SONIC SPEED AND SHOCK WAVE IN HIGH VELOCITY AERATED FLOWS FROM HIGH HEAD DISCHARGE STRUCTURES

The compressible characteristics in aerated flows at the high velocity ofabout 50m/s were analyzed. Based on the theory of compressible the relations between the sonic speedand shock wave in high-velocity aerated flow were theoretically deduced. And comparisons withmeasured data were made. The theoretical and experimental results show the sonic speed in aeratedflow is merely of the order of several-dozen meters per second, and its minimum value is only 20m/s, which is far much less than that in water or air alone. So high subsonic flow, supersonic flowand transonic flow as well as compression wave, shock wave and expansion wave similarly toaerodnamics may be produced in high velocity aerated flow at the speed of the order of 50m/s. Hencethe influences of these compressible characteristics on high head discharge structures can not beneglected, especially on super high dams over 200m high.

Numerical simulation of transient turbulent cavitating flows with special emphasis on shock wave dynamics considering the water/vapor compressibility

The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at ？= 6？ and ？= 1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages：（1） the growth of the attached cavity sheet,（2） development of re-entrant flow and attached cavity sheet breakup,（3） attached cavity sheet rolling up and cavity cloud shedding, and（4） cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.

THE INTERACTION BETWEEN SHOCK WAVES AND SOLID SPHERES ARRAYS IN A SHOCK TUBE

When a shock wave interacts with a group of solid spheres,non-linear aerodynamic behaviors come into effect.The complicated wave reflections such as the Mach reflection occur in the wave propagation process.The wave interactions with vortices behind each sphere's wake cause fluctuation in the pressure profiles of shock waves.This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres.A schlieren photography was applied to visualize the various shock waves passing through solid spheres.Pressure measurements were performed along different downstream positions.The experiments were conducted in both rectangular and circular shock tubes.The data with respect to the effect of the sphere array, size,interval distance,incident Mach number,etc.,on the shock wave attenuation were obtained.

Decomposition of mean skin friction in incident shock wave/turbulent boundary layer interaction flows at Mach 2.25

The evolution characteristics of the mean skin friction beneath the supersonic turbulent boundary layer that interacts with incident shock waves at Mach 2.25 are analyzed using Direct Numerical Simulation(DNS). The separated and attached boundary layers in the interaction region that respectively correspond to 33.2° and 28° incident shock angles are considered. The mean skin friction recovery rate for the separated boundary layer is much gentler and distinctly less than that for the attached case where the skin friction completes its recovery within one boundary layer thickness. The novel mean skin friction decomposition method for compressible flows proposed by the recent research is applied in the interaction region to investigate the internal evolution characteristics quantitatively. The results reveal that the three decomposition components are distinctly unequal between the two cases. The contributions of the turbulent motions at different scales to the associated term are focused on using empirical mode decomposition technology. It indicates that the outer large-scale structures dominate separation and reattachment regions, while contributions from inner small-scale structures are limited. In contrast, contributions from the outer largescale structures are dramatically reduced in the attached case, which results in the outer large-scale and inner small-scale motions being of equal importance.

Effects of Supersonic Nozzle Geometry on Characteristics of Shock Wave Structure

Interaction between the normal shock wave and the turbulent boundary layer in a supersonic nozzle becomes complex with an increase of a Mach number just before the shock wave. When the shock wave is strong enough to separate the boundary layer, the shock wave is bifurcated, and the 2nd and 3rd shock waves are formed downstream of the shock wave. The effect of a series of shock waves thus formed, called shock train, is considered to be similar to the effect of one normal shock wave, and the shock train is called pseudo-shock wave. There are many researches on the configuration of the shock wave. However, so far, very few researches have been done on the asymmetric characteristics of the leading shock wave in supersonic nozzles. In the present study, the effect of nozzle geometry on asymmetric shock wave in supersonic nozzles has been investigated experimentally.

Optical Measurements of Shock Waves in Critical Nozzles at Low Reynolds Numbers

Two-dimensional critical nozzle flows at low Reynolds numbers are visualized by the rainbow schlieren deflectometry. Experiments have been performed in a region of overexpanded nozzle flow. The variation of the shock structure against the back pressure ratio can be clearly visible with color gradation. Static pressure rises due to the shock-induced flow separation are compared with the previous theories. The unsteady characteristics of overexpanded critical nozzle flows at low Reynolds numbers are quantitatively and qualitatively visualized using laser schlieren and Mach-Zehnder interferometer systems combined with a high-speed digital camera. It was found that an oscillating normal shock wave appears inside the nozzle, and that the shock wave has a specified dominant frequency. Also the time-history of the oscillating shock wave is obtained from both the systems and compared with each other.

Subsonic impulsively starting flow at a high angle of attack with shock wave and vortex interaction

Impulsively starting flow, by a sudden attainment of a large angle of attack, has been well studied for incompressible and supersonic flows, but less studied for subsonic flow. Recently,a preliminary numerical study for subsonic starting flow at a high angle of attack displays an advance of stall around a Mach number of 0.5, when compared to other Mach numbers. To see what happens in this special case, we conduct here in this paper a further study for this case, to display and analyze the full flow structures. We find that for a Mach number around 0.5, a local supersonic flow region repeatedly splits and merges, and a pair of left-going and right-going unsteady shock waves are embedded inside the leading edge vortex once it is sufficiently grown up and detached from the leading edge. The flow evolution during the formation of shock waves is displayed in detail. The reason for the formation of these shock waves is explained here using the Laval nozzle flow theory. The existence of this shock pair inside the vortex, for a Mach number only close to 0.5, may help the growing of the trailing edge vortex responsible for the advance of stall observed previously.

Passive Control of Condensation Shock Wave in Prandtl-Meyer Expansion Flow

In this paper, the effects of the passive technique by using the slotted wall on the characteristics of a condensation shock wave generated in a Prandtl-Meyer flow were investigated experimentally. Furthermore, in order to clarify the variation of condensation properties in the flow field, Navier-Stokes equations were solved numerically using a 3rd-order MUSCL type TVD finite-difference scheme with a second-order fractional-step for time integration. Baldwin-Lomax model was used as a turbulence model in the computations. From experimental results, it was found that the shock strength on the slotted wall became weak in comparison with no passive case (solid wall), and the present passive technique was the most effective when a foot of the condensation shock wave was located at the middle of slotted wall. Furthermore, it was confirmed numerically that the passive technique was also effective for the unsteady condensation shock wave.

Shock Wave in Supersonic Moist Air Jet for a Low Pressure Ratio

In the present study,a computational fluid dynamics work was performed to investigate the occurrence of the shock wave by condensation in supersonic moist air jet.The unsteady,compressible axisymmetric Navier-Stokes equation is solved by TVD(Total Variation Diminishing) scheme in this study.The numerical simulations have been performed for low pressure ratio and various humidities.The results show the occurrence of the shock wave in supersonic moist air jet for a low pressure ratio when Mach disk does not occur,depending on humidity of the air.

Hysteretic Phenomenon of Shock Wave in a Supersonic Nozzle

In recent years, hysteretic phenomena in fluid flow systems drew attention for their great variety of industrial and engineering applications. When the high-pressure gas is exhausted to atmosphere from the nozzle exit, the expanded supersonic jet with the Mach disk is formed at a specific condition. In two-dimensional expanded supersonic jet, the hysteresis phenomenon for the reflection type of shock wave is occurred under the quasi-steady flow and the transitional pressure ratio between the regular reflection and Mach reflection is affected by this phe- nomenon. However, so far, there are very few researches for the hysteretic phenomenon of shock wave in a supersonic internal flow and the phenomenon has not been investigated satisfactorily. The present study was concemed with the experimental and numerical investigations of hysteretic phenomena of shock wave in a supersonic nozzle, and discussed the relationship between hysteresis phenomenon and rate of the change of pressure ratio with time.

Effect of Non-Equilibrium Condensation of Moist Air on Unsteady Behaviour of Shock Waves around a Circular Arc Blade

The unsteady phenomena in the transonic flow around airfoils are observed in the flow field of fan, compressor blades and butterfly valves, and this often causes serious problems such as the aeroacoustic noise, the vibration. In the transonic or supersonic flow where vapour is contained in the main flow, the rapid expansion of the flow may give rise to a non-equilibrium condensation. However, the effect of non-equilibrium condensation on the transonic internal flows around the airfoil has not yet been clarified satisfactorily. In the present study, the effect of non-equilibrium condensation of moist air on the self-excited shock wave oscillation on a circular arc blade was investigated numerically. The results showed that in the case with non-equilibrium condensation, frequencies of the flow oscillation became smaller than those without the non-equilibrium condensation.

Discharge of a Shock Wave from an Open End of a Tube

When a Pressure wave propagates along a constant area straight tube and reaches at the open end, an impulsive wave is emitted outward from the tube exit toward the surrounding area and causes an impulsive noise like a sonic boom. In order to clarify the magnitude of an impulsive wave obtained by the discharge of a weak shock wave born an open end of a tube in relation to the noise problem and the industrial devices, the experimental and numerical investigations have been carried out for various strength of a shock wave. A simple open end shock tube with the flange at the tube exit.was used and the numerical calculation using the TVD scheme was performed. The effective equations which concerns with the magnitude of an impulsive wave generated by the emission of a shock wave have been obtained from the procedure of the open end correction based on the aeroacoustic theory and the numerical results. The influence of open end correction length and the diameter of a flange on the magnitude of an impulsive wave has been discussed.

Effect of Duct Geometry on Shock Wave Discharge

This paper describes computational work to understand the unsteady flow-field of a shock wave discharging from an exit of a duct and impinging upon a flat plate. A flat plate is located downstream, and normal to the axis of the duct. The distance between the exit of the duct and flat plate is changed. In the present study, two different duct geometries （i.e., square and cross section） are simulated to investigate the effect of duct geometry on the un-steady flows of a shock wave. In computation, the total variation diminishing （TVD） scheme is employed to solve three-dimensional, unsteady, compressible, Euler equations. Computations are performed over the range of shock Mach number from 1.05 to 1.75. Computational results can predict the three-dimensional dynamic behaviour of the shock wave impinging upon the flat plate. The results obtained show that the pressure increase generated on the plate by the shock impingement depends on the duct geometry and the distance between the duct exit and plate, as well as the shock Mach number. It is also found that for the duct with cross-section, the unsteady loads acting on the flat plate are less, compared with the square duct.

A Study of the Weak Shock Wave Propagating over a Porous Wall/Cavity System

The present computational study addresses the attenuation of the shock wave propagating in a duct, using a porous wall/cavity system. In the present study, a weak shock wave propagating over the porous wall/cavity system is investigated with computational fluid dynamics. A total variation diminishing scheme is employed to solve the unsteady, two-dimensional, compressible, Navier-Stokes equations. The Mach number of an initial shock wave is changed in the range from 1.02 to 1.12. Several different types of porous wall/cavity systems are tested to investigate the passive control effects. The results show that wall pressure strongly fluctuates due to diffraction and reflection processes of the shock waves behind the incident shock wave. From the results, it is understood that for effective alleviation of tunnel impulse waves, the length of the perforated region should be sufficiently long.

A numerical study for WENO scheme-based on different lattice Boltzmann flux solver for compressible flows

In this paper,the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows,including inviscid LBFS Ⅰ,viscous LBFS Ⅱ,hybrid LBFS Ⅲ and hybrid LBFS Ⅳ.Hybrid LBFS can automatically realize the switch between inviscid LBFS Ⅰ and viscous LBFS Ⅱ through introducing a switch function.The resultant hybrid WENO-LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS.We investigate the performance of WENO scheme based on four kinds of LBFS systematically.Numerical results indicate that the devopled hybrid WENO-LBFS scheme has high accuracy,high resolution and no oscillations.It can not only accurately calculate smooth solutions,but also can effectively capture contact discontinuities and strong shock waves.

Study of Interaction between Supersonic Flow and Rods or Jets Surrounded by Porous Cavity

In this experiment, the effects of the combination of jets or rods and a porous cavity on the supersonic flow field are studied by means of visualization of schlieren method and the measurements of wall static pressures and the flow direction in the cavity with the thermal tuft probe. Three cases of jets or rods arrangements are tested in the experiments. As a result, a bow shock wave which is generated by the jets or rods is observed by mean of schlieren method. And it is confirmed that the expansion region appears downstream of the rods but is not in case of the jets pattern. Moreover the pressure ratios of starting shock wave passing through porous cavity for jets pattern differ from that of rods pattern. In the cavity, the flow direction at the measurement position in the cavity is always opposite to the main flow, as long as the starting shock wave is located upstream of the porous cavity for all cases. Difference in the backward flow ratio between the jets and rods patterns is observe after the starting shock wave passes through the porous cavity.

Experimental Study of the Response of Transonic Diffuser Flow to a Piezoceramic Actuator at Diffuser Throat

An experimental study of the response of a piezoceramic actuator set at the throat to a transonic diffuser is carried out by measuring wall static pressure fluctuations and by visualizing the flow field using schlieren technique. The visualized flow fields are captured with a digital still camera and a digital high speed video camera. The piezo ceramic actuator is attached at the throat of the diffuser and driven by sinusoidal amplified voltage signals. The diffuser used in this experiment is circular arc half nozzle with the height h* and width w of 3 mm and 25 mm, respectively. The blockage factor of the piezoceramic actuator to the diffuser throat is 9.2% assuring the effect of change in the throat area rather than the boundary layer disturbances. The piezoceramic actuator is driven at the frequency of 100 Hz, 200 Hz, and 300 Hz and its amplitude is about 1 mm. It is found that the wall static pressure fluctuations and the behavior of the shock wave clearly correspond to the vibration of the piezo ceramic actuator for all the frequency ranges whereas the averaged shock position remains almost unchanged. All the results mentioned above suggest that driving the piezo ceramic actuator at the diffuser throat can be one of the promising techniques to control unsteady transonic diffuser flow.

Configuration of Shock Waves in Two-Dimensional Overexpanded Jets

An experimental and analytical study has been carried out to obtain the clear understanding of a shock wave transition associated with a steady two-dimensional overexpanded flow. Two-dimensional inviscid theory with respect to a shock wave reflection is used in the present study on the characteristic of shock waves. The results obtained from the flow analysis are compared with those obtained from flow visualizations. It is shown that in the region of regular reflection, the angle of an incident shock wave becomes lower than that calculated by two shock theory with an increment in the ratio PJPb of the nozzle exit pressure Pc to the back pressure Pb. It is indicated that the configuration of shock waves in overexpanded jets is influenced by the divergent angle at the nozzle exit. Also it is shown from the flow visualization that a series of shock waves move into the nozzle inside with a decrease in pressure ratio Pc/Pb, even if the Pc/Pb is under overexpanded conditions.

Study of Interaction between Supersonic Flow and Rods Surrounded by Porous Cavity

In this paper, some preliminary calculations and the experiments were performed to figure out the flow field, in which some rods were normally inserted into the main flow surrounded by a porous cavity. As a result, it is found that the starting shock wave severely interacts with the rods, the bow shock wave, its reflections, and the porous wall, which are numerically well predicted at some conditions. Moreover, inserting the rods makes the pressure on the upper wall in the porous region increase when the main flow in the porous region is completely supersonic. The calculations also suggest that three rods cause the widest suction area.

基于改进SST模型的分离流动数值模拟

对SST湍流模型进行了改进,并通过对典型分离流动进行数值模拟,来检验和提高模型预测分离流动的能力。基于亚声速分离流动,提出了提高雷诺应力的模拟精度和分离流修正的改进方法,并进行了对比研究得出结论;在亚声速分离流动分析结论基础上,采用了可压缩性修正方法,开展了跨声速、超声速和高超声速激波/边界层干扰分离流动的数值模拟研究。结果表明:提高雷诺应力的模拟精度和采用分离流修正明显地提高了SST湍流模型对分离流动的模拟能力;适当地可压缩性修正对超声速和高超声速分离流动的计算精度有改善作用。