On the convective instability of a thermal boundary layer

When the surface temperature of a liquid is a harmonic function of time with a frequency, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2/)^1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient.In an earlier work [2] we considered the problem of the stability of a horizontal layer of liquid with a periodically varying temperature gradient. It was assumed that the thickness of the layer was much smaller than the penetration depth of the thermal wave, so that the temperature gradient could be assumed to be independent of position. In the present work we consider the opposite case, in which the liquid layer is assumed to be much larger than the penetration depth, i. e., a thermal boundary layer can be defined. The temperature gradient at equilibrium, which is a parameter in the equations determining the onset of perturbations, is here a periodic function of time and a relatively complicated function of the depth coordinate z. The periodic oscillations are solved by the Fourier method; the equations for the amplitudes are solved by the approximate method of KarmanPohlhausen.The authors are grateful to L. G. Loitsyanskii for helpful criticism.     

Absolute and convective instability of a supersonic boundary layer

Using the saddle-point method, asymptotics of time evolution for spatially localized three-dimensional intrinsic disturbances are determined. Criteria of absolute instability are established for the case of a branching dispersion relationship. Calculation results for the regions of existence of instability for a flat-plate boundary layer forRe→∞ andM=10 are presented. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika Vol. 40, No. 3, pp. 104–108, May–June, 1999.     

Three-dimensional instability analysis of boundary layers perturbed by streamwise vortices

A parametric study is presented for the incompressible, zero-pressure-gradient flat-plate boundary layer perturbed by streamwise vortices. The vortices are placed near the leading edge and model the vortices induced by miniature vortex generators (MVGs), which consist in a spanwise-periodic array of small winglet pairs. The introduction of MVGs has been experimentally proved to be a successful passive flow control strategy for delaying laminar-turbulent transition caused by Tollmien–Schlichting (TS) waves. The counter-rotating vortex pairs induce non-modal, transient growth that leads to a streaky boundary layer flow. The initial intensity of the vortices and their wall-normal distances to the plate wall are varied with the aim of finding the most effective location for streak generation and the effect on the instability characteristics of the perturbed flow. The study includes the solution of the three-dimensional, stationary, streaky boundary layer flows by using the boundary region equations, and the three-dimensional instability analysis of the resulting basic flows by using the plane-marching parabolized stability equations. Depending on the initial circulation and positioning of the vortices, planar TS waves are stabilized by the presence of the streaks, resulting in a reduction in the region of instability and shrink of the neutral stability curve. For a fixed maximum streak amplitude below the threshold for secondary instability (SI), the most effective wall-normal distance for the formation of the streaks is found to also offer the most stabilization of TS waves. By setting a maximum streak amplitude above the threshold for SI, sinuous shear layer modes become unstable, as well as another instability mode that is amplified in a narrow region near the vortex inlet position.     

A laser interferometric measurement of the temperature distribution in convective thermal transfer boundary layers

By means of a double mirror interferometry a two-dimensional temperature distribution measurement in convective thermal boundary layers is presented. When the cold air flows along a hot plate model, the interferometric fringe inside the boundary layer will bend. According to the displacement of the fringe and the relation between temperature and index of refraction, a two-dimensional temperature profile is obtained. All is accomplished by optical device with the help of micro-computer without any contact with the flow field. The project supported by the National Natural Science Foundation of China     

Experimental study for reliability of electronic packaging under vibration

An automated fatigue-testing system was developed for an experimental study on the integrity of the electronic packaging subjected to mechanical vibration. The fatigue-testing machine utilized the electromagnetic device as an actuator. A data acquisition system was developed for the fatigue test of the electronic board. The fixture for the specimen was designed to be suitable for measuring the fatigue life of a typical module/lead/card electronic system subjected to vibration. With this automated fatiguetesting machine, the mechanical integrity of surface mount component with the spider gullwing leads has been studied by a mechanical flexural fatigue test. An experimental method was developed to measure the changes in electrical resistance in the lead, which is used to indicate a fatigue failure. Finally, a relationship between the loading force and the fatigue life of high-cycle region was discussed for the lead of spider gullwing type surface-mounted component. With the relation, the fatigue life of the surface-mounted component (SMC) subjected to vibration environment was predicted successfully.This paper was presented at the 1995 SEM Spring Conference on Experimental Mechanics, Grand Rapids, MI, June 12–14.     

Maximum density effects on thermal instability of horizontal laminar boundary layers

Linear stability theory is used to investigate the onset of longitudinal vortices in laminar boundary layers along horizontal semi-infinite flat plates heated or cooled isothermally from below by considering the density inversion effect for water using a cubic temperature-density relationship. The analysis employs non-parallel flow model incorporating the variation of the basic flow and temperature fields with the streamwise coordinate as well as the transverse velocity component in the disturbance equations. Numerical results for the critical Grashof number Gr _L ^* =Gr _X ^* /Re _X< ^{Emphasis>/3/2} are presented for thermal conditions corresponding to –0.5 ₁–2.0 and –0.8 ₂1.2.Nomenclature a wavenumber, 2/ - D operator, d/d - F (f–f)/2 - f dimensionless stream function - g gravitational acceleration - G eigenvalue, Gr _L/Re_L - Gr _L Grashof number based on L - Gr _X Grashof number based on X - L characteristic length, (X/U)^1/2 - M number of divisions in y direction - P pressure - Pr Prandtl number, / - p dimensionless pressure, P/( ² /Re _L) - Re _L, Re_X Reynolds numbers, (U L/)=Re _X< ^1/2 and (U), respectively - T temperature - U, V, W velocity components in X, Y, Z directions - u, v, w dimensionless perturbation velocities, (U, V, W)/U - X, Y, Z rectangular coordinates - x, y, z dimensionless coordinates, (X, Y, Z)/L - thermal diffusivity - coefficient of thermal expansion - ₁, ₂ temperature coefficients for density-temperature relationship - similarity variable, Y/L=y - dimensionless temperature disturbance, /T - dimensionless wavelength of vortex rolls, 2/a - ₁, ₂ thermal parameters defined by equation (12) - kinematic viscosity - density - dimensionless basic temperature, (T _b T )/T - –1 - T temperature difference, (T _w–T ) - * critical value or dimensionless disturbance amplitude - prime, disturbance quantity or differentiation with respect to - b basic flow quantity - max value at a density maximum - w value at wall - free stream condition     

Vibrational and convective instability of a plane horizontal fluid layer at finite vibration frequencies

The vibrational-convective instability of a plane horizontal fluid layer subject to longitudinal harmonic vibrations of finite frequency and transverse stratification in a static gravity field is studied. The analysis is based on the complete convection equations in the Boussinesq approximation. It is demonstrated that in the limiting case of high-frequency vibrations the results thus obtained coincide with those obtained earlier on the basis of the averaged equations. In the limiting low-frequency case the nature of the instability is quite different being due to the instability of oscillating counterstreams.Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 44–51, September–October, 1996.     

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wallcooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1- 1/M a or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.     

PSE as applied to problems of secondary instability in supersonic boundary layers

Parabolized stability equations (PSE) approach is used to investigate prob-lems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.     

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

The nth-order expansion of the parabolized stability equation(EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation(LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE(EPSE1) and the second-order EPSE(EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory(LST),the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE.In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient e~N prediction tool for the crossflow instability in swept-wing boundary-layer flows.     

Experimental studies of the dynamic behavior of gas-liquid media in spherical shells under the action of vibration

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 1, pp. 68–73, January, 1995.     

On the problem of the stability of convective two-phase medium flows under high-frequency vibration

The principles and methods of constructing a model of vibrational convection in a medium consisting of a liquid (gas) and a solid admixture are discussed. A closed system of averaged equations is first obtained. The system admits passage to the limits of the equations of both vibrational convection in a homogeneous fluid and convection in a dusty medium in the static case. As a measure of the difference with respect to the homogeneous fluid, in addition to the sedimentation parameter, which also manifests itself in the absence of vibrational accelerations, it is possible to take the inhomogeneity parameter introduced in this study and responsible for the pulsatory transport of the average fields. The problem of the stability of plane parallel flow in a vertical layer of a two-phase medium under horizontal longitudinal vibration with respect to infinitesimal perturbations is considered. It is shown that the introduction of particles into the flow leads to qualitatively novel effects which cannot be predicted within the framework of the homogeneous fluid model.     

Deformation of a viscoelastic coating under the action of convective pressure fluctuations

The measurement method for complex compliance of viscoelastic coatings based on direct determination of deformation amplitude and pressure fluctuations was suggested. The value of dynamic deformation was about 0.02%. The frequency range was from 200 Hz to 2 kHz. Complex compliance of a viscoelastic coating measured was experimentally compared with calculations made on the basis of the measured modulus of elasticity and loss factor of the coating material. The resonance frequency was shown to not depend on the ratio between the diameter of the contact area and the coating thickness. According to the suggested explanation, coating deformation is defined by a stationary wave with an oscillation node on solid basement and loop on the coating outside. Analysis showed that to obtain maximum coating deformation under the action of pressure fluctuations, two conditions should be satisfied and the influence frequency should be equal to resonance the frequency of the coating (time factor). The length scale of convective pressure wave should also be equal to quadruple the thickness of the coating (spatial factor).     

Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE

It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e ^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D-LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.     

Experimental study of shock-accelerated liquid layers

An experimental investigation of a shock wave interacting with one, or several, liquid layer(s) is reported with a motivation towards first wall protection in inertial fusion energy reactor chamber design. A 12.8 mm or 6.4 mm thick water layer is suspended horizontally in a large vertical shock tube in atmospheric pressure argon and subjected to a planar shock wave of strength ranging from M = 1.34 to 3.20. For the single water layer experiments, the shock-accelerated liquid results in a significant increase in end-wall pressure loading (and impulse) compared with tests without water. The end-wall loading can be reduced by more than 50% for a given volume of water when it is divided into more than one layer with interspersed layer(s) of argon. A flash X-ray technique is employed to measure the volume fraction of the shocked water layer and multiple water layers are found to dissipate more energy through the liquid fragmentation process resulting in increased shock mitigation.     

弯矩作用下薄板振动的仿真分析

针对工程中广泛存在的弯矩作用下板结构的振动问题,分别建立四边固定、三边固定一边自由、两对边固定两对边自由的3种不同边界条件下板的振动模型;基于有限元法计算振动板的频率响应,计算了各节点振动速度的平方和;运用部分追加法正交试验方案分别对板厚、边界条件、板的损耗因子三因素三水平、激励点位置四水平进行了正交试验。实例结果表明,以速度平方和的大小为目标,影响薄板振动的主次因素顺序为:损耗因子、板厚、边界、激励点位置;当振动板两对边固定另两对边自由支承、板厚为0.014m、在(0.5m,0.4m)点处激励且板的损耗因子为0.0008时,此组合为薄板结构振动最小的最优组合。     

Experimental study of shear flow instability

The results of experiments carried out in order to study the instability of a free shear layer of rotating barotropic fluid at high Reynolds numbers are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 167–173, May–June, 1992.     

An experimental study of turbulent boundary layers approaching separation

The present paper deals with the experimental analysis of a strong decelerated turbulent boundary layer developed on a flat plate. The aim of the study was to examine the effects of pressure gradient on a non-equilibrium boundary layer while indicating local areas of equilibrium flow. The effect of the Reynolds number on a turbulent boundary layer developed with matching the external pressure gradient conditions was also analysed. The emphasis was on the analysis of mean flow statistics i.e. mean velocity profiles, streamwise Reynolds stress and the effect of large- and small-scale interactions by analysing the skewness factor and energy isocontours maps. The comparative analysis of the external data indicated that the structure of the turbulent boundary layer depends not only on local effects of pressure gradient but also on the upstream history of the flow. For the same condition of pressure gradient, the increased momentum is observed near the wall with the increase of the Reynolds number at the Incipient Detachment, where increased turbulence production is also observed, leading to the failure of the outer scaling methods. Surprisingly, the effect of the Reynolds number decays at the intermittent transitory detachment where similar profiles were observed. The upper inflection point in the mean profile corresponded well with the outer maximum of the Reynolds stress and zero crossing of skewness factor. Position of this point occurs at different locations, depending on the flow history effects. The last observation demonstrates that the inflection points results from large- and small-scale interactions, which led to the increased convection velocity of small scales near the wall.     

A parametric study of adverse pressure gradient turbulent boundary layers

There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.