Conjugate heat transfer within a concentric annulus filled with micropolar fluid

This paper investigates numerically the conjugate heat transfer in an annulus between two concentric cylinders. The annulus contains micropolar fluid and is heated isothermally from its inner wall. The effect of Rayleigh number, thickness of inner wall, inner wall-fluid thermal conductivity ratio, and material parameters of micropolar fluid on heat transfer rate within the annulus has been investigated. The study has shown that for low Rayleigh number regimes and for thermal conductivity of the inner wall greater than that of the fluid, the increase of inner wall thickness increases the heat transfer rate through the annulus and vice versa. While for convection dominating regimes Ra ≥ 10⁴ the increase of inner wall thickness decreases the heat transfer rate. Moreover, the study has shown that for fixed geometrical and flow parameters the heat transfer decreases in case of micropolar fluids in comparison with that of Newtonian fluids.     

LES of turbulent flow in a concentric annulus with rotating outer wall

Fully-developed turbulent flow in a concentric annulus, r₁/r₂ = 0.5, Re_h = 12,500, with the outer wall rotating at a range of rotation rates N = U_θ,wall/U_b from 0.5 up to 4 is studied by large-eddy simulations. The focus is on the effects of moderate to very high rotation rates on the mean flow, turbulence statistics and eddy structure. For N up to ∼2, an increase in the rotation rate dampens progressively the turbulence near the rotating outer wall, while affecting only mildly the inner-wall region. At higher rotation rates this trend is reversed: for N = 2.8 close to the inner wall turbulence is dramatically reduced while the outer wall region remains turbulent with discernible helical vortices as the dominant turbulent structure. The turbulence parameters and eddy structures differ significantly for N = 2 and 2.8. This switch is attributed to the centrifuged turbulence (generated near the inner wall) prevailing over the axial inertial force as well as over the counteracting laminarizing effects of the rotating outer wall. At still higher rotation, N = 4, the flow gets laminarized but with distinct spiralling vortices akin to the Taylor–Couette rolls found between the two counter-rotating cylinders without axial flow, which is the limiting case when N approaches to infinity. The ratio of the centrifugal to axial inertial forces, Ta/Re² ∝ N² (where Ta is the Taylor number) is considered as a possible criterion for defining the conditions for the above regime change.     

Study on steady surge pressure for Yield-Pseudoplastic fluid in a concentric annulus

Surge pressure caused by pipe moving through the wellbore full of drilling fluid is the main factor affecting wellbore stability, on which the additional mud density is designed. Thus it is desired to predict the surge pressure with high accuracy. While this is closely related with the selection of mud rheological models. Yield-Pseudoplastic model which has three parameters and is famous for its higher accuracy has been used to describe the mud rheological properties in recent years. Based on this model the paper presents a new theoretical model for calculating surge pressure caused by mud viscosity during tripping or casing in a concentric annulus of directional wells under steady laminar situation. For convenience, the paper plots the distribution of the coefficients of surge pressure for different conditions. An example is given. These results provide the basis for controlling pressure surges and tripping velocity.     

Unsteady flow in an annulus between two concentric rotating spheres

An analysis is presented for the unsteady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric spheres rotating about a common axis of symmetry. A solution of the Navier-Stokes equations is obtained by employing an iterative technique. The solution is valid for small values of Reynolds numbers and acceleration parameters of the spheres. In applying the results of this analysis to a rotationally accelerating sphere, a virtual moment of inertia is introduced to account for the local inertia of the fluid.     

Unsteady flow of a second-order fluid between concentric cylinders

The unsteady motion of an incompressible second-order fluid contained between two finite coaxial cylinders is examined when the outer cylinder is held fixed while the inner cylinder is constrained to execute an arbitrary angular velocity. A solution is obtained in closed form with the aid of transforms and an expression is obtained for the couple experienced. The particular case of a periodic angular velocity is then examined and some numerical work done. There is a marked difference between the results obtained and their classical counterparts.     

Unsteady flow in an annulus between two concentric rotating spheres

An analysis is presented for the unsteady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric spheres rotating about a common axis of symmetry. A solution of the Navier-Stokes equations is obtained by employing an iterative technique. The solution is valid for small values of Reynolds numbers and acceleration parameters of the spheres. In applying the results of this analysis to a rotationally accelerating sphere, a virtual moment of intertia is introduced to account for the local inertia of the fluid.Nomenclature R _i radius of the inner sphere - R _o radius of the outer sphere - radial coordinate - r dimensionless radial coordinate, - meridional coordinate - azimuthal coordinate - time - t dimensionless time, - Re _i instantaneous Reynolds number of the inner sphere, _i R _k ² / - Re _o instantaneous Reynolds number of the outer sphere, _o R _o ² / - radial velocity component - V _r dimensionless radial velocity component, - meridional velocity component - V dimensionless meridional velocity component, - azimuthal velocity component - V dimensionless azimuthal velocity component, - viscous torque - T dimensionless viscous torque, - viscous torque at surface of inner sphere - T _i dimensionless viscous torque at surface of inner sphere, - viscous torque at surface of outer sphere - T _o dimensionless viscous torque at surface of outer sphere, - externally applied torque on inner sphere - T _p,i dimensionless applied torque on inner sphere, - moment of inertia of inner sphere - Z _i dimensionless moment of inertia of inner sphere, - virtual moment of inertia of inner sphere - Z _i,v dimensionless virtual moment of inertia of inner sphere, - virtual moment of inertia of outer sphere - _i instantaneous angular velocity of the inner sphere - _o instantaneous angular velocity of the outer sphere - density of fluid - viscosity of fluid - kinematic viscosity of fluid,/ - radius ratio,R _i/R _o - swirl function, - dimensionless swirl function, - stream function - dimensionless stream function, - _i acceleration parameter for the inner sphere, - _o acceleration parameter for the outer sphere, - shear stress - _r dimensionless shear stress,      

Heat transfer and pressure drop of a transversely finned concentric annulus with longitudinal flow

The characteristics of heat transfer and pressure drop have been experimentally studied for the fully developed concentric annular flow with transverse fins normal to the flow direction by the naphthalene sublimation technique. Correlations for calculating the heat transfer coefficient with different inner diametersD ₀ of the outer tube are presented. A characteristic Reynolds number has been proposed, by which the predominant role of the transverse fins can be evaluated. It has been indicated that the inner diameterD ₀ has much more effect on pressure drop than on heat transfer. The effect ofD ₀ on the overall performance is also compared under the same flow velocity or flow rate. It has been found that the effect of developing flow on heat transfer is significant and should be taken into account during experiment.

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Wärmeübergang und Druckverlust in einem querberippten konzentrischen Ringkanal bei Längsströmung

Zusammenfassung Mit Hilfe der Naphthalin-Sublimationstechnik werden die Wärmeübergangs- und Druckverlustcharakteristiken in quer zur voll ausgebildeten Strömung bei berippten Ringkanälen experimentell ermittelt und Korrelationen zur Berechnung des Wärmeübergangskoeffizienten bei variablen InnendurchmesserD ₀ des umschließenden Rohres angegeben. Ferner wird eine charakteristische Reynolds-Zahl vorgeschlagen, über die sich der dominierende Einfluß der Querrippen erfassen läßt. Es zeigte sich, daß der InnendurchmesserD ₀ den Druckverlust wesentlich mehr beeinflußt als den Wärmeübergang. Auch wurde die Abhängigkeit des Gesamt-Übertragungsverhaltens vonD ₀ bei gleicher Strömungsgeschwindigkeit bzw. Volumenstromdichte ermittelt. Es zeigte sich, daß die Ausbildung des Strömungsprofils bei Einlaufströmung den Wärmeübergang signifikant beeinflußt und deshalb im Experiment zu berücksichtigen ist.

     

Axial laminar flow of viscoplastic fluids in a concentric annulus subject to wall slip

The flow of non-Newtonian fluids in annular geometries is an important problem, especially for the extrusion of polymeric melts and suspensions and for oil and gas exploration. Here, an analytical solution of the equation of motion for the axial flow of an incompressible viscoplastic fluid (represented by the Hershel–Bulkley equation) in a long concentric annulus under isothermal, fully developed, and creeping conditions and subject to true or apparent wall slip is provided. The simplifications of the analytical model for Hershel–Bulkley fluid subject to wall slip also provide the analytical solutions for the axial annular flows of Bingham plastic, power-law, and Newtonian fluids with and without wall slip at one or both surfaces of the annulus.     

Flow of shear-thinning fluids in a concentric annulus

Distributions of mean axial velocity, axial and tangential turbulence intensities together with friction factor versus Reynolds number (f-Re) data are presented for three non-Newtonian liquids in fully developed laminar, transitional and turbulent flow in an annular geometry in the absence of centrebody rotation. Each of the non-Newtonian fluids was shear thinning and to some extent elastic and one was also thixotropic in character. For comparison purposes, measurements are also reported for a Newtonian fluid.In the case of the Newtonian fluid, a mixture of glucose syrup and water, the f-Re data in both laminar and turbulent flow follow the appropriate relationships for the annular geometry, with a clear demarcation at transition which is confirmed independently by a measured increase in the centre-channel axial turbulence intensities. The measured velocity profiles for laminar flow are in good agreement with those predicted theoretically, whilst the turbulent profiles obey the log-law relationship over much of the mid-channel region and tend to the u ⁺=y ⁺ relationship in the immediate vicinity of both walls.For the first non-Newtonian fluid, an aqueous solution of sodium carboxymethylcellulose (CMC), good agreement with theoretical predictions for a power-law fluid was observed in the f-Re data in the laminar regime with evidence of drag reduction in turbulent flow. Velocity profiles, determined in two planes, indicate minor circumferential asymmetry in laminar flow. Law-of-the-wall plots for fully turbulent flow indicate an upward shift in the data in the log-law region of the annulus consistent with the drag-reduction behaviour, as also observed in pipe-flow experiments for this fluid (Escudier et al. 1992). In the near-surface regions of both the outer and inner tubes the data again tend towards the u ⁺=y ⁺ relationship.Anomalous behaviour was observed in the f-Re curves for the second non-Newtonian fluid, 0.125% and 0.2% aqueous solutions of Xanthan gum, with data for both concentrations falling significantly below the appropriate f-Re relationship for a power-law fluid. The anomalies are attributed to the elastic character of Xanthan gum. In the near-surface region of the outer tube the velocity-profile data again tend towards the u ⁺=y ⁺ relationship but it proved impossible to obtain data in the near vicinity of the inner wall due to slight turbidity of the fluid.The third non-Newtonian fluid, a Laponite/CMC blend, again exhibits anomalous f-Re behaviour, attributed to the thixotropic nature of this fluid. Velocity profiles determined in two planes again indicate some circumferential asymmetry in the laminar regime. Law-of-the-wall plots for the transitional and turbulent profiles tend towards the u ⁺=y ⁺ relationship in both near-wall regions, again with an upward shift in the core of the annulus, consistent with drag reduction.In general terms, the experimental results are consistent with previous work for non-Newtonian fluid flow in circular pipes and with limited data for an annular geometry (Nouri et al. 1993), with regard to drag reduction, modified turbulence structure and scale effects.List of Symbols D _i centrebody diameter (m) - D _o outer pipe diameter (m) - (D _o -D _i ) hydraulic diameter (m) - f friction factor (2 · _A /U²) - n power-law exponent (-) - p fluid static pressure (Pa) - Q volumetric flow rate (m³/s) - r radial distance from pipe centreline (m) - R _i centrebody radius (m) - R _o outer pipe radius (m) - R _n refractive index (-) - Re Reynolds number U(D _o -D _i )/ _s - s geometric scaling factor (-) - u mean axial velocity (m/s) - u rms fluctuation in axial velocity (m/s) - u _c1 rms fluctuation in centreline axial velocity (m/s) - u non-dimensional value of u (u/u ) - u friction velocity (m/s) - w rms fluctuation in tangential velocity (m/s) - x axial distance along pipe (m) - y distance from pipe or centrebody wall (m) - y ⁺ non-dimensional value of y (u y/v _s ) - p/L pressure drop per unit length (N/m²/m) - shear rate (s^-1) - radius ratio R _i /R _o - _C constant in Cross model (s) - _CA constant in Carreau model (s) - _HB constant in Herschel-Bulkley model (s) - _n constant in power-law model (s) - _S constant in Sisko model (s) - dynamic viscosity (Pa · s) - _ref reference viscosity (1 Pa · s) - _s viscosity at wall at prevailing surface shear stress (Pa · s) - ₀ zero shear-rate viscosity (Pa · s) - infinite shear-rate viscosity (Pa · s) - v kinematic viscosity (/) (m²/s) - v _s kinematic viscosity at wall (m²/s) - non-dimensional radial location (R _o -r)/(R _o -R _i ) - fluid density (kg/m³) - shear stress (Pa) - _A weighted average wall shear stress (Pa) - _i shear stress on centrebody (Pa) - _o shear stress on outer wall (Pa) - _s surface shear stress (Pa) - _ref reference shear stress (1 Pa) - _y fluid yield stress (Pa) - ^* geometry function of Jones and Leung (1981) The work reported here represents part of programme of research which has received financial support from SERC (GR/F 87813), BP Exploration Company Ltd, Shell Research BV and AEA Petroleum Services. This support is gratefully acknowledged. Frequent meetings with Professor J. H. Whitelaw, Imperial College of Science, Technology and Medicine, Dr. C. F. Lockyear and Dr. D. Ryan, BP Research, Ms. B. Kampman, Shell Research BV, and Dr. W. J. Worraker, AEA Technology, were of considerable benefit to the research.     

The instantaneous slow flow of a visco-elastic fluid between two concentric spheres

Summary A theoretical analysis is made of the flow of an incompressible viscoelastic fluid contained between two concentric spheres when the outer sphere is moved instantaneously in a given direction, whilst the inner sphere remains at rest. The solution is developed by successive approximations, the first corresponding to the instantaneous slow flow of a Newtonian viscous fluid. By allowing the radius of the outer sphere to approach infinity, the result obtained can be used to give an approximate solution to the equations of motion of a visco-elastic fluid flowing slowly past a fixed sphere.     

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

Summary When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan²).     

Axial Couette flow of an Oldroyd-B fluid in an annulus

This paper establishes the velocity field and the adequate shear stress corresponding to the motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders by means of finite Hankel transforms. The flow of the fluid is produced by the inner cylinder which applies a time-dependent longitudinal shear stress to the fluid. The exact analytical solutions, presented in series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. The general solutions can be easily specialized to give similar solutions for Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material parameters on the behavior of the fluid motion are graphically illustrated.     

Natural-convection heat transfer in a nonuniform finite annulus with concentric heat source

In this paper, the mechanisms of natural-convection heat transfer inside a nonuniform finite annulus have been numerically investigated. The system is actually a streamlined, water-filled latex balloon with a coaxial cylindrical heating element. The balloon can be applied as a local hyperthermia treatment device for the removal of undesirable tissue if sufficiently high temperatures and preferably uniform surface heat fluxes can be maintained. A validated control-volume-based method has been employed to solve the coupled transient three-dimensional transport equations for laminar free convection. The effects of heat-source temperature distributions and device orientations on the heat transfer have been studied. Possible design improvements of this device are discussed.     

Stability of a fluid interface under tangential vibrations

The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386).