The effect of wall cooling on compressible Görtler vortices

It is known that in adiabatic boundary layer flow over a curved surface the detailed structure of the spanwise periodic Görtler vortex instability varies markedly over the range of spanwise wavelength. At short wavelengths the modes tend to be concentrated in a well-defined thin zone located within the boundary layer. As the vortex wavenumber diminishes so the region of vortex activity is first driven to the bounding wall but subsequently expands to cover the entire boundary layer at which stage the modes take on a principally inviscid form. At yet longer wavelengths the vortices are given by the solution of an interactive multi-deck structure which has some similarities with that for Tollmien–Schlichting waves.In this work we investigate how the application of wall cooling affects the above scenario. It is shown how cooling both restricts the range of mode types and gives rise to two new structures. The first, for moderate cooling and which relates to longer wavelengths, is interactive in nature. Here the viscous–inviscid interaction between an essentially inviscid Görtler problem, albeit for an effective basic flow which in its general form has a non-standard near-wall structure, and a viscous sublayer is provided by novel boundary conditions. Shorter wavelength vortices are largely unaffected by wall cooling unless this is quite severe. However when this degree of cooling is applied, the vortices take on a fully viscous form and are confined to a thin region next to the bounding wall wherein the basic flow assumes an analytic form. Numerical solutions are obtained and we provide evidence as to how the two new structures are related both to each other and to the previously known uncooled results.     

An experimental study of circular sand–water wall jets

Laboratory experiments were carried out to study the effects of sand particles on circular sand–water wall jets. Mean and turbulence characteristics of sand particles in the sand–water wall jets were measured for different sand concentrations c_o ranging from 0.5% to 2.5%. Effects of sand particle size on the centerline sand velocity of the jets were evaluated for sand size ranging from 0.21 mm to 0.54 mm. Interesting results with the range of measurements are presented in this paper. It was found that the centerline sand velocity of the wall jets with larger particle size were 15% higher than the jets with smaller particle size. Concentration profiles in the vertical direction showed a peak value at x/d = 5 (where x is the longitudinal distance from the nozzle and d is the nozzle diameter) and the sand concentration decreased linearly for x/d > 5. Experimental results showed that the turbulence level enhanced from the nozzle to x/d = 10. For sand–water wall jets with a higher concentration (c_o = 1.5–2.5%), the turbulence intensity became smaller than the corresponding single-phase wall jets by 34% due to turbulent modulation. A modified logarithmic formulation was introduced to model the longitudinal turbulent intensity at the centerline and along the axis of the jet.     

Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies

The mathematical modelling of highly compressible unsteady flows has been of interest for some years. In order to obtain tractable solutions of the governing equations, investigators have made various simplifying assumptions such as presuming isothermal or isentropic flow of ideal gases, etc. The present review, with dense phase gas tranmission systems of particular interest, briefly develops the basic equations without such assumptions and includes the effects of wall friction and heat transfer. After re-expressing the equations in terms of the measurable quantities of pressure, temperature and velocity, previously published work is reviewed for their solution. Relevant experimental work is somewhat limited but contributions from 20 references are included.     

Analytical and experimental investigations of the pulsed air–water jet

This paper describes a new way of generating pulsed air–water jet by entraining and mixing air into the cavity of a pulsed water jet nozzle. Based on the theory of hydro-acoustics and fluid dynamics, a theoretical model which describes the frequency characteristic of the pulsed air–water jet is outlined aimed at gaining a better understanding of this nozzle for generating pulses. The calculated result indicates that as the air hold-up increases, the jet oscillation frequency has an abrupt decrease firstly, and then reaches a minimum gradually at α (air hold-up)=0.5, finally it gets increased slightly. Furthermore, a vibration test was conducted to validate the present theoretical result. By this way, the jet oscillation frequency can be obtained by analyzing the vibration acceleration of the equal strength beam affected by the jet impinging. Thereby, it is found that the experimental result shows similar trend with the prediction of the present model. Also, the relationship between vibration acceleration and cavity length for the pulsed water jet follows a similar tendency in accord with the pulsed air–water jet, i.e. there exists a maximum for each curve and the maximum occurs at the ratio of L/d₁ (the ratio of cavity length and upstream nozzle diameter) =2.5 and 2.2, respectively. In addition, experimental results on specimens impinged by the pulsed water jet and pulsed air–water jet show that the erosion depth increases slightly with air addition within a certain range of cavity length. Further, this behavior is very close to the vibration test results. As for erosion volume, the air entrained into the cavity significantly affects the material removal rate.     

Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.     

Condensation of an argon—monosilane mixture in a free jet

A mass–spectrometric study of the condensation of pure Ar and a 5% SiH₄ + 95% Ar mixture in a supersonic pulse free jet in a broad interval of stagnation pressures is performed. It is shown that a small content of monosilane in argon leads to the fact that condensation in the mixture begins at lower stagnation pressures than in pure argon; at high stagnation pressures, mixed argon—silane complexes are formed in the flow. The sequence of the stages of cluster formation in the mixture is determined.     

Combined phosphor and CARS thermometry at the wall–gas interface of impinging flame and jet systems

For the determination of surface normal temperature gradients, a generic system was built up consisting of two opposed, vertical nozzles impinging onto a flat, horizontal copper plate. From below, the plate was heated by non-reacting, turbulent air jets (Re = 5,000) and by a laminar flame (λ = 0.7, Re = 350), respectively. For well-defined boundary conditions, the plate was cooled by a turbulent cold jet from above in both cases. Wall temperature as well as gas temperature distributions within and outside of the thermal boundary layer of the hot side of the system were determined. The radial surface temperature profile of the plate was measured by coating it with thermographic phosphors (TP), materials whose phosphorescence decay time is dependent on their temperature. The TP was excited electronically by a frequency-tripled Nd:YAG laser (355 nm). The temporal decay of the phosphorescence intensity was measured pointwise by a photomultiplier tube. In this case, the 659 nm emission line of Mg₄FGeO₆:Mn was monitored. Non-intrusive point measurements of the gas temperature close to the surface were performed by rovibrational coherent anti-Stokes Raman spectroscopy (CARS) of diatomic nitrogen. Beams from a seeded, frequency-doubled Nd:YAG laser (532 nm) and from a modeless broadband dye laser (607 nm) were phase-matched into a surface-parallel, planar-boxcars configuration. The temperature data could be collected as close as 300 μm to the surface. Thermographic phosphors as well as CARS proved to be consistent for wall temperature and boundary layer measurements in all test cases. The results and challenges of this approach are discussed.     

Mathematical modeling and experimental investigation of an embedded vibro-impact system

The subject of this work is the experimental investigation and the mathematical modeling of the impact force behavior in a vibro-impact system, where a hammer is mounted on a cart that imposes a prescribed displacement. By changing the hammer stiffness and the impact gap it is possible to investigate the impact force behavior under different excitation frequencies. The experimental data will be used to validate the mathematical model. The hammer behavior is studied in more detail using a nonlinear analysis, which shows the various responses of the hammer, such as dynamical jumps, bifurcations and chaos.     

Air–water flow in a vertical pipe: experimental study of air bubbles in the vicinity of the wall

This study deals with the influence of bubbles on a vertical air–water pipe flow, for gas-lift applications. The effect of changing the bubble size is of particular interest as it has been shown to affect the pressure drop over the pipe. Local measurements on the bubbles characteristics in the wall region were performed, using standard techniques, such as high-speed video recording and optical fibre probe, and more specific techniques, such as two-phase hot film anemometry for the wall shear stress and conductivity measurement for the thickness of the liquid film at the wall. The injection of macroscopic air bubbles in a pipe flow was shown to increase the wall shear stress. Bubbles travelling close to the wall create a periodic perturbation. The injection of small bubbles amplifies this effect, because they tend to move in the wall region; hence, more bubbles are travelling close to the wall. A simple analysis based on a two-fluid set of equations emphasised the importance of the local gas fraction fluctuations on the wall shear stress.     

Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: “Towards an accurate description of compressibility effects in supersonic free shear flows”

A compressible supersonic mixing layer at convective Mach number (Mc) equal to 1 has been studied experimentally in a dual stream supersonic/subsonic wind-tunnel. Laser Doppler Velocimetry (L.D.V.) measurements were performed making possible a full estimation of the mean and turbulent 3D velocity fields in the mixing layer. The Reynolds stress tensor was described. In particular, some anisotropy coefficients were obtained. It appears that the structure of the Reynolds tensor is almost not affected by compressibility at least up to Mc = 1.The turbulent kinetic energy budget was also experimentally estimated. Reynolds analogies assumptions were used to obtain density/velocity correlations in order to build the turbulent kinetic energy budget from LDV measurements. Results have been compared to other experimental and numerical results. Compressibility effects on the turbulent kinetic energy budget have been detected and commented. A study about thermodynamics flow properties was also performed using most recent DNS results experimentally validated by the present data. A non-dimensional number is then introduced in order to quantify the real effect of pressure fluctuations on the thermodynamics quantities fluctuations.     

DPIV, HPTV and visualization study of a vortex ring–moving wall interaction

This paper presents an experimental study of the interaction between a vortex ring and a moving wall. This type of flow can be considered as modeling, in a simplified way, the interaction between a "typical eddy" and the viscous sublayer of a turbulent boundary layer. In the present study, the vortex ring is considered as a three-dimensional (3D) perturbation of a viscous Stokes layer. The interaction was first characterized by visualization. To obtain quantitative information, digital particle image velocimetry (DPIV) and holographic particle-tracking velocimetry (HPTV) were used. These different techniques led to a precise and detailed characterization of the vortex ring alone and of an interaction in which a hairpin vortex is generated in the Stokes layer. The results obtained show a good similarity between the observed vortex ring and the Oseen model. They also validate the Stokes layer model and show that in the present conditions, the hairpin vorticity is comparable to that of the Stokes layer. The holographic study, which was undertaken to obtain full 3D three-component (3D3C) velocity maps, showed the present limitations of HPTV.     

Results of an experimental and numerical study of the aerodynamic heating of the undersurface of delta wings with sharp leading edges at mach numbers M∞=6.1 and 8

The heat transfer between a supersonic flow and the undersurface of delta wings with leading-edge sweep angles x=65 and 70° is investigated in a shock tunnel at angles of attack 15°. The supersonic inviscid flow over these wings in regimes in which the bow shock is attached to the sharp leading edges is calculated numerically. The compressible boundary layer problem is solved for the calculated inviscid flow fields in the laminar, transition and turbulent flow zones. The calculations and experimental values of the heat flux on the surface of the wings are compared. The calculations are in satisfactory agreement with the experimental data in the laminar and transition zones, but diverge significantly (by up to 20%) in the turbulent zone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–188, July–August, 1991.The authors wish to thank A. A. Golubinskii for assisting with the solution of the problem of supersonic inviscid gas flow over a wing.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.     

Assessment of structural integrity and durability—a task of experimental mechanics

The necessity of health-monitoring and supervising structures will be justified under aspects of reliability and safety as well as with regard to economical reasons. Considering the achievements in measurement techniques combined with computer techniques, the requirements on the evolution of efficient monitoring systems will be indicated. The prerequisite will be pointed out, to conceive such systems in close co-ordination with the mathematical modelling of the structure. This is inalienable with concern to system-identification, as generally the control-parameters cannot be measured directly; they are to calculate on the basis of the mathematical model and the measurable structural response symptoms. This requires mathematical complicate solution of inverse problems. During service/operation many effects give rise for degradation of the structural resistance, reducing the safety and the life-time as well. The results of system identification enable the determination of damage indicators, which provide information on the scale of degradation in the course of time to estimate the limit of service-life and the residual life-time.     

The exact theory of bending of prismatic shells — an application of transfer matrices

Conclusion In this paper a new application of transfer matrices has been made in connection with the exact theory of bending of prismatic shells. It is shown that use of transfer matrices reduces the number of unknowns from 8 n to four, where n is the total number of walls, for a given integer m. This simplification is specially applicable to structures with open or simply connected closed sections.     

The study of a ratio-dependent predator–prey model with stage structure in the prey

In this paper, a ratio-dependent predator–prey model with stage structure in the prey is constructed and investigated. In the first part of this paper, some sufficient conditions for the existence and stability of three equilibriums are obtained. In the second part, we consider the effect of impulsive release of predator on the original system. A sufficient condition for the global asymptotical stability of the prey-eradication periodic solution is obtained. We also get the condition, under which the prey would never be eradicated, i.e., the impulsive system is permanent. At last, we give a brief discussion.

     

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e., the dynamic stiffness). However, the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system. Therefore, this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system. Then,the numerical study and experimental verification are conducted on...     

Void nucleation and growth in mineral-filled PVC – An experimental and numerical study

The nucleation and growth of voids in mineral-filled PVC have been investigated through experimental and numerical studies. Uniaxial tensile specimens were deformed in tension to different elongation levels and then unloaded. The macroscopic strain fields were recorded by use of digital image correlation. After the test, the microstructure of the deformed specimens was investigated in a scanning electron microscope. It was found that the observed volume strain on the macroscale is related to void growth on the microscale. In addition, finite element simulations were performed on unit cell models representing the microstructure of the material in a simplified manner. The numerical simulations demonstrate macroscopic dilation as a result of void growth. Moreover, the numerical simulations indicate that the experimentally observed stress-softening response of the PVC composite material may result from matrix-particle debonding.     

Interaction of an unsteady two‐phase jet with a layer of a disperse medium

Discharge of a twophase jet from a cylindrical channel into a bounded layer of a disperse medium is numerically simulated using the equations of the mechanics of heterogeneous media with allowance for the differences in velocity, temperature, and phase stresses. The effect of separation of the gas phase from the disperse phase in the layer is revealed and verified experimentally. A comparison with a similar process of gas discharge at equal initial pressures shows that in the interaction with the disperse layer, the twophase flow has a longer momentum and direction.