CFD for prediction of k-factors of duct fittings

The k-factors of duct fittings provided by CIBSE and ASHRAE are used extensively by HVAC system designers. Existing guides published by the two institutions do not include many of the duct fittings used in HVAC systems and they neglect to consider parameters, such as Reynolds numbers, which affect k-factors. More importantly, there are large errors in some of the data. This paper presents a study in which the computational fluid dynamics or CFD was applied to predict k-factors. Flow fields in duct fittings have been simulated by solving three-dimensional Navier-Stokes equations with the standard k-ε model. The finite volume approach was adopted and the SIMPLE algorithm has been used. It was found that the accuracy of k-factors is sensitively dependent on the presure sampling position, which may vary with many variables such as duct dimensions, type of fitting and flow speed. The predicted k-factors were compared with the CIBSE and ASHRAE data and although some close agreement were encountered for individual cases, in general there is no consistent agreement with either the CIBSE or the ASHRAE data set. It was shown that the knowledge of detailed flow patterns in individual duct fittings is crucial for accurate measurements of k-factors and should be acquired before the test is set up and carried out. Such an approach is important both for improving k-factor data accuracy and for providing a reliable basis for the development of CFD application.     

K-factor data of interacting duct fittings based on measurement and CFD modelling

Energy use and the environment in mechanically-ventilated buildings are strongly influenced by the performance of heating, ventilation and air-conditioning (HVAC) systems, which is in turn governed by the accurate prediction of pressure loss. This paper presents the results of an investigation of pressure loss and associated loss coefficient (k-factor) for a number of interacting duct fittings in close proximity as commonly found in HVAC systems. The constant-injection tracer-gas technique and pitot-tube were used to measure the mean air velocity in ducts and the pressure distribution along the ducts was measured using static pressure tappings. k-Factors were calculated from the measured pressure loss and air velocity for each interacting duct fitting. Computational fluid dynamics (CFD) was used for prediction of air flow and pressure distribution in ducts. Predictions were compared with results obtained experimentally and CFD was found to be a useful method for the prediction of the k-factors of duct fittings. It will also be shown that duct fittings in close proximity interact in such a way that it is difficult to predict their behaviour based on evidence of the fittings' individual characteristics. The behaviour of interacting duct fittings as described in this investigation appears to be isolated to fittings of similar individual loss coefficients placed in close proximity without the effect of spacers. To establish this characteristic and fully to understand the complexity of interacting duct fittings there is an obvious need for further work in this area.     

Analysis of heat transfer augmentation and flow characteristics due to rib roughness over absorber plate of a solar air heater

A computational analysis of heat transfer augmentation and flow characteristics due to artificial roughness in the form of ribs on a broad, heated wall of a rectangular duct for turbulent flow (Reynolds number range 3000–20,000, which is relevant in solar air heater) has been carried out. Shear stress transport k−ω turbulence model is selected by comparing the predictions of different turbulence models with experimental results available in the literature. A detailed analysis of heat transfer variation within inter rib region is done by using the selected turbulence model. The analysis shows that peak in local heat transfer coefficient occurs at the point of reattachment of the separated flow as observed experimentally. The results predict a significant enhancement of heat transfer in comparison to that for a smooth surface. There is a good matching between the predictions by SST k−ω and experimental results. In this work, nine different shapes of rib are examined using SST k−ω model and compared on the basis of heat transfer enhancement, friction characteristics and performance index considering heat transfer enhancement with the same pumping power.     

Experimental investigation on heat-transfer enhancement due to a gap in an inclined continuous rib arrangement in a rectangular duct of solar air heater

Artificial roughness in the form of repeated ribs has been proposed as a convenient method for enhancement of thermal performance of solar air heaters. This paper presents the experimental investigation of heat transfer and friction factor characteristics of a rectangular duct roughened with repeated square cross-section split-rib with a gap, on one broad wall arranged at an inclination with respect to the flow direction. The duct has a width to height ratio (W/H) of 5.84, relative roughness pitch (P/e) of 10, relative roughness height (e/D_h) of 0.0377, and angle of attack (α) of 60°. The gap width (g/e) and gap position (d/W) were varied in the range of 0.5–2 and 0.1667–0.667, respectively. The heat transfer and friction characteristics of this roughened duct have been compared with those of the smooth duct under similar flow condition. The effect of gap position and gap width has been investigated for the range of flow Reynolds numbers from 3000 to 18,000. The maximum enhancement in Nusselt number and friction factor is observed to be 2.59 and 2.87 times of that of the smooth duct, respectively. The thermo-hydraulic performance parameter is found to be the maximum for the relative gap width of 1.0 and the relative gap position of 0.25.     

DRBEM Solution of the Natural Convective Flow of Micropolar Fluids

The main purpose of this article is to present the use of the dual reciprocity boundary element method (DRBEM) in the analysis of the unsteady natural convective flow of micropolar fluids in a differentially heated rectangular cavity. The finite-difference method (FDM) is used for time discretization. All the convective terms and vorticity boundary condition are evaluated in terms of DRBEM coordinate matrix. Solutions are obtained for several values of microstructure parameter (k), Rayleigh number (Ra), and aspect ratio (A). Prandtl number values are taken as 0.71 and 7.0. The heat transfer rate (average Nusselt number) of micropolar fluids is found to be smaller than that of Newtonian fluid. Numerical results at steady-state are given in terms of streamlines, isotherms, vorticity contours, and velocity profiles, as well as a table containing Nusselt number values for several Ra and k.     

Design and analysis of a split reaction water turbine

This paper explores the performance characteristics of a split reaction water turbine. The governing equations are derived by using the principles of conservation of mass, momentum and energy for a practical case, which includes consideration of frictional losses. The optimum diameter for a simple reaction turbine is defined and an equation for the optimum diameter is derived. Design and building procedures for a split reaction turbine are described. Using the equation for optimum diameter and assuming a loss factor (k-factor) of 0.05, optimum rotor diameters for different operating heads and rotational speeds are plotted and discussed. Measured performance of a 122 mm diameter split reaction water turbine rotor is presented. The relationship between k-factor and relative velocity for a split reaction turbine model is discussed with reference to experimental data.     

A Study of the Effect of Duct Width on Fully Developed Turbulent Flow Characteristics in a Corrugated Duct

Abstract

In this article, the effect of duct width on fully developed turbulent air flow characteristics in a corrugated duct is investigated numerically. The k-? model is adopted for turbulent closure, and the governing equations in three dimensions are solved using a finite volume technique. The calculations were performed with the width aspect ratio (interwall spacing/channel width) ranging from 0.1 to 1.0, with the Reynolds numbers ranging from about 2000 to 15000, and corrugation angles of 30° and 45°. An experimental study was also performed for pressure drop, velocity, and flow visualization. The detailed predictions are compared with the experimental measurements, and a good agreement between the two is obtained.     

Simulation of Swirling Turbulent Heat Transfer in a Vortex Heat Exchanger

ABSTRACT

This article presents a numerical simulation of swirling turbulent flow and heat transfer in a novel vortex heat exchanger. A new algebraic Reynolds stress/heat flux model (ASM/AFM) is applied to the simulation. The computation is performed under different air flow rates for both swirling and nonswirling flows. The calculated mean heat transfer coefficients on both inner and outer walls of the annular duct are compared with the measured data. They are generally improved over the results predicted by the new ASM/k–? model. The effects of swirl on enhancing heat transfer in the annular duct are illustrated. The heat transfer performance of the vortex heat exchanger under different air flow rates is obtained.     

Heat transfer coefficient and friction factor correlations for rectangular solar air heater duct having transverse wedge shaped rib roughness on the absorber plate

As is well known, the heat transfer coefficient of a solar air heater duct can be increased by providing artificial roughness on the heated wall (i.e. the absorber plate). Experiments were performed to collect heat transfer and friction data for forced convection flow of air in solar air heater rectangular duct with one broad wall roughened by wedge shaped transverse integral ribs. The experiment encompassed the Reynolds number range from 3000 to 18000; relative roughness height 0.015 to 0.033; the relative roughness pitch 60.17φ^−1.0264<p/e<12.12; and rib wedge angle (φ) of 8, 10, 12 and 15°. The effect of parameters on the heat transfer coefficient and friction factor are compared with the result of smooth duct under similar flow conditions. Statistical correlations for the Nusselt number and friction factor have been developed in terms of geometrical parameters of the roughness elements and the flow Reynolds number.     

Forecasting electricity spot market prices with a k-factor GIGARCH process

In this article, we investigate conditional mean and conditional variance forecasts using a dynamic model following a k-factor GIGARCH process. Particularly, we provide the analytical expression of the conditional variance of the prediction error. We apply this method to the German electricity price market for the period August 15, 2000–December 31, 2002 and we test spot prices forecasts until one-month ahead forecast. The forecasting performance of the model is compared with a SARIMA–GARCH benchmark model using the year 2003 as the out-of-sample. The proposed model outperforms clearly the benchmark model. We conclude that the k-factor GIGARCH process is a suitable tool to forecast spot prices, using the classical RMSE criteria.     

Numerical Study of Heat Transfer Around the Small Scale Airfoil Using Various Turbulence Models

A numerical investigation of low-Reynolds number flows with thermal effect around the MAV airfoils using various turbulence models, including an algebraic Baldwin-Lomax model, Spalart-Allmaras one equation, and two equation (k-ω and SST-k-ω) turbulence models, is presented. First, the thermal effect on the aerodynamic efficiency is studied for flow around a rectangular MAV wing, based on the NACA0012 airfoil section at low-aspect ratio (AR = 2) and an angle of attack equal to 0°. Second, details of the thermal effect are limited to the two-dimensional NACA0012 airfoil with chord length of 3.81 cm. This study shows that the improvement of aerodynamic efficiency (increase lift and reduce drag) is achieved by the generation of a temperature difference between extrados and intrados of the airfoil (by cooling the upper surface and heating the lower surface). The numerical results obtained with various turbulence models are in good agreement with experiment data, except the k-ω turbulence model. These results are performed with the CFD-FASTRAN code, using the fully implicit scheme for time integration and the upwind Roe flux difference splitting scheme for space discretization augmented by a high order Osher-Chakravarthy limiter.     

EFFECTS OF ASPECT RATIO ON VORTEX FLOW PATTERNS IN MIXED CONVECTION OF AIR THROUGH A BOTTOM-HEATED HORIZONTAL RECTANGULAR DUCT

Abstract

Buoyancy-induced vortex flow structures and the associated heat transfer were numerically investigated in a mixed convective airflow in a bottom-heated horizontal rectangular duct of different aspect ratios. The unsteady three-dimensional Navier-Stokes and energy equations were directly solved by a higher order upwind finite difference scheme. Results were presented in particular for Reynolds numbers ranging from 5 to 15, Rayleigh numbers up to 9000, and aspect ratios from 4 to 12. The predicted results clearly show significant differences in vortex structures induced in ducts with small and large aspect ratios. For an aspect ratio less than 6 the transverse vortex rolls are periodically generated in the duct entry and gradually transform into longitudinal rolls when moving downstream. The resulting vortex flow eventually evolves to a time periodic state with the upstream and downstream portions of the duct dominated by the transverse rolls and longitudinal rolls, respectively. For a large aspect ratio (A > 9) the transverse rolls prevail in the duct core, with two to three longitudinal rolls existing near each sidewall. The flow oscillation in the region dominated by the transverse rolls is much higher than that dominated by the longitudinal rolls. At high Ra the flow becomes chaotic in time, and the duct is filled with unstable irregular vortex rolls.     

Correlations for solar air heater duct with V-shaped perforated baffles as roughness elements on absorber plate

An experimental investigation has been carried out to study the effect of heat transfer and friction characteristics of air passing through a rectangular duct which is roughened by V-down perforated baffles. The experiment encompassed Reynolds number (Re) from 3800 to 19,000, relative roughness height (e/H) values of 0.285–0.6, relative roughness pitch (P/e) range of 1–4 and open area ratio values from 12% to 44%. The effect of roughness parameters on Nusselt number (Nu) and friction factor (f) has been determined and increase in heat transfer and friction loss has been observed for ducts having a roughened test plate. Maximum Nusselt number is observed for the relative roughness pitch ranging from 1.5 to 3 for flow and geometrical parameters under consideration. The experimental data have been used to develop Nusselt number and friction factor correlations as a function of roughness and flow parameters.     

Influence of inclination angle,attack angle,and arrangement of rectangular vortex generators on heat transfer performance

We have studied the enhancement of heat transfer by vortex generators. Experiments were performed on rectangular‐type vortex generators mounted on a parallel‐plate heater, and the heat transfer coefficient of the heater surface and pressure drop in the duct were measured. These measurements indicated that a rectangular vortex generator (called a double‐inclined winglet), with inclination angle of the vortex generator surface to the heater surface (β) at 60°, and the attack angle to the flow direction (γ) at 45°, maximizes the local Nusselt number of the heater surface. It was also found that a group of double‐inclined winglets has an optimal arrangement in a winglet array, longitudinal pitch and transverse pitch, that maximizes the ratio [Colburn's dimensionless heat transfer coefficient J_H]/[friction factor f]. The results of numerical calculations showed that the double‐inclined winglet was superior to the conventional rectangular vortex generator in heat transfer. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 253–267, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10089     

Laminar heat transfer between parallel plates as the limiting solution for the rectangular duct

This paper is aimed at demonstrating that the velocity and the temperature distributions of a Newtonian fluid in fully developed laminar flow between infinite parallel plates with uniform wall heat flux, can be derived from the rectangular duct analysis, in H2 boundary conditions, in the limit of the aspect ratio β tending to infinity. Hence the 2-D analytical distributions of fluid velocity and temperature for the rectangular duct are elaborated to obtain the well known 1-D distributions for the slab geometry. The main outcome regards the Nusselt number; it is calculated for the rectangular duct, in the limit of β → ∞, and coincides with the Nusselt number of the infinite parallel plates.     

Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method

This study presents the determination of optimum values of the design parameters in a heat exchanger with a rectangular duct by using Taguchi method. The heat exchanger has plate-fins containing periodically interrupted diverging and converging channel flow domains. The experimental investigation for the established heat exchanger involves short rectangular fins attached in 8 × 8 arrays to a surface having various inclination angles. The effects of the six design parameters such as the ratio of the duct channel width to height, the ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity and pressure drop are investigated. In the Taguchi experimental design method, Nusselt number and friction factor are considered as performance parameters. An L₂₅ (5⁶) orthogonal array is chosen as an experimental plan for the design parameters. The analysis of Taguchi method conducted with an optimization process to reach minimum pressure drop (friction factor) and maximum heat transfer (Nusselt number) for the designed heat exchanger. Experimental results validated the suitability of the proposed approach.     

A comparative study of four low-Reynolds-number k-ε turbulence models for periodic fully developed duct flow and heat transfer

ABSTRACT

In this study, streamwise-periodic fully developed turbulent flow and heat transfer in a duct is investigated numerically. The governing equations are solved by using the finite-control-volume method together with nonuniform staggered grids. The velocity and pressure terms of the momentum equations are solved by the SIMPLE algorithm. A cyclic tri-diagonal matrix algorithm (TDMA) is applied in order to increase the convergence rate of the numerical solution. Four versions of the low-Reynolds-number k-ε model are used in the analysis: Launder-Sharma (1974), Lam-Bremhorst (1981), Chien (1982), and Abe-Kondoh-Nagano (1994). The results obtained using the models tested are analyzed comparatively against some experimental results given in the literature. It is discussed that all the models tested failed in the separated region just behind the ribs, where the turbulent stresses are underpredicted. The local Nusselt numbers are overpredicted by all the models considered. However, the Abe-Kondoh-Nagano low-Re k-ε model presents more realistic heat transfer predictions.     

Measured shortwave sky radiance in an urban atmosphere

An extensive data set of measurements of the shortwave sky radiance at Toronto, Canada, was compiled by the authors in 1984. A pyroelectric radiometer with a half-angle field of view of 5 degrees was used to make a total of more than 100,000 sky radiance measurements. This paper presents an analysis of almost 40,000 of these measurements in the form of a set of plots showing means and percentiles of sky radiance as a function of position in the sky; atmospheric clearness index, k_t; diffuse fraction, k; and solar zenith angle, θ_z. The data show (i) that, in the circumsolar region, the highest observed values of sky radiance occur for partly cloudy sky conditions characterized by intermediate values of k and k_t, (ii) that, in the regions of the sky away from the solar position, sky radiance tends to increase monotonically both with increasing k and with increasing k_t, (iii) that there is a progressive transition with increasing k, from the horizon brightening for skies with low diffuse fractions to horizon darkening for skies with diffuse fractions approaching unity, (iv) that the shape of the sky radiance distribution is a strong function of the elevation of the sun in the sky, and (v) that the sky radiance is highly variable, with a positively skewed probability density function.     

Effects of a kind of surface groove on flow loss in both rectangular and circular ducts at different Reynolds numbers

Pipes are widely used to transport gas,oil and water in industries.Drag reduction in pipes is an increasingly concerned problem to save energy.Some researches have indicated that the non-smooth surface with special structures can reduce flow loss.In this paper,an experimental investigation has been performed on the effects of a kind of surface groove on the drag in both rectangular and circular duct at different Reynolds numbers.In the experiment of the rectangular duct,total pressure at both inlet and outlet were measured.Static pressure on the wall was measured on the surface with smooth and grooved film respectively.In the circular duct,a boundary layer pressure probe was used to measure the total pressure distribution at both inlet and outlet.Four taps at inlet and outlet were used to measure static pressure.The loss coefficient is used to evaluate the effects of the surface groove on drag reduction.The experiment was conducted with the Reynolds number range from 1.28×10~4 to 2.57×10~4.The result shows a maximum drag loss reduction of approximately 2.4% in rectangular duct at Reynolds number of 2.4×10~4.A 10%reduction of pipe pressure loss by grooved surface is measured in circular duct at a Reynolds number of 3.0×10~5.