J. Hernández

Survey of modelling methods for wind turbine wakes and wind farms

This article provides an overview and analysis of different wake-modelling methods which may be used as prediction and design tools for both wind turbines and wind farms. We also survey the available data concerning the measurement of wind magnitudes in both single wakes and wind farms, and of loading effects on wind turbines under single- and multiple-wake conditions. The relative merits of existing wake and wind farm models and their ability to reproduce experimental results are discussed. Conclusions are provided concerning the usefulness of the different modelling approaches examined, and difficult issues which have not yet been satisfactorily treated and which require further research are discussed. Copyright

Experimental validation of the UPM computer code to calculate wind turbine wakes and comparison with other models

Abstract The UPM Computer Code to calculate wind turbine wakes is applied to test cases, both in wind tunnel and in field experiments with full scale machines, in order to validate the model used in the code. In the UPM model the wake of the wind turbine is supposed to be immersed in a non-uniform air stream corresponding to the atmospheric boundary layer. The turbulent transport coefficients are modelled by the k-ϵ method. Relevant parameters describing the process are wind velocity at turbine height, ground roughness, atmospheric stability, turbine dimensions and initial momentum deficit. The wind tunnel measurements correspond to experiments carried out at TNO. The full scale experiments chosen for comparison are those from Nibe wind turbines in Denmark. The results of the UPM Code are also compared with those obtained with other simpler models.

Short Note: Analytical and geometrical tools for 3D volume of fluid methods in general grids

It is well known that volume of fluid (VOF) methods in three-dimensions, especially those based on unsplit advection schemes, involve highly complex geometrical operations. The objective of this work is to propose, for general grids and three-dimensional Cartesian geometry, simple and efficient geometrical tools for volume truncation operations that typically arise in VOF methods and an analytical method for local volume enforcement. The results obtained for different tests and grid types show that the proposed analytical method may be as much as three times faster than Brents iterative method. Advection tests were carried out using hexahedral grids obtained from deformation of a cubic grid to assess the accuracy of the proposed tools in combination with a recently proposed unsplit PLIC-VOF method.

Influence of variable property effects on natural convection flows in asymmetrically-heated vertical channels

The influence of variable property effects on the laminar air flow induced by natural convection in a vertical, asymmetrically-heated channel is investigated. A full-elliptic model that accounts for variations of viscosity and thermal conductivity with temperature and determines the density from the state equation, has been solved numerically for cases for which variable property effects are important, particularly for conditions for which flow reversals may appear. The corresponding numerical results are compared with those obtained from an alternative model in which all thermophysical properties are assumed to be constant and the Boussinesq approximation is used. It has been found that variable property effects have a strong influence, not reported in previous works, on the recirculation patterns, and may produce, for certain ranges of parameters that roughly coincide with those for which flow reversals exist, an increase in the mass flow rate induced in the channel.

On the optimum plunger acceleration law in the slow shot phase of pressure die casting machines

The objective of this paper is to analyse a plunger acceleration law that is expected to minimize air entrapment in the slow shot phase of pressure die casting in horizontal cold chambers, and thus to reduce porosity in manufactured parts. The study is carried out using results from an analytical model of the flow of molten metal in the shot sleeve, which is based on the shallow-water approximation, and whose predicted optimum acceleration parameters are in good agreement with available experimental results. The results for the surface profiles of the wave formed during plunger movement using plunger acceleration laws which are typically used in pressure die casting are compared with those corresponding to the proposed law. Some analytical predictions for the wave profiles and for the mass of trapped air are compared with numerical results obtained from a finite-element code, which solves momentum and mass conservation equations. The limiting values of the initial filling fraction required for appropriate operating conditions are determined for wide ranges of acceleration parameters and pouring hole locations.

Short Note: On reducing interface curvature computation errors in the height function technique

A detailed analysis of the errors involved in computing the interface curvature from volume fraction distributions using a height function technique is presented. An improved version of the height function technique is proposed, based on introducing a correction of the height function discretization error estimated from the local osculating spheres at interface points. By using this error correction and an appropriate discretization of the partial derivatives of the height function, a substantial improvement in the accuracy of the interface curvature computation can be efficiently achieved.

Influence of upstream conduction on the thermally optimum spacing of isothermal, natural convection-cooled vertical plate arrays

Abstract The influence of upstream conduction on the thermal optimization of the spacing used in arrays of equally spaced, natural convection-cooled vertical plates is investigated. The optimization is carried out analytically by maximizing the total heat transfer rate per unit horizontal area with respect to plate spacing. Correlations for the average Nusselt number are taken from the literature, derived analytically or obtained from results of an elliptic numerical model. Ranges of the Rayleigh number (based on the channel length) for which upstream conduction effects modify the optimum spacing obtained using the Elenbaas asymptote, are determined for two different Prandtl numbers.

Shot Sleeve Wave Dynamics in the Slow Phase of Die Casting Injection

An analysis is carried out on the wave formed during the slow phase of die casting injection processes. Viscous effects are assumed to be negligible and the problem is treated two-dimensionally using finite amplitude wave theory. Two commonly used types of plunger movements are considered, for which all the possible wave profiles are analyzed in depth as a function of the parameters which characterize the law of acceleration applied to the plunger, the initial shot sleeve filling fraction, and the geometrical characteristics of the problem. Different relationships between the relevant dimensionless parameters of the system are proposed, which make it possible to optimize the injection process, and so reduce the entrapment of air which leads to porosity. The validity of such relationships is analyzed in detail for different ranges of parameters. Some of the results obtained for the optimum acceleration are compared with those of other authors and experimental measurements. Finally, a law of plunger acceleration which would completely eliminate the air from the shot sleeve at the end of the slow phase of injection and minimizes the filling time is derived.

On the Critical Plunger Speed and Three-Dimensional Effects in High-Pressure Die Casting Injection Chambers

During the initial slow stage of the injection process in high-pressure die casting machines with horizontal cold chamber, a plunger pushes the molten metal which partially fills the injection chamber, causing the formation of a gravity wave. The evolution of the wave surface profile, which depends on the plunger acceleration law, may trap air in the molten metal, causing porosity when the metal solidifies. In this work, a one-dimensional shallow-water model, which is solved numerically using the method of characteristics, and a three-dimensional numerical model, based on a finite element formulation and the volume of fluid (VOF) method for treating the free surface, are used to analyze the flow of molten metal in an injection chamber of circular cross section. The results for the evolution of the free surface obtained from both models for different plunger motion laws and initial filling fractions of the injection chamber were in good agreement for broad ranges of operating conditions. The existence of a critical plunger speed, above which the reflection of the wave of molten metal against the chamber ceiling might appreciably increase air entrapment effects, is investigated. The results for the wave profiles in chambers of circular cross section are compared with those obtained in an equivalent two-dimensional configuration of the injection chamber, for which the shallow-water model is solved analytically. It is shown how the results obtained by applying the one-dimensional model to a two-dimensional chamber configuration can be used to reproduce, with an acceptable degree of accuracy, the salient characteristics of the flow of molten metal in a real injection chamber of circular cross section.

Numerical modeling of turbulent jet diffusion flames in the atmospheric surface layer

The evolution of turbulent jet diffusion flames of natural gas in air is predicted using a finite-volume procedure for solving the flow equations. The model is three dimensional, elliptic and based on the conserved-scalar approach and the laminar flamelet concept. A laminar flamelet prescription for temperature, which is in agreement with measurements in methane/air flames and accounts for radiative heat losses, has been modified and adapted to natural-gas flames. The k-e-g turbulence model has been used. Different probability-density functions for the conserved scalar and an alternative method which does not require the use of a pdf are employed. The model has been applied to flames in the buoyancy-momentum transition regime, in both cases where the fuel jet is immersed in a co-flowing or in a cross-flow air stream whose properties correspond to the atmospheric surface layer. Experiments have been carried out for a horizontal flame in a wind tunnel with simulated atmospheric boundary layer, and measurements of temperature distributions are compared with the numerical results; a good agreement is found. The influence of wind properties on flame shape has been investigated. For horizontal flames, a correlation is proposed for the stoichiometric flame length as a function of the Froude number and the wind to jet velocity ratio. Flame length predictions have been compared with available experimental data and correlations proposed in the literature.