**Study on Multiple-Time-Scale Reynolds Stress Model**

(Second Report, Verification for Grid Turbulence)

Conventional turbulence models have a single time-scale of turbulence. Therefore, they can not predict the flows that are influenced by a lot of time-scales of turbulence. In simulating such flows it is necessary to introduce some information about the scales of turbulence.

In order to overcome this problem, I proposed a multiple-time-scale Reynolds model and the model coefficients were determined for a grid turbulent flow. In this study, the model was applied to a variety of grid turbulent flows to verify the model performance. The numerical results for turbulent energy, Reynolds stresses, second and third invariants were compared with the experimental data. The temporal change of large and small scale components for Reynolds stresses and energy transport rates were also checked (Fig.1). It was found that the model can satisfactorily predict a wide range of grid turbulent flows. In addition, it was verified that the method used in setting initial conditions is reasonable.

*Key Words*: Computational Fluid Dynamics, Turbulent Flow, Turbulence,Reynolds Stress Model, Multiple-Time-Scale Model

Fig.1

**Computation of Turbulent Flow in a Cyclone Chamber with a Reynolds Stress Model**

(Second Report, Numerical Prediction of Cyclone Performance)

The Reynolds stress model and the standard k-e eddy viscosity model were applied to highly swirling confined flows in six types of cyclones, which are widely used as the centrifugal separators in industrial applications (Fig.2), in order to predict numerically the collection efficiency of dust particles and the pressure loss across the cyclone. The Reynolds stress model can capture the feature of the highly swirling turbulence field correctly, while the standard k-e model misrepresents the flow characteristics due to the defect in its eddy viscosity hypothesis. Prediction of the collection efficiency is, therefore, improved by the Reynolds stress model against the standard k-e model. In addition, the pressure losses obtained by the Reynolds stress model calculation are in good agreement with experimental data (Fig.3).

*Key Words*: Numerical Analysis, Turbulent Flow, Swirling Flow, Reynolds Stress Model,Cyclone Separator, 2-Dimensional Axisymmetric Flow, Collection Efficiency, Pressure Loss

Fig.2

Fig.3

**Acceleration of Computations with Fuzzy Reasoning**

(Fuzzy Reasoning for General Coordinate System)

Numerical simulations for every flow require enormous computing time during iterations. In order to solve this problem several techniques have been proposed, as for example a multigrid technique. A method using fuzzy reasoning is one such technique. We studied the possibility of accelerating computation with fuzzy reasoning in two dimensional incompressible laminar flow calculations. In order to obtain qualitatively correct velocity distributions some rules were constructed on the basis of human reasoning. Viscous and obstacle effects were introduced. In addition, the recognition of walls was programmed to find the separation point and the recirculation region. It was found that (i)our procedure can reproduce the channel flows which have some convexities and the backward-facing step flow (Fig.4) and (ii)it can realize a considerable acceleration in all calculations (Table 1).

Fig.4

Table 1