No abstract

Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work analytically defined Gas-Kinetic schemes based on the Shakhov and Rykov models, for monoatomic and diatomic gas flows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for rarefied gas flows at high velocities it is necessary to take into account the non-equilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models with rotational relaxation is a mandatory first step towards realistic simulations. Compared to previous works of Xu and co-workers the presented scheme is defined directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum flows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rarefied flows.

The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance.Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way to include transitional effects into practical CFD simulations. However, the model involves coefficients to be tuned to match the required application. In this paper, the γ−equation transition model is assessed and calibrated, for a wide range of Reynolds numbers at low Mach, as needed for wind turbine applications. Different aerofoils are used to evaluate the original model and calibrate it; while a large scale wind turbine blade is employed to show that the calibrated model can lead to reliable solution for complex three-dimensional flows. The calibrated model shows promising results for both two-dimensional and three-dimensional flows, even if cross-flow instabilities are neglected.

Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work analytically defined Gas-Kinetic schemes based on the Shakhov and Rykov models, for monoatomic and diatomic gas flows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for rarefied gas flows at high velocities it is necessary to take into account the non-equilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models with rotational relaxation is a mandatory first step towards realistic simulations. Compared to previous works of Xu and co-workers the presented scheme is defined directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum flows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rarefied flows.

SUMMARYAt the University of Liverpool, the Helicopter Multi‐Block (HMB2) CFD code is used for studies of various subsonic and transonic flows. This paper presents the implicit implementation in HMB2 of the AUSM +  and AUSM + up, with a fully analytical Jacobian, so that a wider range of Mach numbers can be modelled, including high‐speed flows. A description of the derivation of the analytical Jacobian is given in this paper along with an evaluation of the performance of the implicit schemes for different test cases, including turbulent flows. As examples of high‐speed flows of aerospace interest, a blunt body, a single cone, a shock wave/turbulent boundary‐layer interaction and the Orion spacecraft have been considered. For the transonic regime, the RAE2822 aerofoil and the ONERA M6 wing have been used as test cases. Finally, for low Mach flows, the S809 wind turbine aerofoil and the MEXICO project wind turbine blade have been chosen. The shear stress transport and κ– ω turbulence models have been employed for the turbulent cases. The proposed implicit implementation of the AUSM +  and AUSM + up schemes proved to have good efficiency and robustness without affecting the reliability of the original schemes.Copyright © 2014 John Wiley & Sons, Ltd.