Vertical Circular Duct Research Articles

Study of Parameters Affecting Thermal Drying Process. (Dept. M)

Parameters affecting drying process has been studied experimentally as it associated with heat and mass transfer between porous bed to be dried and air which flows through the porous bed. To perform this study, a test rig is designed and constructed as it consists of vertical circular duct packed with wet porous bed which is made from clay balls of 20 mm in diameter. Drying process occurs as a result of forcing hot air vertically to pass through the wet porous bed, evaporation of moisture is existed in the bed due to the simultaneous heat and mass transfer. The studied operating parameters are inlet air temperature, inlet air mass flux, porous bed depth and porosity of balls. The average heat and mass transfer coefficients are estimated for flow of hot air through the wet porous bed. The results indicated that, the drying rate is directly proportional to inlet air temperature, mass flux of air, dimensionless bed depth and ball porosity. So, Drying process can be achieved in lower time as increasing both air mass flux and or inlet air temperature and decreasing bed depth. Also, heat transfer coefficient and mass transfer coefficient increase with increasing inlet air temperature, inlet air mass flux, and ball porosity, but they decrease with increasing bed depth. Comparison between the obtained experimental results and the previous work gave the same trend.

Bubble behavior in liquid-gas two-phase flow behind a cross-shaped obstacle in a vertical circular duct

Grid spacers installed in subchannels of fuel assemblies for nuclear reactors can promote heat transfer. However, the fluid velocity and bubble behavior are greatly affected as the cross-sectional area of the flow passage changes. Therefore, the void fraction distribution behind the obstacle that simulates the grid spacer shape simply was measured by using a wire mesh sensor (WMS) system. Moreover, a two-phase flow analysis was performed to investigate the effect of the obstacle on the bubble behavior in a vertical duct.

Buoyancy-Opposed Darcy’s Flow in a Vertical Circular Duct with Uniform Wall Heat Flux: A Stability Analysis

An analytical and numerical study is presented to show that buoyancy-opposed mixed convection in a vertical porous duct with circular cross-section is unstable. The duct wall is assumed to be impermeable and subject to a uniform heat flux. A stationary and parallel Darcy’s flow with a non-uniform radial velocity profile is taken as a basic state. Stability to small-amplitude perturbations is investigated by adopting the method of normal modes. It is proved that buoyancy-opposed mixed convection is linearly unstable, for every value of the Darcy–Rayleigh number, associated with the wall heat flux, and for every mass flow rate parametrised by the Peclet number. Axially invariant perturbation modes and general three-dimensional modes are investigated. The stability analysis of the former modes is carried out analytically, while general three-dimensional modes are studied numerically. An asymptotic analytical solution is found, suitable for three-dimensional modes with sufficiently small wave number and/or Peclet number. The general conclusion is that the onset of instability selects the axially invariant modes. Among them, the radially invariant and azimuthally invariant mode turns out to be the most unstable for all possible buoyancy-opposed flows.

Buoyant Flow with Viscous Heating in a Vertical Circular Duct Filled with a Porous Medium

Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature, and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its maximum, no axisymmetric solutions exist.

Combined forced and free flow in a vertical circular duct subjected to non-axisymmetric wall heating conditions

The fully developed mixed convection flow in a vertical circular duct is investigated analytically, under the assumption of laminar parallel flow. A wall heat flux uniform in the axial direction and dependent on the angular coordinate is considered. As a consequence, the fluid temperature is three dimensional, since it changes in the radial, axial and angular directions. An analytical method based on Fourier series expansions of temperature and velocity fields is adopted to determine the velocity and the temperature distributions as well as the friction factor and the average Nusselt number. The general solution, expressed in terms of Bessel functions, is applied to study a case that has a special importance in technical applications: a duct whose wall is half subject to a uniform heat flux and half adiabatic. The positive and negative threshold values of the ratio between the Grashof number Gr and the Reynolds number Re for the onset of the flow reversal phenomenon are determined. A comparison between the average Nusselt number for the considered non-axisymmetric case and that for the case of a duct subject to a uniform wall heat flux is performed.

Mixed convection flow in a vertical circular duct with time-periodic boundary conditions: steady-periodic regime

Mixed convection flow in a vertical circular duct subjected to a periodic sinusoidal temperature change at the wall is investigated. The analysis is performed by considering fully-developed parallel flow and steady-periodic regime. The local momentum and energy balance equations, together with the constraint equations which arise from the definition of mean velocity and mean temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically, and the velocity and temperature distributions are obtained as functions of three parameters: the Prandtl number, Pr, the dimensionless frequency Ω, the ratio between the Grashof number Gr and the Reynolds number Re. The Fanning friction factor and the dimensionless heat flux are evaluated.

Non-axisymmetric forced and free flow in a vertical circular duct

The fully developed laminar mixed convection in a vertical circular duct is studied analytically, with reference to non-axisymmetric boundary conditions such that the fluid temperature does not change along the axial direction. The Boussinesq approximation is applied by taking the average temperature in a duct section as the reference fluid temperature. The dimensionless momentum and energy balance equations are solved by employing Fourier series expansions of the temperature and the velocity fields. The solution shows that the temperature field is not influenced by the velocity distribution and that the Fanning friction factor is not affected by buoyancy. On the other hand, the velocity field is strongly influenced by the buoyancy forces and may display flow reversal phenomena. Two special cases are studied in detail: a duct with a sinusoidal wall temperature distribution; a duct subjected to an external convection heat transfer with two environments having different reference temperatures.

Combined forced and free convection with viscous dissipation in a vertical circular duct

Laminar flow heat transfer in a vertical circular duct is investigated by taking into account both viscous dissipation and the effect of buoyancy. The temperature on the duct wall is considered as uniform and the velocity field is assumed to be parallel. A perturbation method is employed to solve the momentum balance equation and the energy balance equation. The radius of convergence of the perturbation series is evaluated by means of Domb–Sykes plots. A comparison with the velocity and temperature profiles in the case of laminar forced convection with viscous dissipation is performed in order to point out the effect of buoyancy. The case of convective boundary conditions is also discussed.

Wave-tank experiments on an immersed vertical circular duct

A series of experiments is described in which a fully-submerged circular duct situated with its axis vertical is subjected to regular incident waves. The resulting wave-interaction effects are defined in terms of reflexion coefficients derived from waveheight measurements, and a pressure coefficient derived from measurements of pressure in the depths of the enclosure. The experiments were conducted in a wide tank, so simulating open-sea conditions, and in a narrow tank where wall effects were important. The particular case when a transverse standing wave was induced above the duct was examined in detail.These three-dimensional experiments complement a previous investigation into the performance of two-dimensional ducts and are of current practical significance in the context of sub-sea wave-energy conversion.

Viscous Dissipation Effects on Combined Free and Forced Convection Through Vertical Circular Tubes

The effect of viscous dissipation on the flow phenomena and heat transfer rate in a vertical circular duct is analyzed for combined free and forced convection. All fluid properties are considered constant, except variation of density in the buoyancy term. It is noted that effect of viscous dissipation is to reduce the temperature differences in the system which in turn counteract the buoyancy effects. Therefore the viscous dissipation reduces the flow velocity near the wall and increases it near the tube center. Viscous dissipation effects reduce the Nusselt numbers. The reduction in Nusselt numbers is about six percent at the high values of the buoyancy rate (Rayleigh number = 1000) and the dissipation effect Eckert number/Reynolds number = 0.0005 was used in the present study.