Asymmetric structure of an isolated flux arch

This paper extends two-dimensional model of symmetric magnetostatic flux arches confined in stratified atmospheres (Zhang and Hu, 1992, 1993) to asymmetric models. Numerical results show that the flux structure is influenced greatly by the boundary condition of magnetic field, the force-free factor, the atmospheric pressure distribution and the position of footpoints (especially the width ratio of outlet to entrance, which differs from symmetric case).

Equilibrium of isolated magnetostatic flux structure

Two-dimensional magnetostatic models of flux structure confined in stratified atmosphere are discussed in the present paper. The magnetic field in the flux structure is assumed to be force-free at the first step. Numerical solutions for this nonlinear free boundary problem are obtained by finite element method. Results show clearly the relation between the inside fields and outside pressure, especially the influence of atmospheric pressure distribution on the flux structure.

Magnetostatic configuration of a confined magnetic-flux tube

In this paper an isolated magnetic flux tube confined in stratified atmosphere is studied for slender and axisymmetric model. The functions of the pressure, density, and temperature are expanded as a Taylor series of magnetic surface function psi. Several models of an isolated magnetic flux tube confined in a stratified atmosphere are constructed, and the external pressure of the stratified atmosphere decreases reasonably with increasing height. The distribution of thermal dynamic quantities and the magnetic pressure in the flux tube are also obtained.

Magnetostatic equilibrium of isolated magnetic-flux tube

In the present paper, an isolated axisymmetric flux tube is discussed for slender magnetic configuration. The magnetostatic model and the stratified atmospheric model are applied, respectively, to the regions inside and outside the flux tube. The problem is described mathematically by the nonlinear partial differential equations under the nonlinear boundary condition at the free boundary of flux tube. According to the approximation of a small expansive angle, the solutions of series expressions are obtained formally. The model of polytropic plasma is discussed in detail especially. The results show the distributions of thermodynamic quantities and magnetic field extending from the high β region to the low β region, and the flux tube may be either divergent or convergent according to the pressure difference outside and inside the flux tube.

A model of an isolated magnetic-flux tube in a stratified atmosphere

A two-dimensional model of a magnetic flux tube confined in a gravitational stratified atmosphere is discussed. The magnetic field in the flux tube is assumed to be force-free. By using the approximation of large scale height, the problem of a free boundary with nonlinear conditions may be reduced to one involving a fixed boundary. The two-dimensional features are obtained by applying the perturbation method and adopting the Luest-Schlueter model as the basic state. The results show that the configuration of a flux tube confined in a gravitational stratified atmosphere is divergent, and the more twisted the magnetic field, the more divergent is the flux tube.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

Prediction of particle distribution in isotropic turbulence by large-eddy simulation

The recent application of large-eddy simulation (LES) to particle-laden turbulence requires that the LES with a subgrid scale (SGS) model could accurately predict particle distributions. Usually, a SGS particle model is used to recover the small-scale structures of velocity fields. In this study, we propose a rescaling technique to recover the effects of small-scale motions on the preferential concentration of inertial particles. The technique is used to simulate particle distribution in isotropic turbulence by LES and produce consistent results with direct numerical simulation (DNS). Key words: particle distribution, particle-laden turbulence, large-eddy simulation, subgrid scale model.

Multi-pipe string electromagnetic detection tool and its applications

The MID-K, a new kind of multi-pipe string detection tool is introduced. This tool provides a means of evaluating the condition of in-place pipe string, such as tubing and casino. It is capable of discriminating the defects of the inside and outside, and estimating the thickness of tubing and casing. It is accomplished by means of a low frequency eddy current to detect flaws on the inner surface and a magnetic flux leakage to inspect the full thickness. The measurement principle, the technology and applications are presented in this paper.

A kinematic subgrid scale model for large-eddy simulation of turbulence generated sound

In the hybrid approach of large-eddy simulation (LES) and Lighthill’s acoustic analogy for turbulence-generated sound, the turbulence source fields are obtained using an LES and the turbulence-generated sound at far fields is calculated from Lighthill’s acoustic analogy. As only the velocity fields at resolved scales are available from the LES, the Lighthill stress tensor, serving as a source term in Lighthill’s acoustic equation, has to be evaluated from the resolved velocity fields. As a result, the contribution from the unresolved velocity fields is missing in the conventional LES. The sound of missing scales is shown to be important and hence needs to be modeled. The present study proposes a kinematic subgrid-scale (SGS) model which recasts the unresolved velocity fields into Lighthill’s stress tensors. A kinematic simulation is used to construct the unresolved velocity fields with the imposed temporal statistics, which is consistent with the random sweeping hypothesis. The kinematic SGS model is used to calculate sound power spectra from isotropic turbulence and yields an improved result: the missing portion of the sound power spectra is approximately recovered in the LES.

Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. Our analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been devel- oped to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries.

Development And Application Of Flexible Substrate Sensors In Instantaneous Heat Flux Measurement

A new type of sensor with the flexible substrate is introduced. It is applicable in measuring instantaneous heat flux on the model surface in a hypersonic shock tunnel. The working principle, structure and manufacture process of the sensor are presented. The substrate thickness and the dynamic response parameter of the sensor are calculated. Because this sensor was successfully used in measuring the instantaneous heat flux on the surface of a flat plate in a detonation-driven shock tunnel, it may be effective in measuring instantaneous heat flux on the model surface.