Sveučilište u Zagrebu
Vizualni identitet
Priručnik grafičkih standarda za
oblikovanje vizualnih identiteta sastavnica
Znak Sveučilišta
Verzija 2
c/b pozitiv
2.2.
Crno – bijeli pozitiv znaka Sveučilišta u Zagrebu (verzija
2) standardno je reproduciran u crnoj boji Pantone
Black, odnosno njenom cmyk ekvivalentu.
Detaljne specifikacije nalaze se u poglavlju Program
boja Priručnika grafičkih standarda za oblikovanje
vizualnih identiteta sastavnica.
FSB
Radi kvalitete i preciznosti reprodukcije, znak
Sveučilišta nije dozvoljeno rekonstruirati (precrtavati,
skenirati...) Vektorizirani znak nalazi se na elektroničkom
mediju koji je sastavni dio Priručnika grafičkih
standarda za oblikovanje vizualnih identiteta sastavnica.
The Harmonic Balance Method in foam-extend
University of Zagreb
Faculty of Mechanical Engineering and Naval Architecture
Department of Energy, Power Engineering and Environment
korekcija znaka za smanjenje od 14 mm
9
Gregor CVIJETIĆ
ERCOFTAC Centrifugal
Pump
KP505 Propeller
Case Setup
A 3D propeller open water test case was
chosen to demonstrate the capabilities of
the Harmonic Balance method in a turbomachinery environment with single rotor.
Turbulence is modelled using the standard
k − ε model, with the prescribed rotational
speed of 60 rpm. The domain is presented
in Figure 4, with radius being r = 10R,
where R is the propeller radius.
ERCOFTAC centrifugal pump is simulated
using Harmonic Balance method and compared against conventional transient solver.
The geometry is a 2D simplified model of a
centrifugal turbomachine, consisting of rotor
(inner) and stator (outer) part. The rotation
speed is 2000 rpm, with k − ε model used
for turbulence. Additionally, in Harmonic
Balance simulations multiple frequency approach was used to account for different
dominant frequencies in the stator and rotor.
Figure 4: KP505 test case domain.
Results
ABSTRACT
This poster presents the capabilities of the
OpenFOAM’s Harmonic Balance solver for
turbomachinery CFD simulations, developed within Prof. Jasak’s CFD group.
The method solves incompressible turbulent periodic flows, while special attention
is given to development of turbomachinery applications. It is implemented and
tested in foam-extend, a community-driven
fork of the open source software OpenFOAM. The Harmonic Balance model is
used for accurate and efficient simulations
of incompressible turbulent periodic flows,
and therefore validated using ERCOFTAC
centrifugal pump case and KP505 propeller
test case. Results are presented and compared with conventional transient simulation. Furthermore, obtained convergence
with increase in number of used harmonics
is presented.
INTRODUCTION
The Harmonic Balance method is a quasisteady state method developed for simulating non-linear temporally periodic flows. It
is based on the assumption that each primitive variable can be accurately represented
by a Fourier series in time, using first n harmonics and the mean value. Such assumption leads to transformation of a single transient equation into a coupled set of steady
state equations, each for a different time
instant. The benefit of the method, compared to steady state methods, is the ability
to capture the transient effects of periodic
flows, while providing significant speed-up
compared to transient simulation.
8th Floor CFD@FSB
Zagreb, 2017
Harmonic Balance simulations were run using 1 and 2 harmonics, comparing the efficiency, head and torque, as well as the local
transient effects in the blade passage with
transient simulation results.
Figure 1: Transient solution.
Open Water Test
Figure 2: Harmonic Balance
with 1 harmonic.
Figure 3: Harmonic Balance with 2 harmonics.
Local transient effects are presented in Figures 1-3. Figure 1 presents the transient
simulation rotor wakes. Wakes can be noticed in the Harmonic Balance solution, Figures 2 and 3, but are not resolved as accurate due to small number of harmonics used.
Table 1: Pump characteristics comparison
Transient HB, 1h error, % HB, 2h error, %
Efficiency 89.72
88.80
1.0
89.76
0.0
t = T3
Head
81.48
81.80
0.4
80.45
1.3
0.0297 0.0302
1.7
0.0294
0.9
Torque
Efficiency 89.92
88.78
1.3
89.81
0.1
t = 2T3
Head
81.48
81.85
0.4
80.6
1.1
Torque
0.0296 0.0302
2.0
0.0295
0.4
Efficiency 89.83
88.85
1.1
89.71
0.1
t=T
Head
81.49
81.79
0.4
80.39
1.3
Torque
0.0297 0.0302
1.6
0.0294
1.0
Table 1 presents a comparison of pump
characteristics obtained using the Harmonic
Balance and a transient solver. Results are
presented at three time instants. It is shown
that all errors are lower than 2%, showing
the capability and accuracy of the Harmonic
Balance method. It should be noted that the
obtained Harmonic Balance simulation with
2 harmonics demonstrated the CPU time
speed-up by factor of 30.
The main focus of the presented test case is
the convergence of results with increasing
number of harmonics. For one flow regime
u
given by advance coefficient J = nD
= 0.5,
four simulations are performed: with 1, 2, 4
and 7 harmonics. Figures 5-8 show the velocity field for each case, where the increasing level of resolved wakes can be noticed.
Figure 5: 1 harmonic,
Figure 6: 2 harmonics,
Figure 7: 4 harmonics,
Figure 8: 7 harmonics.
Table 2 shows the comparison of thrust and
torque coefficients within a period. For all
cases, average Kt and Kq coefficients are
obtained and compared to experimental
results. It can be noticed that the achieved
convergence is oscillatory, with experimental values being Kt = 0.285 and Kq = 0.0437,
and maximum error being 4.67%.
Table 2: Propeller coefficients comparison
1 harmonic
2 harmonics 4 harmonics 7 harmonics
Kt
Kq
Kt
Kq
Kt
Kq
Kt
Kq
Avg. 0.2914 0.0444 0.293 0.0457 0.290 0.0448 0.286 0.0449
Error, % 2.26
1.61
2.81
4.67
1.89
2.55
0.26
2.82
Conclusion
The Harmonic Balance method is presented
for unsteady periodic non–linear flows in turbomachinery applications. The comparison
presented shows that the Harmonic Balance
method is capable of capturing the transient
flow field accurately even in multi-frequential
environment. What is more, it can be used
as a part of a design process with accurate
flow predictions and significant CPU time
savings.
Supervisor: Prof. Hrvoje Jasak
www.fsb.hr/cfd
Feel free to contact us at [email protected] or take a look at our YouTube channel: 8th Floor CFD@FSB.