Direct numerical simulation of the turbulent MHD channel flow at low magnetic Reynolds number for electric correlation characteristics

Abstract

Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption. The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations. The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner. The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations. The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model. The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation, while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation. low magnetic Reynolds number assumption, magnetohydrodynamic turbulence, DNS, velocity-electric field correlation, electric-electric field correlation, channel flow PACS: 47.65.-d, 47.27.ek, 47.27.nd Research on magnetohydrodynamic (MHD) turbulence is motivated by the following two applications: The first one is that the numerical predictions of aerothermodynamic performance of MHD enhanced scramjet engine are conducted under the laminar flow assumption at the present stage [1]. Nevertheless, the real flows in the engine under operation are in essence turbulent. Thus, MHD turbulence studies and modeling become necessary in order to acquire more accurate performance predictions and obtain an optimal design for the MHD enhanced scramjet engine. Second, studies readily show that the presence of magnetic field affects the drag, and suppresses the velocity fluctuations of the turbulent flows [2]. The applications of magnetic field in the active/passive flow control of turbulence require the knowledge of turbulence-magnetic field interaction mechanisms.Experiment has long been a reliable means in turbulence research to provide data for practical applications. However, liquid metals are frequently used in MHD experiments. Due to their high operational temperatures together with opaque or corrosive properties, the ordinary measurement techniques such as PIV, LDV would not be applicable. As a result, the experimental data presently available are found to be much less than the ordinary turbulence flows. The direct numerical simulation (DNS) which contains no experiential parameter is the only numerical means compatible to the experiment. Extensive work using DNS has been accomplished. Noguchi and Kasagi [3,4] from THT Lab carried out a DNS of turbulent channel flows with streamwise and wall-normal magnetic fields, and published the DNS data at THT Lab website (ftp.thtlab.t.u-tokyo.ac.jp/DNS). Lee [5] reported a DNS of turbulent channel flows with different

Nonlinear eddy viscosity <italic>k-ω</italic> turbulence model for incompressible low <italic>Re</italic><sub>M</sub> magnetohydrodynamic flows

“…在本模型方程(9)和(10)中, 雷诺 应力引用了 Song 等人 [11] 提出的 k-  非线性涡黏模型. 略去表达曲率效应的三次项有 2), (9)和(10)中对流项为 0, 并且可以证明 [8] , 此时电势方程存在解析解, 可以显式给出槽道中的 平均电场:…”