开放剪切流空间全局动力学与空间相位斑图间的关系

开放流动空间动力学可基于两类全局能量关系式进行研究；而空间相位斑图则可通过互谱空间演化加以测定。全局能量关系式以时间Fourier系数的形式建立流场任意两点问速度脉动能量间的关系，籍此可定义全局意义上的线性、非线性和线性一非线性机制。基于轴对称剪切流、变密度轴对称圆射流以及平面对称剪切流的实验发现：轴对称旋涡结构的配对由线性、线性一非线性机制表征，对应有序空间相位斑图；并且能量可通过线性一非线性机制在具有相同相速度的扰动间传递。螺旋结构由线性机制表征，对应有序相位斑图。全局自激励振荡由非线性的能量共振表征，对应无序相位斑图。籍此，有序空间相位斑图对应线性和线性一非线性机制；而混沌相位斑图则对应非线性机制。     

Limitations of temperature measurements with holographic interferometry in the presence of pressure variations

In recent years oscillatory flows have shown to be a promising strategy to enhance heat transfer. However, the mechanisms underlying oscillatory heat transfer enhancement are not yet completely understood. One problem, when investigating heat transfer in oscillatory flows experimentally, is to resolve the temperature distribution as a function of time. This is one reason that most studies reported in the literature so far were restricted to frequencies of a few hertz. As shown in this paper, an appropriate tool to investigate oscillatory heat transfer phenomena at higher frequencies (1000 Hz) is real time holographic interferometry (HI) combined with high-speed cinematography. In the present paper HI was applied to study acoustically driven flow. To apply HI to such a physical situation it was necessary to expand its applicability to cases where changes in the refractive index are caused not only by temperature changes but also by pressure variations. For this purpose a new evaluation formula that accounts for pressure variations was derived. On the example of the acoustic field, we discuss the impact of the pressure variations on temperature measurements. Additionally, an image processing algorithm was developed that allows the measurement of time dependent temperature distributions. The uncertainties of the temperature measurements introduced by the image processing algorithm were found to be in the range of thermocouple measurements.     

Numerical simulation on compressible turbulence by spectral method

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.     

Efficient implicit algorithm for the equations of 2-D viscous compressible flow: application to shock-boundary layer interaction

A fully implicit algorithm has been developed to time integrate the equations of 2-D compressible viscous flow. The algorithm was constructed so as to optimize computational efficiency. The time-consuming block matrix inversions usually associated with implicit algorithms have been reduced to the trivial non-iterative inversion of four sets of scalar bidiagonal matrices. Thus, the algorithm requires virtually no more computer storage than an explicit algorithm. The efficient structure of the implicit algorithm is reflected in comparative timings which slow that it requires only a factor of two more computer time per point per time step than a typical explicit algorithm. Therefore, the algorithm allows more economical solution of given flows than existing explicit methods and also allows more difficult problems to be attempted using available computer resources. Application of the algorithm to the problem of shock-boundary layer interaction produces results consistent with both experimental measurements and other calculations.     

Wall Versus Centerline Polymer Injection in Turbulent Channel Flows

This experimental study compares the mean and turbulence characteristics of turbulent channel flows with polymer injection at the wall and at the centerline to assess the impact of the injection location on drag reduction. It also contrasts the drag reduction performance of a hydrolyzed polymer versus a non-ionic polymer under the same conditions. Wall injection of non-ionic and hydrolized polymers resulted in 23% and 9% larger drag reduction than corresponding centerline injection, respectively. In all cases, the polymer was structured and the presence of macromolecular polymer structures, even when concentrated mostly away from the wall, seemed to be able to affect the turbulence structure in the flow.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.     

Removing of vortices in incompressible flows by distributed controls

We consider an optimal control problem of fluids flow. The fluid motion is governed by the incompressible time-dependent Navier-Stokes equations. A new optimal control formulation for the reduction and possibly extinction of vortices is proposed. A cost functional based on a local dynamical systems characterization of vortices is investigated. The resulting functional is a non-convex function of the velocity gradient tensor. The optimality system describing first order necessary optimality conditions is derived. The gradient and the second derivative of the cost functional with respect to the distributed control are established.     

Similarity solutions for the flow behind an exponential shock in a non-ideal gas

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law are obtained. Similarity solutions exist only when the surrounding medium is of constant density. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. It is found that the assumption of zero temperature gradient brings a profound change in the density distribution as compare to that of the adiabatic case. Effects of the non-idealness of the gas on the flow-field between the shock and the piston are investigated. The variations of density-ratio across the shock and the location of the piston with the parameter of non-idealness of the gas are also obtained.     

Transient flows of a second grade fluid

Exact analytical solutions for a class of unsteady unidirectional flows of an incompressible second-order fluid are constructed. The flows are generated impulsively from rest by motion of a plate or two plates or by sudden application of a pressure gradient. Expressions for velocity, flux and skin friction are obtained for both large and small times. It is found that large and small times solutions are dependent on the coefficient of viscoelasticity. The solutions corresponding to Newtonian fluids can be easily obtained from those for fluids of second order by letting the viscoelastic parameter to be zero.     

Quelques modèles diffusifs capillaires de type KortewegSome diffusive capillary models of Korteweg type.

The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004).