., Cabot, W.
H., 1991, "A dynamic subgrid-scale eddy
viscosity model", Physics Fluids Vol. 3, No. 7.
pp. 1760-1765.
[6] Schlatter, P., Stolza, S., Kleisera, L., 2004, "LES
of transitional flows using the approximate
deconvolution model", International Journal of
Heat and Fluid Flow, Vol. 25, No. 3, pp. 549558.
[7] Schlatter, P., Stolz, S., Kleiser, L., 2006, "Largeeddy simulation of spatial transition in plane
channel flow", Journal of Turbulence, Vol. 7,
No. 33 pp. 1-24.
[8] Kim, S. E., 2004, “Large Eddy Simulation using
unstructured meshes and dynamic subgrid-scale
turbulence models” 34th AIAA Fluid Dynamics
Conference and Exhibit, Portland Oregon.
[9] Lohász, M.M., Rambaud, P., Benocci, C., 2006,
„Flow features in a fully developed ribbed duct
flow as a result of MILES“ Applied Scientific
Research, Vol. 77, No. 1-4, pp. 59-76(18)
[10] Tóth P., Lohász, M. M., 2008, "Anisotropic
grid refinement study for LES" Springer
Netherlands, Vol 12. pp. 167-178.
[11] Nagy L., Lohász M. M., Vad J., 2008,
„Hybrid/Zonal RANS/LES computation of an
airfoil“ Sixth Conference on Mechanical
Engineering, Gépészet 2008
[12] Yang, Z., Voke, P.R., 2001, “Large-eddy
simulation of boundary-layer separation and
transition at a change of surface curvature”
Journal of Fluid Mechanics, Vol. 439, pp. 305333.
[13] Lamballaisa, E., Silvestrini J., Laizeta, S.,
2008, "Direct numerical simulation of a
separation bubble on a rounded finite-width
leading edge" International Journal of Heat
and Fluid Flow Vol. 29, No. 3, pp. 612-625.
[14] Hunt J. C. R., Wray A. A., Moin, P., 1988,
“Eddies, streams, and convergence zones in
turbulent flows”, Center for Turbulence
Research, Annual Research Briefs, pp. 193202.