Koichi Nakabayashi

Direct Numerical Simulation of Compressible Turbulent Channel Flow between Adiabatic and Isothermal Walls

In this paper, the effects of adiabatic and isothermal conditions on the statistics in compressible turbulent channel flow are investigated using direct numerical simulation (DNS). DNS of two compressible turbulent channel flows (Cases 1 and 2) are performed using a mixed Fourier Galerkin and B-spline collocation method. Case 1 is compressible turbulent channel flow between isothermal walls, which corresponds to DNS performed by Coleman et al. (1995). Case 2 is the flow between adiabatic and isothermal walls. The flow of Case 2 can be a very useful framework for the present objective, since it is the simplest turbulent channel flow with an adiabatic wall and provides ideal information for modelling the compressible turbulent flow near the adiabatic wall. Note that compressible turbulent channel flow between adiabatic walls is not stationary if there is no sink of heat. In Cases 1 and 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5, and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000. To compare compressible and incompressible turbulent flows, DNS of two incompressible turbulent channel flows with passive scalar transport (Cases A and B) are performed using a mixed Fourier Galerkin and Chebyshev tau method. The wall boundary conditions of Cases A and B correspond to those of Cases 1 and 2, respectively. Case A corresponds to the DNS of Kim & Moin (1989). In Cases A and B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150. The mean velocity and temperature near adiabatic and isothermal walls for compressible turbulent channel flow can be explained using the non-dimensional heat flux and the friction Mach number. It is found that Morkovins hypothesis is not applicable to the near-wall asymptotic behaviour of the wall-normal turbulence intensity even if the variable property effect is taken into account. The mechanism of the energy transfers among the internal energy, mean and turbulent kinetic energiesis investigated, and the difference between the energy transfers near isothermal and adiabatic walls is revealed. Morkovins hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall.

Transition of Taylor–Görtler vortex flow in spherical Couette flow

The critical Taylor number, phenomena accompanying the transition to turbulence, and the cellular structure of Taylor–Gortler vortex in the flow between two concentric spheres, of which the inner one is rotating and the outer is stationary, are investigated using three kinds of flow-visualization technique. The critical Taylor number generally increases with the ratio β of clearance to inner-sphere radius. For β [les ] 0.08, the critical Taylor number in spherical Couette flow is smaller than in circular Couette flow, but vice versa for β > 0.08. A pair of toroidal Taylor–Gortler vortices occurs first around the equator at the critical Reynolds number R ec (or critical Taylor number T c ). More Taylor–Gortler vortices are added with increasing Reynolds number R e . After reaching the maximum number of vortex cells, as R e is increased, the number of vortex cells decreases along with the various transition phenomena of Taylor–Gortler vortex flow, and the vortex finally disappears for very large R e , where the turbulent basic flow is developed. The instability mode of Taylor–Gortler vortex flow depends on both β and R e . The vortex flows encountered as R e is increased are toroidal, spiral, wavy, oscillating (quasiperiodic), chaotic and turbulent Taylor–Gortler vortex flows. Fourteen different flow regimes can be observed through the transition from the laminar basic flow to the turbulent basic flow. The number of toroidal and/or spiral cells and the location of toroidal and spiral cells are discussed as a means to clarify the spatial organization of the vortex. Toroidal cells are stationary. However, spiral cells move in relation to the rotating inner sphere, but in the reverse direction of its rotation and at about half its speed. The spiral vortices number about six, and the spiral angle is 2–10°.

Low Reynolds number fully developed two-dimensional turbulent channel flow with system rotation

Theoretical and experimental studies have been performed on fully developed two-dimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u * D/v (u * is the friction velocity, D the channel half-width) and Ωv/u * 2 (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u * for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u * 2 ≤ 0.0030 (these values correspond to Re = 2U m D/v from 1700 to 10000 and rotation number Ro = 2 |Ω|D/U m up to 0.055 ; U m is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.

Dynamics of anisotropy on decaying homogeneous turbulence subjected to system rotation

The dynamics of the anisotropy of the Reynolds stress tensor and its behavior in decaying homogeneous turbulence subjected to system rotation are investigated in this study. Theoretical analysis shows that the anisotropy can be split into two parts: polarization and directional anisotropies. The former can be further separated into a linear part and a nonlinear part. The corresponding linear solution of the polarization anisotropy is derived in this paper. This solution is found to be equivalent to the linear solution of the anisotropy. While proposing a method to introduce the polarization anisotropy into an isotropic turbulence, direct numerical simulation (DNS) of the rotating turbulence with or without the initial anisotropy is carried out. The linear solution of the anisotropy agrees very well with the DNS result, showing that the evolution of the polarization anisotropy is mainly dominated by the linear effect of the system rotation. With an immediate rotation rate, the coupling effect between the s...

Turbulence characteristics of two-dimensional channel flow with system rotation

Turbulence quantities have been measured for a low-Reynolds-number fully developed two-dimensional channel flow subjected to system rotation. Turbulence intensities, Reynolds shear stress, correlation coefficient, skewness and flatness factors, four-quadrant analysis, autocorrelation coefficient and power spectra are investigated. According to the dimensional analysis, the relevant parameters of this flow are the Reynolds number

A DNS algorithm using B-spline collocation method for compressible turbulent channel flow

\hbox{\it Re}^{\ast}\,{=}\,u^{*}D/\nu

Flow-history effect on higher modes in the spherical Couette system

and the Coriolis parameter

Similarity laws of velocity profiles and turbulence characteristics of Couette-Poiseuille turbulent flows

Rc\,{=}\,\Omega \nu/u^{*2}

A new DNS algorithm for rotating homogeneous decaying turbulence

for the wall region, and

Modulated and unmodulated travelling azimuthal waves on the toroidal vortices in a spherical Couette system

Re^*