Initial Development of the Prefracture Zone Near the Tip of a Crack Reaching the Interface Between Dissimilar Media

The Wiener–Hopf method is used to analyze, within the framework of a plane static problem, the prefracture zone near the tip of a mode I crack reaching the interface separating two isotropic media and containing a corner point     

Computational and Experimental Investigation of the Development of Turbulent Mixing in a Gas Layering in Passage of a Shock Wave

The experimental data and the results of direct numerical simulation of the flow developed in a constant-cross-section tube in passage of a shock wave through a three-layer gas system are presented. The three-layer systemis formed as a result ofmounting two thin films in the tube and filling the space between them with gases of different densities. The first interface (thin film) makes an angle of 45? with the shock front and the second interface is located in parallel to the front. The shock wave is formed at the left tube end and moves towards the first interface at the Mach number M = 2.4. The results of simulation of the problem are compared with the experimental data.     

An Experimental Database for Benchmarking Simulations of Turbulent Premixed Reacting Flows: Lean Extinction Limits and Velocity Field Measurements in a Dump Combustor

This contribution is aimed at drawing the attention of the computational fluid dynamics community on the availability of an experimental database regarding turbulent lean premixed prevaporised (LPP) reacting flows stabilised behind a double symmetric, plane sudden expansion fed by two fully developed turbulent channel flows of air plus propane. This flow configuration can be thought of as a relevant benchmark for testing turbulence and/or combustion models aimed at helping for the design of reliable LPP combustion chambers. This database contains a large amount of raw and processed data regarding essentially the velocity field for one inert and three different reacting flows configurations. Additional pieces of information are available and concern the lean extinction properties and the wall static pressure evolution in the feeding channels. For the reacting flows, the presence of a large scale coherent motion is clearly visible in the velocity spectra and it is shown how a data processing based on the semi-deterministic approach that decomposes the velocity signal into the sum of its steady time average, its coherent fluctuations and its stochastic fluctuations can permit to evaluate their respective contribution to the total velocity fluctuations.     

Thermal-drag and Transition from Quasi-steady to Highly-unsteady Combustion of a Fuel Droplet in the Presence of Upstream Velocity Oscillations

Numerical studies on the behaviors of combustion of 1-butanol fuel droplet at presence of upstream velocity oscillation are performed. Fuel droplet has an initial diameter of 1.25 mm and ambiance pressure and temperature are 0.4 MPa and 300 K, respectively. These conditions are those in which the microgravity experiments in literature conducted. In the excellent agreement with the experimental data, numerical results show a significant enhancement of the burning rate of droplet compared to what is predicted by quasi-steady film theory models. The mechanism of the enhancement of burning rate is clarified then by observation of a new mechanism that is named thermal-drag, TD. It is shown, depending on the amplitude and frequency of the upstream velocity oscillation, the flame in wake region of droplet can move toward the droplet surface by the force of vortex flow motions produced by the TD mechanism. It is verified that such movement of the flame is responsible for the enhancement of the burning rate and deviation of the response of the evaporation process form the predictions of the quasi-steady model. Frequency analysis of the burning rate reveals that at low frequency and amplitude the FFT diagram of the burning rate contains of only one main peak synchronies with the frequency of upstream velocity oscillation, which implies a quasi-steady response. However; at high frequency and amplitude the diagram includes of wide range of frequencies beside of the main peak that readily shows deviation from the quasi-steady conditions. In the latter, the study on the response of the combustion to the upstream velocity fluctuations in which the fluctuations contains of three wave numbers shows the amplification of the effects of low frequency fluctuations rather than that of damping of the effects of high frequency fluctuations on the evaporation processes.     

Experimental study and mathematical simulation of the characteristics of a turbulent flow in a straight circular pipe rotating about its longitudinal axis

The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal axis decreases the values of the turbulent stresses, turbulence energy, and dissipation rate along the pipe. The results of laboratory experiments and calculations by the second-order closure model of turbulent transfer are presented. On the whole, the model using a system of transport equations yields better agreement with experimental data than the models with algebraic relations for second-order moments. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 103–116, March–April, 1998.     

Similarity Laws for the Velocity Distribution and the Reynolds Tensor Components in the Wall Region of a Turbulent Boundary Layer with Injection and Suction

Similarity laws of the distributions of the average velocity, tangential stress, and mean-square transverse velocity fluctuation are established in an intermediate zone of a turbulent boundary layer with injection and suction. This zone is located in the neighborhood of the wall outside the viscous sublayer. The similarity relationship for the velocity profile is a generalization of the well-known logarithmic law to include the case of the presence of a mass flow at the wall.     

Approximate method for determining the momentum in a wedge-shaped notch with the instantaneous dispersion of a thin layer of matter from its surface

The article proposes a geometric method, based on the superposition of elementary momenta with the repeated reflection of particles scattered from the surface of the notch. The results of the calculation are in good agreement with experiment.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 159–163, September–October, 1974.     

An Analytical Solution and Nonlinear Regression Analysis for Sandface Temperature Transient Data in the Presence of a Near-Wellbore Damaged Zone

Throughout this study, we present a dual-continuum model of transport of the natural gas in shale formations. The model includes several physical mechanisms such as diffusion, adsorption and rock stress sensitivity. The slippage has a clear effect in the low-permeability formations which can be described by the apparent permeability. The adsorption mechanism has been modeled by the Langmuir isotherm. The porosity-stress model has been used to describe stress state of the rocks. The thermodynamics deviation factor is calculated using the equation of state of Peng–Robinson. The governing differential system has been solved numerically using the mixed finite element method (MFEM). The stability of the MFEM has been investigated theoretically and numerically. A semi-implicit scheme is employed to solve the two coupled pressure equations, while the thermodynamic calculations are conducted explicitly. Moreover, numerical experiments are performed under the corresponding physical parameters of the model. Some represented results are shown in graphs including the rates of production as well as the pressures and the apparent permeability profiles.

     

Experimental investigation of convective flows in a plane horizontal fluid layer heated from below and rotating about the vertical axis

The convective coherent structures in a plane horizontal fluid layer, heated from below and capable of rotation about the vertical axis, are experimentally investigated. It is shown that with increase in the supercriticality the time it takes for the convective structures to be formed decreases sharply. Rotation and an increase in the layer thickness-to-diameter ratio lead to an increase in the steady-state attainment time.     

Slow flow of gas past a strongly heated sphere in the presence of blowing and evaporation from its surface

A solution is obtained to the problem of the simultaneous influence of blowing (evaporation) and large temperature differences on the flow past a sphere and on the force acting on it with allowance for the Burnett thermal stresses in the momentum equation. It is assumed that the Reynolds numbers calculated using the blowing velocity and the velocity of the oncoming flow, respectively, have the order Re_w 1 and Re 1. The temperature difference is determined by the boundary conditions, namely, a constant temperature T_w T on the surface of the sphere (VT/T 1). The problem is solved by the method of matched asymptotic expansions with respect to the small parameter Re. The equations reduce to a system of ordinary differential equations, which are solved numerically by the orthogonal sweep method [1]. It is found that under certain conditions the drag of the sphere can become negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 128–134, July–August, 1982.I thank O. G. Fridlender for valuable advice and interest in the work.     

Experimental investigation of vortex formation in the wake of a flat plate for subsonic and supersonic freestream Mach numbers

The wake of a flat plate with thickness H = 6 mm whose surface was either smooth or rough by pasting smooth or rough paper on to it was investigated with optical methods. The studies showed that for supersonic freestream Mach numbers the wake of the smooth flat plate seems to be turbulent in the observation field. In contrast the wake of the rough plate can exhibit a vortex street if certain conditions are met. The most important parameters are the roughness of the paper and the distance from the location where the rough paper ends to the trailing edge, abbreviated with d. It turned out that a vortex street develops in the wake if the roughness exceeds a critical value and if the distance d is of the order of some millimeters. If these conditions are not met the wake of the rough plate is turbulent in the observation field. The dependence of the vortex formation upon the Mach number, the roughness and the distance d was investigated with holographic interferometry, two component laser-Doppler-anemometry and a laser-optics for measuring the vortex shedding frequency.     

A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid

A general solution for 3D Stokes flow is given which is different from, and more compact than the existing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape translating along the direction normal to it in an unbounded fluid.The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the velocity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and elliptic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences.     

Experimental investigation of the resistance to the flow of a conducting fluid in flat insulated ducts in the presence of a transverse magnetic field with allowance for fringe effects and wall roughness

The distribution of pressure, velocity, and electrical potential has been investigated for a mercury flow in insulated rectangular ducts with a large side ratio (Hartmann-type flow). The ranges of variation of the Reynolds, Hartmann, and Stewart numbers were 7·10²R5·10⁵, 0H490, and 0N24, respectively. Special attention is given to the sections of the channel where the flow enters and leaves the magnetic field. In these zones the pressure is sharply nonuniform and the velocity profiles in a plane perpendicular to the field acquire an M shape. A relation is established between the length of the entrance section, where the flow is three-dimensional, and the MHD similarity criteria. It is shown that ducts which are hydraulically smooth in the absence of a magnetic field become increasingly rough as the field grows stronger. Data are obtained on the resistance coefficient for a stabilized flow measured in a magnetic field and on the dependence of the critical Reynolds number on the Hartmann number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–21, July–August, 1971.     

A calibration technique for multiple-sensor hot-wire probes and its application to vorticity measurements in the wake of a circular cylinder

A calibration technique for multiple-sensor hot-wire probes is presented. The technique, which requires minimal information about the probe geometry, is tested using a four-sensor and a twelve-sensor probe. Two data reduction algorithms are introduced. The first one assumes a uniform velocity over the probe sensing-volume and is applied to the four-sensor probe measurements. The second one assumes a uniform velocity gradient over the sensing volume of the probe. The procedure, when applied to the twelve-sensor probe, is shown to measure the velocity gradient components successfully. In both algorithms, the unknowns (velocity and velocity gradient components) are obtained by solving the resulting systems of nonlinear algebraic equations in a least-squares sense. The performances of the probes and the algorithms are tested with measurements in the wake of a circular cylinder. The statistics and spectra show that the twelve-sensor probe is successful in the simultaneous measurement of all three components of the velocity and all three components of the vorticity vectors.     

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.     

An analytical method for the determination of stress and strain concentrations in textile-reinforced GF/PP composites with elliptical cutout and a finite outer boundary and its numerical verification

Stress concentrations in the vicinity of cutouts can often be regarded to be the limiting factor for a whole structure. As a further development of prior research at the Institute of Lightweight Engineering and Polymer Technology, an analytical method for the determination of the whole stress-strain fields in the vicinity of holes in multilayered textile-reinforced composites has been developed, which takes into consideration the influences of a finite outer boundary of the specimen. The analytical method is based on the classical laminate theory and the use of complex-valued potential functions. To account for the shape of the specimen, the method of conformal mappings is applied for the inner boundary, while a combination of boundary collocation and least squares method is used for the outer boundary. The method allows a layer-by-layer analysis of stress concentrations. For the verification of the developed calculation model, extensive experimental and numerical finite-element (FE) studies have been carried out on multilayered GF/PP plates with different laminate layups, notches, and specimen dimensions. The comparison of the experimentally or numerically determined results with the analytically calculated ones shows a very good correlation, of which the numerical studies are presented here for the first time. In a second step, the applicable boundary conditions on the outer boundary have been extended in such a way that varying stress and moment resultants can be applied, so that the calculation method can be used as an analytical sub-model in combination with FE techniques.