Evolution of perturbations on the surface of a viscoelastic liquid

The stability of a layer of a viscoelastic liquid on an inclined plane is studied within the framework of the model with a time-dependent “memory” in the presence of surface tension. It is shown analytically and numerically that these flows can be stable or unstable depending on the Reynolds number. Profiles of the free surface are found as functions of the Reynolds and Weber numbers. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 86–91, May–June, 2000.     

The behavior of viscoelastic squeeze films subject to normal oscillations, including the effect of fluid inertia

The problem of the squeeze film flow of a viscoelastic fluid between parallel, circular disks is analyzed. The upper disk is subject to small, axial oscillations. Lodge's “rubber-like liquid” is used as the viscoelastic fluid model, and fluid inertia forces are included. An exact solution to the equations of motion is obtained involving in-phase and out-of-phase components of velocity field and load, with respect to the plate velocity. Peculiar resonance phenomena in the load amplitude are exhibited at high Deborah number. At certain combinations of Reynolds number and Deborah number, the in-phase and/or out-of-phase velocity field components may attain an unusual circulating type of motion in which the flow reverses direction across the film. In the low Deborah number limit, and in the low Reynolds number limit, the results of this study reduce to those obtained by other workers.     

Convective heat transfer characteristics of laminar pulsating pipe air flow

 Heat transfer characteristics to laminar pulsating pipe flow under different conditions of Reynolds number and pulsation frequency were experimentally investigated. The tube wall of uniform heat flux condition was considered. Reynolds number was varied from 780 to 1987 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by pulsation frequency while it is slightly affected by Reynolds number. The results showed enhancements in the relative mean Nusselt number. In the frequency range of 1–4 Hz, an enhancement up to 30% (at Reynolds number of 1366 and pulsation frequency of 1.4 Hz) was obtained. In the frequency range of 17–25 Hz, an enhancement up to 9% (at Reynolds number of 1366 and pulsation frequency of 17.5 Hz) was indicated. The rate of enhancement of the relative mean Nusselt number decreased as pulsation frequency increased or as Reynolds number increased. A reduction in relative mean Nusselt number occurred outside these ranges of pulsation frequencies. A reduction in relative mean Nusselt number up to 40% for pulsation frequency range of 4.1–17 Hz and a reduction up to 20% for pulsation frequency range of 25–29.5 Hz for Reynolds numbers range of 780–1987 were considered. This reduction is directly proportional to the pulsation frequency. Empirical dimensionless equations have been developed for the relative mean Nusselt number that related to Reynolds number (750 < Re < 2000) and the dimensionless frequency (3<Ω<18) with about 10% rms. Received on 16 May 2000 / Published online: 29 November 2001     

Reynolds number dependence of the inertial range scaling of energy dissipation rate and enstrophy in a cylinder wake

The full energy dissipation rate and enstrophy are measured simultaneously using a probe consisting of four X-wires in the intermediate region of a cylinder wake for Taylor microscale Reynolds number in the range of 120–320. Longitudinal and transverse velocity increments are also obtained temporally using Taylor’s hypothesis. The inertial range scaling exponents indicate that the full enstrophy field has a stronger intermittency than does the full dissipation field for all the Reynolds numbers considered. The approximations of the energy dissipation rate and enstrophy based on isotropy are more intermittent than their corresponding true values. While the scaling exponents of the full energy dissipation rate remain approximately constant for different Reynolds numbers, those of the enstrophy decrease slightly and consistently with the increase of Reynolds number. It is conjectured that the scaling of the energy dissipation rate and the enstrophy may be the same when Reynolds number is extremely high, a trend that is consistent with that suggested by Nelkin (Phys Fluids 11:2202–2204, 1999; Am J Phys 68:310–318, 2000).     

Finite-Amplitude Equilibrium Solutions for Plane Poiseuille–Couette Flow

Two-dimensional nonlinear equilibrium solutions for the plane Poiseuille–Couette flow are computed by directly solving the full Navier–Stokes equations as a nonlinear eigenvalue problem. The equations are solved using the two-point fourth-order compact scheme and the Newton–Raphson iteration technique. The linear eigenvalue computations show that the combined Poiseuille–Couette flow is stable at all Reynolds numbers when the Couette velocity component σ₂ exceeds 0.34552. Starting with the neutral solution for the plane Poiseuille flow, the nonlinear neutral surfaces for the combined Poiseuille–Couette flow were mapped out by gradually increasing the velocity component σ₂. It is found that, for small σ₂, the neutral surfaces stay in the same family as that for the plane Poiseuille flow, and the nonlinear critical Reynolds number gradually increases with increasing σ₂. When the Couette velocity component is increased further, the neutral curve deviates from that for the Poiseuille flow with an appearance of a new loop at low wave numbers and at very low energy. By gradually increasing the σ₂ values at a constant Reynolds number, the nonlinear critical Reynolds numbers were determined as a function of σ₂. The results show that the nonlinear neutral curve is similar in shape to a linear case. The critical Reynolds number increases slowly up to σ₂∼ 0.2 and remains constant until σ₂∼ 0.58. Beyond σ₂ > 0.59, the critical Reynolds number increases sharply. From the computed results it is concluded that two-dimensional nonlinear equilibrium solutions do not exist beyond a critical σ₂ value of about 0.59. Received: 26 November 1996 and accepted 12 May 1997     

Stability of Poiseuille flow in the presence of a longitudinal magnetic field

The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds numbers is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008.     

Parameter determination and response analysis of viscoelastic material

The parameter determination of viscoelastic material is a multi-variable, multi-aim nonlinear optimization problem, which made the optimization process very complicated. In this paper a hybrid optimal algorithm was proposed to determine the viscoelastic parameters in the constitutive relation according to the experimentally obtained mechanical properties. This algorithm merges the Broydon–Fletcher–Goldfarb–Shanno search into a genetic algorithm framework as a basic operator in order to enhance the local search capability. The proposed hybrid algorithm not only can reduce the iterative times greatly but can abolish the limitation of initial parameter values. Nonlinear material characteristic curve-fitting was carried out using the proposed algorithm and other existing approaches. And the comparison results show this algorithm is accurate and effective. The numerical simulation and experimental study of viscoelastic cantilever beam also indicates that the finite element formulation and the calculative viscoelastic model parameters are reliable. The proposed optimization method can be extended to further complex parameter estimation researches.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

Conjugate heat transfer study of incompressible turbulent offset jet flows

In the present case, the conjugate heat transfer involving a turbulent plane offset jet is considered. The bottom wall of the solid block is maintained at an isothermal temperature higher than the jet inlet temperature. The parameters considered are the offset ratio (OR), the conductivity ratio (K), the solid slab thickness (S) and the Prandtl number (Pr). The Reynolds number considered is 15,000 because the flow becomes fully turbulent and then it becomes independent of the Reynolds number. The ranges of parameters considered are: OR = 3, 7 and 11, K = 1–1,000, S = 1–10 and Pr = 0.01–100. High Reynolds number two-equation model (k–ε) has been used for turbulence modeling. Results for the solid–fluid interface temperature, local Nusselt number, local heat flux, average Nusselt number and average heat transfer have been presented and discussed.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.     

Experimental study on influence of microscale effects on liquid flow characteristic in microtubes

Using deioned water as a working fluid, the influence of the microscale effects on liquid flow resistance in microtubes with inner diameters of 19.6 and 44.2 μm, respectively, is experimentally studied. The temperature rise resulted from the microscale effects, such as viscous dissipation, electric double layer, wall rough on the wall surface, etc., is obtained by an IR camera with a special magnified lens adopting micro-area thermal image technology and the corresponding pressure drop and the flux are also measured, so the relationship among friction factor, temperature rise and Reynolds number is obtained. Investigation shows that experimental data are almost equal to those of Hagen–Poiseuille when Reynolds number is low. With the increase of Reynolds number, the values of the friction factor depart from that of classical theory due to the microscale effects. Moreover, the values of the experimental friction factor considering various microscale effects is the maximal 10–15% deviation from that of friction factor without considering various microscale effects with further increase of Reynolds number.     

Investigation of steady laminar flows with an initial disturbance

Results of a parametric study of steady asymmetric flows are analyzed. Three-dimensional unsteady equations of hydromechanics for a compressible medium are solved by a time-dependent method. The range of the characteristic Reynolds number Re = 60–350 is considered. It is shown that a symmetric flow becomes asymmetric at Re = 90. This value can be considered as a threshold value for air. In the examples considered, the upper separation region is always smaller than the lower separation region owing to flow asymmetry in the vicinity of the left boundary of the domain of integration. The dependence of the separation region size on the Reynolds number is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 11–19, May–June, 2008.     

Response to Comments on the Article Titled ‘The Starting Flow in Ducts Filled with a Darcy–Brinkman Medium’

The fully developed flow and constant flux heat transfer in super-elliptic ducts filled with a porous (Darcy–Brinkman) medium are studied. Super-elliptic ducts resemble rectangular ducts with rounded corners. An efficient Ritz method is used to determine the velocity and temperature fields. Extensive tables for friction factor–Reynolds number product and Nusselt number are given.     

Dynamic stability of a viscoelastic plate with concentrated masses

The paper addresses the geometrically nonlinear problem of dynamic stability of a viscoelastic plate with concentrated masses. The Bubnov-Galerkin method based on polynomial approximation is used to reduce the problem to a system of nonlinear Volterra-type integro-differential equations with singular relaxation kernels. This system is solved by numerical method based on quadrature formulas. The critical loads are found and their dependence on the arrangement and number of concentrated masses is studied for a wide range of mechanical and geometrical parameters of the plate. The choice of a relaxation kernel for dynamic problems for viscoelastic thin-walled plate-like structures is justified. Results produced by different theories are compared __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 109–118, February 2008.     

Effects of coincidence window and measuring volume size on laser Doppler velocimetry measurement of turbulence

The effects of coincidence window and measuring volume size on two-component laser velocimeter measurement of turbulence in an isothermal liquid flow through a concentric annular channel were studied. Three different coincidence windows (100–500 μs) and three different measuring volume sizes (diameter, 5–9 wall units; spanwise length, 24–91 wall units) were used in a flow of Reynolds number 31,500 and data density spanning the high end of intermediate to the low end of high (3–6). While no significant effects of the coincidence window and measuring volume size were found on the time-mean velocity and turbulence intensities, the streamwise Reynolds shear stress measured near a wall was found to be markedly affected by both. The smallest feasible measuring volume along with an appropriate coincidence window provides good measurement of the shear stress. Received: 8 September 1999/Accepted: 11 July 2000     

Polymer “threads” and drag reduction

A number of different polymer fluids were ejected on the centerline of a water pipe-flow facility. Two distinct flow regions were identified: Reynolds numbers above 25000, where centerline injection acted as a rather efficient mixing device for water-soluble polymer — and no drag-reduction resulted from non water-soluble materials; and Reynolds numbers from 10000 to 25000, where strong evidence exists that under certain conditions, a viscoelastic fluid thread can interact with turbulence eddies and reduce the overall flow friction in the pipe.On Sabbatical leave from San Diego State University.     

Hydrodynamic and heat transfer characteristics of laminar flow past a parabolic cylinder with constant heat flux

 Steady, two-dimensional, symmetric, laminar and incompressible flow past parabolic bodies in a uniform stream with constant heat flux is investigated numerically. The full Navier–Stokes and energy equations in parabolic coordinates with stream function, vorticity and temperature as dependent variables were solved. These equations were solved using a second order accurate finite difference scheme on a non-uniform grid. The leading edge region was part of the solution domain. Wide range of Reynolds number (based on the nose radius of curvature) was covered for different values of Prandtl number. The flow past a semi-infinite flat plate was obtained when Reynolds number is set equal to zero. Results are presented for pressure and temperature distributions. Also local and average skin friction and Nusselt number distributions are presented. The effect of both Reynolds number and Prandtl number on the local and average Nusselt number is also presented. Received on 5 July 2000     

Investigation of the heat transfer and Reynolds analogy in a turbulent boundary layer at a high freestream turbulence level

The results of a systematic experimental study of the flow turbulence level effect on the heat transfer and Reynolds analogy coefficients over a wide range of the relevant parameters (the turbulence intensity and scale and the Reynolds number) are presented. The notion of the equivalent flow turbulence, which unifies the above-mentioned parameters, is introduced. It is established that the skin friction and heat transfer coefficients increase with the equivalent turbulence, while the Reynolds analogy coefficient remains unchanged. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 61–71, January–February, 2000.     

On the fluid–structure interaction of a splitter plate: vibration modes and Reynolds number effects

Previous work (Eloranta et al. in Exp Fluids 39:841–855, 2005) has shown that flow separation from the trailing edge of a splitter plate in a convergent channel involves a fluid–structure interaction (FSI), which modifies the fundamental instability related to vortex shedding. Under certain conditions, the FSI induces cellular vortex shedding from the trailing edge. This paper reports detailed measurements of the plate vibration mode and studies the effect of the Reynolds number on the FSI. Experimental techniques including laser vibrometer and digital imaging are used to measure the response of the plate and particle image velocimetry is used to measure the flow field in the near wake. Combining data from these techniques, the development of the vibration frequency and mode can be addressed together with the imprint of the vibration mode in the flow. The results show that over most of the Reynolds numbers measured, the plate vibrates in a distinct mode characterized by a spanwise standing wave along the plate trailing edge. The vibration frequency and the spacing between the nodes of the standing wave depend on the Reynolds number. As the Reynolds number is increased, the frequency of the dominant vibration mode does not increase linearly. The plot of the vibration frequency as a function of the Reynolds number shows that the vibration tends to lock to a rather constant frequency over of range of Reynolds numbers. After certain Reynolds number if threshold is exceeded, the frequency jumps to a new level, which also involves a new vibration mode.