1,721,016 research outputs found
UNSTRUCTURED PERIODIC GRID GENERATION AROUND 2D TURBINE CASCADES
No full textA novel grid generation algorithm for periodic unstructured grid around two-dimensional highly-staggered turbine cascades, including multiply connected blade geometries, is presented. The idea is to generate the mesh in a transformed space in which the periodic boundaries are coincident and internal to the computational domain so that no special treatment along these curves is required. The mesh in the transformed u-v space is computed by means of front-advancing/Delaunay technique and the resulting grid is transformed back into the x-y space of physical variables after introducing a suitable cut, which translates to periodic boundaries in the x-y plane. The cut is not arbitrary and it is automatically managed by the algorithm. The proposed transformation is conformal and therefore no elements are distorted in the process. In this way, the prescribed element size and mesh quality are easily attained and the uniqueness of the periodic nodes is guaranteed by the fact that they are indeed coincident in the space u-v. Numerical simulations of a VKI LS-89 turbine blade are presented to support the present approach
A Novel Interpolation-Based Method for Thermodynamic Properties Calculation in Dense-Gas Flow Simulations
No full textThe 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
An implicit three-dimensional discontinuos Galerkin method for the numerical solution of the Navier-Stokes equations on hybrid grids
No full textECCOMAS CFD2001, University of Wales Swansea U
Influence of Thermodynamic Models in Two-Dimensional Flow Simulations of Turboexpanders
No full textThis paper presents a quantitative comparison of the effect of using thermodynamic models of various degrees of complexity if applied to fluid-dynamic simulations of turboexpanders operated at conditions affected by strong real-gas effects. The 2D flow field of a standard transonic turbine stator is simulated using the state-of-the-art inviscid ZFLOW computational fluid-dynamic solver coupled with a fluid property library containing the thermodynamic models. The considered thermodynamic models are, in order of increasing complexity, the polytropic ideal-gas (PIG) law, the Peng-Robinson-Stryjek-Vera (PRSV) cubic equation of state, and the highly accurate multiparameter equations of state (MPEoSs), which are adopted as benchmark reference. The fluids are steam, toluene, and R245fa. The two processes under scrutiny are a moderately nonideal subcritical expansion and a highly nonideal supercritical expansion characterized by the same pressure ratio. Using the PIG model for moderately nonideal subcritical expansions leads to large deviations with magnitudes of up to 18-25% in density, sound speed, velocity, and total pressure loss, and up to 4-10% in Mach number, pressure, temperature, and mass flow rate. The PIG model applied to highly nonideal supercritical expansions leads to a doubling of the deviations' magnitudes. The advantage of the PIG model is that its computational cost is roughly 1/11 (or 1/3 if saturation-checks in the MPEoS are omitted) of the cost of the MPEoSs. For the subcritical expansion, adopting the physically more correct cubic PRSV model leads to comparatively smaller deviations, namely, <2% (toluene and R245fa) and <4% (steam) in all flow parameters, except for the total pressure loss error, which is comparable to that of the PIG model. The PRSV model is reasonably accurate even for the highly nonideal supercritical expansion, for which the errors are at most 4%. The computational cost of the PRSV model is roughly nine times higher than the cost of the PIG model (or twice as high if saturation-checks in the PRSV are omitted). Contrary to low-complexity fluids like water, for complex fluids like toluene and R245fa the deviations in density, speed of sound, and velocity ensuing from the use of the PIG model vary strongly along the isentropic expansions. This invalidates the approach commonly used in practice of correcting the PIG model with a properly chosen constant compressibility factor. [DOI: 10.1115/1.3192146
High-Order Discontinuous Galerkin approximation of compressible flows on polyhedral grids
No full textSolutori impliciti in un metodo agli elementi finiti discontinui applicato a flussi turbolenti
No full text55° Congresso nazionale Associazione Termotecnica Italiana, Bari, Mater
A penalty formulation for the throughflow modeling of turbomachinery
No full textDespite the widespread use of fully three-dimensional Computational Fluid Dynamics (CFD) techniques, axisymmetric flow models still represent a key tool in turbomachinery design. In this paper, a novel method for the numerical solution of axisymmetric flow models for turbomachinery is presented and demonstrated for two cases, both relevant for the industrial perspective. The key feature of the proposed method is that the flow tangency condition to the blade mean line is enforced with a penalty term, which can also be interpreted as an immersed boundary technique. Differently from the techniques commonly applied for the solution of this kind of flows, the proposed method does not require additional constraint equations to be solved in bladed regions and is therefore very simple to be implemented into existing axisymmetric CFD codes. The techniques employed to deal with flows of high incidence angle (misalignments between the actual flow and the direction imposed by the blade) and to account for the aerodynamic losses and the blade blockage are also thoroughly discussed.
The method has been implemented as an extension of the zFlow code for the numerical solution of the Euler equations in cylindrical coordinates, which is based on an hybrid finite element/finite volume space approximation, an implicit time integration scheme, and can deal with fluids of arbitrarily complex equations of state. The details of the numerical method are fully described in the paper.
The performance of the developed code is demonstrated by the results obtained in the simulation of a single-stage axial fan, compared against a fully three-dimensional CFD simulation. The potentialities for more complex transonic flow conditions are finally demonstrated by the calculation of a double-stage low pressure steam turbine
Consistent look-up table interpolation method for real-gas flow simulations
Full text linkNowadays the reliable modeling of real fluid flows is of paramount importance in many industrial
applications, especially in the energy field with the growing diffusion of Organic Rankine Cycles,
supercritical CO2 compressors, and advanced refrigeration systems. In these applications the assumption
of flow ideality is profoundly inaccurate and may lead to erroneous physical interpretations. As a
consequence thereof, various thermodynamic models have been recently developed for real gases and
a number of tools are by now available to accurately predict the thermodynamic properties of fluids in
presence of relevant non-ideal effects. However, these thermodynamic libraries are frequently
computationally inefficient when coupled with existing simulation codes, such as in process modeling
and computational fluid-dynamics (CFD).
An effective alternative is proposed in this paper. The equations of state embedded in the thermodynamic
programs are used, at preliminary level, to construct a grid of nodes storing a subset of
thermo-physical properties, i.e. v; s; e; k; l, required by the method for a given region of interest. Then,
an interpolation-based method is conceived for determining the remaining properties in any other point.
A key feature is as follows: the nodal values of the basic thermodynamic quantities are used to locally
construct, i.e., within each cell of the table, a model of the fundamental relation, assuming a differentiable
functional form of at least C2 class.
The presented Look-up Table (LuT) approach is intrinsically consistent and guarantees thermodynamic
stability, with inherent high accuracy and very limited computational costs, as demonstrated by the quantitative
examples reported in the paper. As a final step, the LuT method is coupled with two in-house flow
solvers and applied to simulate real gas transonic flow in Organic Rankine Cycle turbines; a comprehensive
assessment of the approach is provided by comparison with direct equations of state implementation
Real-Gas Effects in Organic Rankine Cycle Turbine Nozzles
No full textOrganic Rankine cycle turbogenerators are a viable option as stationary energy converters for external heat sources, in the low power range (from a fewkWup to a few MW). The fluid-dynamic design of organic Rankine cycle turbines can benefit from computational fluid dynamics tools which are capable of properly taking into account realgas effects occurring in the turbine, which typically expands in the nonideal-gas thermodynamic region. In addition, the potential efficiency increase offered by supercritical organic Rankine cycles, which entails even stronger real-gas
effects, has not yet been exploited in current practice. In this paper, real-gas effects occurring in subcritical and supercritical organic Rankine cycle nozzles have been investigated. Two-dimensional Euler simulations of an existing axial organic Rankine cycle stator nozzle are carried out using a computational fluid dynamics code, which is linked to an accurate thermodynamic model for the working fluid octamethyltrisiloxane C8H24O2Si3). The cases analyzed include the expansions starting from actual subcritical conditions, that is, the design point and part-load operation, and three expansions starting from supercritical conditions. Results of the simulations of the existing
nozzle for current operating conditions can be used to refine its design. Moreover, the simulations of the nozzle expansions starting from supercritical conditions show that a nozzle geometry with a much higher exit-to-throat area ratio is required to obtain an efficient expansion. Other peculiar characteristics of supercritical expansions such as low sound speed and velocity, high density, and mass flow rate, are discussed
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