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Paper ID: ETC2019-047 Proceedings of 12th European Conference on Turbomachinery Fluid dynamics & Thermodynamics ETC13, April 8-12, 2019; Lausanne, Switzerland
N. Casimir1 - Z. Xiangyuan2– G. Ludwig3– R. Skoda1
1Chair of Hydraulic Fluid Machinery, Ruhr University Bochum, Germany
2 School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, P. R. China
3Chair of Fluid Systems, Technical University Darmstadt, Germany
ABSTRACT
The accuracy of linear eddy-viscosity URANS turbulence modelling is assessed for off-
design operation of a single stage radial centrifugal pump. The open source software
OpenFOAM is utilized. Hot wire probes have been utilized for measurement of spatially and
temporally resolved validation data at the impeller discharge of the air-operated pump. The
ensemble-averaged mean flow angle is in qualitatively good agreement to data for the entire
operation range, while minor deviations occur close to the volute tongue due to impeller-volute
interaction. Turbulence statistics from the simulation are compared to ensemble-averaged
velocity RMS from measurements. RMS distribution is also qualitatively well reproduced for
near-design and overload operation. A more pronounced RMS mis-prediction occurs in part
load in the region of high impeller-volute tongue interaction and reveals limitations of
turbulence modelling in highly unsteady flow regions of centrifugal pumps.
KEYWORDS
URANS, OPENFOAM, PART LOAD, PUMP, TURBULENCE MEASUREMENTS
NOMENCLATURE
Latin characters
b Volute inlet width [m] Tp Periodic time scale [s] c Velocity [m/s] TT Integral turbulent time scale [s]
d Diameter [m] t Blade spacing [m]
n Rotational speed [1/s] TI Turbulent Intensity [-]
G1 Coarse mesh [-]
u Impeller circumferential
velocity [m/s]
G2
Fine mesh [-] x Circumferential distance [m] k
Turbulent kin. Energy [m2/s2] between trailing edge and ns Specific speed [-] measurement point p Pressure [Pa] y Axial direction [m] Q Flow rate [m3/s] Z Number of blades [-] q Flow rate related to [-] nominal Flow rate
2
Greek characters
α Flow-angle [°] TKE Turbulent Kinetic ε Volute angle [°] Energy ν Kinematic viscosity [m2/s] u Circumferential
Ψ Pressure coefficient [-] Abbreviations
ρ Density [kg/m3] CFD Computational Fluid Dynamics
ω Turbulent frequency [1/s] Exp Experimental Data
Subscripts GGI Generalized Grid Interface
0 Nominal value Hub Hub side
1 Impeller inlet LES Large Eddy Simulation
2 Impeller outlet MP Measurement Point
3 Measurement plane Num Numerical data
abs Absolute PISO Pressure Implicit with
exp Experimental Separation of Operators
m Meridional SIMPLE Semi Implicit Method for
num Numerical Pressure Linked Equations
out Outlet property Shr Shroud side
ref Reference position SST Shear-Stress-Transport
RMS Root Mean Square URANS Unsteady Reynolds Averaged
t Total Navier-Stokes
INTRODUCTION
Increasing demands on centrifugal pumps, e. g. by legislature, require higher efficiencies even at
off-design operation, i.e. part load and overload, which are characterized by a highly unsteady and
turbulent flow field due to flow separation and impeller-stator interaction. CFD methods are
increasingly integrated in the design and optimization process of pumps. Statistical (i.e. URANS)
eddy-viscosity turbulence models are widely used for pump flow simulations. In this class of
turbulence models, a significant simplification is introduced by an a-priori time-average of the
turbulent fluctuations. Thus, the resulting Reynolds-stress tensor has lost any spectral information of
the turbulence field. Although statistical models may yield a good prediction of pump characteristics
at close-to-design operation, they may increasingly fail towards off-design pump operation. There are
several studies that show such limitations of statistical models and benefits of scale-resolving models
(LES), e.g. for the prediction of in-homogenous flow distribution through impeller blade channels at
part load (Byskov et al., 2002, 2003), head characteristics instability by Kato et al. (2003), part load
instabilities and flow separation (Tang et al., 2007; Tokay et al., 2006; Zhang, 2010; Wang et al.,
2013; Posa et al., 2011, 2015; Si et al. 2014) or tip vortices by Shen et al. (2013). However, the
computational effort of LES is tremendous because at least 80 % of the spectral energy must be
resolved (Pope, 2000; Fröhlich et al., 2008). Since Reynolds numbers typically encountered in
centrifugal pumps are high, and thus the spectrum of turbulent eddies spreads over several spatial and
temporal orders of magnitude, a soundly resolved LES demands an extensively high number of
computational cells and time steps. It is thus attractive to exploit the moderate computational effort
of statistical models after their careful validation on spatially and temporally resolved flow field data
and thorough evaluation of their particular limitations. Spence and Amaral-Teixeira (2008, 2009) and
Barrio et al. (2010) presented URANS simulations and a validation on measured integral
characteristics i.e. head, power and efficiency. However, a comparison with measured spatially and
temporally resolved velocity has not been presented yet for centrifugal volute casing pumps, to the
knowledge of the authors, and is thus the aim of the present study.
A single stage volute casing radial centrifugal pump (𝑛𝑆 = 26 𝑚𝑖𝑛−1) is investigated including
off-design operation. The pump is operated with air in order to use hotwire anemometry for a high
temporal and spatial resolution of the velocity field near the impeller discharge and thus enables a
comparison with turbulence statistics from the simulation. Experimental data origins from
3
measurements at the Chair of Fluid Systems, Technical University Darmstadt, see Hergt et al. (2004)
and Meschkat and Stoffel (2002) and is reviewed and re-edited within the present study to yield
ensemble-averaged mean flow angle and turbulence field (velocity RMS) at the impeller discharge
for comparison with CFD results. The statistical, linear eddy-viscosity SST turbulence model by
Menter (1994) is employed due to its wide use for pump flow simulation.
EXPERIMENTAL SETUP
Details of the measurements were presented by Hergt et al. (2004) and Meschkat and Stoffel
(2002) and briefly summarized here. A centrifugal pump with a specific speed of 𝑛𝑆 = 26 𝑚𝑖𝑛−1 and a trapezoidally shaped volute casing is operated in an open test rig with air. A special volute casing
construction allows circumferential and axial probe traversals across a cylindrical plane 6 𝑚𝑚
downstream of the impeller trailing edge, see Figure 1 a and b, with a spatial resolution of 2 𝑚𝑚 in
axial and 1.8° in circumferential direction. Since the maximum Mach number is evaluated to be below
0.3, it is assumed that compressibility effects on the velocity field are of minor relevance. The volute
casing is designed for about 80 % nominal impeller flow rate because a nearly constant
circumferential distribution of the static volute wall pressure has been achieved for that flow rate, see
Hergt et al., 2004. Thus, 𝑞 = 𝑄 𝑄0 = 80 %⁄ is considered to be the design operation of the pump. Pump
impeller data are summarized in Table 1, and more details can be found in Hergt et al. (2004) and
Meschkat and Stoffel (2002).
Table 1: Pump impeller data.
Parameter Notation Value Unit
Specific speed (water and air) 𝑛𝑆 = 𝑛[𝑚𝑖𝑛−1] ∙√𝑄0[
𝑚3
𝑠]
(𝐻)3/4 26 𝑚𝑖𝑛−1
Specific speed (non- 𝑛𝑆 = 𝑛[𝑠−1] ∙
√𝑄0[𝑚3
𝑠]
(𝐻𝑔)3/4 0.08 -
dimensional)
Number of blades 𝑍 7 -
Rotational speed (air) 𝑛 3000 𝑚𝑖𝑛−1
Nominal flow rate (air) 𝑄0 879 𝑚3 ℎ⁄
Suction flange diameter 𝑑1 230 𝑚𝑚
Impeller diameter 𝑑2 405 𝑚𝑚
Measurement plane diameter 𝑑3 417 𝑚𝑚
Impeller discharge width 𝑏 34 𝑚𝑚
The spatially and temporally resolved velocity field in the measurement plane was recorded for
operation points from 𝑞 = 20 % to 𝑞 = 130 %, while only the range of 𝑞 = 40 % to 𝑞 = 120 % is
considered in the present study. The transient flow angle was evaluated by single wire measurements
with a sampling frequency of 42 𝑘𝐻𝑧 and ensemble-averaged in dependence on the angular impeller
position. Velocity RMS was determined by cross wire probe measurements with a sampling rate of
37 𝑘𝐻𝑧 and also ensemble-averaged. By the cross wire probe arrangement, it was ensured that the
velocity fluctuations in all three spatial directions are detected to reflect the three dimensional
turbulence field. The uncertainties of both, single and cross wire probe measurements, are 5 % of the
measured value, according to Meschkat (2004), which are suitably low for the assessment of
qualitative velocity and turbulence distributions. The flow-angle 𝛼 was evaluated with Equation 1
and ranges from −180° to 180°.
𝛼 =
|𝑐𝑚|
𝑐𝑚∙ 𝑎𝑐𝑜𝑠 (
𝑐𝑢
𝑐𝑎𝑏𝑠) (1)
4
Negative angles indicate a meridional backflow into the impeller. Values between 0° and 90° indicate that 𝑐𝑢 is oriented towards impeller rotation direction, and values between 90° and 180° in
the opposite direction.
Mean flow angle and RMS velocities are presented as functions of the axial position 𝑦 𝑏⁄ , see
Figure 1 a, and the circumferential coordinate 𝑥 𝑡⁄ , which corresponds to the time range when one
blade spacing passes the measurement position, see Figure 1 c. Results are presented for selected
circumferential measurement positions 𝜀 = 0° and 120° in the volute casing, see Figure 1 b.
The total pressure cross-area distribution was recorded 2,5 ∙ 𝐷 upstream of the impeller inlet
(position 𝑟𝑒𝑓) as well as at the volute discharge by transient single-hole cylindrical pneumatic probes
and was area-averaged for the evaluation of the pressure coefficient according to Equation 2.
Ψ𝑡 =𝑝𝑡,𝑜𝑢𝑡 − 𝑝𝑡,𝑟𝑒𝑓
0,5 ∙ �̅� ∙ 𝑢22 (2)
An averaged density �̅� is evaluated between suction pipe and discharge and assumed to be
constant within the pump. According to Meschkat (2004) uncertainties of pressure coefficient
measurements are at 1.4 % at 𝑞 = 40% partial load and increasing to 4% at 𝑞 = 120% overload,
illustrated in Figure 3c as error bars.
Figure 1. a) Meridional contour and radial probe position; b) Circumferential probe positions;
c) Illustration of coordinate 𝒙, which corresponds to the time range when one blade spacing
passes the measurement position.
NUMERICAL SET-UP
Numerical method
URANS simulations are performed with the open source software Foam-Extend version 4.01. The
pimpleDyMFoam solver is utilized, i.e. a combined PISO (Issa, 1986) and SIMPLE (Patankar and
Spalding, 1972) algorithm for incompressible unsteady flows, combined with moving mesh
capabilities. The statistical eddy-viscosity SST turbulence model by Menter (1994) with automatic
wall functions is employed due to its wide use for pump flow simulation.
The computational domain contains the impeller, volute casing, side chambers and the suction
and pressure pipe, see Figure 2 d. The suction pipe has been elongated to a length of 5 ∙ 𝐷 to avoid an
impact of boundary conditions on the part load vortex. A block structured hexahedral grid as shown
in Figure 2 a, b and c with approximately 3 million nodes (named G1) is generated with the software
1 https://foam-extend.fsb.hr/
d2
d3
d1
Measurement
plane
Hub
b
Front shroud
Rear shroud
Volute
Casing
a) Pump meridional view b) Volute axial view
120 d1 d3
c) Tongue region axial view
𝑦 Measurement
plane
.
.
MP: ε=0
MP: ε=0
Measurement
position:ε=0°y
Impeller
rotation
5
ANSYS ICEM 182. For a grid study, the grid G1 is successively refined to approximately 24 million
nodes (named G2) by bisection of node distances in each direction. For G1, average and maximum
𝑦+ values equal about 10 and 60, and for G2 about 5 and 30.
A Dirichlet inlet boundary condition is set for velocity according to flow rates from experiment,
together with a Neumann (zero-gradient) condition for static pressure. At the volute discharge, a
Neumann boundary conditions is set for velocity (zero gradient) and a Dirichlet condition for static
pressure. Temporal and spatial second order discretization methods are used according to table 2.
Time step is set according to an impeller rotation of 1° on the coarse and 0.5° on the fine grid to maintain a constant Courant number during the grid study.
For the evaluation of convergence of the non-linear iterative SIMPLE-PISO algorithm,
preliminary investigations have shown that a drop of the non-linear non-dimensional residual sum
norm of each equation below a value of 10-5 is a suitable convergence criterion. It is noteworthy that
we evaluate the residual of the pressure equation in the first PISO loop and not in the last one, which
is a more stringent convergence evaluation. For assessment of the temporal convergence, an
ensemble-average of velocity magnitude in the measurement plane in the same way as in the
experiment is performed. Temporal convergence is defined when the standard deviation of ensemble-
averaged velocity is below 1 % which is achieved after less than one revolution at design point 𝑞 =80 %, about two revolutions in overload 𝑞 = 120 % and about four revolutions in part load 𝑞 = 40 %.
Figure 2. a) Computational grid near volute tongue, b) Conformal interface meshing between
rotor and stator domain, c) Computational grid at the blade leading edge; d) Computational
domain.
2 https://www.ansys.com
Volute
Impeller and side
chambers
Outlet
Suction pipe Inlet
c) Computational domain
a) Polyhedral interface meshing (schematic) b) Blade leading edge meshing
Polyhedral Interface
Conformal Interface
Homogeneous interface grid
Rotor
Stator
Volu
te
Impel
ler
and
side
cham
ber
s
Outl
et
Suct
ion
pip
eIn
let
c) C
om
puta
tional
dom
ain
a) P
oly
hed
ralin
terf
ace
mes
hin
g(s
chem
atic
)b)
Bla
de
lead
ing
edge
mes
hin
g
Poly
hed
ral
Inte
rfac
e
Confo
rmal
Inte
rfac
e
Hom
ogen
eous
inte
rfac
egri
d
Roto
r
Sta
tor
Trailing edge
a) Volute tongue meshing (G1) b) Polyhedral interface meshing (G1)
c) Blade leading edge meshing d) Computational domain
Fine
G2
Coarse
G1
6
Table 2: Overview of the numerical setup
Parameter Description
Fluid Incompressible air, 𝜐 = 1.54 ∙ 10−5 𝑚2 𝑠⁄
Simulation type Transient, 1° time step (G1), 0.5° time step (G2)
Time discretization Second-order backward Euler
Spatial discretization of convection Momentum equations: Warming and Beam (1976)
The correlation term 𝑐′𝑐′̂ is described in terms of the turbulent kinetic energy 𝑘:
2𝑘 = (𝑐𝑚′𝑐𝑚
′̂ + 𝑐𝑢′𝑐𝑢
′̂ + 𝑐𝑎𝑥′𝑐𝑎𝑥
′̂ ) = (𝑐′𝑐′̂ ) (6)
The Reynolds-averaged turbulence intensity (𝑇𝐼) is calculated inserting Equation (5) and
Equation (6) into (4) and dividing by the impeller circumferential trailing edge velocity 𝑢2:
1.1
1.2
1.00 π/2 π 3/2π 2π
a) ANSYS-CFX: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
b) Foam-Extend: Q/Q0=40%P
ress
ure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
c) FE Conformale: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]Rotation [rad] Rotation [rad] Rotation [rad]
b) Ψ𝑡, with conformal Interface
1.1
1.2
1.00 π/2 π 3/2π 2π
a) ANSYS-CFX: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
b) Foam-Extend: Q/Q0=40%P
ress
ure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
c) FE Conformale: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]Rotation [rad] Rotation [rad] Rotation [rad]
Impeller position [-] Impeller position [-]
Ψ𝑡[-
]
Ψ𝑡[-
]Q/Q0 [-]
c) Head characteristicsa) Ψ𝑡, w/o conformal Interface
Ψ𝑡[-
]
Ψ𝑡 [
-]
Ψ𝑡 [
-]
Ψ𝑡 [
-]
𝑞 [-]Impeller position[-]Impeller position[-]
a) Ψ𝑡, w/o conformal Interface b) Ψ𝑡, with conformal Interface c) Head characteristics
Sim-G2Sim-G1
Exp
1.1
1.2
1.00 π/2 π 3/2π 2π
a) ANSYS-CFX: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
b) Foam-Extend: Q/Q0=40%P
ress
ure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
c) FE Conformale: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]Rotation [rad] Rotation [rad] Rotation [rad]
b) Ψ𝑡, with conformal Interface
1.1
1.2
1.00 π/2 π 3/2π 2π
a) ANSYS-CFX: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
b) Foam-Extend: Q/Q0=40%P
ress
ure
Co
eff.
Ψ(t
) [-
]
1.1
1.2
1.00 π/2 π 3/2π 2π
c) FE Conformale: Q/Q0=40%
Pre
ssure
Co
eff.
Ψ(t
) [-
]Rotation [rad] Rotation [rad] Rotation [rad]
Impeller position [-] Impeller position [-]
Ψ𝑡[-
]
Ψ𝑡[-
]Q/Q0 [-]
c) Head characteristicsa) Ψ𝑡, w/o conformal Interface
Ψ𝑡[-
]
8
𝑇𝐼𝑆𝑖𝑚 =
√𝑅𝑀𝑆2(�̂�) + 2�̅�
𝑢2 (7)
Ensemble averaged turbulent kinetic energy and the variance (RMS²) of the unsteady Reynolds-averaged
velocity are used for 𝑇𝐼𝑆𝑖𝑚 according to Equation (7), which can immediately be compared with
measured 𝑇𝐼𝐸𝑥𝑝 in Equation (8):
𝑇𝐼𝐸𝑥𝑝 =
𝑅𝑀𝑆(𝑐𝑎𝑏𝑠)
𝑢2 (8)
RESULTS
Grid study
The grid influence is assessed by the pump head characteristics in terms of the time-averaged total
pressure coefficient (Figure 3 c) and the spatial-temporal distribution of mean flow angle 𝜶 (Figure 4
a) as well as 𝑻𝑰 (Figure 4 b). The head shows slight differences between G1 and G2 towards overload,
see Figure 3 c. Since the grid dependence of head is lower than the difference to measurement data,
sufficient grid independence of total pressure coefficient is assumed.
Since 𝛼 and 𝑇𝐼 are time dependent, their ensemble-averaged distribution is presented. Ensemble-
averaged results vs. the axial coordinate 𝑦 and direction of blade spacing 𝑥 are discussed in Figure 4. Note that this kind of illustration should not be confused with a snapshot of the flow field in the
measurement plane in direction of blade spacing 𝑡. Rather, the 𝑥 𝑡⁄ axis illustrates the time range when
one blade spacing passes the measurement position 𝜀. Grid dependence is exemplarily presented for
𝑞 = 40 %, since at the other operation points the deviations between both grids are lower than at part
load. Two exemplary measurement locations, 𝜀 = 0° and 120° are discussed. The flow angle 𝛼 is
essentially grid independent, see Figure 4 a. A more pronounced grid dependence is present for 𝑇𝐼, see Figure 4 b. 𝑇𝐼 increases with higher grid resolution. Since these differences are again lower than
the difference to measurement (as will be shown further below) and the qualitative distribution is
essentially unaffected, also for 𝑇𝐼 a sufficient grid independence is assumed. In what follows, G2
results are presented.
Figure 4. Grid dependency of mean flow angle 𝜶 (a) and turbulence intensity 𝑻𝑰 (b) for part
load 𝒒 = 𝟒𝟎 %.
Spatially and temporally resolved flow angle and turbulence intensity
In Figure 5, the flow angle 𝛼 is illustrated for 𝑞 = 40 %, 80 % and 120 % for two circumferential
measurement location, a close-to volute tongue location 𝜀 = 0° and far away from the tongue 𝜀 =120°. Note that for 𝜀 = 0°, flow angle results at 𝑞 = 100 % are presented to illustrate overload
operation instead of 120 % due to defective measurement data for 𝑞 = 120 % near the volute tongue.
It was approved, that turbulence intensity measurements were not affected by the defective