The surface hot wire as a means of measuring mean and fluctuating wall shear stress

 The paper describes some applications of a wall shear stress sensor technique which is based on hot-wire anemometry. The “surface hot wire” is a flush-mounted thermal resistive wire with a tiny slot underneath. The arrangement of this sensor guarantees an improved signal-to-noise ratio compared to a common surface hot film. The setup and the application of single sensors and of surface hot-wire arrays are shown. Some results are presented that were acquired in several experiments in the field of laminar-turbulent transition. Received: 26 May 2000/Accepted: 7 February 2001     

Chaos in Acoustic Subspace Raised by the Sommerfeld–Kononenko Effect

This paper deals with vibrations of an infinite plate in contact with an acoustic medium where the plate is subjected to a point excitation by an electric motor of limited power-supply. The whole system is divided into two “exciter - foundation” and “foundation-plate-medium”. In the system “motor-foundation” three classes of steady state regimes are determined: stationary, periodic and chaotic. The vibrations of the plate and the pressure in the acoustic fluid are described for each of these regimes of excitation. For the first class they are periodic functions of time, for the second they are modulated periodic functions, in general with an infinite number of carrying frequencies, the difference between which is constant. For the last class they correspond to chaotic functions. In another mathematical model where the exciter stands directly on an infinite plate (without foundation) it was shown that chaos might occur in the system due to the feedback influence of waves in the infinite hydro-elastic subsystem in the regime of motor shaft rotation. In this case the process of rotation can be approximately described as a solution of the fourth order nonlinear differential equation and may have the same three classes of steady state regimes as the first model. That is the electric motor may generate periodic acoustic waves, modulated waves with an infinite number of frequencies or chaotic acoustic waves in a fluid.     

Transient conjugate heat transfer from a hemispherical plate during free liquid jet impingement on the convex surface

This paper considers the analysis of transient heating of a hemispherical solid plate of finite thickness during impingement of a free liquid jet. A constant heat flux was imposed at the inner surface of the hemispherical plate at t = 0 and heat transfer was monitored for the entire duration of the transient until a steady state condition was reached. Calculations were done for Reynolds number (Re) ranging from 500 to 1,500 and dimensionless plate thicknesses to nozzle diameter ratio (b/d _n) from 0.083 to 1.5. Results are presented for local and average Nusselt number using water as the coolant and various solid materials such as silicon, constantan, and copper. It was detected that increasing the Reynolds number decreases the time for the plate to achieve the steady-state condition. Also, a higher Reynolds number increases the Nusselt number. Hemispherical plate materials with higher thermal conductivity maintain lower temperature non-uniformity at the solid–fluid interface. Increasing the plate thickness decreases the maximum temperature in the solid and increases the time to reach the steady-state condition.     

A finite element analysis for the temperature field produced by a moving heat source

Using moving mesh finite element method we discuss the temperature field produced by a moving heat source with the variable thermal conductivity and with the raUioative and convective boundary conditions in a wide range of the velocity. The temperature-time relationships at various velocities in the static and moving coordinate systems are studied. The steady-state temperature distributions at various velocities in the moving coordinate systems are given. The temperature field produced by the plastic deformation at the process region (a region very near the crack tip) is also studied, and the results show that the highest temperature at the process region is lower than 1000℃ or 1832℉     

Slow viscoelastic radial flow between parallel disks

A perturbation analysis is presented for the steady-state radial flow of a third-order fluid between two parallel disks. The results include previous perturbation analyses in which various other rheological models were used. The pressure drop needed to maintain the radial flow is less than that for the Newtonian creeping-flow solution because of fluid inertia and shear-thinning viscosity, whereas the normal stresses have the opposite effect. Possible use of the “radial flow viscometer” for experimental evaluation of second-order constants is also discussed. Finally, molecular stretching in the flow system is examined using the elastic dumbbell model for a polymer molecule.     

An analogue rotated vector field of polynomial system

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Thermal explosion during the flow of a viscous liquid

Frank-Kamenetskii has discussed a steady-state formulation of thermal explosions [1]. Bostandzhiyan et al. [2] and Bostandzhiyan and Chernyaeva [3] have shown, for the flow in a cylindrical tube of Newtonian and non-Newtonian liquids having a strong (nonlinear) temperature dependence of the viscosity, that a phenomenon analogous to thermal explosion may occur during the flow of a chemically inert liquid. Bostandzhiyan et al. [4] have also studied Couette flow and the flow between two rotating circular cylinders of a Newtonian liquid having the same temperature dependence for its viscosity. It was shown that, although the heat balance equation reduces to the equations of the steady-state theory of thermal explosion for the corresponding region, hydrodynamic thermal “explosion” was not observed in these cases. This phenomenon was found to be characteristic of only pressurized flows. Below, we study thermal explosions during the Poiseuille flow of a viscous, chemically reactive liquid in an infinite circular cylindrical tube, and during the motion of the liquid between infinite rotating cylinders. The combined effect of chemical and mechanical heat cources are considered. Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, Vol. 9, No. 5, pp. 38–43, 1968     

Dynamics of a “collective” bubble in a magma melt flow behind the decompression wave front

Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100 m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the free surface.     

Influence of some design parameters on the thermal performance of domestic refrigerator appliances

This paper presents a thermal study on chest-freezers, the small refrigerators used in domestic and supermarket applications. A thermal and energy model of a particular kind of these refrigerators, the “hot-wall” (or “skin condenser”) refrigerator, is developed and used to perform sensitivity and design optimisation analysis for given working temperatures and useful volume of the refrigerated cell. A finite-element heat transfer model of the refrigerator box is coupled to the complete thermodynamic model of the refrigerating plant, including real working conditions (compressor efficiency, friction pressure losses and so on). A sensitivity study of the main design parameters affecting the global refrigerator performance has been developed (for fixed working temperatures) with reference to the thickness of the metallic plates, to the evaporator and condenser tube diameters and to the evaporator tube pitch (with fixed evaporator-to-condenser tube pitch ratio). The results obtained show that the proposed sensitivity analysis can yield quite reliable results (in comparison with much more complex, albeit more accurate mathematical optimisation algorithms) using small computational resources. The great importance of 2-D heat conduction in the metallic plates is shown, evidencing how the plate thickness and the evaporator and condenser tube diameters affect the global performance of the system according to the well-known “fin efficiency” effect. The influence of the evaporator and condenser tube diameters on the friction pressure losses is also outlined. Some practical suggestions are made in conclusion, regarding the criteria which should be adopted in the thermal design of a hot-wall refrigerator.     

The flow field near the triple point in steady shock reflection

This paper investigates the flow field near three intersecting shock waves appearing in steady Mach reflection. Results of numerical computations reveal a “von Neumann Paradox”—like feature for weak shock waves, in which the flow field between the reflected and the Mach stem is smooth with no distinct slip flow region and changes rather smoothly. An analytical solution of the Navier–Stokes equations constructed using a polar–coordinate system gives a flow field with the same properties as the numerical simulation.     

A new approach to predicting interfacial crack growth

I.Intr0ductionItisknownthatthenear-tipstressfieldforaninterfacecrackbetweendissimilarelasticsolidsisalinearcombinationoftwotypesofsingularities,namelyacoupledoscillatoryfieldscaledbyacomplexK(K=K1 iK,whichiscalledinterfacialstressintensityfactor)andanonos…     

Thermal convection initiated by the quasistatic component of the microacceleration field on the “Mir” orbital station

The three-dimensional unsteady thermal convection developing in a cubic cavity on board the “Mir” station under the action of the quasistatic component of the microacceleration caused by the earth’s gravity field strength gradient and the motion of the station about the centre of mass is investigated numerically. The calculations are carried out for two real time intervals of motion of the station about the centre of mass using actual values of the quasistatic component. Moscow, Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–45, May–June, 2000.     

Effective thermal conductivity of heterogeneous multi-component materials: an SPH implementation

Modeling heat transfer and fluid flow in materials with complicated micro-structures is a major challenge to numerical methods due to their multiscale and multiphysics nature. A relatively novel numerical technique—the meshless smoothed particle hydrodynamics (SPH) method has the potential of making a significant contribution to this research field. In the present SPH modeling effort, a 2D modeling system is devised for the prediction of the effective thermal conductivity in heterogeneous materials containing two or three different components. The microscopic component configuration inside the materials is constructed in the SPH methodology by randomly assigning particles as a certain component to meet the required macroscopic composition. For heterogeneous two-component materials, the effective thermal conductivity predicted by the modified effective medium theory model with the so-called “flexible” factor f equal to 4.5 agrees well with the SPH data. On the basis of a simple “step-process” concept, the effective thermal conductivity of a heterogeneous multi-component material can be derived from the corresponding “degenerate” materials which consist of fewer components.     

Nucleation and growth of a gas bubble in magma

The dynamics of a “collective” gas bubble in the magma melt during its decompression was numerically studied on the basis of a complete mathematical models of an explosive volcanic eruption. It is shown that the bubble size distribution obtained for the nucleation process has one peak, which allows considering a “collective” bubble. The main stages of bubble growth due to gas diffusion and changes in the viscosity of the medium are determined. It is shown that the high viscosity of the melt makes possible the transition from the Rayleigh equation to a simpler relation for the radial velocity of the bubble.     

Visual observations of flow structure and melting front morphology in horizontal ice plate melting from above into a mixture

Visual observations reveal a complicated flow in the liquid melt and a melting front configuration resulting from horizontal ice plate melting from above into a 20 wt% calcium chloride aqueous solution. The initial temperature of the ice plate and the mixture are both −5°C. Small scale “mountain and valley” structures (∼1 mm) appear on the flat melting front just after melting begins, which have been called “sharkskin”. Innumerable upward and downward flows appear near the sharkskin and are controlled by its “mountain and valley” structure. These typical flows will considerably promote the melting of the ice plate to be 30% larger as compared to the numerically predicted results assuming a flat melting front (i.e., without the sharkskin), and also by three times larger compared with the results for melting from below.     

Numerical and experimental investigation of transverse injection flows

The flow field resulting from a transverse injection through a slot into supersonic flow is numerically simulated by solving Favre-averaged Navier–Stokes equations with κ − ω SST turbulence model with corrections for compressibility and transition. Numerical results are compared to experimental data in terms of surface pressure profiles, boundary layer separation location, transition location, and flow structures at the upstream and downstream of the jet. Results show good agreement with experimental data for a wide range of pressure ratios and transition locations are captured with acceptable accuracy. κ − ω SST model provides quite accurate results for such a complex flow field. Moreover, few experiments involving a sonic round jet injected on a flat plate into high-speed crossflow at Mach 5 are carried out. These experiments are three-dimensional in nature. The effect of pressure ratio on three-dimensional jet interaction dynamics is sought. Jet penetration is found to be a non-linear function of jet to free stream momentum flux ratio.     

A comparison of PIV measurements of canopy turbulence performed in the field and in a wind tunnel model

Particle image velocimetry (PIV) has been used to compare between turbulence characteristics just within and above a mature corn canopy and those of a model canopy setup in a wind tunnel (WT). The laboratory normalized mean velocity profile is adjusted using variable mesh screens to match the normalized mean shear of the corn field (CF) data. The smallest resolved scale in the field is about 15 times the Kolmogorov length scale (η_CF ≈ 0.4 mm), whereas in the WT it is 5 times η_WT (η_WT ≈ 0.15 mm). In both cases, the mean velocity and turbulence statistics are consistent with those measured using single point sensors. However, the profiles of normalized Reynolds shear stress in the field and the laboratory differ. Turbulent spectral densities calculated from PIV spatial and time series in the field display an inertial range spanning three decades. In the laboratory due to lower Reynolds numbers, the inertial range shrinks to two decades. Quadrant-Hole analysis is applied to Reynolds shear stress, vorticity magnitude and dissipation rates. In quadrants 1–3, the WT and field conditionally sampled stresses show similar trends. However, a conflicting trend is found in the sweep quadrant. The analysis confirms that sweep and ejections dominate the momentum flux and dissipation rate.The content of this paper, entitled “Applying PIV for Measuring Turbulence just within and above a Corn Canopy,” was presented at the 6th International Symposium on Particle Image Velocimetry at Pasadena, CA, USA, September 21–23, 2005.     

On the Kinetics of Polymer Crystallization in Opposite-Nozzle Flow

The present work was encouraged by the successes obtained previously in this laboratory with short-term shearing experiments on slightly undercooled melts of i-PP: post-shearing lamellar growth on (inconspicuous) thread-like precursors. For the present purpose (evaluation of the influence of extensional flow) the pioneering work by Mackley and Keller is taken as the point of departure. Our own machine of the same type has been adapted for creep experiments (adjustment to steady flow in fractions of the time needed in the original machine). The range of extension rates, where a transition takes place from a mere multiplication of the number of nuclei to the induction of highly oriented structures, appears to be quite narrow in undercooled i-PP melts. In the range of high extension rates (≅50 s⁻¹ ) the critical time for the formation of an oriented structure could not be measured because of its shortness (less than 0.2 s). It turns out that the flow pattern in the opposite-nozzle machine is far from ideal. A proposal had to be made for a redesign. In spite of the preliminary nature of some of our results, several interesting insights should not be “bottled up”. First of all, there is the usefulness of creep flow (because of its fast transition into steady state, after an almost instantaneous compliance). Secondly, there is the quite unexpected ineffectiveness of lower stretching rates for the formation of oriented structures. Thirdly, there is the overwhelming influence of a change of the geometry: the provisional introduction of trumpet-shaped (nearly hyperbolic) entrance regions to the nozzles caused a remarkable broadening of the birefringent zone, which was previously observed as a very thin “string” connecting the nozzles. Finally, the almost certain usefulness of the revised machine for other (sometimes purely rheological) purposes, e.g., for steady-state flow birefringence measurements in extensional flow should be mentioned. Received: 22 June 1999 Accepted: 28 September 2000     

Oscillatory Couette flow in the presence of an inclined magnetic field

Oscillatory MHD Couette flow of electrically conducting fluid between two parallel plates in a rotating system in the presence of an inclined magnetic field is considered when the upper plate is held at rest and the lower plate oscillates non-torsionally . An exact solution of the governing equations has been obtained by using Laplace transform technique. Asymptotic behavior of the solution is analyzed for M ² ≪1, K ² ≪1 and ω ≪1 and for large M ², K ² and ω. Numerical results of velocities are depicted graphically and the frictional shearing stresses are presented in tables. It is found that a thin boundary layer is formed near the lower plate, for large values of rotation parameter K ², Hartman number M ² and frequency parameter ω. The thickness of this boundary layer increases with increase in inclination of the magnetic field with the axis of rotation.     

Electroelastic field for an impermeable anti-plane shear crack in a piezoelectric ceramics plate

Electroelastic behavior of a cracked piezoelectric ceramics plate subjected to four cases of combined mechanical-electrical loads is analyzed. The integral transform method is applied to convert the problem involving an impermeable anti-plane crack to dual integral equations. Solving the resulting equations, the explicit analytic expressions for electroelastic field along the crack line and the intensity factors of relevant quantities near the crack tip and the mechanical strain energy release rate are obtained. The known results for an infinite piezoelectric ceramics plane containing an impermeable anti-plane crack are recovered from the present results only if the thickness of the plate h → ∞. Biography: LI Xian-fang (1964-)