Ken-ichi Abe

Towards the development of a Reynolds-averaged algebraic turbulent scalar-flux model

Abstract In order to derive a possible direction for developing Reynolds-averaged algebraic turbulent scalar-flux models, a priori explorations are attempted by processing the LES data presently performed for channel flows under several flow-boundary conditions including shear-free boundaries. The present calibration has elucidated that the turbulent scalar-flux vectors obtainable from the simple generalized gradient-diffusion hypothesis (GGDH) hardly align with the simulation results in wall-shear flows at Pr ⩾0.71. However, the GGDH form returns a quite reasonable approximation in shear-free flow regions and/or lower Pr fluid cases. In the former flow cases, it has been found that an introduction of quadratic products of the Reynolds-stress tensor into the gradient diffusion model may improve the predictive performance.

An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models

Abstract New closure approximations are proposed, within the framework of non-linear eddy-viscosity modeling, which aim specifically at an improved representation of near-wall anisotropy in both shear and stagnation flows. The main novel element is the introduction of tensorial terms, alongside strain and vorticity, which depend on wall-direction indicators and which procure the correct asymptotic near-wall behavior of the Reynolds stresses. The newly formulated non-linear constitutive equation for the Reynolds stresses is combined with low-Reynolds-number forms of equations for the rate of dissipation e or the specific dissipation ω, the latter incorporating a number of new features into the established form of the equation. The predictive performance of three model variants is investigated by reference to three test flows: a plane channel flow, a separated flow in a channel with periodic hill-shaped obstacles on one wall and a plane impinging jet. It is shown that the new model elements result in a substantially improved representation of the Reynolds-stress field at the wall, especially in the wall-normal Reynolds stress. One of the variants includes the use of the modified ω-equation, and it is shown that this model performs especially well in the presence of separation.

On Reynolds-stress expressions and near-wall scaling parameters for predicting wall and homogeneous turbulent shear flows

Abstract In this paper, a new type of two-equation turbulence model that incorporates some essential characteristics of second-order closure models is proposed. The present model belongs to a nonlinear k−ϵ model taking into account low-Reynolds-number effects originating from the physical requirements, and is applicable to complex turbulent flows with separation and reattachment. The model successfully predicts both wall-turbulent and homogeneous shear flows, the latter of which has been very difficult to simulate with existing two-equation turbulence models. Channel flows with injection and suction at wall surfaces and separated and reattaching flows downstream of a backward-facing step are also calculated. Comparisons of the computational results with the measurements and the direct numerical simulation data indicate that the present model is effective in calculating complex turbulent flows of technological interest. Furthermore, the parameters for scaling the near-wall region in the low-Reynolds-number model functions are re-evaluated, yielding some insights into the near-wall scaling parameters for application to complex turbulent flows.

Nonlinear eddy viscosity modelling for turbulence and heat transfer near wall and shear-free boundaries

Abstract New turbulence and turbulent heat flux models are proposed for capturing flow and thermal fields bounded by walls or free surfaces. The models are constructed using locally definable quantities only, without any recourse to topographical parameters. For the flow field, the proposed model is a cubic nonlinear k–e–A three equation eddy viscosity model. It employs dependence on Lumleys stress flatness parameter A, by solving its modelled transport equation as the third variable. Since A vanishes at two-component turbulence boundaries, introducing its dependency enables a turbulence model to capture the structure of turbulence near shear-free surfaces as well as wall boundaries. To close the modelled A equation, an up-to-date second-moment closure is applied. For the thermal field, an explicit algebraic second-moment closure for turbulent heat flux is proposed. The new aspect of this heat flux model is the use of nonlinear Reynolds stress terms in the eddy diffusivity tensor. This model complies with the linearity and independence principles for passive scalar. The proposed models are tested in fully developed plane channel, open channel and plane Couette–Poiseuille flows at several fluid Prandtl numbers. The results show the very encouraging performance of the present proposals in capturing anisotropic turbulence and thermal fields near both wall and shear-free boundaries in the range of 0.025⩽Pr⩽95.

A two-equation heat transfer model reflecting second-moment closures for wall and free turbulent flows

Abstract A new two-equation heat transfer model which incorporates some essential features of second-order modeling is proposed. The present model is applicable to heat transfer problems in both wall and free turbulent flows not unusually deviating from the equilibrium state. Furthermore, by introducing the Kolmogorov velocity scale, the model can appropriately express the low Reynolds number effects in the near-wall region and is also applicable to complex heat transfer fields with flow separation and reattachment. It is shown that the proposed model predicts quite successfully heat transfer in both wall and free turbulent flows; i.e., a homogeneous isotropic decaying flow, a homogeneous shear flow, a boundary-layer flow heated from the origin, and a boundary-layer flow subjected to a sudden change in the wall-heating condition; whereas, such predictions have been almost impossible with existing two-equation heat transfer models.

Numerical prediction of fluid-resonant oscillation at low Mach number

A method (governing equation set and numerical procedure) suited to the numerical simulation of fluid-resonant oscillation at low Mach numbers is constructed. The new equation set has been derived under the assumption that the compressibility effect is weak. Because the derived equations are essentially the same as the incompressible Navier-Stokes equations, except for an additional term, we can apply almost the same numerical procedure developed for incompressible flow equations without difficulty. With application of a pressure-based method that treats the continuity equation as a constraint equation for pressure, the stiffness problem that arises in solving the usual compressible flow equations under low Mach number conditions has been alleviated. To verify the present method, we apply it to the flows over a three-dimensional open cavity

The effects of radiative heat transfer in arc-heated nonequilibrium flow simulation

Numerical simulation of a 20 kW constrictor-type arc-heated flow was carried out, and the distribution of the nonequilibrium flow-field properties was obtained. The flow field was described by the Navier–Stokes equations with a multi-temperature model, tightly coupled with the electric-field and radiation-field calculations. As a radiation model, an accurate and low-cost model was introduced into the flow-field simulation. It was confirmed that the plasma flow inside the arc-heated facility is in a state of high nonequilibrium and the arc discharge plays a critical role. By comparing the computational results with/without the radiation model, it was clarified that the radiation exerts significant effects on the heat transport in the constrictor section. Additionally, to validate the present numerical model, the numerical solutions were compared with the experimental data. It was indicated that the present flow-field simulation with a radiation model tends to be in good agreement with the corresponding experimental data.

Numerical Investigation of Nonequilibrium Plasma Flows in Constrictor- and Segmented-Type Arc Heaters

Numerical simulations are carried out and the distributions of flowfield properties are obtained for nonequilibrium flows in a 20 kW constrictor-type and a 750 kW segmented-type arc-heated wind tunnel. In these arc heaters, it is confirmed that each plasma flow is highly in nonequilibrium and arc discharge plays critical roles. The flowfield is described by the Navier-Stokes equations with a multitemperature model. To validate the present numerical model, the numerical solutions are compared with the corresponding experimental data. The flow characteristics in the 20 and 750 kW arc heaters (e.g., the arc discharge and the supersonic expansion) become clear through the present simulations. In particular, the computed results for the 20 kW arc heater indicate almost full dissociation/ionization reactions and thermochemical equilibrium in the constrictor section, while strong nonequilibrium clearly appears in the nozzle section.

Turbulence and radiation behaviours in large-scale arc heaters

Turbulent plasma flow in large-scale arc heaters such as JAXA 750 kW and NASA 20 MW facilities was investigated and distributions of flow-field properties were successfully obtained. The turbulent flow field was described by the Navier–Stokes equations with a multitemperature model, which was tightly coupled with electric-field and radiation-field calculations. An accurate and low-cost radiation model, and a low Reynolds number two-equation turbulence model were introduced into the flow-field simulation. It was confirmed that the plasma flows in the arc-heating facilities were in a highly thermochemical nonequilibrium state in the expansion section and that the arc discharge plays a critical role in the heating section. It was quantitatively clarified that radiation and turbulence phenomena were very important in transferring heat and momentum from the high-temperature flow near the core to the cold gas region near the facility wall. To confirm the effectiveness of the present numerical model, the obtained results were compared with experimental data for the arc voltage, mass-averaged enthalpy, chamber pressure and heat efficiency. The present flow-field model was found to give good agreement for various operating conditions of the facilities.

Modeling the turbulent heat and momentum transfer in flows under different thermal conditions

Two-equation turbulence models for velocity and temperature (scalar) fields are developed to calculate wall shear flows under various flow conditions and related turbulent heat transfer under various wall thermal conditions. In the present models, we make the modified dissipation rates of both turbulent energy and temperature variance zero at a wall, though the wall limiting behavior of velocity and temperature fluctuations is reproduced exactly. Thus, the models assure computational expediency and convergence. Also, the present k- model is construted using a new type of expression for the Reynolds stress ūiūj proposed by Abe et al. [Trans. JSME B 61 (1995) 1714–1721], whose essential feature lies in introducing the explicit algebraic stress model concept into the nonlinear k- formulation, and the present two-equation heat transfer model is constructed to properly take into account the effects of wall thermal conditions on the eddy diffusivity for heat. The models are tested with five typical velocity fields and four typical thermal fields. Agreement with experiment and direct simulation data is quite satisfactory.