Engineering topics

Knaepen, B.

Publications and source records attributed to Knaepen, B..

6 records

NASA NTRS2004

Anisotropy of MHD Turbulence at Low Magnetic Reynolds Number

Turbulent fluctuations in MHD flows are known to become dimensionally anisotropic under the action of a sufficiently strong magnetic field. We consider the technologically relevant case of low magnetic Reynolds number and apply the method of DNS of forced flow in a periodic box to generate velocity fields. The analysis based on different anisotropy characteristics shows that the dimensional anisotropy is virtually scale-independent. We also find that, except for the case of very strong magnetic field, the flow is componentally isotropic. Its kinetic energy is practically uniformly distributed among the velocity components.

Zikanov, O.↗

NASA NTRS2004

MHD Turbulence Sheared in Fixed and Rotating Frames

We consider homogeneous turbulence in a conducting fluid that is exposed to a uniform external magnetic field while being sheared in fixed and rotating frames. We take both the frame-rotation axis and the applied magnetic field to be aligned in the direction normal to the plane of the mean shear. Here a systematic parametric study is carried out in a series of Direct Numerical Simulations (DNS) in order to clarify the main effects determining the structural anisotropy and stability of the flow.

Kassinos, S. C.↗

NASA NTRS2004

Sampling Versus Filtering in Large-Eddy Simulations

A LES formalism in which the filter operator is replaced by a sampling operator is proposed. The unknown quantities that appear in the LES equations originate only from inadequate resolution (Discretization errors). The resulting viewpoint seems to make a link between finite difference approaches and finite element methods. Sampling operators are shown to commute with nonlinearities and to be purely projective. Moreover, their use allows an unambiguous definition of the LES numerical grid. The price to pay is that sampling never commutes with spatial derivatives and the commutation errors must be modeled. It is shown that models for the discretization errors may be treated using the dynamic procedure. Preliminary results, using the Smagorinsky model, are very encouraging.

Debliquy, O.↗

NASA NTRS2003

Large-Eddy Simulation of Conductive Flows at Low Magnetic Reynolds Number

In this paper we study the LES method with dynamic procedure in the context of conductive flows subject to an applied external magnetic field at low magnetic Reynolds number R(sub m). These kind of flows are encountered in many industrial applications. For example, in the steel industry, applied magnetic fields can be used to damp turbulence in the casting process. In nuclear fusion devices (Tokamaks), liquid-lithium flows are used as coolant blankets and interact with the surrounding magnetic field that drives and confines the fusion plasma. Also, in experimental facilities investigating the dynamo effect, the flow consists of liquid-sodium for which the Prandtl number and, as a consequence, the magnetic Reynolds number is low. Our attention is focused here on the case of homogeneous (initially isotropic) decaying turbulence. The numerical simulations performed mimic the thought experiment described in Moffatt in which an initially homogeneous isotropic conductive flow is suddenly subjected to an applied magnetic field and freely decays without any forcing. Note that this flow was first studied numerically by Schumann. It is well known that in that case, extra damping of turbulence occurs due to the Joule effect and that the flow tends to become progressively independent of the coordinate along the direction of the magnetic field. Our comparison of filtered direct numerical simulation (DNS) predictions and LES predictions show that the dynamic Smagorinsky model enables one to capture successfully the flow with LES, and that it automatically incorporates the effect of the magnetic field on the turbulence. Our paper is organized as follows. In the next section we summarize the LES approach in the case of MHD turbulence at low R(sub m) and recall the definition of the dynamic Smagorinsky model. In Sec. 3 we describe the parameters of the numerical experiments performed and the code used. Section 4 is devoted to the comparison of filtered DNS results and LES results. Conclusions are presented in Sec. 5.

Knaepen, B.↗

NASA NTRS2003

MHD Turbulence at Moderate Magnetic Reynolds Number

In the present article we will consider the decay of MHD turbulence under the influence of a strong external magnetic field at moderate magnetic Reynolds numbers. Typical values of R(sub m) that are considered here range from R(sub m) approx. 0.1 to R(sub m) approx. 20. As a comparison, the initial kinetic Reynolds number common to all our simulations is Re(sub L) = 199. This means that the range of Prandtl numbers explored is 5 x 10(exp -4) to 10(exp -1). Our motivation is mainly to exhibit how the transition from the QS approximation to FMHD occurs. At the lowest values of R(sub m) studied here, the QS approximation is shown to model the flow faithfully. However, for the higher values of R(sub m) considered, it is clearly inadequate but can be replaced by another approximation which will be referred to as the Quasi-Linear (QL) approximation. Another objective of the present study is to describe how variations in the magnetic Reynolds number (while maintaining all other parameters constant) affect the dynamics of the flow. This complements past studies where variations in either the strength of the external magnetic field or the kinetic Reynolds number were considered. This article is organized as follows. In section 2 we recall the definition of the quasi-static approximation. Section 3 is devoted to the description of the numerical experiments performed using the quasi-static approximation and full MHD. In section 4 we describe the quasi-linear approximation and test it numerically against full MHD. A concluding summary is given in section 5.

Knaepen, B.↗

NASA NTRS2003

DNS and LES of a Shear-Free Mixing Layer

The purpose of this work is twofold. First, given the computational resources available today, it is possible to reach, using DNS, higher Reynolds numbers than in Briggs et al.. In the present study, the microscale Reynolds numbers reached in the low- and high-energy homogeneous regions are, respectively, 32 and 69. The results reported earlier can thus be complemented and their robustness in the presence of increased turbulence studied. The second aim of this work is to perform a detailed and documented LES of the shear-free mixing layer. In that respect, the creation of a DNS database at higher Reynolds number is necessary in order to make meaningful LES assessments. From the point of view of LES, the shear-free mixing-layer is interesting since it allows one to test how traditional LES models perform in the presence of an inhomogeneity without having to deal with difficult numerical issues. Indeed, as argued in Briggs et al., it is possible to use a spectral code to study the shear-free mixing layer and one can thus focus on the accuracy of the modelling while avoiding contamination of the results by commutation errors etc. This paper is organized as follows. First we detail the initialization procedure used in the simulation. Since the flow is not statistically stationary, this initialization procedure has a fairly strong influence on the evolution. Although we will focus here on the shear-free mixing layer, the method proposed in the present work can easily be used for other flows with one inhomogeneous direction. The next section of the article is devoted to the description of the DNS. All the relevant parameters are listed and comparison with the Veeravalli & Warhaft experiment is performed. The section on the LES of the shear-free mixing layer follows. A detailed comparison between the filtered DNS data and the LES predictions is presented. It is shown that simple eddy viscosity models perform very well for the present test case, most probably because the flow seems to be almost isotropic in the small-scale range that is not resolved by the LES.

Knaepen, B.↗