Low-velocity viscous incompressible fluid flow around a hollow porous sphere

The problem of a viscous incompressible fluid flow around a hollow porous sphere in the Stokes approximation, in which the filtration flow through the sphere shell obeys the Darcy law, is solved. The force acting on the sphere from the fluid is calculated. The limiting cases are considered. The stream function is constructed.     

Very slow flow of Bingham viscoplastic fluid around a circular cylinder

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.     

Numerical investigation of flow structures around a sphere

A numerical investigation of flow around a sphere is performed and compared with previous studies. Here, a second-order accurate, finite volume method is used in order to predict the instantaneous and time-averaged flow characteristics using large eddy simulation (LES) on the multi-block grid system. Namely, the objectives of this article are: (i) the presentation of flow structures in the wake region downstream of the sphere with a wide variety of flow properties such as the distribution of velocity vectors, patterns of streamlines, Reynolds stress correlations, root mean square of velocity components and other time-averaged flow data in order to reveal the vortical flow structures in detail and (ii) to demonstrate the abilities of computational methods in simulation of vortical flow data. Finally, it has been concluded that there are good agreements between the experimental results and numerical predictions.     

Creeping flow of a power law fluid past a fluid sphere

The stress variational principle is employed to obtain the lower bound for the drag offered by the creeping flow of a power law fluid past a Newtonian fluid sphere. In spite of the unprescribed interfacial velocity, a bound-on-bound approach yields bounds that are close to the upper bound obtained by Mohan (1974). Furthermore, for very viscous drops (solid behavior) the theory gives lower bounds that differ considerably from those of Wasserman & Slattery (1964) and show good agreement with the results of Yoshioka & Adachi (1973). The approach presented in this work provides an insight into the method of analyzing multiphase flow situations involving non-Newtonian fluids.     

Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method (OHAM). The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.     

The slow rotation of a sphere submerged in a fluid with a surfactant surface layer

The effect of a layer of an adsorbed surfactant monomolecular film of fluid which covers the surface of a large volume of a different substrate fluid is considered with respect to the fluid motion caused by the slow rotation of a submerged sphere. For a semi-infinite substrate, the boundary value problem posed with the surfactant boundary condition of Scriven and Goodrich is solved exactly for any depth of the submerged sphere. Comprehensive numerical calculations are given for the torque and surface velocity for various values of the parameters defining the depth of the sphere and the surface shear viscosity. Asymptotic expressions for the solution are given for the cases of a deeply submerged sphere or when the substrate has a finite depth. The relevance of the work to providing an experimental technique for measuring surface shear viscosity is also considered.     

A comparative assessment of fluid flow and heat transfer parameters in laminar flow around a circular cylinder and a sphere

Theoretical studies have been carried out for a comparative assessment of hydrodynamic boundary layer thickness, displacement thickness and shear stress at the wall for laminar flow around a circular cylinder and a sphere with the help of the approximate method due to Karman and Pohlhausen for two dimensional flow and the method as applied to bodies of revolution based on the work of F. W. Scholkemeier, respectively. Thermal boundary layer thickness and Nusselt number have been evaluated around the surface of the solids. Comparison is made with available solutions. The graphical presentation of the results depicts a concise and relative assessment of fluid flow and heat-transfer parameters for flow around cylinder and sphere.     

Flow of a viscous fluid around a sphere of finite radius

We consider the stead y flow of a viscous fluid around a sphere of finiteradius in non-linear formulation. The equations of motion are written in non-dimensional terms. We seek their solution as the expansion of the unknown stream function in a series of powers of the Reynolds number, the coefficients of which are polynomials in associated Legendre functions of the first kind. Recurrence relations are given for the sequential determination of all coefficients. The velocity and pressure fields are determined. The drag is calculated. Numerical calculations are carried out.     

A power-law fluid flow past a porous sphere

Summary A model has been developed for the flow of a non-Newtonian fluid past a porous sphere. The drag force exerted on a porous sphere moving in a power-law fluid is obtained by an approximate solution of equations of motion in the creeping flow regime. It is predicted that the effect of the pseudoplastic anomaly on the drag force is more pronounced at large porosity parameters.

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Zusammenfassung Es wird ein Modell für die Strömung einer nichtnewtonschen Flüssigkeit längs einer porösen Kugel entwickelt. Die auf die in einer Ostwald-DeWaele-Flüssigkeit bewegte Kugel ausgeübte Reibungskraft wird durch eine Näherungslösung der Bewegungsgleichungen für schleichende Strömung gewonnen. Man findet, daß der Einfluß der Abweichung vom newtonschen Verhalten um so ausgeprägter wird, je größer die Porosität ist.

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A, B, C, D a, b, c, d coefficients in eqs. [10] and [18] - F _D drag force - K consistency index in power-law model - k ₁ ,k ₂ coefficients defined by eq. [18] - m porosity parameter - n flow index in power-law model - P pressure - P ^* dimensionless pressure defined by eq. [4] - P pressure difference - R radius of porous sphere - r radial distance from the center of the sphere - U velocity of uniform stream - u _i velocity component - u _i ^* dimensionless velocity component defined by eq. [4] - Y drag force correction factor defined by eq. [27] - _ij rate of deformation tensor - _ij ^* dimensionless rate of deformation tensor defined by eq. [4] - , spherical coordinates - dimensionless radial distance defined by eq. [4] - second invariant of rate of deformation tensor - ^* dimensionless second invariant of rate of deformation tensor defined by eq. [4] - _ij stress tensor - _ij ^* dimensionless stress tensor defined by eq. [4] - stream function - ^* dimensionless stream function defined by eq. [4] - i inside the surface of the sphere - o outside the surface of the sphere With 1 figure and 1 table     

Creeping flow of an ellis fluid past a Newtonian fluid sphere

Upper and lower bounds on the drag offered to a Newtonian fluid sphere placed in an Ellis model fluid in creeping flow have been found using variational principles. For a solid sphere, the bounds are in good agreement with those reported by earlier investigators.     

Experimental investigation of the separation of flow around a sphere

The results of an experimental investigation of the flow around a sphere over a broad range of Mach numbers M=0.3–3 and Reynolds numbers Re=3·10⁴–3·10⁷ are presented. The experiments were carried out on a ballistic test stand and in a wind tunnel. Flow patterns and pressure distributions were obtained. In particular, the effect of the Mach and Reynolds numbers on the position of the separation point and the edge shock was studied; the pressure distribution on the sphere was measured; and a nonmonotonic displacement of the flow separation point upon passage through the speed of sound was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 152–156, January–February, 1991.     

One example of magnetohydrodynamic stokes flow around a self-propelled sphere

Magnetohydrodynamic flow around a sphere equipped with an internal source of electromagnetic fields in the form of a variable megnetic dipole is investigated in the Stokes approximation. This dipole is capable of imparting translational motion to the sphere relative to the liquid. The properties of streamline flow in the self-propelled mode of operation of the source due to the influence of distributed volumetric forces on the character of the flow are demonstrated. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 3–11, July–August, 1998.