Singular fields of a mode III interface crack in a power-law hardening bimaterial

A high order of asymptotic solution of the singular fields near the tip of a mode III interface crack for pure power-law hardening bimaterials is obtained by using the hodograph transformation. It is found that the zero order of the asymptotic solution corresponds to the assumption of a rigid substrate at the interface, and the first order of it is deduced in order to satisfy completely two continuity conditions of the stress and displacement across the interface in the asymptotic sense. The singularities of stress and strain of the zeroth order asymptotic solutions are −1/(n ₁+1) and −n/(n ₁+1) respectively. (n=n ₁,n ₂ is the hardening exponent of the bimaterials.) The applicability conditions of the asymptotic solutions are determined for both zeroth and first orders. It is proved that the Guo-Keer solution^[10] is limited in some conditions. The angular functions of the singular fields for this interface crack problem are first expressed by closed form. The project supported by National Natural Science Foundation of China     

First visualization of temperature fields in liquids at high pressure using thermochromic liquid crystals

A first application of encapsulated thermochromic liquid crystals (TLCs) for visualizing temperature fields in pressurized liquids was studied experimentally. By means of a tempered high-pressure optical cell, investigations were performed in a wide temperature range and at pressures up to 7000 bar. The measured calibration curves of isochromes in the pressure/temperature domain as well as photographically documented temperature fields at high pressure are presented and discussed. The results found illustrate that TLCs provide an efficient instrument for investigating thermofluiddynamical processes even at high pressure. Received: 13 February 1998/Accepted: 9 December 1999     

Coefficient-by-Coefficient Averaging in a Problem of Laminar Gas Flow in a Well

This paper describes the problem of determining the temperature of laminar gas flow, in which the equation of convective heat transfer contains two variable coefficients, is reduced to nonclassical problems for zeroth and first asymptotic expansion coefficient with respect to a formal parameter. The Laplace–Carson transform are used to obtain analytical expressions for the temperature field of ascending laminar gas flow in a well with account for the relationships of density and velocity with spatial coordinates in zeroth and first asymptotic approximations. Expressions for the temperature asymptotically averaged along the cross section of the well and temperature distributions over the cross-sectional radius are obtained.     

Exact solutions for the unsteady flow of a Burger’s fluid in a duct induced by time-dependent prescribed volume flow rate

In this investigation, some unsteady flows in a circular duct have been studied. The fluid obeys viscoelastic non-Newtonian model with the Burgers’ constitutive equation and all fluid properties are constant. The flows in a duct are due to the prescribed arbitrary time dependent inlet volume flow rates. Four types of flow situations are considered. The governing equations are first developed and then solved using Laplace transform technique. Results indicate the strong effect of Burgers’ fluid parameter on the velocity fields and pressure gradients.     

The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders

We develop the Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential equations of the first order is analyzed, and tensor fields of special structure are constructed for defining characteristic vector fields naturally related with nonlinear partial differential equations of higher orders. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 26–36, January–March, 2007.     

Efficient estimation of power spectral density from laser Doppler anemometer data

 A non-biased estimator of power spectral density (PSD) is introduced for data obtained from a zeroth order interpolated laser Doppler anemometer (LDA) data set. The systematic error, sometimes referred to as the “particle-rate filter” effect, is removed using an FIR filter parameterized using the mean particle rate. Independent from this, a procedure for estimating the measurement system noise is introduced and applied to the estimated spectra. The spectral estimation is performed in the domain of the autocorrelation function and assumes no further process parameters. The new technique is illustrated using simulated and measured data, in the latter case with direct comparison to simultaneously acquired hot-wire data. Received: 9 June 1997/Accepted: 14 October 1997     

Solution of statistical problems in elasticity theory in the singular approximation

A method of calculating elastic fields and effective moduli of microheterogeneous solids is developed in the random field theory. The solution is obtained in the form of an operator series, each term of which is constructed on the basis of the regular component of the second derivative tensor of the equilibrium Green function. The zeroth approximation of such a series consists of the local part of the interaction between inhomogeneity grains. The possibilities of the method are illustrated on the example of an isotropic mixture of two isotropic components.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 98–102, January–February, 1972.     

On stagnation pressure increases in calorically perfect,ideal gases

When stagnation pressure rises in a natural or numerically simulated flow it is frequently a cause for concern, as one usually expects viscosity and turbulence to cause stagnation pressure to decrease. In fact, if stagnation pressure increases, one may suspect measurement or numerical errors. However, this need not be the case, as the laws of nature do not require that stagnation pressure continually decreases. In order to help clarify matters, the objective of this work is to understand the conditions under which stagnation pressure will rise in the unsteady/steady flows of compressible, viscous, calorically perfect, ideal gases. Furthermore, at a more practical level, the goal is to understand the conditions under which stagnation pressure will increase in flows simulated with the Reynolds averaged Navier–Stokes equations and eddy-viscosity turbulence models. In order to provide an improved understanding of increases in stagnation pressure for both these scenarios, transport equations are derived that govern its behavior in the unaveraged and Reynolds averaged settings. These equations are utilized to precisely determine the relationship between changes in stagnation pressure and zeroth, first, and second derivatives of fundamental flow quantities. Furthermore, these equations are utilized to demonstrate the relationship between changes in stagnation pressure and fundamental non-dimensional quantities that govern the conductivity, viscosity, and compressibility of the flow. In addition, based on an analysis of the Reynolds averaged equation (for eddy-viscosity turbulence models), it is shown that stagnation pressure is particularly likely to experience a spurious rise at the outer edges of shear layers that are undergoing convex curvature. Thereafter, numerical experiments are performed which confirm the primary aspects of the theoretical analysis.     

Hydrothermal convection in a thin porous ring

Natural convection of the fluid in a thin porous ring on whose boundaries steady temperature distributions are maintained is considered. For this problem on the basis of the two-dimensional equations an integrodifferential equation is obtained in the zeroth approximation in terms of a small parameter, namely the relative thickness of convection. A parametric numerical investigation of the flow and temperature fields is carried out.Makhachkala, Kaspiisk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 4–8, November–December, 1994.     

Wall pressure fluctuations and topology in separated flows over a forward-facing step

Laboratory measurements of wall pressure fluctuations and aerodynamic fields were made in separated flows over a forward facing step (h = 30, 40 and 50 mm with U _e = 15–40 m/s). An array of 16 off-set pressure probes extending in the streamwise and the spanwise directions was especially developed for sensing the wall pressure fluctuations. The flow field was also investigated by wall flow visualizations and PIV to analyze the flow topology in an open section wind tunnel. The results show a different behavior of the flow depending on the aspect ratio l/h and δ/h for high Reynolds numbers. The space time correlations between the wall pressure and the velocity fields were highlighted. The results show that high levels of these correlations are located at the top of the recirculation bubble, mainly in the shear layer and are extended downstream of the re-attachment point. Indeed, the results indicate that the flapping motion at the separation is important in the flow organization at the re-attachment point.     

Comparative evaluation of three heat transfer enhancement strategies in a grooved channel

 Results of a comparative evaluation of three heat transfer enhancement strategies for forced convection cooling of a parallel plate channel populated with heated blocks, representing electronic components mounted on printed circuit boards, are reported. Heat transfer in the reference geometry, the asymmetrically heated parallel plate channel, is compared with that for the basic grooved channel, and the same geometry enhanced by cylinders and vanes placed above the downstream edge of each heated block. In addition to conventional heat transfer and pressure drop measurements, holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in the self-sustained oscillatory flow. The locations of increased heat transfer within one channel periodicity depend on the enhancement technique applied, and were identified by analyzing the unsteady temperature distributions visualized by holographic interferometry. This approach allowed gaining insight into the mechanisms responsible for heat transfer enhancement. Experiments were conducted at moderate flow velocities in the laminar, transitional and turbulent flow regimes. Reynolds numbers were varied in the range Re = 200–6500, corresponding to flow velocities from 0.076 to 2.36 m/s. Flow oscillations were first observed between Re = 1050 and 1320 for the basic grooved channel, and around Re = 350 and 450 for the grooved channels equipped with cylinders and vanes, respectively. At Reynolds numbers above the onset of oscillations and in the transitional flow regime, heat transfer rates in the investigated grooved channels exceeded the performance of the reference geometry, the asymmetrically heated parallel plate channel. Heat transfer in the grooved channels enhanced with cylinders and vanes showed an increase by a factor of 1.2–1.8 and 1.5–3.5, respectively, when compared to data obtained for the basic grooved channel; however, the accompanying pressure drop penalties also increased significantly. Received on 5 April 2001     

Laser-pulse interferometry applied to high-pressure fluid flow in micro channels

The miniaturization of hydraulic systems together with ever increasing static and dynamic fluid pressure as is happening in fuel injection systems leads to complex flow effects with very high local and temporal pressure gradients. System optimization for hydraulic efficiency, components durability or spray formation quality needs the understanding of relevant flow properties. Fluid flow simulation models support such understanding, but with the complex nature of flow conditions, they are in need for precise and comprehensive verification and validation data. This work reports on measurement methods and analysis results for local fluid density and pressure measurements under overall stationary, highly turbulent and cavitating flow conditions in planar, optically accessed, model flow experiments. Laser-pulsed interferometry is applied for the measurement of fluid density fields under high spatial (∼3 μm) and temporal (∼5 ns) resolution. Interferometric imaging and image evaluation techniques provide ensemble mean pressure field data, local pressure fluctuation and differential pressure data. This yields information about local flow features such as flow vortex generation frequency, spatial size and shape of vortices and local pressure distribution inside of vortex structures. Features of bubble collapse process and corresponding pressure shock waves have been observed. The analysis method is applied to a forward-facing step and a target flow geometry. Experimental method, evaluation procedures and results are presented in this paper.     

Nonlinear oscillations of combustion velocity of powder

The combustion of powder, where the surface temperature T_s depends on the pressure p and the initial temperature T₀, is studied under the condition of sinusoidally varying pressure. The nonlinearity of the heat conduction equation together with the dependence of the combustion velocity u and the surface temperature on both the pressure and initial temperature affects the zeroth harmonic and gives rise to higher harmonics in the combustion velocity and the temperature of the powder. The present paper considers the case of nonlinear resonance, when the frequency of the pressure fluctuations is close to the natural vibration frequency of the powder. It has been shown that an autonomous oscillatory regime of combustion is possible under constant pressure.The author wishes to thank Ya. V. Zel'dovich, G. I. Barenblatt, A. S. Kompaneits, and O. I. Leipunskii for fruitful discussion and advice.     

Marangoni Mixed Convection Boundary Layer Flow

The paper deals with a steady coupled dissipative layer, called Marangoni mixed convection boundary layer, which can be formed along the interface of two immiscible fluids, in surface driven flows. The mixed convection boundary layer is generated when besides the Marangoni effects there are also buoyancy effects due to gravity and external pressure gradient effects. We shall use a model proposed by Golia and Viviani (L’ Aerotecnica missili e Spazio 64 (1985) 29–35, Meccanica 21 (1986) 200–204) wherein the Marangoni coupling condition has been included into the boundary conditions at the interface. The similarity equations are first determined, and the pertinent equations are solved numerically for some values of the governing parameters and the features of the flow and temperature fields as well as the interface velocity and heat transfer at the interface are analysed and discussed.     

Complex-potential method in the nonlinear theory of elasticity

For materials characterized by a linear relation between Almansi strains and Cauchy stresses, relations between stresses and complex potentials are obtained and the plane static problem of the theory of elasticity is thus reduced to a boundary-value problem for the potentials. The resulting relations are nonlinear in the potentials; they generalize well-known Kolosov's formulas of linear elasticity. A condition under which the results of the linear theory of elasticity follow from the nonlinear theory considered is established. An approximate solution of the nonlinear problem for the potentials is obtained by the small-parameter method, which reduces the problem to a sequence of linear problems of the same type, in which the zeroth approximation corresponds to the problem of linear elasticity. The method is used to obtain both exact and approximate solutions for the problem of the extension of a plate with an elliptic hole. In these solutions, the behavior of stresses on the hole contour is illustrated by graphs. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 133–143, January–February, 2000.     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

A Conceptual Study of Cavity Aeroacoustics Control Using Porous Media Inserts

In this study, an integrated flow simulation and aeroacoustics prediction methodology is applied to testing a sound control technique using porous inserts in an open cavity. Large eddy simulation (LES) combined with a three-dimensional Ffowcs Williams–Hawkings (FW–H) acoustic analogy is employed to predict the flow field, the acoustic sources and the sound radiation. The Darcy pressure – velocity law is applied to conceptually mimic the effect of porous media placed on the cavity floor and/or rear wall. Consequently, flow in the cavity could locally move in or out through these porous walls, depending on the local pressure differences. LES with “standard” subgrid-scale models for compressible flow is carried out to simulate the flow field covering the sound source and near fields, and the fully three-dimensional FW–H acoustic analogy is used to predict the sound field. The numerical results show that applying the conceptual porous media on cavity floor and/or rear wall could decrease the pressure fluctuations in the cavity and the sound pressure level in the far field. The amplitudes of the dominant oscillations (Rossiter modes) are suppressed and their frequencies are slightly modified. The dominant sound source is the transverse dipole term, which is significantly reduced due to the porous walls. As a result, the sound pressure in the far field is also suppressed. The preliminary study reveals that using porous-inserts is a promising technology for flow and sound radiation control.     

Application of Chebyshev polynomials to the theory of thin bodies

The application of shifted Chebyshev polynomials of the second kind to the construction of the thin-body theory is considered. Some basic and additional recurrence relations for Chebyshev polynomials are given. Arbitrary-order moments are obtained for the first and second derivatives of a tensor field and for some expressions. Several equations of motion expressed in terms of the moments of displacement and rotation vectors are derived for the moment theory; a number of constitutive relations of the zeroth approximation are obtained.     

A first‐order volume of fluid convection model in three‐dimensional space

To improve the numerical analysis of free surface convections and reconstruction in a three‐dimensional space, a first‐order algorithm is developed based on the volume of fluid (VOF) theory. The methodology applied to the first‐order method (FOM) is to define a first‐order surface as near to the horizontal as possible while satisfying the defined volume fraction of a cell. The developed method is compared against the donor cell method of zeroth‐order through simulation of the transitional and rotational convection of liquid spheres. Although the donor cell method shows relatively good predictions for the sphere of a large diameter, it shows poor performance of large distortions for a sphere of a relatively small diameter. However, the FOM developed in this study always shows quite satisfactory prediction results for free surface convection. Copyright © 2001 John Wiley & Sons, Ltd.     

Generation of geostrophic motions of an inhomogeneous fluid by surface pressure

The conditions of generation of a geostrophic flow by a pressure zone applied to the free surface of an undisturbed continuously stratified fluid layer of constant depth are determined in the general linear formulation. At large times the spatial external pressure distribution is assumed to tend to the steady state. In the axisymmetric case the geostrophic vortex is qualitatively analyzed on the basis of a numerical calculation of integral representations of the hydrodynamic fields for a fluid with an exponential density stratification. Sevastopol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 51–59, January–February, 1999.