In this work we simulate the non-cavitating and cavitating flow around the PPTC (Potsdam Propelle... more In this work we simulate the non-cavitating and cavitating flow around the PPTC (Potsdam Propeller Test Case) model scale propeller. The calculations are carried out using the commercial CFD solver ANSYS CFX 12, and for the prediction of the cavitating behaviour three different mass transfer models, previously calibrated, are employed.
Lo studio si propone la previsione numerica dei campi termici e dinamici di convezione naturale p... more Lo studio si propone la previsione numerica dei campi termici e dinamici di convezione naturale prodotti da schede elettroniche disposte all'interno di cabinets ermetici per elettronica, sia per regimi stazionari che tempovarianti. I risultati dimostrano la praticabilit\ue0 dell'estensione a geometrie complesse di un metodo numerico gi\ue0 sviluppato per la simulazione di regimi di convezione naturale e mista in cavit\ue0 e condotti a sezione rettangolare
A novel two-equations turbulence model is presented for the analysis of turbulent natural convect... more A novel two-equations turbulence model is presented for the analysis of turbulent natural convection in internal flows. The case of a two-dimensional differentially heated vertical cavity is presented
The numerical predictions of a model scale propeller working in uniform and oblique flow are pres... more The numerical predictions of a model scale propeller working in uniform and oblique flow are presented. Both non-cavitating and cavitating flow conditions are numerically investigated using homogeneous (mixture) model. Two previously calibrated mass transfer models are alternatively used to model the mass transfer rate due to cavitation. The turbulence effect is modelled using the Reynolds Averaged Navier Stokes (RANS) approach. The simulations are performed using an open source solver. The numerical results are compared with the available experimental data. For a quantitative comparison the propeller thrust is considered, while for a qualitative comparison, snapshots of cavitation patterns are shown. From the overall results it seems that, with the current simulation approach it is possible to predict with a reasonable accuracy the propeller performances. Nevertheless, for detailed reproduction of complex cavitation phenomena, such as bubble cavitation for instance, a more sophisticated modelling approach is probably required
Si descrivono alcuni algoritmi basati sulla discretizzazione delle equazioni di Navier-Stokes con... more Si descrivono alcuni algoritmi basati sulla discretizzazione delle equazioni di Navier-Stokes con il metodo ai volumi di controllo, con riferimento a casi di convezione naturale non stazionari
International Journal of Multiphase Flow, Jul 1, 2011
Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide ra... more Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide range of methods. One strategy consists of using the RANS (Reynolds Averaged Navier Stokes) equations and an additional transport equation for the liquid volume fraction, where mass transfer rate due to cavitation is modelled by a mass transfer model. In this study, we compare three widespread mass transfer models available in literature for the prediction of sheet cavitation around a hydrofoil. These models share the common feature of employing empirical coefficients, to tune the models of condensation and evaporation processes, that can influence the accuracy and stability of the numerical predictions. In order to compare the different mass transfer models fairly and congruently, the empirical coefficients of the different models are first well tuned using an optimization strategy. The resulting well tuned mass transfer models are then compared considering the flow around the NACA66(MOD) and NACA009 hydrofoils. The numerical predictions based on the three different tuned mass transfer models are very close to each other and in agreement with the experimental data. Moreover, the optimization strategy seems to be stable and accurate, and could be extended to additional mass transfer models and further flow problems.
Direct numerical simulations - DNS hereafter - of a fully developed, turbulent horizontal pipe fl... more Direct numerical simulations - DNS hereafter - of a fully developed, turbulent horizontal pipe flow in the presence of buoyancy forces were carried out in order to investigate the interactive shear and buoyancy effects on the turbulent momentum and heat transport. Similar studies were carried out for the channel flow configuration [1,2], while, to the authors best knowledge, no investigation has been reported so far for the pipe flow. The isoflux wall thermal conditions were imposed, which generated a sort of stable stratification and a complex secondary flow pattern, affecting both the hydraulic and the thermal efficiency. While knowledge of synthetic parameters, like the friction factor and the Nusselt number, is valuable for practical applications, DNS studies produce a wide variety of higher-order statistics, which can be used to develop a better physical comprehension of the phenomenon, or even to improve the existing turbulence models. The modest influence of buoyancy on both the Nusselt number and the friction factor does not reflect the relevant modifications, which, at the considered values of the Richardson number, characterize the velocity and the temperature fields
The present work reports the comparison of different k-eps turbulence models for two-dimensional,... more The present work reports the comparison of different k-eps turbulence models for two-dimensional, differentially heated, rectangular enclosures. The comparison is related to the proiposed Benchmark excercise for the 22o Eurotherm/Ercoftac Workshop, i.e. a side-heated square cavity with a fluid with a Prandtl number of 0.71 and a Rayleigh number of 5x10^10, but further results are reported for enclosures with different aspect ratios and different Pr and Ra numbers, when experimental data are available. From the comparison, it is concluded that the standard k-eps turbulence model leads to severe errors in the prediction of mean quantities very close to the wall, like the heat transfer rate, while better agreement with the experiments is obtained with selected low-Reynolds-Number k-eps models
The numerical predictions of the cavitating flow around two model scale propellers in uniform inf... more The numerical predictions of the cavitating flow around two model scale propellers in uniform inflow are presented and discussed. The simulations are carried out using a commercial CFD solver. The homogeneous model is used and the influence of three widespread mass transfer models, on the accuracy of the numerical predictions, is evaluated. The mass transfer models in question share the common feature of employing empirical coefficients to adjust mass transfer rate from water to vapour and back, which can affect the stability and accuracy of the predictions. Thus, for a fair and congruent comparison, the empirical coefficients of the different mass transfer models are first properly calibrated using an optimization strategy. The numerical results obtained, with the three different calibrated mass transfer models, are very similar to each other for two selected model scale propellers. Nevertheless, a tendency to overestimate the cavity extension is observed, and consequently the thrust, in the most severe operational conditions, is not properly predicted.
Transient simulations of flow in a Francis turbine were performed with a goal to predict pressure... more Transient simulations of flow in a Francis turbine were performed with a goal to predict pressure pulsation frequencies and amplitudes caused by rotating vortex rope at part load operating regime. Simulations were done with the SAS SST turbulence model with curvature correction on basic and refined computational meshes. Without cavitation modelling too small values of frequency and amplitudes were obtained. With mesh refinement the calculated amplitudes were a bit closer to the measured values, while the accuracy of predicted frequency did not improve at all. Agreement between measured and numerical values was significantly improved when cavitation was included in simulations. In addition, the predicted value of the dominant frequency was slightly more accurate when, in the Zwart et al. cavitation model, the default condensation and evaporation model constants were replaced with previously calibrated ones. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Numerical Heat Transfer Part B-fundamentals, Oct 1, 1996
A time-accurate, additive-correction multigrid method for the prediction of two-dimensional unste... more A time-accurate, additive-correction multigrid method for the prediction of two-dimensional unsteady flows is presented in this article. The method makes use of the additive-correction multigrid strategy, which, originally proposed for steady-flow problems, is extended to the calculation of time-dependent and chaotic flows at high Reynolds or Rayleigh numbers. The numerical algorithm guarantees absolute, to machine accuracy, mass conservation at every time step, and it is characterized by second-order accuracy in space and time. In a companion article [1], the method is applied to the calculation of unsteady flow in cavities, i.e., the lid-driven cavity problem at high Reynolds number, and the buoyant flow in differentially heated cavities at high values of the Rayleigh number. Although the method has been implemented and tested for two-dimensional flows, it can also be extended to three-dimensional problems.
Numerical Heat Transfer Part B-fundamentals, Oct 1, 1996
An additive-correction multigrid method for the prediction of two-dimensional unsteady flows, des... more An additive-correction multigrid method for the prediction of two-dimensional unsteady flows, described in a previous article [1], is applied to selected cavity flow problems. The cases considered are the lid-driven cavity problem and the buoyant flow in differentially heated cavities. Accurate results are obtained for the lid-driven cavity, where fine-grid, high-Reynolds-number calculations, indicate that the steady flow bifurcates to a periodic regime for a Reynolds value in the range 7,500-10,000. The results for side-heated rectangular enclosures are presented first for a Prandtl number equal to zero, and corresponding values of Grashof number of 1.2 × 10 and 1.6 × 10. In addition, a Prandtl number of 0.71 is considered, with values of the Rayleigh number of 1 × 10, 2 × 10, and 2 × 10. The study demonstrates that the additive-correction multigrid method is computationally efficient, and is capable of performing accurate simulations of time-dependent, and possibly chaotic, flows in enclosures.
In this work we illustrate the combined use of the modeFRONTIER optimization system, together wit... more In this work we illustrate the combined use of the modeFRONTIER optimization system, together with the unstructured finite element FEMLAB package, for some selected conduction and convection heat transfer problems. The conductive problems are relative to optimization of cylindrical fins, and direct design of shape for a heated substrate cooled by convection. The multiobjective optimization of two-dimensional convective flow passages, representative of subsystems for compact heat exchangers, is considered, where maximization of heat transfer rate and minimization of friction losses are the main goals. It is concluded that our approach is accurate and robust, and provides a flexible and user-friendly environment for design tasks of heat transfer systems and devices. The multiphysics capabilities of FEMLAB, coupled with the modeFRONTIER optimization system, constitute a convenient and powerful tool for complex design tasks and research activities
The time-dependent, buoyancy-driven flow in cavities heated and cooled from the side, with adiaba... more The time-dependent, buoyancy-driven flow in cavities heated and cooled from the side, with adiabatic horizontal walls, is investigated with an implicit, two-dimensional finite volume scheme. The numerical algorithm integrates the Navier-Stokes equations, in primitive form, with a second-order accurate time-stepping scheme, and it is characterized by absolute, to machine accuracy, mass conservation. The results are presented for a Prandtl number, Pr, of 0.005, and corresponding values of Grashof number, Gr, of 1x10^6 and 3x10^6 and a value of Pr of 0.71, with a value of the Rayleigh number, Ra, of 2x10^9. For the results with Pr = 0.005, the effects of time-stepping order and spatial and temporal resolutions are identified and discussed. For the Pr = 0.71 case, the results are qualitatively compared with spectral-code predictions with favorable agreement. It is concluded that first-order time-stepping schemes should not be used when dealing with time-dependent buoyant flows, and that the proposed algorithm is capable of performing accurate simulations of unsteady, and possibly chaotic, convective flows in side-heated cavities
The numerical predictions of a cavitating model scale propeller working in uniform and oblique fl... more The numerical predictions of a cavitating model scale propeller working in uniform and oblique flow conditions are presented. The cavitating phenomena are numerically reproduced using a homogeneous (mixture) model where three previously calibrated mass transfer models are alternatively used to model the mass transfer rate. The turbulence effect is modelled using the Reynolds Averaged Navier Stokes (RANS) approach. The simulations are performed using an open source solver. The numerical results are compared with available experimental data. For a quantitative comparison the propeller thrust is considered, while for a qualitative comparison, snapshots of cavitation patterns are shown. The thrust values obtained with the three different mass transfer models are very close to each other, however differences in the predicted cavitation patterns are observed. Moreover, some discrepancies between the numerical results and experimental data are reported.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
International Journal of Thermal Sciences, Sep 1, 2006
In this paper, a numerical study of natural convection in a 2D-enclosure is presented. The enclos... more In this paper, a numerical study of natural convection in a 2D-enclosure is presented. The enclosure is bounded by two vertical isothermal walls, kept at different temperatures, and by two adiabatic walls which are either straight and horizontal (rectangular cavity) or elliptic (modified rectangular cavity). The dimensionless mass, momentum and energy balance equations are solved by means of two different software packages based on Galerkin finite element methods. An excellent agreement between the solutions is found and provides a cross-validation of the results. Two basic geometries are considered: a square geometry and a rectangular one with height double the width. For each basic geometry, three cavities are investigated: a rectangular cavity, and two modified rectangular cavities. Dry air is considered, with several values of the Rayleigh number. The results show that the elliptic boundaries enhance the mean Nusselt number and the dimensionless mean kinetic energy of the fluid.
In this work we simulate the non-cavitating and cavitating flow around the PPTC (Potsdam Propelle... more In this work we simulate the non-cavitating and cavitating flow around the PPTC (Potsdam Propeller Test Case) model scale propeller. The calculations are carried out using the commercial CFD solver ANSYS CFX 12, and for the prediction of the cavitating behaviour three different mass transfer models, previously calibrated, are employed.
Lo studio si propone la previsione numerica dei campi termici e dinamici di convezione naturale p... more Lo studio si propone la previsione numerica dei campi termici e dinamici di convezione naturale prodotti da schede elettroniche disposte all'interno di cabinets ermetici per elettronica, sia per regimi stazionari che tempovarianti. I risultati dimostrano la praticabilit\ue0 dell'estensione a geometrie complesse di un metodo numerico gi\ue0 sviluppato per la simulazione di regimi di convezione naturale e mista in cavit\ue0 e condotti a sezione rettangolare
A novel two-equations turbulence model is presented for the analysis of turbulent natural convect... more A novel two-equations turbulence model is presented for the analysis of turbulent natural convection in internal flows. The case of a two-dimensional differentially heated vertical cavity is presented
The numerical predictions of a model scale propeller working in uniform and oblique flow are pres... more The numerical predictions of a model scale propeller working in uniform and oblique flow are presented. Both non-cavitating and cavitating flow conditions are numerically investigated using homogeneous (mixture) model. Two previously calibrated mass transfer models are alternatively used to model the mass transfer rate due to cavitation. The turbulence effect is modelled using the Reynolds Averaged Navier Stokes (RANS) approach. The simulations are performed using an open source solver. The numerical results are compared with the available experimental data. For a quantitative comparison the propeller thrust is considered, while for a qualitative comparison, snapshots of cavitation patterns are shown. From the overall results it seems that, with the current simulation approach it is possible to predict with a reasonable accuracy the propeller performances. Nevertheless, for detailed reproduction of complex cavitation phenomena, such as bubble cavitation for instance, a more sophisticated modelling approach is probably required
Si descrivono alcuni algoritmi basati sulla discretizzazione delle equazioni di Navier-Stokes con... more Si descrivono alcuni algoritmi basati sulla discretizzazione delle equazioni di Navier-Stokes con il metodo ai volumi di controllo, con riferimento a casi di convezione naturale non stazionari
International Journal of Multiphase Flow, Jul 1, 2011
Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide ra... more Cavitating flows, which can occur in a variety of practical cases, can be modelled with a wide range of methods. One strategy consists of using the RANS (Reynolds Averaged Navier Stokes) equations and an additional transport equation for the liquid volume fraction, where mass transfer rate due to cavitation is modelled by a mass transfer model. In this study, we compare three widespread mass transfer models available in literature for the prediction of sheet cavitation around a hydrofoil. These models share the common feature of employing empirical coefficients, to tune the models of condensation and evaporation processes, that can influence the accuracy and stability of the numerical predictions. In order to compare the different mass transfer models fairly and congruently, the empirical coefficients of the different models are first well tuned using an optimization strategy. The resulting well tuned mass transfer models are then compared considering the flow around the NACA66(MOD) and NACA009 hydrofoils. The numerical predictions based on the three different tuned mass transfer models are very close to each other and in agreement with the experimental data. Moreover, the optimization strategy seems to be stable and accurate, and could be extended to additional mass transfer models and further flow problems.
Direct numerical simulations - DNS hereafter - of a fully developed, turbulent horizontal pipe fl... more Direct numerical simulations - DNS hereafter - of a fully developed, turbulent horizontal pipe flow in the presence of buoyancy forces were carried out in order to investigate the interactive shear and buoyancy effects on the turbulent momentum and heat transport. Similar studies were carried out for the channel flow configuration [1,2], while, to the authors best knowledge, no investigation has been reported so far for the pipe flow. The isoflux wall thermal conditions were imposed, which generated a sort of stable stratification and a complex secondary flow pattern, affecting both the hydraulic and the thermal efficiency. While knowledge of synthetic parameters, like the friction factor and the Nusselt number, is valuable for practical applications, DNS studies produce a wide variety of higher-order statistics, which can be used to develop a better physical comprehension of the phenomenon, or even to improve the existing turbulence models. The modest influence of buoyancy on both the Nusselt number and the friction factor does not reflect the relevant modifications, which, at the considered values of the Richardson number, characterize the velocity and the temperature fields
The present work reports the comparison of different k-eps turbulence models for two-dimensional,... more The present work reports the comparison of different k-eps turbulence models for two-dimensional, differentially heated, rectangular enclosures. The comparison is related to the proiposed Benchmark excercise for the 22o Eurotherm/Ercoftac Workshop, i.e. a side-heated square cavity with a fluid with a Prandtl number of 0.71 and a Rayleigh number of 5x10^10, but further results are reported for enclosures with different aspect ratios and different Pr and Ra numbers, when experimental data are available. From the comparison, it is concluded that the standard k-eps turbulence model leads to severe errors in the prediction of mean quantities very close to the wall, like the heat transfer rate, while better agreement with the experiments is obtained with selected low-Reynolds-Number k-eps models
The numerical predictions of the cavitating flow around two model scale propellers in uniform inf... more The numerical predictions of the cavitating flow around two model scale propellers in uniform inflow are presented and discussed. The simulations are carried out using a commercial CFD solver. The homogeneous model is used and the influence of three widespread mass transfer models, on the accuracy of the numerical predictions, is evaluated. The mass transfer models in question share the common feature of employing empirical coefficients to adjust mass transfer rate from water to vapour and back, which can affect the stability and accuracy of the predictions. Thus, for a fair and congruent comparison, the empirical coefficients of the different mass transfer models are first properly calibrated using an optimization strategy. The numerical results obtained, with the three different calibrated mass transfer models, are very similar to each other for two selected model scale propellers. Nevertheless, a tendency to overestimate the cavity extension is observed, and consequently the thrust, in the most severe operational conditions, is not properly predicted.
Transient simulations of flow in a Francis turbine were performed with a goal to predict pressure... more Transient simulations of flow in a Francis turbine were performed with a goal to predict pressure pulsation frequencies and amplitudes caused by rotating vortex rope at part load operating regime. Simulations were done with the SAS SST turbulence model with curvature correction on basic and refined computational meshes. Without cavitation modelling too small values of frequency and amplitudes were obtained. With mesh refinement the calculated amplitudes were a bit closer to the measured values, while the accuracy of predicted frequency did not improve at all. Agreement between measured and numerical values was significantly improved when cavitation was included in simulations. In addition, the predicted value of the dominant frequency was slightly more accurate when, in the Zwart et al. cavitation model, the default condensation and evaporation model constants were replaced with previously calibrated ones. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Numerical Heat Transfer Part B-fundamentals, Oct 1, 1996
A time-accurate, additive-correction multigrid method for the prediction of two-dimensional unste... more A time-accurate, additive-correction multigrid method for the prediction of two-dimensional unsteady flows is presented in this article. The method makes use of the additive-correction multigrid strategy, which, originally proposed for steady-flow problems, is extended to the calculation of time-dependent and chaotic flows at high Reynolds or Rayleigh numbers. The numerical algorithm guarantees absolute, to machine accuracy, mass conservation at every time step, and it is characterized by second-order accuracy in space and time. In a companion article [1], the method is applied to the calculation of unsteady flow in cavities, i.e., the lid-driven cavity problem at high Reynolds number, and the buoyant flow in differentially heated cavities at high values of the Rayleigh number. Although the method has been implemented and tested for two-dimensional flows, it can also be extended to three-dimensional problems.
Numerical Heat Transfer Part B-fundamentals, Oct 1, 1996
An additive-correction multigrid method for the prediction of two-dimensional unsteady flows, des... more An additive-correction multigrid method for the prediction of two-dimensional unsteady flows, described in a previous article [1], is applied to selected cavity flow problems. The cases considered are the lid-driven cavity problem and the buoyant flow in differentially heated cavities. Accurate results are obtained for the lid-driven cavity, where fine-grid, high-Reynolds-number calculations, indicate that the steady flow bifurcates to a periodic regime for a Reynolds value in the range 7,500-10,000. The results for side-heated rectangular enclosures are presented first for a Prandtl number equal to zero, and corresponding values of Grashof number of 1.2 × 10 and 1.6 × 10. In addition, a Prandtl number of 0.71 is considered, with values of the Rayleigh number of 1 × 10, 2 × 10, and 2 × 10. The study demonstrates that the additive-correction multigrid method is computationally efficient, and is capable of performing accurate simulations of time-dependent, and possibly chaotic, flows in enclosures.
In this work we illustrate the combined use of the modeFRONTIER optimization system, together wit... more In this work we illustrate the combined use of the modeFRONTIER optimization system, together with the unstructured finite element FEMLAB package, for some selected conduction and convection heat transfer problems. The conductive problems are relative to optimization of cylindrical fins, and direct design of shape for a heated substrate cooled by convection. The multiobjective optimization of two-dimensional convective flow passages, representative of subsystems for compact heat exchangers, is considered, where maximization of heat transfer rate and minimization of friction losses are the main goals. It is concluded that our approach is accurate and robust, and provides a flexible and user-friendly environment for design tasks of heat transfer systems and devices. The multiphysics capabilities of FEMLAB, coupled with the modeFRONTIER optimization system, constitute a convenient and powerful tool for complex design tasks and research activities
The time-dependent, buoyancy-driven flow in cavities heated and cooled from the side, with adiaba... more The time-dependent, buoyancy-driven flow in cavities heated and cooled from the side, with adiabatic horizontal walls, is investigated with an implicit, two-dimensional finite volume scheme. The numerical algorithm integrates the Navier-Stokes equations, in primitive form, with a second-order accurate time-stepping scheme, and it is characterized by absolute, to machine accuracy, mass conservation. The results are presented for a Prandtl number, Pr, of 0.005, and corresponding values of Grashof number, Gr, of 1x10^6 and 3x10^6 and a value of Pr of 0.71, with a value of the Rayleigh number, Ra, of 2x10^9. For the results with Pr = 0.005, the effects of time-stepping order and spatial and temporal resolutions are identified and discussed. For the Pr = 0.71 case, the results are qualitatively compared with spectral-code predictions with favorable agreement. It is concluded that first-order time-stepping schemes should not be used when dealing with time-dependent buoyant flows, and that the proposed algorithm is capable of performing accurate simulations of unsteady, and possibly chaotic, convective flows in side-heated cavities
The numerical predictions of a cavitating model scale propeller working in uniform and oblique fl... more The numerical predictions of a cavitating model scale propeller working in uniform and oblique flow conditions are presented. The cavitating phenomena are numerically reproduced using a homogeneous (mixture) model where three previously calibrated mass transfer models are alternatively used to model the mass transfer rate. The turbulence effect is modelled using the Reynolds Averaged Navier Stokes (RANS) approach. The simulations are performed using an open source solver. The numerical results are compared with available experimental data. For a quantitative comparison the propeller thrust is considered, while for a qualitative comparison, snapshots of cavitation patterns are shown. The thrust values obtained with the three different mass transfer models are very close to each other, however differences in the predicted cavitation patterns are observed. Moreover, some discrepancies between the numerical results and experimental data are reported.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
International Journal of Thermal Sciences, Sep 1, 2006
In this paper, a numerical study of natural convection in a 2D-enclosure is presented. The enclos... more In this paper, a numerical study of natural convection in a 2D-enclosure is presented. The enclosure is bounded by two vertical isothermal walls, kept at different temperatures, and by two adiabatic walls which are either straight and horizontal (rectangular cavity) or elliptic (modified rectangular cavity). The dimensionless mass, momentum and energy balance equations are solved by means of two different software packages based on Galerkin finite element methods. An excellent agreement between the solutions is found and provides a cross-validation of the results. Two basic geometries are considered: a square geometry and a rectangular one with height double the width. For each basic geometry, three cavities are investigated: a rectangular cavity, and two modified rectangular cavities. Dry air is considered, with several values of the Rayleigh number. The results show that the elliptic boundaries enhance the mean Nusselt number and the dimensionless mean kinetic energy of the fluid.
Uploads
Papers by Enrico Nobile