Abstract: Within a continuum framework, flows featuring shock waves can be modelled by means of either shock-capturing or shock-fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock-capturing and contribute towards making shock-fitting on unstructured meshes a versatile technique.
Abstract: The analysis of the rarefaction effects in the prediction of the main aerothermal loads of a space re-entry vehicle is presented. It is well known that the Navier-Stokes equations fail in rarefied regimes and therefore other approaches must be used. In the present paper different configurations have been simulated by using the Direct Simulation Monte Carlo method. Moreover, slip flow boundary conditions have been implemented in a Navier-Stokes code in order to extend the validity of such a continuum method in the transitional flow regime. Finally, bridging-formulae for the high altitude aerodynamics of winged bodies have also been used. For the tuning of the methodologies, two simple geometries have been analysed, specifically designed to study the phenomenon of shock wave boundary layer interaction: the first one is a hollow cylinder flare, for which experimental data are also available; the second one is the geometry of a test article that was designed and tested at the Italian Aerospace Research Centre. The other two configurations that have been taken into account are an experimental winged re-entry vehicle and a capsule, for which global aerodynamic coefficients and local wall heating have been determined using different computational approaches. The Navier-Stokes code with slip flow boundary conditions has shown good predictive capabilities of the size of the recirculation bubble compared with the experimental results in the hollow cylinder flare test case; however, for the winged vehicle and capsule case, the CFD results are not fully satisfactory and the Monte Carlo method remains the most reliable approach, together with the bridging formulae, that provide good results for the global aerodynamic coefficients.
Abstract: A new shock-fitting technique has been recently proposed and implemented by the authors in conjunction with an unstructured shock-capturing solver. In the present paper, the attention is addressed towards the computation of shock-shock and shock-wall interactions by means of this novel computational technique.
Abstract: Weak steady Mach reflections are numerically simulated using unstructured grids by means of either âshock-fittingâ or âshock-capturingâ techniques. It is shown that shock-fitting allows using coarser meshes than those required by shock-capturing, since the latter needs mesh refinement in the direction normal to the discontinuities, which is not needed using the former approach. The shock-fitted solution is also free from the numerical disturbances that arise along the captured discontinuities and pollute the captured solution in the smooth flowfield region. Finally, the shock-fitting solutions show the presence of a small region next to the Mach stem and the reflected shock downstream of the triple point, characterized by very high gradients.
Notes: This paper was based on work that was presented at the 27th International Symposium on Shock Waves, St. Petersburg, Russia, 19-24 July 2009.
Abstract: This article addresses two modelling aspects of wind turbine aerofoil aerodynamics based on the solution of the Reynolds-averaged NavierâStokes (RANS) equations. One of these is the effect of an a priori method for structured grid adaptation aimed at improving the
wake resolution. The presented results emphasize that the proposed adaptation strategy greatly improves the wake resolution in the far field, whereas the wake is completely diffused by the nonadapted grid with the same number and spacing patterns of grid nodes.The proposed adaptation approach can be easily included in the structured generation process of both commercial and in-house-structured mesh generators. The other numerical aspect examined herein is the impact of particular choices for turbulence modelling on the predicted solution. This includes the comparative analysis of numerical solutions obtained by using different turbulence models, and also aims at quantifying the solution inaccuracy arising from not modelling the laminar-to-turbulent transition. It is found that the drag forces obtained by considering the flow as transitional or fully turbulent may differ by 50 per cent. All these issues are investigated using a special-purpose hyperbolic grid generator and two multi block structured finite volume RANS codes. The numerical experiments consider the flow field past a wind turbine aerofoil for which an exhaustive campaign of steady and unsteady experimental measurements was conducted. The predictive capabilities of the CFD solvers are validated by comparing experimental data and numerical predictions for selected flow regimes. The incompressible analysis and design code XFOIL is also used to support the findings of the
comparative analysis of numerical RANS-based results and experimental data.
Abstract: A new floating shock-fitting technique featuring the explicit computation of shocks by means of the RankineâHugoniot relations has been implemented on two-dimensional unstructured grids. This paper illustrates the algorithmic features of this original technique and the results obtained in the computation of the hypersonic flow past a circular cylinder and a steady Mach reflection.
Abstract: This paper describes an accurate, robust and efficient methodology for solving twodimensional steady transonic turbomachinery flows. The Euler fluxes are discretized in space using a hybrid multidimensional upwind method, which, according to the local flow conditions, uses the most suitable fluctuation splitting (FS) scheme at each cell of the computational domain. The viscous terms are discretized using a standard Galerkin finite element scheme. The eddy viscosity is evaluated by means of the Spalart-Allmaras turbulence transport equation, which is discretized in space by means of a mixed FS-Galerkin approach. The equations are discretized in time using an implicit Euler scheme, the Jacobian being evaluated by two-point backward differences. The resulting large sparse linear systems are solved sequentially using a preconditioned GMRES strategy. The proposed methodology is employed to compute subsonic and transonic turbulent flows inside a high-turning turbine-rotor cascade.
Abstract: The ERCOFTAC junction flow is numerically simulated with both a structured and an unstructured RANS solver for incompressible flows. The structured code adopts a finite volume, cell-centered formulation while the unstructured code uses residual distribution schemes and a vertex centered storage of the unknowns. Two differential eddy viscosity models, based on local quantities, are considered in the computations: the one-equation Spalart Allmaras model and the two equations k-e model proposed by Lam and Bremhorst. The grid dependence of the numerical solutions is evaluated by means of a convergence analysis based on computation of the GCI and a code-to-code comparison. The numerical results provided by both turbulence models are compared with the experimental measurements of the pressure and velocity fields.
Abstract: Introduced in the late eighties by Roe, fluctuation splitting (or residual distribution) schemes have recently emerged as a viable alternative to Finite Volume and Finite Element methods for PDE based, fluid dynamics simulations using unstructured meshes. Their application to the numerical approximation of the compressible and incompressible Euler and Navier-i Stokes equations is described, emphasizing low Mach
number and incompressible applications. The advantages provided by time-preconditioning techniques are discussed and details of the implementation are given.
Abstract: The reflection of weak shocks constitutes an interesting problem from a modeling point of view. The discussion about the von Neumann paradox and the Guderleyâs triple shock wave solution are an example of this interest. In the present paper the attention is focused on
those steady state reflections where the Von Neumann theory fails or does not provide the âclassicalâ solution with incident and reflected shocks belonging to opposite families. Contrarily to the theory, numerical solutions of these problems show a Mach reflection similar to von Neumann triple point solution, provided that the computed shocks have a physical or numerical thickness. These special cases of Mach reflections are discussed with the help of numerical solutions obtained by different approaches based on shock capturing and shock fitting, respectively.
Notes: 26th International Symposium on Shock Waves, Volume 2
Abstract: A new floating shock-fitting technique featuring the explicit computation of shocks by means of the Rankine-Hugoniot relations has been implemented in an unstructured solver. This paper briefly illustrates the algorithmic features of this orginal technique and the results
obtained in the computation of the hypersonic flow past a circular cylinder.
Notes: 26th International Symposium on Shock Waves
Abstract: We consider iterative solution strategies for solving the Reynolds-Favre averaged Navier-Stokes (RANS) equations on 2D and 3D flow configurations. The novelty of this study is the coupling of an hybrid class of methods for the space discretization, called Fluctuation Splitting (or residual distribution) schemes, and a fully coupled Newton algorithm for solving the RANS equations. This approach is particularly attractive for parallel computations because it gives rise to discretization matrices with a compact stencil resulting in a limited number of nonzero entries. In this paper, we present the solution approach and report on results of numerical experiments with particular emphasis on the design of preconditioners for the inner linear system, which is a critical computational issue of the iterative solution.
Notes: XVI, 826 p. 247 illus., Hardcover http://www.springer.com/math/cse/book/978-3-540-69776-3
Abstract: We present results with a parallel CFD code that computes steady-state solutions of the Reynolds-Favre averaged Navier-Stokes equations for the simulation of the turbulent motion of compressible and incompressible Newtonian fluids. We describe solution techniques adopted for the discretization, algorithmic details of the implementation and report on preliminary experiments on 2D and 3D problems, for both internal and external flow configurations.
Notes: Proceedings of the 8th International Workshop, PARA 2006, Umea, Sweden, June 2006. Lecture Notes in Computer Science
Abstract: Following previous work on the canonical decomposition of the subsonic, compressible Euler equations into their steady hyperbolic and elliptic components, a similar decomposition for the incompressible equations is proposed. The artificial compressibility approach is used make the incompressible Euler equations hyperbolic in time. The canonical form of this pseudo-compressible system consists in an hyperbolic component corresponding to the convection of total pressure along the streamlines and a Cauchy-Riemann system corresponding to the omni-directional propagation of the (artificial) acoustic waves.
The discretization of the pseudo-unsteady system is accomplished using Fluctuation Splitting schemes and unstructured meshes.
Abstract: A compressible flow solver [Bonfiglioli and Deconinck (96)] for unstructured triangular and tetrahedral meshes has been extended to deal with incompressible flows using Chorinâs artificial compressibility [Chorin (67)]
Abstract: Matrix distribution schemes, originally developed and tested in two dimensions, have been extended to three dimensions. Preliminary numerical evidence shows great promise for these methods, but addition work is still needed to improve robustness near stagnation points and discontinuities.
Abstract: Owing to the maturity nowadays reached by computational geometry, shock-fitting, i.e. treating shock waves as true surfaces of discontinuity may no longer be prohibitively complex, as commonly believed by CFD practitioners.
In this paper we report on some newly implemented features and algorithmic improvements of an unstructured, shock-fitting algorithm
for three-dimensional flows that has been recently proposed by the authors.
The shock wave is described using a double-sided triangulated surface which is allowed to float over a background tetrahedral grid while obeying to the Rankine-Hugoniot jump relations. A constrained, Delaunay tetrahedralization is applied in the neighbourhood of the shock-front to make sure that the triangular faces that make up the shock surface are part of the tetrahedral
mesh that covers the entire computational domain. A shock-capturing, vertex-centred solver is used to discretise the governing PDEs
in the smooth regions of the flow-field; it also allow to ``capture'' those shock waves that may not have been fitted and/or the interaction between different fitted shock surfaces.
The capabilities of the technique are demonstrated by reference to the high speed flow past a blunt-nosed cylinder with a conical flare for which experimental and other numerical results are available.
When the technique is compared with shock-capturing on un-adapted meshes of comparable resolution, it is shown that fitting the strong shocks allows to considerably improve the solution quality in the entire shock layer and over the body surface.
Abstract: CRAS is taking part to the ESA FLPP program contributing significantly to the computation of numerical simulations for to the aerothermodynamic database of the IXV vehicle.
Numerical simulation of hypersonic flows represents surely a strong point for CRAS. Indeed, in this field CRAS boasts researchers with long experience and availability of state-of-art software tools. In addition to this, a new computing technique which promises significantly improvements in the simulation of flows with strong shocks is presently under development at CRAS.
The paper is a brief overview of the numerical techniques presently, used in the contract activities related to the IXV program or under development at CRAS together with a selection of the most significant results.
Abstract: A recently developed parallel three-dimensional
flow solver of the turbulent Navier-Stokes equations is presented. The space discretization of the continuous equations is performed by means of the Fluctuation Splitting algorithm, and the implicit integration process of the discrete equations is based on an eectively preconditioned Newton-Krylov subspace algorithm. The high computational performance is demonstrated using a suite of two- and three-dimensional test cases with grids featuring up to 6.5 million nodes.
Abstract: A novel unstructured shock-fitting algorithm for three-dimensional flows is presented in this paper.
The fitted shock front is described using a double-sided, triangulated surface. Two sets of flow states, corresponding to the upstream and dowsntream sides of the discontinuity, are assigned to the gridpoints located on either side of the triangulated shock surface. This is allowed to move, while obeying to the Rankine-Hugoniot jump relations, throughout a background tetrahedral mesh which covers the entire computational domain.
At each time step, a local, constrained Delaunay tetrahedralization is applied in the neighbourhood of the shock front to ensure that the triangles make up the shock surface are part of the overall tetrahedral grid.
The fitted shock surface acts as an interior boundary for a shock-capturing solver that is used to solve the discretized governing equations in the smooth regions of the flowfield.
Despite the intrinsic complexity of the algorithm and the need to include the extra computational nodes that make up the triangulated shock-surface, the algorithm is shown to provide high quality results even with the coarse grain tetrahedralizations used in the example provided.
Moreover, the re-meshing step is limited to the region close to the shock surface and the fitting algorithm is only weakly coupled with the flow solver used in the simulation.
Abstract: The analysis of the rarefaction effects in predicting the main aero-thermal loads of a Space re-entry vehicle is presented. It is well known that the Navier-Stokes equations fail in rarefied regimes and other approaches must be used.
In the present paper different configurations have been simulated by using the Direct Simulation Monte Carlo method. Moreover, slip flow boundary conditions have been implemented in a Navier-Stokes code in order to extend the validity
of the continuum approach to the transitional flow regime. Finally, bridging formulas for high altitude aerodynamics of winged bodies have been used. Firstly, two simple geometries have been analysed, specifically designed to study the
phenomenon of shock wave boundary layer interaction: a hollow cylinder flare, for which some experiments are available; and a blunt-nosed flat plate/flap model designed and tested at the Italian Aerospace Research Centre. The other
configurations taken into account are, respectively, an experimental winged re-entry vehicle and a capsule, for which global aerodynamic coefficients and local wall heating have been determined with different approaches. The Navier-
Stokes code with slip flow boundary conditions has shown good predicting capabilities compared with experiments in the hollow cylinder flare case; however, for the winged vehicle and capsule cases, the CFD results are not fully satisfactory
and the Monte Carlo method remains the most reliable approach, together with the bridging formula, that provides good results for the aerodynamic coefficients.
Notes: ISBN 978-0-7354-0889-0, Two Volume, Print; 1452 pages; 8.5 X 11 inches, single column; $398.00
Abstract: Capturing strong shocks is a difficult task. It is also known that it leads to accuracy degradation in the entire region downstream of the captured shock wave. Things get even worst when unstructured grids are used. In this paper we try to assess whether these drawbacks may be circumvented by combining shock-fitting and unstructured grids. Achievements, current difficulties and un-solved problems are
presented and discussed.
Abstract: The reflection of weak shocks constitutes a challenging problem from a modelling and numerical point of view. Indeed, there exist
certain combinations of free-stream Mach number and flow deflection angle for which the Von Neumann theory admits no
solution. However, numerical solutions for these same flow parameters show a flow pattern which is very similar to
the von Neumann's triple point solution. This inconsistency is referred to as the von Neumann paradox, and the observed reflection pattern is called the von Neumann reflection. In the paper these issues will be investigated by computing von Neumann reflections using different computational approaches including an unstructured shock-fitting technique.
Abstract: A recently developed parallel three-dimensional flow solver of the turbulent Navier-Stokes equations is presented. The implicit integration process of the discrete equations is based on an effectively preconditioned Newton-Krylov subspace algorithm. The space discretization of the continuous equations is performed by means of the Fluctuation Splitting algorithm. This method can be viewed as a mixed finite volume/finite element discretisation of the system of conservation laws. The presented Computational Fluid Dynamics solver has a very high computational performance. Such a performance as well as the accuracy of the code are highlighted by considering a suite of two- and three-dimensional test cases, among which the calculation of the flow past the DPW-W1 wing configuration of the 3rd AIAA Drag Prediction Workshop. This analysis is carried out with a grid featuring about 1 million nodes.
The use of Newton-Krylov subspace solvers in implicit CFD codes has a great potential for dramatically reducing the computational cost
associated with the analysis of complex aerodynamic problems. Included results also highlight the remarkable computational effectiveness of Newton's solution procedure in the case of unsteady flows. The theoretical and numerical results reported
herein will contribute to highlight this potential and enrich the database of this technology.
Abstract: The two-dimensional, hypersonic (M = 17.605), laminar flow (Re = 376930) past the forebody of a circular cylinder has been simulated
by means of a vertex-centred CFD code using linear triangular elements. Two different approaches have been used to simulate the strong detached bow shock: shock-capturing on anisotropically refined meshes and shock-fitting. Concerning the boundary layer mesh, the distribution of gridpoints has been kept constant, while three different connectivity patterns have been examined. When looking at wall quantities such as pressure, skin friction and heat transfer these appear to be more heavily affected by the boundary layer mesh than by the numerical model used to simulate the detached shock wave.
Abstract: A new shock-fitting technique has been recently proposed and implemented by the authors in conjunction with an unstructured shock-capturing solver. In the present paper, the attention is addressed towards the computation of shock-shock interactions by means of
this novel computing technique. Different computing approaches are considered and their performances are assessed through the computation of a type IV shock-shock interaction.
Abstract: This paper focuses on novel unsteady and low-speed algorithmic developments of a structured explicit Euler solver and an unstructured implicit Euler/RANS solver for wind turbine CFD. The central topics are a) a discussion on the definition of optimal low-speed preconditioning for explicit solvers featuring state-of-the-art convergence acceleration methods, b) the presentation of a simple optimal mixed preconditioning strategy, and c) the novel implementation in the implicit unstructured code of a preconditioning method which thus far has only been used for steady problems. These technologies are thoroughly validated by considering a low-speed vortex convection problem and the low-speed flow field past a pitching wind turbine airfoil. The excellent computational performance of the implicit approach is also demonstrated by computing the stalled flow past the same airfoil. All results demonstrate the accuracy and computational efficiency of these algorithms.
Abstract: This paper reports the first findings of an ongoing research programme on wind turbine computational aerodynamics at the University of Glasgow. Several modeling aspects of wind turbine airfoil aerodynamics based on the solution of the Reynoldsaveraged Navier-Stokes (RANS) equations are addressed. One of these is the effect of an a priori method for structured grid adaptation aimed at improving the wake resolution. Presented results emphasize that the proposed adaptation strategy greatly improves the wake resolution in the far-field, whereas the wake is completely diffused by the non-adapted grid with the same number and distribution of grid nodes. A grid refinement analysis carried out with the adapted grid shows that the improvements of flow resolution thus achieved are of a smaller magnitude with respect to those accomplished by adapting the grid keeping constant the number of nodes. The proposed adaptation approach can be easily included in the structured generation process of both commercial and in-house structured mesh generators systems. The study also aims at quantifying the solution inaccuracy arising from not modeling the laminar-to-turbulent transition. It is found that the drag forces obtained by considering the flow as transitional or fully turbulent may differ by 50%. The impact of various turbulence models on the predicted aerodynamic forces is also analyzed. All these issues are investigated using a special-purpose hyperbolic grid generator and a multi-block structured finite volume RANS code. The numerical experiments consider the flow field past a wind turbine airfoil for which an exhaustive campaign of steady and unsteady experimental measurements was conducted. The predictive capabilities of the CFD solver are validated by comparing experimental data and numerical predictions for selected flow regimes. The incompressible analysis and design code XFOIL is also used to support the findings of the comparative analysis of numerical RANS-based results and experimental data.
Abstract: A new floating Shock-Fitting technique featuring the explicit computation of shocks by means of the Rankine-Hugoniot relations has been implemented on unstructured grids. This paper illustrates the algorithmic features of this orginal technique and the results obtained in the computation of the hypersonic flow past a circular cylinder and a Mach reflection.
Abstract: In the present work the results of a preliminary computational fluid dynamics (CFD) simulation of the flow past a marine propeller are presented. The principal aim of the study is to verify the ability of a CFD method, solving the Reynolds-Averaged Navier-Stokes Equations (RANSEs), to predict the performances of a marine propeller. The complexity in the mesh generation is one of the main obstacles for CFD. Following an hybrid mesh generation approach, prisms have been generated in the boundary layer, where viscous phenomena are dominant, and tetrahedra in the remaining regions. A parallel RANS solver has been used, employing a cell-centered, finite-volume method that allows the use of computational cells of arbitrary polyhedral shape. Boundary conditions were given to simulate the flow past a rotating propeller in open water conditions. The equations have been written in a moving reference frame fixed on the propeller blades. The steady-rotating reference frame source terms, i.e., the centrifugal and Coriolis force terms, therefore, are added to the RANS equations derived in the inertial frame. The k-w model has been employed for turbulence closure. Different values of advance ratios are considered, at design and off-design conditions. Computational results have been obtained for all the four-quadrant operational conditions: forward, backing, crashback and crashahead, considering also non-positif values for the advance ratio J. The thrust and torque coefficients, k_T and k_Q, have been selected as global quantities and compared with available experimental data. Pressure and velocity distributions and turbulent quantities were also used to analyze the computed flow field. The results show a good qualitative agreement with the experimental data. Important issues need to be addressed like an extensively improvement in the mesh generation techniques and in turbulence modeling.
Abstract: Progress on the development and the application of an accurate and efficient flow solver for steady turbomachinery flows is reported. The code uses unstructured tetrahedral grids, its space-discretization is based on a fluctuation splitting scheme and an implicit strategy is used for the time integration. Results include the three-dimensional analysis of the flow field of a compressor stator and thorough comparisons with experimental data and numerical results obtained with other codes.
Abstract: A parallel finite element model for incompressible laminar two-phase flows is presented. A two-fluid model, describing the laminar non-equilibrium flow of two incompressible phases, is discretized by means of a properly designed Streamline Upwind Petrov-Galerkin (SUPG) finite element procedure. Such a procedure is consistent with a continuous pressure equation. The design and the implementation of the algorithm are presented together with its validation throughout a comparison with simulations available in literature.
Abstract: Viene descritta lâimplementazione dellâalgoritmo di Newton per risolvere i sistemi di equazioni algebriche non-lineari che si ottengo dalla discretizzazione delle equazioni della fluidodinamica. In particolare, vengono studiate le equazioni di Navier-Stokes mediale a la Reynolds-Favre (RANSE) in cui la turbolenza `e descritta tramite il modello ad una equazione dovuto a Spalart e Allmaras. Le applicazioni considerate, entrambe bidimensionali, riguardano il flusso attraverso una schiera anulare di turbina, International Standard Configuration 11 (STCF 11), ed il flusso esterno attorno al profilo RAE 2822. Vengono confermate le eccellenti qualit`a di convergenza dellâalgoritmo che non solo consente di raggiungere la soluzione stazionaria in poche decine di iterazioni non-lineari, ma inoltre permette di raggiungere livelli di convergenza dellâordine dello zero macchina, difficilmente ottenibili utilizzando metodi iterativi meno sofisticati. Dâaltro canto, vengono evidenziati alcuni limiti dellâimplementazione descritta.
Abstract: This paper provides an accurate, robust, and efficient methodology for solving steady transonic turbomachinery flows. The Euler fluxes are discretized in space using a hybrid multidimensional upwind method, which, according to the local flow conditions, uses the most suitable Fluctuation Splitting (FS) scheme at each cell of the computational domain. The viscous terms are discretized using a standard Galerkin finite element scheme. The eddy viscosity is evaluated by means of the Spalart-Allmaras turbulence transport equation, which is discretized in space by means of a mixed FS-Galerkin approach. The equations are discretized in time using an implicit Euler scheme, the Jacobians being evaluated by two-point backward differences. The resulting large sparse linear systems are solved sequentially using a preconditioned GM-RES strategy. The proposed methodology is employed to compute the 2D subsonic and transonic turbulent flows inside a high-turning turbine-rotor cascade, as well as a 3D subsonic turbulent flow inside the Stanitz elbow.
Abstract: This paper addresses a number of numerical issues associated with Finite Volume (FV) discretisation of the incompressible Navier-Stokes (NS) equations on unstructured meshes. This is done in the context of a numerical scheme which is based on a cell-centred, fully collocated storage arrangement, adopts equal-order interpolation for pressure and velocity, and determines the pressure from the solution of the Pressure-Poisson equation. The performance of the method as a whole is then illustrated by reference to the 2D computations for laminar and turbulent vortex shedding behind prismatic cylinders, with turbulence effects represented by linear and cubic low-Reynolds-number two-equation eddy-viscosity models.
Abstract: In questo lavoro si è sviluppato un modello di previsione delle prestazioni di una turbina marina ad asse verticale seguendo un approccio di tipo teorico-numerico. E` stato utilizzato, come strumento di analisi, un codice di calcolo che risolve le equazioni di Navier-Stokes non stazionarie per campi di moto bidimensionali incomprimibili, adottando un metodo ai volumi finiti. Si è dapprima verificata lâesatta impostazione del metodo utilizzato per confronto con varie configurazioni di flusso per le quali sono reperibili in letteratura dati numerici e sperimentali. Successivamente si è utilizzato il codice, opportunamente modificato, per predire le caratteristiche di funzionamento di un modello semplice di turbina ad asse verticale, del tipo Darrieus, costituito da unâunica pala avente un profilo alare di tipo simmetrico con corda rettilinea, appartenente alla serie NACA. Lâanalisi delle prestazioni di questo modello semplificato di turbina è stata effettuata sia mediante visualizzazioni del campo di moto che si instaura intorno alla pala, sia calcolando lâevoluzione temporale della potenza disponibile allâasse. Eâ stata condotta unâanalisi parametrica al variare del numero di Reynolds e del rapporto l tra la velocità periferica del rotore e la velocità della corrente indisturbata. Per ciascuna coppia di valori di questi due parametri si è analizzato lâandamento dei coefficienti aerodinamici e del coefficiente di coppia al variare della posizione assunta dalla pala durante la rotazione, ottenendo così lâandamento del coefficiente di potenza in funzione del parametro lambda. Sono stati infine eseguiti confronti con risultati sperimentali disponibili in letteratura mettendo in evidenza lâattendibilità del modello numerico.
Abstract: This report describes the research activity carried out in the framework of the Standard HPC Grant 2009. The key thread of this activity lies in demonstrating the effectiveness of Newtonâs rootfinding method in solving the large system of non-linear algebraic equations arising from the discretization of the Navier-Stokes and Reynolds Averaged Navier-Stokes equations using unstructured tetrahedral grids. The aforementioned technique has been applied to both
steady and un-steady flow simulations. In this latter case, a dual time-stepping technique is used to advance the solution in physical time. Last, but not least,
this research activity offered the opportunity to validate the un-steady capability that has been recently implemented within the EulFS code.
Abstract: This document reports numerical experiments addressing grid dependence issues that
arise in the simulation of hypersonic
ow past blunt bodies. For a given distribution
of gridpoints, dierent connectivity patterns are investigated. Some of these give rise
to unexpected features such as: strong asymmetries, the onset of recirculation regions,
multiple stagnation points. While a convincing explanation for the occurence of these
phenomena is not yet available, there seem to be evidence that at least some of these
problems are peculiar to hypersonic
ows, or at least to the presence of shock waves,
since analogous calculations using the same grids in the subsonic regime produce far
more reasonable results.
Abstract: A numerical method for solving the incompressible, Reynolds averaged, Navier-Stokes equations is presented.
The method is based on a conservative, Finite Volume discretisation of the momentum and turbulence transport equations and pressure-Poisson equation is used to enforce the continuity constraint.
The computational domain is discretised using unstructured meshes made of polyhedral elements. The primitive variables, velocity and pressure, are representative of cell-averages and are associated with the elements of the mesh. A piece-wise linear representation of the dependent variables is used to derive the discrete form of the governing conservation equations. Due to the equal order interpolation (or co-located storage) used for both velocity and pressure, the pressure field needs to be stabilised and this is accomplished by the addition of a discrete bi-harmonic pressure operator in the continuity equation. The theoretical foundations of the method are described is some detail and several computational experiments are presented. These involve steady and un-steady laminar testcases that allow to assess the range of applicability and current limitations of the method.
A linear and a cubic eddy viscosity models are then validated on a boundary layer flow and applied to simulate the un-steady vortex shedding behind a bluff body for which extensive experimental and numerical data are available.
Finally, the method is used to simulate the flowfield inside an hydraulic spool valve.
Abstract: Il presente rapporto analizza le prestazioni di diversi metodi iterativi per la risoluzione di sistemi lineari a matrice sparsa di grandi dimensioni.
I sistemi lineari vengono generati in ciascun passo di un metodo di Newton utilizzato per risolvere i sistemi di equazioni non lineari ottenuti dalla discretizzazione delle equazioni della fluidodinamica (equazioni di Eulero e Navie-Stokes) su reticoli di calcolo di tipo non strutturato.
La risoluzione dei sistemi lineari è affidata alla libreria PETSc, sviluppata presso l'Argonne National Laboratory e liberamente disponibile in rete.
Le prove sono state effettuate sia su workstation uniprocessore che su architetture parallele considerando problemi con un numero di incognite
variabile fra 1000 e 1000000.
