William W. Liou

Heat transfer in microchannel devices using DSMC

The heat transfer characteristics of supersonic flows in microchannels is studied using direct simulation Monte Carlo (DSMC) method. The velocity components and the spatial coordinates of the simulated particles are calculated and recorded by using a variable-hard-sphere (VHS) collision model. The effects of Knudsen number (Kn) on the heat transfer of the microchannel flows are examined. The results show that the magnitude of the temperature jump at the wall increases with increasing Kn. The heat transfer to the isothermal wall is found to increase significantly with Kn. The possible causes for the increase of wall heat transfer are discussed.

Turbulence model assessment for shock wave/turbulent boundary-layer interaction in transonic and supersonic flows

Abstract Comparisons of the performance of several state-of-the-art low-Reynolds number turbulence models in the prediction of shock wave/turbulent boundary-layer interactions in transonic and supersonic flows are reported in this paper. The models include a realizable k - e model, a k - e / k - ω hybrid model, and a one-equation ν t model. Several flow experiments focused on the shock wave/turbulent boundary-layer interaction phenomena are chosen for model comparisons. The selected flows represent a range of flow conditions with the turbulent boundary layers being fully attached, incipiently separated, or displaying large region of flow separation. Care has been taken to obtain solutions on sufficiently refined grids in all calculations. The model predictions are compared with experimental data and with the results obtained using Chien’s low-Reynolds number model. The results show that the models tested provide improvements over Chien’s model in the predictions of shock wave/turbulent interactions.

Linear instability of curved free shear layers

The linear inviscid hydrodynamic stability of slightly curved free mixing layers is studied in this paper. The disturbance equation is solved numerically using a shooting technique. Two mean velocity profiles that represent stably and unstably curved free mixing layers are considered. Results are shown for cases of five curvature Richardson numbers. The stability characteristics of the shear layer are found to vary significantly with the introduction of the curvature effects. The results also indicate that, in a manner similar to the Gortler vortices observed in a boundary layer along a concave wall, instability modes of spatially developing streamwise vortex pairs may appear in centrifugally unstable curved mixing layers.

Analytical modeling of capillary flow in tubes of nonuniform cross section.

The interface rise for the flow in a capillary with a nonuniform cross section distribution along a straight center axis is investigated analytically in this paper. Starting from the Navier-Stokes equations, we derive a model equation for the time-dependent rise of the capillary interface by using an approximated three-dimensional flow velocity profiles. The derived nonlinear, second-order differential equation can be solved numerically using the Runge-Kutta method. The nonuniformity effect is included in the inertial and viscous terms of the proposed model. The present model is validated by comparing the solutions for a circular cylindrical tube, rectangular cylindrical microchannels, and convergent-divergent and divergent-convergent capillaries. The validated model has been applied to capillaries with parabolic varying wall, sinusoidal wall, and divergent sinusoidal wall. The inertial and viscous effects on the dynamic capillary rise and the equilibrium height are investigated in detail.

Lift Enhancement by Static Extended Trailing Edge

A static extended trailing edge attached to a NACA0012 airfoil section is studied for achieving lift enhancement at a small drag penalty. It is indicated that the thin extended trailing edge can enhance the lift, whereas the zero-lift drag is not significantly increased. Experiments and calculations are conducted to compare the aerodynamic characteristics of the extended trailing edge with those of the Gurney flap and the conventional flap. The extended trailing edge, as a simple mechanical device added on a wing without altering the basic configuration, has a good potential to improve the cruise flight efficiency.

Transonic turbulent flow predictions with new two-equation turbulence models

Solutions of the Favre-averaged Navier-Stokes equations for two well-documented transonic turbulent flows are compared in detail with existing experimental data. While the boundary layer in the first case remains attached, a region of extensive flow separation has been observed in the second case. Two recently developed k-epsilon, two-equation, eddy-viscosity models are used to model the turbulence field. These models satisfy the realizability constraints of the Reynolds stresses. Comparisons with the measurements are made for the wall pressure distribution, the mean streamwise velocity profiles, and turbulent quantities. Reasonably good agreement is obtained with the experimental data.

Weakly nonlinear models for turbulent mixing in a plane mixing layer

New closure models for turbulent free shear flows are presented in this paper. They are based on a weakly nonlinear theory with a description of the dominant large‐scale structures as instability waves. Two models are presented that describe the evolution of the free shear flows in terms of the time‐averaged mean flow and the dominant large‐scale turbulent structure. The local characteristics of the large‐scale motions are described using linear theory. Their amplitude is determined from an energy integral analysis. The models have been applied to the study of an incompressible mixing layer. For both models, predictions of the mean flow development are made. In the second model, predictions of the time‐dependent motion of the large‐scale structures in the mixing layer are made. The predictions show good agreement with experimental observations.

Modeling of compressible effects on the Reynolds stress using a Markovianized two-scale method

Compressibility effects on the Reynolds stress are modeled using a Markovianized two-scale method. These effects occur twofold. One is the effect on the turbulent viscosity, which is expressed in terms of the ratio of the normalized density variance to the squared turbulent Mach number. Another comes from the deviation of the Reynolds stress from a turbulent-viscosity representation, which is written using the Langrange derivative of the mean velocity and the spatial derivatives of the mean density and internal energy. A simple model with the former compressibility effect incorporated is applied to fully developed free-shear layers and is shown to capture the steep decrease in the growth rate with the increasing convective Mach number.

Rough-wall layer modeling using the Brinkman equation

A flow model to facilitate the Reynolds-averaged Navier-Stokes (RANS) type of calculations of the turbulent flow over rough walls is proposed. Given that the roughness region is thin compared to the thickness of the boundary layer, the turbulent flow is viewed as consisting of two regions: (1) where the medium is entirely fluid and the RANS equations can be applied, and (2) a region of two phases where the fluid meanders around the solid roughness elements. The method of volume-averaging often used in the study of porous medium flows is applied in the rough-wall layer region. The resulting parameters such as porosity allow a direct inclusion of the geometric characteristics of the roughness element and their pattern in the model equations. In this formulation, the Brinkman equation, a reduced form of the volume-averaged Navier-Stokes (VANS) equations has been used. We have experimented with adapting an existing low Reynolds number eddy-viscosity, two-equation turbulence model developed for smooth walls, to provide closure to the RANS equations. The results shown are for a NACA 0012 airfoil with three different surface coverage using the same roughness.

New Two-Equation Closure for Rough-Wall Turbulent Flows Using the Brinkman Equation

A new flow-physics-based modeling of surface-roughness effects is developed for the Reynolds-averaged Navier-Stokes equations numerical calculations of high-Reynolds-number turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume-averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness, and the permeability is modeled. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, and a low-Reynolds-number k-e model is employed in all regions. In this paper, we present the computational results, including the skin-friction coefficient, the log-law mean velocity, the roughness function, the turbulent kinetic energy, and the Reynolds shear stress. The results show that the new rough-wall-layer modeling approach well predicts the skin-friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress.