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International Journal of Engines
was evaluated by using an eddy current probe (with a • a short inlet pipe (from section 0 to 1); the end section of
precision of 0.009% of the full scale) mounted close to the the inlet pipe is characterized by a sudden area contraction,
compressor wheel. Two high speed synchronized data taking into account the impeller eye obstruction. This will
acquisition cards were used to record instantaneous signals. A cause some inlet losses, as explained in the following;
Hall sensor mounted on the driving cam shaft of the cylinder
head provided a trigger signal, corresponding to 40 crank • the impeller (from section 1 to 2), consisting of Z rotating
angle degrees after TDC related to cylinder no. 1 overlap. pipes, Z being the number of blades. The profile of the blade-
to-blade duct is assigned in terms of the local blade angle,
All measured signals reported in the paper are an ensemble equivalent and hydraulic diameters and radius. The latter are
average of several complete cycles. estimated perpendicularly to the meanline profile. Since
upstream and downstream conditions are the same, the flow
rate within a single impeller duct is really computed and then
1D COMPRESSOR MODEL multiplied by the number of blades. A numerical procedure
In the following, the 1D compressor model is recalled, has been developed to reproduce the 3D impeller geometry
including a brief description of its geometrical basing on a reduced set of data (inlet and outlet flow angles,
schematization, of the 1D flow equations holding in diameters, number of blades, etc.), which can be measured
stationary and rotating ducts, and of the boundary conditions easily on the impeller wheel. The comparison between the
and flow losses. A more detailed model discussion can be actual impeller geometry and the CAD reproduced
found in [17]. reconstruction is reported in Figure 4. The equivalent 1D
profile of blade-to-blade duct, to be employed in 1D flow
GEOMETRICAL MODEL equations, is then easily derived from the 3D CAD model;
The compressor is schematized as follows (Fig. 3): • the vaneless diffuser (from section 2 to 3). It is considered
as a diverging pipe of constant width in the radial direction;
(1)
SLIP EFFECT
Even under ideal (inviscid) conditions, the flow leaving the
impeller is said to ‘slip’. Secondary flows (relative eddies)
determine an increase of the exit flow angle, respect to the
blade angle. As a consequence, the tangential component
(c2u‘) varies with respect to the ideal value c2u, determining a
decrease of the energy transfer, quantified by the slip factor,
σ:
(3) (5)
(4) (8)
INLET AND INCIDENCE LOSSES cinc being the tuning constant affecting the total incidence
First of all, the absolute velocity c1 is computed in the end loss.
section of the inlet pipe. The flow is assumed to non-
isentropically expand up to the impeller eye section. Part of RECIRCULATION FLOW
the produced kinetic energy is assumed to be dissipated at A recirculating flow from the impeller outlet occurs near the
constant pressure, as a consequence of the impeller eye case tip clearance because of pressure difference. It alters the
obstruction. The absolute and peripheral velocities at the total temperature at the inlet and the related work exchange.
impeller inlet so define the flow angle characterizing the The recirculating flow is computed as a function of the
direction of the approaching flow. When the flow angle φ1 instantaneous pressure difference downstream and upstream
differs from the blade angle φ1c, it is assumed that the kinetic the impeller.
energy associated with the flow component normal to the
blade direction w1n (Fig. 5) is completely dissipated at a ADDITIONAL IMPELLER LOSSES
constant pressure (NASA shock model) [24]. Secondary loss mechanisms are considered in the model, too.
The first concerns the flow separation deriving from a high
blade loading level. Leakage losses due to blades tip
clearance are taken into account. Moreover, losses due to
local sonic flow on the blade surface are evaluated. More
details are reported in [17, 24].
VOLUTE LOSSES
The kinetic energy associated with the radial velocity
component at volute inlet is assumed to be completely
dissipated. The one associated to the tangential velocity
component is indeed assumed to be partly lost at low flow
rate according to [25].
Figure 8. Effect of varied inlet flow angle, due to an upstream swirling flow, on the performance maps.
[27, 28]. Experimental data on the pre-whirl flow can be as well, whilst displacing the surge margin to the left. These
obtained introducing a swirl meter in the upstream pipe. This results qualitatively agree with the experimental findings in
information can be utilized in the 1D model to estimate the [27] and [28].
actual inlet flow angle and, correspondingly predict the new
operating conditions. Figure 8 shows an example of the In the present case, the experimental maps in Fig. 6 were
influence of the inlet flow angle on the performance maps. A directly measured coupled to the complete intake system. For
negative pre-whirl (defined as pre-whirl in the same sense of this reason, they reflect the actual compressor behavior on the
the compressor rotation) determines lower inlet flow angles considered engine. In addition, due to the presence of a
and relative velocities at the impeller eye. Consequently, it straight pipe of about 7 diameters length upstream to the
reduces the mass flow rate range and the adiabatic efficiency, compressor, no swirl flow was assumed in the computed data.
UNSTEADY OPERATION RESULTS • Discharge pressure in the downstream plenum: this value is
imposed as boundary condition for the outlet flow through
The results in Fig. 6 authorize to conclude that a good the valves.
reproduction of the steady operating condition has been
obtained in the tested compressor operating range and the • Throttle opening: both tests and numerical analyses are
model can be hence employed to analyze its unsteady carried out at WOT conditions. The small losses introduced
operation, too. To this aim, a 1D representation of the by the fully opened throttle are however considered in the
upstream and downstream compressor circuit is realized, as model.
shown in Fig. 9. • Valve lift profile and discharge coefficients: actual values of
the valve lift are employed in the calculations. Experimental
values of the discharge coefficient were provided by the
engine manufacturer.
Figure 9. 1D representation of the compressor test In order to verify the capabilities of the model in capturing
bench, for its unsteady analysis the unsteady compressor behavior, two different numerical
procedures are utilized: a classical approach, based on the
employment of the tuned steady map in Fig. 6, and the more
Three different operating conditions (CASES A, B and C) are refined unsteady procedure, based on the direct time
analyzed. They are characterized by different values of the integration of systems (1), (2) and (3). In the following
pressure in the downstream plenum, realizing different values figures, the above approaches are referred as ‘Steady Map
of the average mass flow rate. Apart from the whole Model’ and ‘Unsteady Model’, respectively.
geometrical details of the external circuit, the sole input data
to the model are: Concerning the operating point A, Fig. 10 reports the
• The compressor rotational speed: the experimental analysis comparisons between numerical and experimental pressure
highlighted a negligible variation of this parameter; for this fluctuations in five different measuring stations located along
reason the latter is kept constant in the model. the external circuit (see Fig. 2), namely: the static pressure
signal downstream the throttle valve (a), the intercooler inlet
• The engine crankshaft rotational speed: this parameter (c) and outlet (b), and the total pressure profiles upstream (e)
defines the opening and closing frequency of the intake and downstream (d) the compressor. As expected, a similar
valves and controls the pressure pulsation in the external pressure wave is repeated every 180° crank angles, since the
circuit. pulse shape is related to the valve opening frequency [10],
which was kept constant during the investigation. The
• Ambient pressure and temperature: these values are pressure wave highlights a shape change due to both the
imposed as boundary condition in the first section of the inlet superimposed variation in the pipe geometry, to wave
pipe, A1. reflection phenomena, and to the concentrated or distributed
In order to further underline the consideration here discussed, Fig. 12d. The map-based model (dashed loop) only partly
it should be remembered that, in a two-stage boosting system, describes the above fluctuations. In addition, a further slight
the employment of a classical map-based approach, without increase in the downstream plenum pressure (from 1.303 bar
any correction, may determine substantial errors at the inlet in CASE C to 1.312 bar), induces a reduction of the mass
section of the high pressure compressor, which reflect in a flow rate, beyond the minimum stable value reported in the
different low pressure compressor behavior and overall map (∼58 kg/h) at the considered speed. In this case, the lack
pressure ratio. In a two-stage boosting system, moreover, of experimental data in the unstable zone absolutely requires
when packaging the 2 turbochargers as closely as is necessary a map extrapolation. On the contrary, the unsteady model
to fit in the car, secondary interstage flow structures (swirling allows to describe the operation in the unstable zone, too
flows) may affect overall efficiency and pressure ratio [29]. (dashed loop with circles). At the lowest mass flow rate, a
The latter, as already pointed out, can indeed be introduced in pressure decrease can now be detected, indicating a close-to-
the 1D model in terms of modified inlet flow angles. surge operation. Any additional pressure increase in the
downstream tank will induce a reverse flow through the
Finally, in Fig. 15, with reference to CASE C, the compressor and the beginning of surging loops. Although still
instantaneous inlet mass flow rate is plotted as a function of not ready to handle reverse flow situations, the unsteady
the instantaneous compressor outlet pressure. On the same model shows the potential to account for local surging
graph, both the stable and the unstable branches of the 1D operation, too.
computed characteristic lines are drawn, too. A typical
unsteady pressure loop occurs in counterclockwise direction.
It consists of a ‘Main Loop’, directly related to the pressure
wave traveling upstream as a consequence of valve opening,
and a ‘Secondary Loop’, due to the wave reflections in the
external circuit. The unsteady model is able to reproduce the
experimental main loop, while pressure fluctuations are
slightly overestimated in the secondary one, as also shown in
CONCLUSION pressure and mass flow rate fluctuations occurring when the
compressor is coupled to the intake circuit of a small-size
In the present paper a detailed experimental analysis and an spark-ignition engine. The above data were then employed to
advanced modeling approach to characterize both the steady validate a recently proposed 1D compressor model based on
and the unsteady behavior of a turbocharger compressor have the direct modeling of the work exchange and main losses
been described. The experimental analysis allowed to occurring inside the device.
measure the steady compressor map and the instantaneous
• The introduction of a small length virtual pipe, accounting 7. Capobianco, M., Gambarotta, A., “Performance of a twin-
for the time delay due to the wave propagation inside the entry automotive turbocharger turbine”, ASME Energy-
device can give results quite comparable with the proposed Sources Technology Conference and Exhibition, paper 93-
1D compressor model. The correct specification of the pipe ICE-2, Houston, 1993.
length and diameter however requires roughly the same 1D 8. Capobianco, M., Marelli, S., “Waste-Gate Turbocharging
geometrical schematization of the device. The above time Control in Automotive SI Engines: Effect on Steady and
delay is indeed automatically captured in the 1D model and is Unsteady Turbine Performance,” SAE Technical Paper
particularly important at high engine/turbocharger speeds, 2007-01-3543, 2007, doi:10.4271/2007-01-3543.
and in a two-stage turbocharging system. 9. Capobianco, M., Polidori, F., “Experimental Investigation
• Finally, the proposed model seems to have the potential in on Open Waste-Gate Behaviour of Automotive
describing surging operation, too: in these conditions, the Turbochargers,” SAE Technical Paper 2008-36-0052, doi:
absence of steady map data simply implies the unfeasibility 10.4271/2008-36-0052.
of map-based simulations. 10. Capobianco, M., Marelli, S., “Experimental Investigation
into the Pulsating Flow Performance of a Turbocharger
The integration of the experimental activity with the Turbine in the Closed and Open Waste-Gate Region”, 9th
numerical analysis presented in the paper represents a International Conference on Turbochargers and
methodology that can be helpful employed during the design Turbocharging, London, 2010.
process for intake systems of internal combustion engines.
The good accuracy of the presented numerical results of 11. Bozza, F., Gimelli, A., Strazzullo, L., Torella, E.,
course implies that experimental work can be minimized and Cascone, C., “Steady-State and Transient Operation
cost saved in the end. Simulation of a ‘Downsized’ Turbocharged SI Engine,” SAE
Technical Paper 2007-01-0381, 2007, doi:
In the future, the introduction of proper loss correlation 10.4271/2007-01-0381.
holding for reverse flow conditions, will allow to employ the 12. Martin, G., Talon, V., Higelin, P., Charlet, A., Caillol,
presented model to describe local surging operation, too. C., “Implementing Turbomachinery Physics into Data Map-
H Z
Total enthalpy per unit mass Number of impeller blades
k Greeks
Specific heat ratio α
Duct area variation term
L
meanline Length γ
Specific heats ratio
M
Mach number δ
Radius variation term along the meanline of the
n impeller duct
Engine Speed
ρ
p Density
Pressure, pressure difference
σ
q Slip factor
Rate of heat exchange
R Crank angle
Gas constant
Ω
r Area of a duct section
Radius
Subscripts
S 0
Vector of the source terms Total conditions, Compressor inlet
s 1
Impeller curvilinear abscissa Intake duct outlet, Inducer inlet
T 2
Temperature Impeller outlet, Diffuser inlet
u 3
Tangential blade velocity Diffuser outlet, Volute inlet
w 4
Relative velocity Volute outlet
W C
Vector of the conservative variables for rotating ducts Referred to stationary ducts
ex Superscripts
Outlet ’
Effective flow condition (after slip)
in
Inlet
CONTACT
i Fabio Bozza (Full Professor), Vincenzo De Bellis (PhD
Impeller Student)
(DIME). Università di Napoli “Federico II”.
Via Claudio 21, 80125 Napoli (Italy).
loss
Tel. +39 081 7683274 - 3264
Referred to a generic loss mechanism
Fax: +39 081 2394165
fabio.bozza@unina.it
r vincenzo.debellis@unina.it
Radial velocity component, spatial derivative for
vaneless diffuser Massimo Capobianco (Full Professor), Silvia Marelli
(Research Assistant)
(DIMSET). Università di Genova.
ref
Via Montallegro 1, 16145 Genova (Italy).
Reference conditions
Tel. +39 010 3532466 - 2454
Fax: +39 010 3532566
s massimo.capobianco@unige.it
Spatial derivative for rotating ducts, Case silvia.marelli@unige.it
t
Temporal derivative
u
Tangential velocity component
x
Spatial derivative for stationary ducts
W
Referred to rotating ducts