Calculation of the drag and heat transfer from a sphere in the gas flow in a cylindrical channel

A numerical experiment on the simulation of heat transfer from a sphere to a gas flow in a cylindrical channel in the Stokes and transient flow regimes has been described. Radial and axial profiles of the gas temperature and the dependences of drag coefficient C_d of the body and Nusselt number Nu on Reynolds number Re have been calculated and analyzed. The problem of the influence of the early drag crisis for a sphere on its heat transfer to the gas flow has been considered. The estimation of this phenomenon has shown that the early drag crisis of the sphere in a strongly turbulent flow causes a reduction in heat transfer from the sphere to the gas by three to six times (in approximately the same proportion as for its drag coefficient).     

Calculation of the flow about a sphere and the drag of the sphere under laminar and strongly turbulent conditions

To investigate the influence of a strongly turbulent incoming flow on the hydrodynamic drag of a body and occurrence of the early crisis of drag, a numerical experiment is conducted in which a free gas flow about a sphere is simulated for two cases, namely, for a laminar flow and for a strongly turbulent flow. Turbulence is simulated by assuming a high kinematic coefficient of turbulent viscosity. Calculation data lead us to conclude that the early crisis of drag at Reynolds numbers near 100, which shows up as a considerable (four-to sevenfold) decrease in the hydrodynamic force and the drag coefficient of the body, can be explained by the strong turbulence of the incoming flow.     

Experimental verification of the early crisis of drag using a single sphere

The recently discovered phenomenon of drag anomaly (early crisis) observed for droplets in a two-phase turbulent flow at transition Reynolds numbers (Re = 10–100) is experimentally supported in the case of a gas flow about a single hard sphere as well. Using a specially designed torsion balance, the drag force of a foam plastic sphere 3 mm in diameter placed in a blower-produced turbulent jet is measured. It is found that the turbulence of the flow about the sphere must be high for the drag anomaly to arise.     

Direct numerical simulation of the turbulent flows of power-law fluids in a circular pipe

Fully developed turbulent pipe flows of power-law fluids are studied by means of direct numerical simulation. Two series of calculations at generalised Reynolds numbers of approximately 10000 and 20000 were carried out. Five different power law indexes n from 0.4 to 1 were considered. The distributions of components of Reynolds stress tensor, averaged viscosity, viscosity fluctuations, and measures of turbulent anisotropy are presented. The friction coefficient predicted by the simulations is in a good agreement with the correlation obtained from experiment. Flows of power-law fluids exhibit stronger anisotropy of the Reynolds stress tensor compared with the flow of Newtonian fluid. The turbulence anisotropy becomes more significant with the decreasing flow index n. An increase in apparent viscosity away from the wall leads to the damping of the wall-normal velocity pulsations. The suppression of the turbulent energy redistribution between the Reynolds stress tensor components observed in the simulations leads to a strong domination of the axial velocity pulsations. The damping of wall-normal velocity pulsations leads to a reduction of the fluctuating transport of momentum from the core toward the wall, which explains the effect of drag reduction.     

Effect of the gas flow geometry and turbulence on the hydrodynamic drag of a body in the flow

The effect of the incoming flow geometry on the hydrodynamic drag of a body is investigated in a numerical experiment simulating a free gas flow past a sphere as well as flows in cylindrical tubes of various radii, in a confuser, and a diffuser. The results of calculations lead to the conclusion that the confinement of the flow by the tube walls, its contraction and expansion may change the hydrodynamic force and the drag acting on the body insignificantly (not more than by 30%). This cannot explain the early drag crisis, in which the values of these quantities decrease by 4–7 times for Reynolds numbers on the order of 100. This phenomenon is explained theoretically by the effect of strong turbulence of the incoming flow to the body.     

Drag and Lift Forces Acting on a Sphere in Shear Flow of Power-Law Fluid

Laminar flow of a power-law fluid over a sphere is considered for unbounded shear flow. The Navier–Stokes equations with power-law viscosity are solved numerically using an in-house developed CFD package. Vorticities structures downstream of particle are suppressed for powerlaw fluid. The shear rate influence on drag force is negligible for power index close to unit, and the drag force appreciably decreases with falling power index. For small Reynolds numbers, the lift force coefficient monotonically decreases against the power index and exhibits an opposite behavior for moderate values of Reynolds numbers. The results of the parametric studies are used to derive correlations for the drag force and to detect the hydrodynamic differences from uniform flow. The investigation parameters varied within the following ranges: power-law index 0.3 ≤ n ≤ 1, Reynolds number 0 < Re ≤ 150, and dimensionless shear rate 0.05 ≤ s ≤ 0.4.     

Simulation of turbulent non-isothermal polydisperse bubbly flow behind a sudden tube expansion

The results of numerical simulation of the structure of non-isothermal polydisperse bubbly turbulent flow and heat transfer behind a sudden tube expansion are presented. The study was carried out at a change in the initial diameter of the air bubbles within d _m1 = 1–5 mm and their volumetric void fraction β = 0–10 %. Small bubbles are available in almost the entire cross section of the tube, while the large bubbles pass mainly through the flow core. An increase in the size of dispersed phase causes the growth of turbulence in the liquid phase due to flow turbulization, when there is a separated flow of liquid past the large bubbles. Adding the air bubbles causes a significant reduction in the length of the separation zone and heat transfer enhancement, and these effects increase with increasing bubble size and their gas volumetric flow rate ratio.     

Crisis of hydrodynamic drag of drops in the two-phase turbulent flow of a spray produced by a mechanical nozzle at transition reynolds Numbers

When processing experimental data for the hydrodynamics of a two-phase flow in a spray produced by a mechanical nozzle, we revealed an anomaly in the behavior of the hydrodynamic drag of drops: the drag coefficient turns out to be four to seven times lower than the previously known values. Several hypotheses are put forward to explain the anomaly. It is found that, when the gas flows around drops under highly turbulent conditions, an “early” (i.e., observed even at transition Reynolds numbers, Re>50) crisis of drag resistance of drops takes place. This new physical phenomenon allows us to account for a number of features of the two-phase flow that are observed in the experiment. Among these features is, in particular, the fact that the momentum transferred to the gas is roughly half the initial momentum of the liquid jet.     

Relaxation of a 2D MHD flow across a magnetic field (2D hydrodynamic flow) in a bounded region

The problem on magnetohydrodynamic (MHD) flow of a solitary vortex across a magnetic field in a volume confined by rigid walls is solved numerically for large Reynolds numbers (including magnetic Reynolds numbers) and small Alfven-Mach numbers M _A . In this case, the MHD problem is reduced to that of two-dimensional hydrodynamic turbulence. It is shown that sound is not generated by a turbulent medium for small values of M _A ; consequently, this kinetic energy dissipation channel is closed in this case. Calculations show that, in contrast to 3D turbulence, kinetic energy dissipation for 2D turbulence occurs, as expected, over time periods on the order of L²/v(L is the characteristic size of the system and v is the kinematic viscosity). In our calculations with numerical viscosity v～vΔx (Δx is the unit cell size), this corresponds to time values on the order of ～(L/Δx)(L/v). In the kinetic energy spectra for a turbulent flow in a bounded region in the inertial interval (lying between the energy-carrying and viscosity regions), the values of E(k) decrease with increasing wave numbers k at a higher rate than in proportion to k^?3. The volume distribution of vorticity becomes narrower with time (the characteristic values of curlv decrease) and is blurred; for large time periods, the distribution approximately retains its shape as well as asymmetry with respect to positive and negative values, which is associated with the asymmetry of the initial conditions.     

Wall Shear Stress and Heat Transfer of Downward Bubbly Flow at Low Flow Rates of Liquid and Gas

The effect of suppression of turbulence in a downward bubbly flow and its impact on the wall shear stress and heat transfer are discussed. Measurements were carried out for Reynolds numbers Re = 5000–10000, which were calculated from the velocity of the liquid phase and with the gas volumetric flow rate ratio β = 0–0.05. Data on the size of bubbles detaching from the edges of an array of capillaries in a liquid flow are given. The influence of the disperse phase dimensions on the wall shear stress and heat transfer is discussed. It is shown that change in the size of the dispersed phase can lead to both intensification and deterioration of heat transfer as compared with a single-phase flow at constant flow rates of liquid and gas at the channel inlet. The cause of the heat transfer deterioration is “laminarization” of the flow in the near-wall region. An analysis of the spectral power of signals is given.     

The evolution of free turbulent spherical gas flames and the generalized Kolmogorov-Obukhov laws

A scenario of self-turbulization and limiting (experimentally observed) laws of accelerated expansion of a free turbulent spherical flame in a preliminarily mixed fuel gas mixture are described. The limiting self-similar law of the growth of a completely turbulized spherical front R ～ 〈?〉^1/2 t ^3/2 was shown to correspond to the generalized Kolmogorov-Obukhov law for a locally isotropic velocity field in a spherical turbulent medium with an immobile center of gravity at a constant rate of internal heat release per 1 kg of the mixture 〈?〉 (in m²/s³). The asymptotic dependences of the kinematic (space-time) characteristics of the evolution of a turbulent macroelement growing according to the Kolmogorov-Obukhov laws on the Reynolds and Peclet numbers obtained from the visible radius R, the rate of its propagation R′, and laminar viscosity (v) and thermal diffusivity (χ) coefficients of the initial mixture were obtained in the criterional form. It was shown that, irrespective of the direction of cloud growth under study (horizontal impurity diffusion in the atmosphere and ocean or an isotropic spherical flame) and the physical nature and value of internal heat release 〈?〉 in this direction (viscous dissipation of the kinetic energy of turbulent vortices in the first case or energy release in combustion in the second), the kinematic parameters of the growth of turbulent macroformations were described by these generalized laws.     

Experimental Study of the Influence of Structured Capillary-Porous Coatings on the Dynamics of Development of Transient Processes and the Crisis Phenomena at Stepwise Heat Release

The effect of structured plasma-sprayed capillary-porous coatings on transient processes and the development of crisis phenomena at boiling under pulsed heat release was studied. The working fluid was liquid nitrogen on the saturation line at atmospheric pressure. It is shown that under unsteady heat release, there is a degeneration of the development of the boiling crisis on heaters with structured capillary-porous coatings at q &lt; q_CHF (critical heat flux at steady heat release). Under unsteady pulsed heat release, no rapid transition to the film boiling regime (without passing through the nucleate boiling stage) is observed on heaters with such coatings until the thermal load is more than two times higher than the critical heat flux for steady heat release. This significantly increases the times of transition to post-critical heat transfer. Analysis of synchronized measurements of surface temperature of heaters and high-speed video recording of transient processes shows that the degeneration of the heat transfer crisis at q &lt; q_CHF on samples with coatings occurs due to significantly lower liquid boiling temperature differences and specific features of the dynamics of propagation of self-sustaining evaporation fronts in comparison with a smooth heater.     

Laminar free convection heat transfer between vertical isothermal plates

The paper represents results on numerical investigation of flow and heat transfer between two isothermal vertical plates under laminar natural convection. A system of complete Navier–Stokes equations is solved for a two-dimensional gas flow between the plates along with additional rectangular regions (connected to inlet and outlet sections), whose characteristic sizes are much greater than the spacing between the plates. The calculations were performed over very wide ranges of Rayleigh number Ra = 10 ÷ 10⁵ and a relative channel length AR = L/w = 1 ÷ 500. The influence of the input parameters on the gas-dynamic and thermal structure of thermogravitational convection, the local and mean heat transfer, and also the gas flow rate between the plates (convective draft. We determined sizes of the regions and regime parameters when the local heat flux on the walls tends to zero due to the gas temperature approach to the surface temperature. It is shown that the mean heat transfer decreases as the relative channel length AR grows, whereas the integral gas flow rate (convective draft) and Reynolds number in the channel Re = 2wUm/ν increase. The use of a modified Rayleigh number Ra* = Ra · (w/L) (Elenbaas number) leads to generalization of calculation data on mean heat transfer. These data are in good agreement with the correlations for heat transfer [1, 2] and gas flow rate [3]. The reasons of variation of the data in the range of low Rayleigh numbers are discussed in detail.     

EXPRIMENTAL STUDY ON EFFECTS OF A SINGLE POROUS-TYPE ROUGHNESS ELEMENT IN A PARALLEL-PLATE DUCT

Experiments were carried out to examine the effects of a single porous-type roughness element on the insulated wall opposite the smooth heated plate on the heat transfer. The local heat transfer and drag coefficients depend on the porous diameter and the porosity. The local heat transfer coefficient takes a peak, PI, under the porous element in laminar flow. On the other hand, in turbulent flow, it takes two peaks, PI and P2, under and after the element, respectively. The position of peak P2 varies with the height of the element and the Reynolds number. The drag coefficient of the porous element is lower than that of the solid element. According to thermal performance at constant pumping power, this kind of element should be used in laminar flow. In addition, it is estimated that the porous element should be utilized in the composite effects (the turbulence increase and the thermal radiation shielding effect) of heat transfer in order to apply the element effectively.     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.     

Effectiveness of blowing for improving the high-speed trains aerodynamics

The promising method of drag reduction with the use of micro-blowing through the streamlined surface has been proposed for its use to the external surface of high-speed train. The advantages of high-speed train as an object of micro-blowing application are introduced. The corresponding RANS-based mathematical model is elaborated, and the computations of the external flow around a long train body are performed. Predictions of the turbulent boundary layer over penetrable surface with different modes of micro-blowing have been presented and analyzed. The developed modifications of mathematical model of turbulence have been used to take into account the micro-blowing influence in the inner region of turbulent boundary layer. The obtained results of parametric analysis of drag reduction depending on the area of permeable sections, intensity of micro-blowing, and high-speed train length have been analyzed. In particular, the dependence between drag reduction effect and length of train body with realized micro-blowing as well as its intensity is established. Realization of micro-blowing with blowing velocity just 0.25 % of train speed (V = 100 m/s) on the 70 % of the streamlined surface area for just one train carriage (L = 25 m) allows one to reduce the aerodynamic drag (including the most actual friction and head-tail pressure components) of the whole train (L = 200 m) by about 5.25 %, so in case of micro-blowing realization on all its 8 carriages, the train’s aerodynamic drag can be reduced approximately by 42 %.     

Handling of temperature dependence of viscosity in problems of incompressible medium flow around a cylinder

The viscous incompressible medium (water, air) flow past a circular cylinder is considered with regard for the temperature T dependent viscosity v. The influence of different boundary conditions for temperature on flow structure, the drag coefficient and its components due to the pressure and viscosity is investigated in the problem of the flow past a cylinder at rest for the (diameter-based) Reynolds number Re_D = 40. A relation between the viscosity gradient along a normal to the body surface and the integral vorticity flux from the body surface into the boundary layer is discussed. Unlike the constant viscosity case the vorticity flux may be different from zero, which must lead because of the integral conservation law for the vorticity to an alteration of the far-field boundary conditions for the velocity. In the same connection, the problem is analysed on the heat spot entry into the computational region under consideration for the flow past a circular cylinder. The examples of the symmetrization of separated flow past a cylinder performing rotation oscillations in a uniform free stream (the Taneda problem) are considered. A comparison with flow computations for low Mach numbers M « 1 for the flow of a medium past a cylinder at rest is carried out. At the computation of the equation for heat transfer under the assumption of incompressibility of such media as air, it is proposed to retain the pressure derivative, which is typical of gases. In this case, a better agreement with the computations of compressible flows (for M « 1) is achieved, for example, at the determination of the sizes of a symmetric zone of flow separation past a circular cylinder. An unsteady flow in the neighborhood of the point of joining the zero streamline bounding a closed region of separated flow (the cavity) in a wake of the cylinder at rest is obtained by a numerical simulation at the Reynolds number equal to 40.     

Elastic stresses in random flow of a dilute polymer solution and the turbulent drag reduction problem

In this short review I argue that the progress in our understanding the mechanism of turbulent drag reduction is conditioned by obtaining experimental data on dynamics and statistics of polymer stretching and elastic stresses in inertial turbulence at high Reynolds numbers that is a technically challenging task. The suggested way out of the currently unresolved technical problem is to collect the same data in elastic turbulence, which is a smooth random flow similar to that found in inertial turbulence below the dissipation scale. Since the polymer stretching and elastic stresses in inertial turbulence are influenced only by small scales, it is appropriate to use information on the polymer stretching and elastic stresses obtained in elastic turbulence. The experimental data on the statistics of the polymer stretching, the coil–stretch transition, and elastic stresses together with spatial distribution and values of the rms of the velocity gradients were collected in elastic turbulence for the last several years. This information serves a basis for a new hypothesis of turbulent drag reduction. To cite this article: V. Steinberg, C. R. Physique 10 (2009).     

Verification of the standard model of shear stress transport and its modified version that takes into account the streamline curvature and estimation of the applicability of the Menter combined boundary conditions in calculating the ultralow profile drag for an optimally configured cylinder–coaxial disk arrangement

A modification of the popular model of shear stress transport aimed at calculating the separation flow of an incompressible viscous liquid is justified. The modification eliminates the nonphysical pumping of the vortex viscosity in the cores of large-scale vortices. It has been verified with regard to the influence of the streamline curvature on the vortex viscosity by introducing a reciprocal linear function of the turbulent Richardson number with the Isaev–Kharchenko–Usachov constant equal to 0.02.Verification is based on solving the test problem an axisymmetric steady flow about a disk–cylinder tandem with an optimally configured nose, which has an ultralow profile drag for a Reynolds number of 5 × 10⁵. It has been shown that the Menter combined boundary conditions are valid if y⁺y of the wall does not exceed two.