Comparison of measured and computed Strehl ratios for light propagated through a channel flow of a He-N(2) mixing layer at high Reynolds numbers

A lateral shearing interferometer was used to measure the slope of perturbed wave fronts after they propagated through a He-N(2) mixing layer in a rectangular channel. Slope measurements were used to reconstruct the phase of the turbulence-corrupted wave front. The random phase fluctuations induced by the mixing layer were captured in a large ensemble of wave-front measurements. Phase structure functions, computed from the reconstructed phase surfaces, were stationary in first increments. A five-thirds power law is shown to fit streamwise and cross-stream slices of the structure function, analogous to the Kolmogorov model for isotropic turbulence, which describes the structure function with a single parameter. Strehl ratios were computed from the phase structure functions and compared with a measured experiment obtained from simultaneous point-spread function measurements. Two additional Strehl ratios were calculated by using classical estimates that assume statistical isotropy throughout the flow. The isotropic models are a reasonable estimate of the optical degradation only within a few centimeters of the initial mixing, where the Reynolds number is low. At higher Reynolds numbers, Strehl ratios calculated from the structure functions match the experiment much better than Strehl ratio calculations that assume isotropic flow.     

Statistical anisotropy in free turbulence for mixing layers at high Reynolds numbers

A lateral shearing interferometer was used to measure the slope of perturbed wave fronts after propagating through free turbulent mixing layers. Shearing interferometers provide a two-dimensional flow visualization that is nonintrusive. Slope measurements were used to reconstruct the phase of the turbulence-corrupted wave front. The random phase fluctuations induced by the mixing layer were captured in a large ensemble of wave-front measurements. Experiments were performed on an unbounded, plane shear mixing layer of helium and nitrogen gas at fixed velocities and high Reynolds numbers for six locations in the flow development. Statistical autocorrelation functions and structure functions were computed on the reconstructed phase maps. The autocorrelation function results indicated that the turbulence-induced phase fluctuations were not wide-sense stationary. The structure functions exhibited statistical homogeneity, indicating that the phase fluctuations were stationary in first increments. However, the turbulence-corrupted phase was not isotropic. A five-thirds power law is shown to fit orthogonal slices of the structure function, analogous to the Kolmogorov model for isotropic turbulence. Strehl ratios were computed from the phase structure functions and compared with classical estimates that assume isotropy. The isotropic models are shown to overestimate the optical degradation by nearly 3 orders of magnitude compared with the structure function calculations.     

Numerical modelling and flow visualization of mixing of stratified layers and rollover in LNG

A numerical model has been developed to study the mixing of two initially stratified layers which are subjected to a uniform lateral heat flux. An important distinction is made between the free surface and the liquid/liquid interface with regard to the different flow characteristics of the two layers. In the upper layer where warm liquid is cooled at the evaporating surface, the convective circulation is featured by a strong downward core flow; in contrast, the fluid flow in the lower layer is mainly confined to the wall boundary and is much weaker. Flow visualization experiments show that mixing of two stratified layers generally involves two stages in sequence: migration of the interface and rapid mixing between the remaining liquids. The interface movement is due to entrainment mixing at the interface. When the two layers approach density equalization, the interface becomes increasingly unstable and the core flow in the upper layer is able to break into the lower layer. The base to side heat flux ratio appears to be a major factor in determining the mode and intensity of the subsequent mixing at a rollover incident.     

Experimental and numerical investigation of the effect of shock wave characteristics on the ejector performance

The entrainment performance and the shock wave structures in a three-dimensional ejector were investigated by Computational Fluid Dynamics (CFD) and Schlieren flow visualization. The ejector performance was evaluated based on the mass flow rates of the primary and secondary flows. The shock wave structures in the ejector mixing chamber were captured by the optical Schlieren measurements. The results show that the expansion waves in the shock train do not reach the mixing chamber wall when the ejector is working at the sub-critical mode. Decreasing of the shock wave wavelength increases the secondary mass flow rate. A three-dimensional CFD model with four turbulence models was then compared with the experimental data. The results show that the RNG k-ε model agrees best with measurements for predictions of both the mass flow rate and shock wave structures.     

Nonstationary phenomena in the region of shock-wave interaction with a boundary layer at transonic flow velocities

Nonstationary characteristics of detached flow have been experimentally studied during interaction of the boundary layer with a shock wave that appears on a profiled bump in transonic flow. The experiments were performed with variable shock-wave intensity and position in a T-325 wind tunnel. The flow was studied using methods of schlieren imaging, measuring average pressure and its pulsations on the surface of a model, and determining velocity fields by particle image velocimetry. Analysis of the experimental data showed that the observed shock-wave oscillations and flow pulsations in the detachment zone were related to disturbances present in the oncoming boundary layer.     

Suppressing a Laminar Flow Separation Zone by Spark Discharge at Mach Number M = 1.43

The influence of flow perturbations generated by an electric discharge on the region of interaction between a shock wave and laminar boundary layer in the flow on a flat plate at a Mach number of M = 1.43 has been experimentally studied. The oblique shock wave generated by a wedge mounted above the plate induced separation of the flow, while perturbations in the flow were introduced by a spark discharge on the model plate surface. It is established that the discharge leads to the formation of turbulent and thermal spots. The turbulent spot suppresses the separation zone, while the thermal spot leads to a local increase in the boundary layer thickness in the interaction zone.

     

Prediction of bed level variations in nonuniform sediment bed channel

In the present study, a numerical model, based on one-dimensional de Saint-Venant equations along with sediment continuity equation, is developed for prediction of bed levels in non-cohesive sediments in aggrading alluvial channels. One-dimensional, unsteady flow equations and sediment continuity equations are solved using ‘shock-capturing’, second order accurate, explicit MacCormack finite difference scheme while considering upstream and downstream boundary conditions in the channel. Series of experimental investigations have been undertaken for measurements of bed and water levels in an aggrading channel due to overloading of nonuniform sediments, extracted from the bed of Tapi River at Surat City, in a flume installed in Advanced Hydraulics Laboratory of SVNIT, Surat, India. A satisfactory coupling between the water flow and sediment flow has been achieved. The sediment continuity equation is used for the each size class to compute the volume of each size class after each time step at any computational node in the computational grid. The fractional bed and suspended load transport capacities for different size fractions have been computed using fractional transport laws for nonuniform sediments. The active bed layer concept has been implemented in finite difference scheme to consider the interaction and exchange of sediment and water flow near the mixing layer. The performance of developed numerical model has been satisfactorily verified with independent experimental data of nonuniform sediment bed. Also, consideration of sediment nonuniformity in computation of bed level variation has been demonstrated by comparing the results based on sediment transport functions of uniform and nonuniform sediments.     

Hydrothermal wave in a shallow liquid layer

The oscillatory thermocapillary convection and hydrothermal wave in a shallow liquid layer, where a temperature difference is applied between two parallel sidewalls, have been numerically investigated in a two-dimensional model. The oscillatory thermocapillary convection and hydrothermal wave appear if the Marangoni number is larger than a critical value. The critical phase speed and critical wave number of the hydrothermal wave agree with the ones given analytically by Smith and Davis in the microgravity environment, and it travels in the direction opposed to the surface flow. Another wave traveled downstream in addition to the hydrothermal wave traveled upstream was observed in the case of earth gravity condition.     

A note on the linear instability of the Blasius flow

Summary It is found that in a ribbon-excited Blasius boundary layer, a wave Reynolds number defined here on the basis of phase speed and wave number of the disturbance remains nearly independent of the local mean flow Reynolds number, and so also of the streamwise distance, under the parallel flow approximation. Consequently, a limited similarity feature of the Orr-Sommerfeld equation has been found to exist for the streamfunction in the outer region of the boundary layer.     

Modelling powder mixing in mass flow discharge: A kinematic approach

The dynamics of a powder flowing in a mass flow regime through a storage bin with a conical hopper, is a well studied problem. However, many challenges remain, including quantification of the mixing that occurs during discharge through the hopper. We have formulated a model based on the conservation of volume of the powder and a semi-empirical expression for velocity profile, (see [1], [2]), and used this to estimate mixing parameters. We have specifically considered the case of an inflow which is disposed in homogeneous horizontal layers as it enters the storage bin. When the powder, in successive layers, enters the hopper, it accelerates and its velocity along the longitudinal axis of the hopper is greater than at the walls. Portions of layers high in the hopper may overtake layers closer to the exit resulting in mixing of the layers. Using this model we are able to quantify the percentage of each layer in a given output volume and present results for typical hopper geometries.     

Shock wave reflection and diffraction on a convex double wedge

We have numerically simulated the interaction of a shock wave with a convex double angle within the framework of a model of inviscid non-heat-conducting gas. The main attention is paid to the stage of a two-shock diffraction configuration on the second face of the wedge. Special features of flow under various condi-tions of diffraction are revealed. We also propose an explanation of the appearance and behavior of a purely gasdynamic layer formally resembling the viscous boundary layer.     

Models for the formation of a critical layer in water wave propagation

A theory is presented which provides a model for the appearance of critical layers within the flow below a water wave. The wave propagates over constant depth, with constant (non-zero) vorticity. The mechanism described here involves adjusting the surface-pressure boundary condition; two models are discussed. In the first, the pressure at the surface is controlled (mimicking the movement of a low-pressure region associated with a storm) so that the speed and development of the pressure region ensure the appearance of a critical layer. In the second, the pressure boundary condition is allowed to accommodate the reduction of pressure with altitude, although the effects have to be greatly enhanced for this mechanism to produce a critical layer. These two problems are analysed using formal parameter asymptotics. In the second problem, this leads to a Korteweg-de Vries equation for the surface wave, and then the evolution of appropriate solutions of this equation gives rise to the appearance of a critical layer near the bottom; the corresponding problem at the surface can be formulated but not completely resolved. The appearance of a stagnation point and then a critical layer, either at the surface or the bottom, are discussed; the nature of the flow, and the corresponding streamlines are obtained and some typical flow fields are depicted.     

Surface wave propagation in sandy layer overlying a liquid saturated porous half-space and lying under a uniform liquid layer

Dispersion of Rayleigh-type surface waves is studied in a sandy layer under a uniform layer of homogeneous liquid lying over liquid-saturated porous solid half-space. The frequency equation in the form of a ninth-order determinant is obtained and evaluated. Special cases have been deduced and dispersion curves for the phase velocity and wave number have been plotted for a particular model.     

Laminar-turbulent transition in a supersonic boundary layer during initiation of a pulsed surface discharge

The near-surface layer structure in a supersonic airflow (M = 1.5) behind the plane shock wave has been experimentally studied in a shock tube. The flow structure was visualized using nanosecond pulsed distributed surface discharge. Different structures of plasma glow have been observed for the laminar and turbulent flow regimes in the boundary layer. The position of a region of the laminar-turbulent transition for different flow densities (0.11 and 0.19 kg/m³) has been determined and the critical Reynolds number (Re _k ～ 2.4 × 10⁵) for this transition has been evaluated.     

Monte Carlo simulation of intermixed layer formed by ion beam enhanced deposition

A Monte Carlo simulation code SIBL has been used to simulate the intermixed layer formed during ion beam enhanced deposition (IBED). Depending on the simple collision cascade mixing model, the relations between the shape of the intermixed layer and the ion energy, the atomic arrival ratio and the incident angle have been investigated. A semi-empirical expression has been established, which is in agreement with Sigmund's analytical expression, indicating a quadratic dependence of the thickness of the intermixed layer on the ion fluence and the total elastic energy deposited in the interface region.     

Temperature distribution over the cross section of liquid heat transfer films

The temperature profiles over the cross sections of vertically flowing films of water and aqueous solutions have been directly measured. It is shown that even in the wall boundary layer heat is transported not only by molecular heat conduction but also as a result of the mixing action of the waves, which increases with increase in flow density and film path.     

Simulation of the turbulent mixing of a passive impurity in a jet mixer

Results of numerical simulation of the mixing of a turbulent jet with a cocurrent incompressible-fluid flow (Schmidt number Sc ≈ 1000) in a cylindrical channel of circular cross section (axisymmetric mixer) with the use of the standard k-ε turbulence model and different models for the averaged value of the mixture fraction and its variance have been given. For the problem of mixing of an inert passive impurity, two regimes of flow — the regime with the formation of a recirculation zone and that without its formation — have been considered. The formulated statistical model has been verified with the use of experimental data and results of calculation by large-eddy simulation. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 4, pp. 666–681, July–August, 2008.     

A Higher-Order Asymptotic Theory for Fully Developed Turbulent Flow in Smooth Pipes

A complete second-order asymptotic theory for fully developed turbulent flow in smooth pipes at high turbulent Reynolds numbers is presented in the paper. The theory is based on Prandtl's mixing-length hypothesis involving a fourth-order polynomial representation for the mixing length and taking into account its dependence on the Reynolds number. Two main contributions with respect to the existing literature have been achieved:(a) the friction law is obtained by asymptotic evaluation of an integral, completely independently of the velocity field, and(b) an axis layer (in addition to the wall layer and the outer layer) has to be included in the analysis in order to remove a nonuniformity appearing in the second-order solution for the velocity fieldClosed-form analytic expressions for all constants and wake functions appearing up to the second-order solution in both the friction law and the velocity field are obtained. The results are in a very good agreement with experiments.     

湍流边界层激励下加筋平板振声响应特性研究

船舶、汽车和飞机等高速运动时,其外壳受湍流边界层壁面脉动压力激励而产生的内场声辐射成为该类交通工具自噪声的重要成分。基于模态叠加法计算结构振动响应。采用湍流壁面脉动压力功率谱Corcos模型,计算了外侧气流或水流湍流边界层激励下简支平板振动及内场辐射声,计算值与解析解和试验值吻合良好,验证了算法的有效性。采用湍流壁面脉动压力功率谱改进型Corcos模型,研究了外侧水流湍流边界层激励下平板及板格的振声响应特性,结果表明:水流马赫数低,壁面脉动压力迁移波数大于平板结构弯曲波数,壁面脉动压力波数-频率谱的迁移脊对平板的激励作用可以忽略;横向或纵向加筋对板格振动速度自功率谱级基本无影响;减小板格宽度与长度之比,适当增大板格流向长度可使平板振动辐射声功率在2 000 Hz以上明显降低。