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Aerodynamics of Centrifugal Turbine Cascades
The centrifugal turbine architecture represents a promising solution for Organic Rankine
Cycle (ORC) Systems, in the small-to-medium power range. ORC expanders operate with
very high volumetric expansion ratios, which can be better accomplished in a centrifugal
machine thanks to the increase of passage area along the
ow path. Furthermore the
centrifugal arrangement allows for assembling a multiplicity of stages in a relatively
compact machine, thus reducing the expansion ratio per stage, with benecial eects on
the performances in both design and o-design operating conditions.
A preliminary design exercise proposed by the authors [1] has recently shown the po-
tential of multistage centrifugal turbines, composed by a succession of xed nozzles and
rotors, for medium power applications (about 1MWel). By limiting the
ow regime to
transonic or slightly supersonic conditions, purely converging ducts can be used with
a certain degree of post-expansion, if necessary; the resulting
ow conguration, char-
acterized by weak oblique shocks, leads to a promising design eciency above 85% ;
the absence of converging-diverging ducts allows to negotiate a certain degree of power
control without the onset of normal shocks which, instead, result in a dramatic increase
of aerodynamic losses in axial ORC turbines.
These promising features, however, were based on estimates performed with preliminary
design tools. In this perspective, the aerodynamic performances of centrifugal cascades
represent the most critical issue, since very few information are available in literature
for centrifugal turbines. In absence of experimental data on this kind of machines, the
correlations used to estimate the aerodynamic losses and the
ow deviation must be
assessed with high-delity computational methods.
In the present work the aerodynamics and performance of centrifugal turbine cascades
are studied by applying a three-dimensional CFD model. The study is focused on the
sixth stage of the transonic centrifugal turbine proposed in [1]. At rst a simple but
eective blade design technique, introduced by the authors in [2], is recalled and applied
to the present conguration. The resulting stage is then analyzed focusing on the
prole aerodynamics, considering both stator and rotor blade rows (in this latter case
discussing the eects of the Coriolis acceleration). Finally the morphology of secondary
ows and the three-dimensional eects of the channel
aring are investigated
Nonideal Compressible Fluid Dynamics of Dense Vapors and Supercritical Fluids
The gas dynamics of single-phase nonreacting fluids whose thermodynamic states are close to vapor-liquid saturation, close to the vapor-liquid critical point, or in supercritical conditions differs quantitatively and qualitatively from the textbook gas dynamics of dilute, ideal gases. Due to nonideal fluid thermodynamic properties, unconventional gas dynamic effects are possible, including nonclassical rarefaction shock waves and the nonmonotonic variation of the Mach number along steady isentropic expansions. This review provides a comprehensive theoretical framework of the fundamentals of nonideal compressible fluid dynamics (NICFD). The relation between nonideal gas dynamics and the complexity of the fluid molecules is clarified. The theoretical, numerical, and experimental tools currently employed to investigate NICFD flows and related applications are reviewed, followed by an overview of industrial processes involving NICFD, ranging from organic Rankine and supercritical CO2 cycle power systems to supercritical processes. The future challenges facing researchers in the field are briefly outlined
A Novel Interpolation-Based Method for Thermodynamic Properties Calculation in Dense-Gas Flow Simulations
The reliable modeling of real-gases is nowadays of great importance in many industrial
applications, especially in the energy eld. The prediction of real-gas thermodynamic
properties based on the direct use of an equation of state (EoS) and of its derivatives,
implies a high computational cost in case of numerical studies, when a set of governing
equations is iteratively solved (e.g. detailed CFD calculations, dynamic plant simula-
tions).
A dierent approach is represented by the use of look-up tables. In the thermodynamic
regions of interest, a grid of nodal points (storing all thermodynamic and transport
properties) is preliminary built. Within the discretized domain, the properties in any
point are computed using fast interpolation methods, with a dramatic reduction in
computational time [2, 3]. However, a proper technique has to be applied to guarantee
the thermodynamic consistency, which is not automatically satised as in the case of
direct EoS application. Finally the desired accuracy can be addressed by selecting the
number of nodes and the interpolation scheme.
This paper presents a novel interpolation method for property calculation of real gases
using look-up tables. Herein, any grid has been built using accurate EoS implemented in
the software FluidProp [4]. The method assigns a selected functional form to the internal
energy e as a function of the specic volume v and of the specic entropy per unit mass
s (e = e(v; s)). Within any cell of the thermodynamic domain, the coecients of the
functional form are calculated referring to the local grid data; therefore, a fundamental
relation is locally established, in such a way that any thermodynamic property of any
internal point is intrinsically consistent. A similar approach has been adopted also for
computing the transport properties. Two dierent functional forms are assigned to the
dynamic viscosity and to the thermal conductivity k as a function of the specic
volume and of the specic entropy per unit mass ( = (v; s), k = k(v; s)); the two sets
of coecients are then computed at any cell on the basis of the transport properties
stored within local grid points.
The method is here presented for the siloxane MDM and for the carbon dioxide CO2.
Both single and two-phase regions close to vapor saturation line have been explored,
for reduced temperature ranging between Tr ' 0:6 and Tr ' 1:05. The accuracy and
the computational cost of the method have been assessed in comparison with those
resulting from direct EoS computation. As an example of application, the through
ow
calculation of a centrifugal turbine operating with MDM is also presented
Design, simulation, and construction of a test rig for organic vapors
A blow-down wind tunnel for real-gas applications has been designed, validated by means of dynamic simulation, and then built. The facility is aimed at characterizing an organic vapor stream, representative of the expansion taking place in organic Rankine cycle (ORC) turbines, by independent measurements of pressure, temperature, and velocity.
The characterization of such flows and the validation of design tools with experimental data, which are still lacking in the scientific literature, is expected to strongly benefit the performance of future ORC turbines. The investigation of flow fields within industrial ORC turbines has been strongly limited by the unavailability of calibration tunnels for real-gas operating probes, by the limited availability of plants, and by restricted access for instrumentation. As a consequence, it has been decided to design and realize a dedicated
facility, in partnership with a major ORC manufacturer. The paper thoroughly discusses the design and the dynamic simulation of the apparatus, presents its final layout, and shows the facility “as built”. A straight-axis planar convergent-divergent nozzle represents
the test section for early tests, but the test rig can also accommodate linear blade
cascades. The facility implements a blow down operating scheme, due to high fluid density
and operating temperature, which prevent continuous operation because of the prohibitive
thermal power required. A wide variety of working fluids can be tested, with
adjustable operating conditions up to maximum temperature and pressure of 400 C and
50 bar, respectively. Despite the fact that the test rig operation is unsteady, the inlet nozzle
pressure can be kept constant by a control valve. In order to estimate the duration of
the setup and experimental phase, and to describe the time evolution of the main process
variables, the dynamic plant operation, including the control system, has been simulated.
Design and simulation have been performed with both lumped-parameter and 1D models,
using siloxane MDM and hydrofluorocarbon R245fa as the reference working fluids,
described by state-of-the-art thermodynamic models. Calculations show how experiments
may last from 12 seconds up to several minutes (depending on the fluid and test pressure),
while reaching the experimental conditions requires few hours, consistently with the performance
of daily-based experiments. Moreover, the economic constraints have been met
by the technical solutions adopted for the plant, allowing the construction of the facility
Entropy generation in laminar boundary layers of non-ideal fluid flows
This paper documents a numerical study on entropy generation in zero-pressure gradient, laminar boundary layers of adiabatic non-ideal compressible fluid flows. The entropy generation is expressed in terms of dissipation coefficient and its dependency on free-stream Mach number, fluid molecular complexity, and flow non-ideality is investigated systematically by means of a boundary layer code extended to treat fluids modeled with arbitrary equations of state. The results of the study show that the trend of dissipation coefficient follows that of an incompressible flow for complex fluid molecules like siloxanes in all thermodynamic and flow conditions. For simpler fluids like CO the trend becomes inversely proportional to the free-stream Mach number and the value can significantly reduce in the non-ideal flow regime, where strong thermo-physical property gradients occur near the wall.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Flight Performance and Propulsio
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