Numerical Predictions of Cavitating Flow Around A Marine Propeller and Kaplan Turbine Runner With Calibrated Cavitation Models
Numerical Predictions of Cavitating Flow Around A Marine Propeller and Kaplan Turbine Runner With Calibrated Cavitation Models
Numerical Predictions of Cavitating Flow Around A Marine Propeller and Kaplan Turbine Runner With Calibrated Cavitation Models
Cavitating phenomena, which may occur in many industrial systems, can be modelled using several approaches. In this study a homogeneous
multiphase model, used in combination with three previously calibrated mass transfer models, is evaluated for the numerical prediction of
cavitating flow around a marine propeller and a Kaplan turbine runner. The simulations are performed using a commercial computational fluid
dynamics (CFD) solver and the turbulence effects are modelled using, alternatively, the Reynolds averaged Navier Stokes (RANS) and scale
adaptive simulation (SAS) approaches. The numerical results are compared with available experimental data. In the case of the propeller the
thrust coefficient and the sketches of cavitation patterns are considered. In the case of the turbine the efficiency and draft tube losses, along
with the cavitation pattern sketches, are compared. From the overall results it seems that, for the considered systems, the three different
mass transfer models can guarantee similar levels of accuracy for the performance prediction. For a very detailed investigation of the fluid
field, slight differences in the predicted shapes of the cavitation patterns can be observed. In addition, in the case of the propeller, the
SAS simulation seems to guarantee a more accurate resolution of the cavitating tip vortex flow, while for the turbine, SAS simulations can
significantly improve the predictions of the draft tube turbulent flow.
Keywords: cavitation, marine propeller, Kaplan turbine, mass transfer models, RANS, SAS
Highlights
• CFD simulations of cavitating flow around a marine propeller and Kaplan turbine runner.
• Homogeneous model used in combination with three previously calibrated mass transfer models.
• Turbulence modelled using RANS and SAS approaches.
• Calibrated mass transfer models guarantee similar levels of accuracy.
• SAS approach improves the local flow field resolution.
empiricism have for instance been proposed by [15] transfer models can be successfully employed. The
and [16]. machine performances can be predicted with a similar
In this study the homogenous transport- equation level of accuracy, even though small differences in the
based model is considered and three different mass predicted cavitation patterns can be observed. As far as
transfer models are employed. More precisely, the the turbulence modelling is concerned, the numerical
mass transfer models originally proposed by Zwart et results show that the SAS simulations could be used
al. [17], Singhal et al. [18] and Kunz et al. [19] with to improve the resolution of certain flow features such
empirical coefficients calibrated according to [20] are as the propeller cavitating tip vortex for example.
employed. Moreover, it seems that in the case of the Kaplan
The scope is to verify the applicability of the turbines, where the efficiency predictions are highly
considered calibrated models to the numerical affected by the proper resolution of the unsteady draft
predictions of the cavitating flow around two different tube turbulent structures, the SAS simulations could
systems: marine propeller and Kaplan turbine. represent a good compromise between standard RANS
The investigation is performed considering the simulations and the computationally more demanding
Potsdam propeller test case (PPTC) model propeller
and more accurate large eddy simulations (LES).
working in uniform inflow [21], and a model Kaplan
The paper is structured as follows. First the
turbine experimentally investigated by researchers at
mathematical model is presented. Then, the numerical
Kolektor-Turboinstitut, Slovenia.
predictions performed for marine propeller and
Even though the present study is carried out
Kaplan turbine are described. The descriptions follow
mainly to evaluate a possible more general character
of the calibrated mass transfer models, related to the same scheme where the considered system is
the systems under consideration the influence of the presented, the numerical and meshing strategies are
turbulence modelling is also briefly evaluated. Thus, described, and the results are discussed. Finally, the
the simulations are performed using the standard concluding remarks are given.
Reynolds averaged Navier Stokes (RANS) approach
and the more accurate and more time consuming 1 MATHEMATICAL MODEL
Scale Adaptive Simulations (SAS). In the case of the
steady state RANS simulations the workhorse Shear Here, the homogeneous model is presented in the
Stress Transport (SST) turbulence model [22] is used fixed frame of reference for convenience.
in combination with all the three different calibrated
mass transfer models. 1.1 Governing Equations
For the evaluation of the possible improvement
related to a more accurate turbulence modelling In the homogeneous multiphase transport equation-
approach, time dependent SAS simulations are based model, the cavitating flow can be described by
carried out using the SST-SAS turbulence model the following set of governing equations:
[23] in combination with only a certain mass transfer
model for convenience. The simulations are carried 1 1
∇ ⋅ U = m −
out using ANSYS-CFX (CFX for brevity) commercial ρl ρ v
CFD solver which is based on the node-centered ∂ ( ρU)
finite volume method (more precisely on the Control +∇ ⋅ ( ρ UU ) = −∇ P −∇ ⋅ τ � + S M . (1)
Volume-Based Finite Element Method (CVFEM)) ∂t
[24] and [25]. ∂γ m
∂t +∇ ⋅ ( γ U ) = ρ
The numerical results are compared with the l
available experimental data. For a quantitative
comparison the thrust is evaluated for the marine Cavitating flow is modelled as a mixture of two
propeller, while the draft tube losses and the efficiency species i.e. vapour and liquid behaving as one. The
are considered for Kaplan turbine. For a qualitative phases are considered incompressible. They share the
comparison the sketches of cavitation patterns same velocity U and pressure fields P.
predicted around the blades are considered for both The mixture density, ρ, and dynamic viscosity, μ,
cases. are scaled, respectively, as:
From this study it seems that for the prediction
of the cavitating flow around a marine propeller and ρ = γρl + (1 − γ ) ρv , µ = γµl + (1 − γ ) µv . (2)
Kaplan turbine all the three different calibrated mass
544 Morgut, M. – Jošt, D. – Škerlavaj, A. – Nobile, E. – Contento, G.
Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554
The interface mass transfer rate due to cavitation, Kunz et al. model:
m , can be modelled using three different calibrated
mass transfer models. + C prod ρvγ 2 (1 − γ )
m =
+ −
t∞
m = m + m : . (5)
m − = Cdest ρvγ min [ 0, P − Pv ]
1.2 Turbulence Modelling
Experiment
Fig. 3. PPTC propeller; RANS simulation performed with three different mass transfer models;
cavitation patterns depicted using isosurfaces of vapour volume fraction equal to 0.2
3 it is possible to note that for a given operational Following [21] the cavitation patterns are here
condition the thrust predicted using the three different presented as isosurfaces of vapour volume fraction
calibrated mass transfer models was in excellent equal to 0.2. From the qualitative comparison of the
agreement with the experimental data. snapshots of the cavitation patterns, presented in
Fig. 3 it is interesting to observe that for J = 1.019,
σn = 2.024, only in the case of the FCM the shape of
the cavitation pattern was correctly reproduced. With
the other models a layer of sheet cavitation on the
blade leading edge, not observed experimentally, was
obtained. Conversely, for J = 1.408, σn = 2.000, the
extent of the sheet cavity developing on the propeller
face was better reproduced with the Zwart and Kunz
models. The extent of the cavitation pattern predicted
Fig. 4. Cavitation pattern predicted using the SST-SAS turbulence with the FCM was minor. The reasons behind these
model in combination with the calibrated FCM differences are still not fully clear. For J = 1.269,
mass transfer model for J = 1.019, σn =2.024 σn = 1.424 there were no differences in the cavitation
Numerical Predictions of Cavitating Flow Around a Marine Propeller and Kaplan Turbine Runner with Calibrated Cavitation Models 547
Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554
patterns predicted using the three different mass point, determined by a certain combination of guide
transfer models. vane blade opening angle and rotor blade angle. For
Since in the case of the RANS simulations the such a point the flow and energy coefficients were
tip-vortex was slightly under-estimated, in this study, φ /φBEP =1.33 and ψ /ψBEP = 0.86, respectively. The
focusing on J = 1.019, σn = 2.024, a brief evaluation Reynolds number, ReT, was 6×106.
of the SAS simulation was performed. An additional
SAS simulation was performed in combination with 3.1 Numerical Strategy
the FCM model, even though the other two models
could also be adopted for this purpose. The FCM was All the simulations were carried out considering the
used, mainly, because in the former RANS simulation computational domain shown in Fig. 5.
the most accurate prediction of the cavitation pattern, Similarly to the propeller case, the numerical
for the specific operational condition, was obtained investigations were first performed using the steady
using this mass transfer model. Fig. 4 shows that with state RANS approach, mainly to evaluate the effect
the SAS simulation the extension of the cavitating of the calibrated mass transfer models on the accuracy
tip-vortex was better reproduced. This improvement of the numerical predictions. Then, further SAS
is related to the less diffusive character of the SAS simulations were carried out in order to improve
simulations where, in general, lower levels of the efficiency predictions.
turbulent viscosity are predicted than those obtained For RANS simulations the SST turbulence model
with the corresponding RANS simulations. was used while for SAS simulations the SST-SAS
model was employed. Both were used in combination
3 MODEL SCALE KAPLAN TURBINE with the automatic wall treatment. Moreover, the
curvature correction [32] and the Kato launder
The numerical predictions of the cavitating flow production limiter [33] were, here, included in all the
in a model scale medium head Kaplan turbine are simulations. For the discretization of the advective
presented. terms high resolution method was used for both
The turbine in question was developed by RANS and SAS simulations. The use of the second
Kolektor-Turboinstitut and consists of a semi-spiral order bounded central difference scheme (BCDS) in
casing with two vertical piers, 11 stay vanes and a the current SAS simulations was precluded by poor
nose, 28 guide vanes, a 6-blade runner, and an elbow solver stability. For time discretization a second order
draft tube with two vertical piers. In CFD simulations implicit time scheme was used.
a draft tube prolongation was added to improve solver For cavitation modelling all the three different
stability as depicted in Fig. 5. mass transfer models were employed in RANS
simulations while for SAS simulations the calibrated
Zwart model was used exclusively.
It is important clarifying that during the design
process of the current turbine, carried out by Kolektor-
Turboinstitut, the standard Zwart model available in
CFX was used. Therefore the SAS simulations were
carried out in combination with the calibrated Zwart
model in order to verify the benefits, in terms of
accuracy, of using an advanced URANS model like
SAS with the same (calibrated) mass transfer model
[35].
The computational domain was properly
Fig. 5. Sketch of the Kaplan turbine used in simulations subdivided in rotating region containing the runner
and in fixed region including the rest of the turbine
The experimental tests were performed on the test parts. In the case of the steady state RANS simulations
rig at Kolektor-Turboinstitut following the IEC 60193 the MRF approach was employed and at the interfaces
[31] international standard. between rotating and fixed regions the frozen rotor
In this study the effect of the severity of the frame change/mixing model was used. In the case of
cavitating phenomena was analysed considering SAS simulations the sliding grid approach (transient
an operating point, close to the local best efficiency rotor stator) available in CFX was used.
548 Morgut, M. – Jošt, D. – Škerlavaj, A. – Nobile, E. – Contento, G.
Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554
3.2 Meshing
3.3 Results
Numerical Predictions of Cavitating Flow Around a Marine Propeller and Kaplan Turbine Runner with Calibrated Cavitation Models 549
Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554
each other. The cavitation patterns are represented the accuracy of the efficiency predictions, additional
using the isosurfaces of the vapour volume fraction SAS simulations were performed in combination with
equal to 0.1 in order to clearly visualize the small the calibrated Zwart mass transfer model.
(initial) cavitation bubbles predicted at . Following [35] a comparison between the
Nevertheless, in the case of standard RANS turbulent flow structures predicted by RANS and SAS
simulations the efficiency was under-predicted, even simulations are presented in Fig. 10.
though the shape of the predicted sigma brake curve
It is possible to note that for the steady state
compared well with the experimental trend. It is worth
RANS simulations, only large turbulent structures
noting that the differences in predicted efficiency
values were, mainly, due to the over estimation of the were obtained.
draft tube losses related to the steady state approach In the case of SAS simulations, as expected,
and turbulence modelling rather than on cavitation smaller turbulent structures were resolved leading to
modelling [35]. more accurate predictions of the draft tube losses.
Thus, in order to better resolve the vortex In Fig. 10 it is also interesting to note the lower
structures in the draft tube and consequently improve level of the viscosity ratio (ratio between the turbulent
Zwart
FCM
Kunz
Fig. 8. Kaplan turbine; steady state simulations performed using the SST turbulence model in combination with three different calibrated
mass transfer models; cavitation patterns depicted as isosurfaces of the vapour volume fraction equal to 0.1.
a) b) c)
Fig. 9. Cavitation patterns for σ = 0.52; a) experimental recording, b) predicted using Zwart mass transfer model in combination with
the SST turbulence model, c) predicted using Zwart mass transfer model in combination with the SST-SAS turbulence model. Numerical
cavitation patterns depicted as isosurfaces of vapour volume fraction equal to 0.1.
a) b)
Fig. 10. Turbulent structures represented using the isosurfaces of velocity invariant equal to 0.1, coloured by viscosity ratio;
a) simulation performed with the SST turbulence model, and b) with the SST-SAS model
and dynamic viscosity) associated with the SAS With transient simulations, as expected, the same
simulation. amount of vapour structures was obtained on all
Regarding the efficiency, from Fig. 7, it is runner blades.
possible to note that with the SAS simulations the
predicted values compared well with the experimental 4 CONCLUSIONS
data even though a premature break down of the
turbine performances was predicted. In this study a homogeneous multiphase model, used
In Fig. 9 the cavitation patterns obtained with in combination with three previously calibrated mass
RANS and SAS simulations are qualitatively transfer models, was evaluated for the numerical
compared with the available experimental recording prediction of the cavitating flow around a marine
for σ = 0.52. It is possible to note that in the case of propeller and Kaplan turbine runner.
the steady state RANS simulation the extension of the The simulations were carried out considering two
cavitation phenomenon was under-predicted. This is different levels of turbulence modelling: the industrial
related to the over prediction of the draft tube losses workhorse steady state RANS approach and the more
which lead to an inaccurate pressure distribution in advanced unsteady SAS approach. In both the cases
the turbine. Actually, in the case of the steady state the governing equations were solved using ANSYS-
RANS simulations for a given cavitation number the CFX 15 commercial CFD solver.
pressure in the runner region was higher compared to The numerical results were compared with the
the experimental one and consequently the predicted available experimental data.
cavitation phenomenon was less severe. For the propeller, the thrust obtained with the
Finally, it is worth clarifying that steady- RANS simulations, performed along with the three
state simulations did not predict the same extent different mass transfer models, compared well with
of cavitation on all blades due to the frozen rotor the available experimental data even though the
conditions, imposed at Guide Vanes-Runner and experimental cavitation patterns were not perfectly
Runner-Draft tube interfaces, which somehow matched. Except for a particular flow condition the
preserved differences in circumferential direction. cavitation patterns associated with the different mass
Numerical Predictions of Cavitating Flow Around a Marine Propeller and Kaplan Turbine Runner with Calibrated Cavitation Models 551
Strojniški vestnik - Journal of Mechanical Engineering 64(2018)9, 543-554
transfer models were very similar to each other. From P pressure, [Pa]
an additional investigation performed using the SAS Pv saturation vapour pressure, [Pa]
approach a better resolution of the cavitating tip- Poutlet pressure on outlet boundary, [Pa]
vortex flow was obtained. Q flow rate, [m3/s]
Also for the Kaplan turbine the three different Rnuc radius of a nucleation site, [m]
mass transfer models predicted similar shapes of SM source term,
the cavitation patterns in the case of the RANS T propeller thrust, [N]
simulations. Nevertheless, using the RANS approach, U velocity, [m/s]
mainly due to the overestimation of the draft tube U∞ free stream velocity, [m/s]
losses, the turbine efficiency was not properly VA propeller advance velocity, [m/s]
predicted. Better prediction of the draft tube losses, as c0.7 chord length (at 0.7/(D/2)), [m]
well as of the efficiency, was obtained using the SAS fv vapour mass fraction,
approach even though in this case a premature break g gravity acceleration, [m/s2]
down of the performance was obtained. k turbulence kinetic energy, [m2/s2]
From the overall results it seems that the m mass transfer rate, [kg/(m3s)]
calibrated mass transfer models in question can be m + mass transfer rate, vapour to liquid, [kg/(m3s)]
successfully applied to the numerical predictions of m – mass transfer rate, liquid to vapour, [kg/(m3s)]
the cavitating flow around a marine propeller and n rotational speed, [rps]
Kaplan turbine. It seems that for the prediction of the rnuc nucleation site volume fraction,
machine’s performance they can guarantee similar t∞ mean flow time scale, [s]
levels of accuracy even though differences in the ρ mixture density, [kg/m3]
predicted cavitation patterns can be observed. ρl, ρv liquid density, vapour density, [kg/m3]
Finally, from this study it emerges that for
η turbine efficiency,
improving the accuracy of numerical predictions,
φ turbine flow coefficients,
SAS simulations could represent a good compromise
φBEP turbine flow coefficients at local best
between standard RANS simulations and the
efficiency point,
computationally more demanding and more accurate
α vapour volume fraction,
large eddy simulations (LES).
γ liquid volume fraction,
𝜅 surface tension, [N/m]
5 ACKNOWLEDGEMENTS
μ mixture dynamic viscosity, [Pa s]
The research leading to these results received funding μl liquid dynamic viscosity, [Pa s]
from the People Programme (Marie Curie Actions) μv vapour dynamic viscosity, [Pa s]
of the European Union’s Seventh Framework σ turbine cavitation number,
Programme FP7/2007-2013/ under REA grant σn propeller cavitation number,
agreement n°612279. From the Slovenian Research τ stress tensor, [N/m2]
Agency ARRS - Contract No. 1000-15-0263. ω turbulence frequency, [1/s]
ψ turbine energy coefficient
6 NOMENCLATURE ψBEP turbine energy coefficient at local best
efficiency point
Ce empirical coefficient (FCM model), NPSE net positive suction energy, [m2/s2]
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