Modeling of steady Herschel–Bulkley fluid flow over a sphere

Characteristics of the incompressible flow of Herschel–Bulkley fluid over a sphere were studied via systematic numerical modeling. A steady isothermal laminar flow mode was considered within a wide range of flow parameters: the Reynolds number 0 < Re ≤ 200, the Bingham number 0 ≤ Bn ≤ 100, and the power index 0.3 ≤ n ≤ 1. The numerical solution to the hydrodynamic equations was obtained using the finite volume method in the axisymmetric case. The changes in flow structures, pressure and viscous friction distribution, and integral drag as a function of the flow rate and fluid rheology are shown. Depending on whether plastic or inertial effects dominate in the flow, the limiting cases were identified. The power law and Bingham fluid flows were studied in detail as particular cases of the Herschel–Bulkley rheological model. Based on the modeling results, a new correlation was developed that approximates the calculated data with an accuracy of about 5% across the entire range of the input parameters. This correlation is also applicable in the particular cases of the power law and Bingham fluids.     

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.     

Calculations of the flow resistance and heat emission of a sphere in the laminar and high-turbulent gas flows

An early drag crisis can occur at high turbulence of incoming gas flow to a sphere. To study the influence of a crisis on heat transfer from a sphere to gas, a numerical experiment was carried out in which the free gas flow around a sphere with a temperature lower than the sphere temperature was simulated for two cases. The flow was laminar in the first case and highly turbulent in the second case. To take into account turbulence, the kinematic coefficient of turbulent viscosity with a value, which is much higher (up to 2000 times) than that for physical viscosity, was introduced. The results of calculations show that the early drag crisis occurs at Reynolds numbers of about 100 and results in considerable (by four to seven times) decrease in the hydrodynamic force and sphere drag coefficient C _d . The early drag crisis is also accompanied by the crisis of heat transfer from a sphere to gas with a decrease in Nusselt numbers Nu by three to six times.     

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.     

TVC effects on flow separation on slender cylinders

Occurrence of flow separation within the boundary-layer is primarily attributed to the growth of adverse pres-sure gradient within the boundary-layer. Such a separating boundary-layer can, however, be made to stay attached to the bounding surface due to various remedies where the surface transverse curvature (TVC) is one of them while the body contour is another. Assistive role of the surface transverse curvature is utilized in delaying the boundary-layer separation in a retarded flow past the slender bodies by assuming different body configurations. Axially-symmetric bodies of revolution of different shapes having a varying cross section in x, following the power-law form, have been considered in this study. It is shown that the point of separation is strongly dependent upon the surface curvature parameter k and the body-shape index n, which in fact control the flow separation. This fact ensures that an increase in the surface curvature parameter k and the body-shape index n leads to an increase in the wall shear stress which consequently delays the flow separation. Significant delay in flow separation is observed on cylinders having sufficiently large transverse curvature. Percent increase in the separation length corresponding to various values of the curvature parameter and the body-shape index has been calculated and reported in the form of Tables.     

Scaling laws of aquatic locomotion

In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion CD(Re)~2 =(Sw)~2 and its corresponding log law and power law. For power scaling law,(Sw)~2 = β_nRe~((2-1)/n), which is valid within the full spectrum of the Reynolds number Re=UL/v from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw=ωAL/v as Re ∝ (Sw)~σ,with σ=2 for creeping flows,σ=4/3 for laminar flows, σ=10/9 and σ=14/13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(lnRe+1.287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer's gait A;ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number.     

Maslov index for power-law potentials

The Maslov index in the semiclassical Bohr–Sommerfeld quantization rule is calculated for one-dimensional power-law potentials V (x) = ?V ₀/x ^s, x > 0, 0 < s < 2 The result for the potential V(x)=-V ₀/x ^1/2 is compared with the recently reported exact solution. The case of a spherically symmetric power-law potential is also considered.     

Acoustic testing of the vortex structure produced by an air flow about an array of cylinders

Results of experiments on the scattering of a plane ultrasonic wave from a vortex wake formed in an air flow behind a lattice of vertical cylinders are presented. The lattice is periodic in the direction perpendicular to the oncoming flow. The experiments are performed in a wind tunnel for two values of the Reynolds number, namely, Re = 75 and 500, and for lattices with different numbers of cylinders and with different lattice periods g = (2.5–15)d (where d is the diameter of the cylinders). The measured parameters of the scattered waves are used to estimate the degree of transverse correlation between the vortex wakes formed behind the cylinders for flows with different Reynolds numbers. The results obtained from an analysis of the characteristics of the scattered sound are compared with the results of direct hot-wire anemometer measurements and with the data obtained by other researchers.     

Mixed convection and entropy generation in a square cavity using nanofluids

In this work, two-dimensional mixed convection and entropy generation of water-(Cu, Ag, Al₂O₃, and TiO₂) nanofluids in a square lid-driven cavity containing two heat sources, have been numerically investigated. The upper lid and bottom wall of the cavity are maintained at a cold temperature T_C, respectively. The governing equations along with boundary conditions are solved using the finite volume method. Comparisons with the previous results were performed and found to be in excellent agreement. The effects of the solid volume fraction (0≤φ≤0.10), Rayleigh (10³≤Ra≤10⁵) and Reynolds (1≤Re≤500) numbers, and different types of nanofluids on the total entropy generation S_t and on entropy generation due to heat transfer S_h are presented and discussed. Moreover, the heat sources positions have an effect on the total entropy generation and Bejan number. It was found that S_t and S_h decrease with increase of φ, Ra, and Re.     

Reciprocal Time Relation of Noncolliding Brownian Motion with Drift

We consider an N-particle system of noncolliding Brownian motion starting from x ₁≤x ₂≤…≤x _N with drift coefficients ν _j , 1≤j≤N satisfying ν ₁≤ν ₂≤…≤ν _N . When all of the initial points are degenerated to be zero, x _j =0, 1≤j≤N, the equivalence is proved between a dilatation with factor 1/t of this drifted process and the noncolliding Brownian motion starting from ν ₁≤ν ₂≤…≤ν _N without drift observed at reciprocal time 1/t, for arbitrary t>0. Using this reciprocal time relation, we study the determinantal property of the noncolliding Brownian motion with drift having finite and infinite numbers of particles.     

Panoramic diagnostics of shear stresses on the channel wall with a step using the liquid crystals

Measurements results on the shear stresses of surface friction by means of thin-film coatings based on cholesteric liquid crystals and specialized software for digital processing of experimental video are presented in the paper. The calibration dependencies of shear stress relative to the hue and azimuth angle as well as shear stress spatial distribution at subsonic turbulent flow (V _∝ = 84 m/s) around a step, trapezoidal in plane (Reynolds number calculated for step height h, Re _h = 2.57?10⁴), with a base angle of 46° were derived for two geometries of experiment. The experiments demonstrated high sensitivity of liquid crystals to rearrangement of the near-wall flow structure and possibility to obtain quantitative data about mean shear stress levels.     

Vacuum self similar anisotropic cosmologies in <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)-gravity

The implications from the existence of a proper Homothetic Vector Field on the dynamics of vacuum anisotropic models in F(R) gravitational theory are studied. The fact that every Spatially Homogeneous vacuum model is equivalent, formally, with a “flux”-free anisotropic fluid model in standard gravity and the induced power-law form of the functional F(R) due to self-similarity enable us to close the system of equations. We found some new exact anisotropic solutions that arise as fixed points in the associated dynamical system. The non-existence of Kasner-like (Bianchi type I) solutions in proper F(R)-gravity (i.e. \(R\ne 0\)) strengthens the belief that curvature corrections will prevent the shear influence into the past thus permitting an isotropic singularity. We also discuss certain issues regarding the lack of vacuum models of type III, IV, VII\(_{h}\) in comparison with the corresponding results in standard gravity.     

Effect of Hall current and chemical reaction on MHD flow along a fluctuating porous flat plate with internal heat absorption/generation

Effect of Hall current on the unsteady free convection flow of a viscous incompressible and electrically conducting fluid past a fluctuating porous flat plate with internal heat absorption/generation in the presence of foreign gasses (such as H₂, CO₂, H₂O, NH₃) was investigated. The results are discussed with the effect of the parameters m, the Hall current, Mt, the hydromagnetic parameter, G _r the Grashoff number for heat transfer, G _c , the Grashoff number for mass transfer, S, the internal heat absorption/generation parameter, α, the transpiration parameter, S _c , the Schmidt parameter, and K _c the chemical reaction parameter for Prandtl number P _r = 0.71, which represents air. Further, the present study accounts for the 1st order chemical reaction affecting the flow characteristics. The governing equations are solved in closed form applying Hh _n (x) function. The effects of pertinent parameters characterizing the flow field are discussed with the help of graphs and tables. The important observation of the present study is that heat generation/absorption modifies the flow of current simultaneously to a magnetic force and thermal bouncy force. Heat generation combined with blowing leads to a sharp fall of temperature.     

Low-Prandtl-number Rayleigh-Bénard convection with stress-free boundaries

Results of direct numerical simulations on Rayleigh-Bénard convection in low-Prandtl-number convection with stress-free horizontal boundaries are presented. Simulations are done in a three dimensional rectangular simulation box of dimensions L _x × L _y × 1. Instabilities and the corresponding fluid patterns near onset of convection are investigated by varying the horizontal aspect ratio η = L _y /L _x in a range 1 ≤ η ≤ 4. Fluid patterns are complex and unsteady at the instability onset for η ≥ 2. They consist of wavy rolls, rhombic patterns and oblique wavy rolls. The patterns near onset are time periodic for η < 2. We observe periodic wavy rolls for η = 4 / 3. Homoclinic bifurcations are observed for η = 1 for 0 ≤ Pr ≤ 0.03. We observe spontaneous breaking of a single limit cycle in two and again spontaneous merging of two limit cycles into one in a simulation box with η = 1, as the reduced Rayleigh number r = Ra/R a _c is raised at a fixed value of Pr. The effect of Prandtl number on the homoclinic bifurcations is also investigated. We also present a low-dimensional model, which captures the instability sequence quite accurately for η = 1.     

Growth of (GaAs)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(ZnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solution films and investigation of their structural and some photoelectric properties

Single-crystal films of the substitutional solid solution (GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) on GaAs substrates have been grown using liquid phase epitaxy. The X-ray diffraction patterns, photoluminescence spectra, and current-voltage characteristics of the n-(GaAs)-p-(GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) heterostructures prepared have been investigated. The lattice parameters of the film a _f = 5.6544 Å and the substrate a _s = 5.6465 Å have been determined, and the profile of the molecular distribution of the solid solution components has been obtained. The photoluminescence spectrum of the (GaAs)_{1 ? x} (ZnSe) _x (0 ≤ x ≤ 0.80) films exhibits a narrow peak (against the background of the broad luminescence band) with a maximum in the luminescence intensity at a photon energy of 2.67 eV due to the presence of Zn-Se bonds in the structure (ZnSe is covalently bonded to the tetrahedral lattice of the GaAs matrix). It has been shown that the direct branch of the current-voltage characteristics of the structures under investigation is described by an exponential dependence I = I ₀exp(qV/ckT) at low voltages (V > 0.3 V) and by a power-law dependence I ～ V ^α with exponents α = 4 at V = 0.4–0.8 V, α = 2 at V = 0.8–1.4 V, and α = 1.5 at V > 2 V. The experimental results have been explained in the framework of the double-injection model for the n-p-p ⁺ structure under the condition that the concentration distribution of nonequilibrium charge carriers has a minimum.     

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.     

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.     

Unsteady analysis of six-DOF motion of a 6:1 prolate spheroid in viscous fluid

Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6.     

Impact of generalized dissipative coefficient on warm inflationary dynamics in the light of latest Planck data

The warm inflation scenario in view of the modified Chaplygin gas is studied. We consider the inflationary expansion to be driven by a standard scalar field whose decay ratio \(\Gamma \) has a generic power-law dependence with the scalar field \(\phi \) and the temperature of the thermal bath T. By assuming an exponential power-law dependence in the cosmic time for the scale factor a(t), corresponding to the intermediate inflation model, we solve the background and perturbative dynamics considering our model to evolve according to (1) weak dissipative regime and (2) strong dissipative regime. Specifically, we find explicit expressions for the dissipative coefficient, scalar potential, and the relevant inflationary observables like the scalar power spectrum, scalar spectral index, and tensor-to-scalar ratio. The free parameters characterizing our model are constrained by considering the essential condition for warm inflation, the conditions for the model evolves according to weak or strong dissipative regime, and the 2015 Planck results through the \(n_s\)–r plane.     

The influence of the thermal wake due to pulsating optical discharge on the aerodynamic-drag force

The influence of a thermal wake due to gas injection and due to a pulsating optical discharge (POD) on the aero-dynamic-drag force of a body in a supersonic air flow with Mach number M = 1.45 are experimentally examined. With the help of a single-component aerodynamic balance, the influence of the injected subsonic jet and the thermal wake produced by POD on the aerodynamic drag of a hemisphere-on-cylinder model was studied. It is shown that the observed aerodynamic-force reduction phenomenon can be made more pronounced by increasing the laser power and pulse repetition frequency, or by decreasing the distance between the model and the pulsating optical discharge. The maximum aerodynamic-force reduction (up to 15%) due to the thermal-wake action was observed at a maximum laser-radiation power of W = 2.3 kW and at a pulse rate of f = 90 kHz. The joint effect due to the argon jet and due to the POD caused an aerodynamic-drag force reduction reaching 30%.