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.

---

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 development of subcooled boiling flow in an internally heated annulus

For the main purpose of database construction in order to develop the interfacial area transport equation, axial developments of local void fraction, interfacial area concentration, bubble Sauter mean diameter, interfacial velocity, and bubble number density were measured in boiling water bubbly flows in a vertical-upward internally heated annulus using a double-sensor conductivity probe. The annulus channel consisted of an inner rod with a diameter of 19.1 mm and an outer round tube with an inner diameter of 38.1 mm, and the hydraulic equivalent diameter was 19.1 mm. A total of 11 data sets were acquired consisting of four inlet liquid velocities, 0.500, 0.664, 0.987 and 1.22 m/s, two heat fluxes, 100 and 150 kW/m², and two inlet liquid temperatures, 95.0 and 98.0°C. The axial developments of the flow parameters were discussed based on the measured data in detail. In addition to the database construction, the measured data validated recently proposed constitutive equations for the distribution parameter, drift velocity, and bubble Sauter mean diameter, which will improve the accuracy of the drift-flux model in subcooled bubbly flow.     

Computation of buoyancy-driven flow in an eccentric centrifugal annulus with a non-orthogonal collocated finite volume algorithm

A computational study is performed on two-dimensional mixed convection in an annulus between a horizontal outer cylinder and a heated, rotating, eccentric inner cylinder. The computation has been done using a non-orthogonal grid and a fully collocated finite volume procedure. Solutions are iterated to convergence through a pressure correction scheme and the convection is treated by Van Leer's MUSCL scheme. The numerical procedure adopted here can easily eliminate the ‘Numerical leakage’ phenomenon of the mixed convection problem whereby strong buoyancy and centrifugal effects are encountered in the case of a highly eccentric annulus. Numerical results have been obtained for Rayleigh number Ra ranging from 7×10³ to 10⁷, Reynolds number Re from 0 to 1200 and Prandtl number Pr from 0.01 to 7. The mixed rotation parameter σ (=Ra/PrRe²) varies from ∞ (pure natural convection) to 0.01 with various eccentricities ε. The computational results are in good agreement with previous works which show that the mixed convection heat transfer characteristics in the annulus are significantly affected by σ and ε. The results indicate that the mean Nusselt number Nu increases with increasing Ra or Pr but decreases with increasing Re. In the case of a highly eccentric annulus the conduction effect becomes predominant in the throat gap. Hence the crucial phenomenon on whereby Nu first decreases and then increases can be found with increasing eccentricity. © 1998 John Wiley & Sons, Ltd.     

Counter current gas-liquid vertical flow, model for flow pattern and pressure drop

Counter-current flow pattern transition and pressure drop are modeled. Emphasis is placed on the understanding of the transition mechanisms from a mechanistic point of view.

Unlike the case of co-current flow, in counter-current flow, the situations of “no solution” as well as “multiple solutions” for the flow pattern and pressure drop exist. These possibilities are discussed and criteria for the actual flow pattern that will take place are suggested.

Some of the results are supported by data (from the literature), others are somewhat tentative suggesting future experimental verification is needed.     

Pressure drop and film height measurements for annular gas-liquid flow

Measurements of the pressure drop and the film height averaged around the circumference are presented for air and water flowing in horizontal 2.54 and 5.08 cm pipelines. Film height measurements are interpreted using relations similar to those that have been developed for vertical flows. The frictional pressure loss is found to be primarily related to properties of the liquid film and to be approximately independent of the amount of entrained liquid.     

Irregularity and singular vector growth of the differentially heated rotating annulus flow

The problem of weather prediction is to a large part determined by the large-scale atmospheric flow. This flow is irregular but not fully turbulent. The irregularity can be related to instability, nonlinear wave–wave interactions, or randomly excited singular vectors. In the present study, the latter mechanism is investigated numerically and experimentally. For this purpose, a baroclinic quasigeostrophic low-order model is adjusted to a differentially heated rotating annulus experiment, an established laboratory analog to the atmospheric circulation. We linearize the low-order model about a time-mean state to study the growth of singular vectors and compare those with singular vectors that have been derived empirically from the experimental data. Qualitative agreement of the numerically and experimentally derived singular vectors form the basis for a deeper analysis of the low-order model. In particular, for a broad range of annulus rotation frequencies and radial temperature differences, we compute the maximal growth rates of the low-order model. These growth rates are displayed as a function of the Taylor and thermal Rossby number, a frame widely used in studies of annulus regime transitions. We can show that most regime transitions defined by E.N. Lorenz in the sixties have their counterpart in the Taylor-Rossby singular value diagram. Most striking is the fact that for the irregular regime by far, the largest growth rates can be found. We suppose that irregularity in the transition region to geostrophic turbulence might for some part result from randomly excited singular vectors with unusual large growth rates. In concert with nonlinear wave–wave coupling, this process might explain the gradual broadening of the wave spectrum that has been found for the route to geostrophic turbulence in annulus flows.     

A numerical investigation of developing flow in an eccentric curved annulus in the presence of gravity

In this article developing incompressible viscous flow in an eccentric curved annulus in the presence of gravity is numerically studied using a second order finite difference method based on the projection algorithm to solve the governing equations including the continuity and full Navier–Stokes equations. The equations written in a bipolar–toroidal coordinate system are discretized in a three dimensional staggered grid. The effects of governing non-dimensional parameters including the eccentricity, non-dimensional curvature ratio, Dean number, Froude number, aspect ratio, and the Reynolds number on the flow field in the entrance and fully developed region are investigated. The numerical results indicate that at the small Froude numbers, the flow field distorts from the symmetrical condition due to the larger body force effect and the axial velocity formation mostly takes place at the lower half of the annulus. In addition, at the constant Froude number, by decreasing the curvature radius, the peak axial velocity and its sharp gradient appear on the outer curvature region due to the larger centrifugal forces and by increasing the eccentricity the flow rate intensifies at the wider region and weakens at the narrower region due to the larger flow resistance. Furthermore, the friction factor increases by decreasing the Froude number and increasing the Dean number.     

Correlations for heat transfer coefficient and pressure drop in the annulus of concentric helical coils

Heat transfer and pressure drop characteristics in the annulus of concentric helical coils heat exchangers were experimentally investigated. The effects of coil curvature ratio, flow configuration, number of turns and addition of surfactant were investigated. Five test coils were designed and manufactured to study the effect of different parameters on heat transfer and pressure drop. The liquids used in the present study were water and oleyl-dihydroxy-etheyl-amine-oxide (ODEAO, C₂₂H₄₅NO₃ = 371) non-ionic aqua surfactant solution flowing through the annulus side. The inner side Reynolds number range 11,000–27,000 and the annulus side range 5,000–19,000. The results showed that the annulus Nusselt number decreases as annulus curvature ratio increases and increases when number of turns decrease. Moreover, the friction factor increases with the curvature ratio and also increases as number of turns decreases. Both Nusselt number and friction factor decrease when ODEAO concentration increases.     

Momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls

An analysis and measurement were made of momentum and heat transfers from fully developed turbulent flow in an eccentric annulus to inner and outer tube walls. The eddy diffusivities of momentum and heat obtained in the turbulent flow in a circular tube were applied to the annular flow in the analysis. The result indicates that the calculated friction factor and average Nusselt numbers on the inner and outer tube walls are in fairly good agreement with the measurements.     

Analytical pressure drop correlation for adiabatic vertical two-phase flow

A new correlation for two-phase wall friction is proposed derived from analytical considerations and based upon an annular flow model. In spite of this basis in annular flow the correlation is consistent for all flow patterns in vertical two-phase flow.The correlation yields a smooth transition from two-phase flow to single-phase liquid flow, mainly because it incorporates the friction factor of the Moody diagram [1] for single-phase flow.The correlation is checked against 236 measurements from various sources and has turned out to be most favourable in comparison with the correlations of Dukler (case 2) [2] and Lockhart-Martinelli [3]. The standard deviation of these 236 measurements is 27.8%, with 68% having a relative error of less than 28.2%.     

Correlations for the pressure drop for flow through metal foam

Steady-state unidirectional pressure-drop measurements for incompressible airflow through nine open-cell aluminum foam samples, having different porosities and pore densities, were undertaken. The pressure drop increased with increasing Darcian velocity following the quadratic Forchheimer equation. The lower-porosity foam produced significantly higher pressure drop. Both the permeability and the form drag coefficient correlated well with the porosity. The correlations predicted the results of some previous studies reasonably well, especially for the low-pore-density foam.     

Numerical analysis of flow and thermal fields in arbitrary eccentric annulus by differential quadrature method

 In the present paper, natural convective heat transfer in horizontal eccentric annulus is numerically studied by applying the differential quadrature (DQ) method to solve the vorticity–stream function formulation. An explicit formulation for computing the stream function value on the inner cylinder wall is derived from the pressure single-value condition. It is demonstrated in this paper that the DQ method is an efficient approach in computing the weak global circulation in the domain. The present method was validated by comparing its numerical results with available experimental data. Very good agreement has been achieved. Then, a systematic study is conducted for the effect of eccentricity and angular position on the flow and thermal fields. Received on 20 September 2000 / Published online: 29 November 2001     

Simultaneous PIV and thermography measurements of partially blocked flow in a differentially heated rotating annulus

A radial barrier has been mounted in a differentially heated rotating annulus that partially blocks the azimuthal flow component. The experiment can be seen as an analog to geophysical flows with constrictions, e.g., the Antarctic Circumpolar Current. However, the experiment has been carried out without a particular natural flow in mind. The main interest was to observe a baroclinic annulus flow that does not become saturated. Hence, in contrast to the annulus flow without a barrier, the partially blocked flow remains transient and surface heat fluxes associated with baroclinic life cycles can be studied. The annulus can be subdivided into the upstream half of the barrier, where waves amplify, and the downstream half of the barrier, where waves decay. In the upstream half, the azimuthal mean flow is moderate but with a significant positive eddy radial heat flux. In the downstream half, we find a strong jet in the mean azimuthal flow and furthermore an increased radial mean temperature gradient. The latter points to a weakened or even reversed radial eddy heat flux in the lee side of the barrier. Temperature anomalies appear as large bulges in the outer part of the annulus. Moreover, an outward shift of vortex centers can be observed with respect to centers of temperature anomalies. This phase shift between pressure and temperature anomalies differs from that of classical Eady modes of baroclinic instability.     

A model for pressure loss, film thickness, and entrained fraction for gas-liquid annular flow

A two-component (air-water) annular flow model is presented requiring only flow rates, absolute pressure, temperature, and tube diameter. Film thicknesses (base film and wave height) are calculated from a critical film thickness model. Modeled pressure gradient is weighted by wave intermittency to compute average pressure gradient. Film flow rate and wave velocity are estimated using the universal velocity profile in the waves and a piecewise linear profile in the base film. For vertical flow, mean absolute errors for film thickness, wave velocity, and pressure gradient are 9%, 9%, and 19%, respectively. In horizontal flow, mean absolute errors for pressure gradient, base film thickness, and disturbance wave velocity are 17%, 10%, and 14%, respectively, on par with those from single-behavior models that require additional film thickness or other data as inputs.     

An experimental study of fluid flow and heat transfer in decaying swirl through a heated annulus

The mean and turbulent structures of turbulent swirling flow in a heated annulus have been measured. Both forced and free vortex swirling flows were generated, and the outer wall of the test section was heated uniformly. The maximum swirl number was 1.39, Reynolds numbers were up to 200000, and heat input was 10.5 kW. Mean and turbulent velocity components, air and wall temperatures, and wall static pressures were all measured. Hot-film techniques were developed to measure turbulence. From these parameters, the flow and temperature fields, pressure distribution, and heat transfer coefficients were determined. The mechanisms of heat transfer were identified.     

Heat transfer by rotational flow in an annulus with porous lining

The flow and heat transfer in an annulus between rotating coaxial cylinders, with non-erodible porous lining, is investigated. The flow in the porous lining is obtained by using Brinkman equation. At the boundary between the porous lining and the free flow (the so called nominal surface), the velocity slip and the temperature slip are used. A quasi-numerical technique developed by the authors is employed in obtaining the solution of the energy equation. The effect of the thickness of the porous lining and the permeability on the velocity and the Nusselt numbers at the walls is studied.

---

Wärmeübergang bei rotierender Strömung in einem Ring mit poröser Wand

Zusammenfassung In dieser Arbeit wird die Strömung und Wärmeübertragung zwischen rotierenden koaxialen Zylindern mit unauswaschbarem porösem Überzug untersucht. Die Strömung innerhalb des porösen Überzugs ist mit Hilfe der Brinkmanschen Gleichung berechnet. An der Grenze (der sogenannten Nominalfläche) zwischen dem Überzug und der freien Strömung wurde die Geschwindigkeitsgleitung und Temperaturgleitung benutzt. Die Energiegleichung ist mit Hilfe eines von den Autoren entwickelten quasi-numerischen Verfahrens gelöst. Der Einfluß der Dicke und der Durchlässigkeit des porösen Überzugs auf die Strömung und die Nusseltschen Zahlen an den Wänden wird untersucht.

---

Nomenclature R ₂ radius of the outer cylinder forming the annulus - ₂ angular velocity of the outer cylinder - T ₂ temperature of the outer cylinder - R _l radius of the inner cylinder forming the annulus - ₁ angular velocity of the inner cylinder - T ₁ temperature of the inner cylinder - h thickness of the porous lining - R radial distance of any point in the annulus - V azimuthal component of velocity in zone 1 (of Fig. 1) - V part of velocity in zone 2 (of Fig. 1) due to transfer of momentum from the main flow - V _p velocity in zone 2 (of Fig. 1) - Q Darcy velocity in the porous medium (zone 2 of Fig. 1) - velocity slip parameter - k absolute permeability of the material used for lining - ₀ nondimensional shearing stress at the outer cylinder - _i nondimensional shearing stress at the inner cylinder - K thermal conductivity in zones 1 and 2 (of Fig. 1) - coefficient of viscosity of the fluid - T temperature in zone 1 (of Fig. 1) - T temperature in zone 2 (of Fig. 1) - temperature slip parameter - (Nu) _o nondimensional Nusselt number at the outer cylinder - (Nu) _i nondimensional Nusselt number at the inner cylinder - radii ratio - nondimensional rotational parameter - nondimensional thickness of the porous lining     

A boundary integral equation method for Navier-Stokes equations—application to flow in annulus of eccentric cylinders

A novel Navier-Stokes solver based on the boundary integral equation method is presented. The solver can be used to obtain flow solutions in arbitrary 2D geometries with modest computational effort. The vorticity transport equation is modelled as a modified Helmholtz equation with the wave number dependent on the flow Reynolds number. The non-linear inertial terms partly manifest themselves as volume vorticity sources which are computed iteratively by tracking flow trajectories. The integral equation representations of the Helmholtz equation for vorticity and Poisson equation for streamfunction are solved directly for the unknown vorticity boundary conditions. Rapid computation of the flow and vorticity field in the volume at each iteration level is achieved by precomputing the influence coefficient matrices. The pressure field can be extracted from the converged streamfunction and vorticity fields. The solver is validated by considering flow in a converging channel (Hamel flow). The solver is then applied to flow in the annulus of eccentric cylinders. Results are presented for various Reynolds numbers and compared with the literature.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.