Temperature and heat flux bounds of convection driven by non-uniform internal heating

Convection driven by a spatially non-uniform internal heat source between two horizontal isothermal walls is studied by theoretical analysis and numerical simulation,in order to explore the bounds of the temperature and the vertical heat flux.Specifically,the rigorous lower bound of the weighted average temperature<QT>is derived analytically,by decomposing the temperature field into a background profile and a fluctuation part.This bound obtained for the first time to consider non-uniform heat sources is found to be compatible with the existing bound obtained in uniform internal heat convection.Of physical importance,an analytical relationship is derived as an inequality connecting<QT>and the average vertical heat flux<wT>,by employing the average heat flux on the bottom wall(qb)as an intermediary variable.It clarifies the intrinsic relation between the lower bound of<QT>and the upper bound of<wT>,namely,these two bounds are essentially equivalent providing an easy way to obtain one from another.Furthermore,the analytical bounds are extensively demonstrated through a comprehensive series of direct numerical simulations.

Numerical Simulations of the Richtmyer-Meshkov Instability of Solid-Vacuum Interface

The Richtmyer-Meshkov instability of interfaces separating elastic-plastic materials from vacuum is investigated by numerical simulation using a multi-material solid mechanics algorithm based on an Eulerian framework.The research efforts are directed to reveal the influence of the initial perturbation and material strength on the deformation of the perturbed interface impacted by an initial shock.By varying the initial amplitude(kx0)of the perturbed interface and the yield stress(sY),three typical modes of interface deformation have been identified as the broken mode,the stable mode and the oscillating mode.For the broken mode,the interface width(i.e.,the bubble position with respect to that of the spike)increases continuously resulting in a final separation of the spike from the perturbed interface.For the stable mode,the interface width grows to saturation and then maintains a nearly constant value in the long term.For the oscillating mode,the wavy-like interface moving forward obtains an aperiodic oscillation of small amplitude,namely,the interface width varies in time slightly around zero.The intriguing difference of the typical modes is interpreted qualitatively by comparing the early-stage wave motion and the commensurate pressure and effective stress.Further,the subsequent interface deformation is illustrated quantitatively via the time series of the interface positions and velocities of these three typical modes.

Length and stiffness effects of the attached flexible plate on the flow over a traveling wavy foil

Flow over a traveling wavy foil attached with a flexible plate has been numerically investigated using the lattice Boltzmann method combined with the immersed boundary method. The influence of the flexibility and length of the caudal fin on the locomotion of swimming fish through this simplified model, whereas the fish body is modeled by the undulating foil and the caudal fin by the plate passively flapping as a consequence of fluid-structure interaction. It is found that the plate flexibility denoted by the bending stiffness, as well as the length ratio of tail and body, plays an important role in improving thrust generation and propulsive efficiency. It is also revealed that there exists a parameter region of the plate length and stiffness, in which positive propeller efficiency can be achieved. The effect of the passively flapping flexible plate on the pressure field and the vortex production on the wake is further discussed. It is found that when the length ratio of caudal fin and body is greater than 0.2, a reverse von Kármán vortex street occurs when the bending stiffness is about greater than 1.0, and a great thrust is generated as a result of a large pressure difference occurring across the flexible plate. This work provides physical insight into the role of the caudal fin in fish swimming and may inspire the design of robotic fish.

Numerical Study of Two-Winged Insect Hovering Flight

The two-winged insect hovering flight is investigated numerically using the lattice Boltzmann method(LBM).A virtual model of two elliptic foils with flapping motion is used to study the aerodynamic performance of the insect hovering flight with and without the effect of ground surface.Systematic studies have been carried out by changing some parameters of the wing kinematics,including the stroke amplitude,attack angle,and the Reynolds number for the insect hovering flight without ground effect,as well as the distance between the flapping foils and the ground surface when the ground effect is considered.The influence of the wing kinematic parameters and the effect of the ground surface on the unsteady forces and vortical structures are analyzed.The unsteady forces acting on the flapping foils are verified to be closely associated with the time evolution of the vortex structures,foil translational and rotational accelerations,and interaction between the flapping foils and the existed vortical flow.Typical unsteady mechanisms of lift production are identified by examining the vortical structures around the flapping foils.The results obtained in this study provide some physical insight into the understanding of the aerodynamics and flow structures for the insect hovering flight.

Numerical Investigation of Supersonic Channel Flow with Oscillatory Backpressures

The investigation of supersonic channel flow with periodic oscillatory backpressures at the outlet of the channel was performed using large-eddy simulation for the inlet free-stream Mach number 4 and the Reynolds number approximately 5.2104 based on the height of the channel.Results have been validated carefully against our experimental data.Three typical backpressures are considered for constant backpressure and both periodic oscillatory backpressures with low and high frequency.The oscillatory backpressure can obviously influence the flow features occurring up to the middle region of the channel for the low frequency case and the downstream region for the high frequency case.Obvious differences of phase-averaged quantities at different phases are observed for the low frequency backpressure while the differences are relatively small for the high frequency backpressure.The spectral analysis reveals that the flow field experiences a periodic-like evolution of flow structures including shocks and vortices for the low frequency backpressure,resulting in the enhancement of turbulence fluctuations due to the complicated interaction of shocks and vortices.