The use of artificial roughness or turbulence promoters on a surface is an effective technique to enhance the rate of heat transfer of the fluid flowing in a duct to aid the cooling of the surface. The main objective of this work is to simulate the effect of rib surfaces on cooling of a finite thickness plate of different shapes, (rectangular, semi-circular and cone) in fluent and to investigate the heat transfer and fluid flow characteristics. The purpose of studying the heat transfer and flow characteristics of different rib shapes is to find the shape that gives the optimum result. In this part of this work, the literature review of some works already done relating to this project has been carried. Taking specifications from these literatures, a 2D analysis was carried out for a square rib and the temperature and velocity fields results were studied. In the result, the effect of the rib on cooling was observed. The other part of this project is intended to carry out a simulation of other rib shape and orientations and campare the results to those found in literatures.
Nomenclature
Dh hydraulic diameter =4 area/perimeter
F friction factor
Gk turbulent kinetic energy due to mean velocity gradient
Gb turbulent kinetic energy due to buoyancy
H heat transfer coefficient
K turbulent kinetic energy
Kair thermal conductivity of air
Nu nusselt number
p/e relative roughness pitch
re Reynolds number
st Stanton number
ρ density of air
sk, se source term
e dissipation rate
w specific dissipation rate
y+ dimensional distance from the wall
t t effective diffusivity of k and e
2. Introduction / literature review
The use of artificial roughness or turbulence promoters on a surface is an effective technique to enhance the rate of heat transfer to the fluid flowing in a duct kamali et al, [1]. The application of Artificial roughness in form of protruded ribs of different shapes up to laminar sub-layer to enhance heat transfer coefficient is used in various applications like gas turbine blade cooling channels, heat exchangers, electrical microchip, nuclear reactors and solar air heaters. A number of experimental studies [2,3] in this area have conducted but very few attempts of numerical investigation have been made so far due to complexity of flow pattern and computational limitations. In this project, an attempt is made to simulate the rib effects on cooling of a finite thickness plate using the fluent software and to predict numerically the details of the velocity and temperature fields. The surface roughness can be produced by several methods, such as sand blasting, machining, casting, forming, welding and processes such as pressing. The presence of rib may enhance heat transfer because of interruption of the viscous sub layer, which yields flow turbulence, separation and reattachment leading to a higher heat transfer coefficient. Formation, development and decay of vertical structures, during flow of water along a rib-roughened surface have been investigated long ago [new]. It was found that the dynamics of vertical structures depends on the dimensionless rib spacing (pitch to height ratio) and on the geometry of rib edge. Zhang et al. [4] reported that the addition of grooves in between adjacent square ribs enhance the heat transfer capability of the surface considerably with nearly same pressure drop penalty. Hence, the efforts of researchers have been directed towards finding the roughness shape and arrangement, which break the laminar sub-layer and enhance the heat transfer coefficient. But later experiments and investigations in stationary flows with rib-roughened and groove surfaces showed that application of any ribs or inserts do not enhance or improve heat transfer as long as the Reynolds number is low [new]. Systematic investigations of the influence of ribs shape on effectiveness of heat transfer in a channel were carried out in [new]. It was found that the most effective rib spacing in turbulent flow is a rib-pitch-to-height ratio of p/e =10. The turbulence promoters show their best effect in the region with Reynolds numbers Re = 1500-6000. It was found that the local heat transfer always has maxima located just before the top of the rib, minima just behind the ribs and intermediate values in the spacing between the ribs. The local heat transfer minima behind the ribs were explained by the stationary air flow bound in recirculation zones behind the ribs. The flow bound in such vortices have only a little exchance with the main flow, and therefore cause poor heat transfer in such areas. Parameters involved in such experimental studies are passage aspect ratio, AR [5,6]; pitch ratio, P/e [7,8]; blockage ratio, e/Dh [8,9]; number of ribbed walls [12]; and the manner by which ribs are positioned with respect to each other [6,13]. The heat transfer measurements results for two different rib spacings, p/e = 14 and 8, indicate the importance of roughness geometry [14]. Liou et al. [15] have performed both the numerical analysis and experimental study to investigate the heat transfer and fluid flow behavior in a rectangular channel flow with stream wise periodic ribs mounted on one of the principal walls. They have concluded that the flow acceleration and the turbulence intensity are two major factors influencing the heat transfer coefficient. The combined effect is found to be optimum for the pitch to rib height ratio equal to 10, which results in the maximum value of average heat transfer coefficient. Rau et al. [16] experimentally found optimum pitch to rib height ratio to be equal to 9. Hence, his investigations reveal that not only the rib geometry but also its geometrical arrangement play a vital role in enhancing the heat transfer coefficient. Karwa [17] has reported an experimental investigation for the same configuration for the Reynolds number range of 4000-16,000. Tanda [18] has carried out experimental investigation of heat transfer in a rectangular channel with transverse and V-shaped broken ribs using liquid crystal thermography. He concluded that features of the inter-rib distributions of the heat transfer coefficient are strongly related to rib shape and geometry; a relative maximum is typically attained downstream of each rib for continuous transverse ribs (due to flow reattachment). The main aim of this project is to investigate the flow and heat transfer characteristics of different rib shapes air flowing through a rectangular duct with only one principal (broad) wall subjected to uniform heat flux by making use of computer simulation. The ribs are provided only on the heated wall. All other walls are smooth (without ribs) and insulated. Such a case is encountered in solar air heaters with artificially roughened absorber plate.
3. Methodology
3.1. Solution domain
The solution domain shown in Fig. 1(a) has been selected as per the experimental details given by tanda [18]. A 2-D analysis of heat transfer and fluid flow through a rectangular duct with transverse ribs provided on a broad, heated wall and other walls smooth and insulated, is carried out using commercially available CFD software, FLUENT 6.1. The inlet velocity is 4.3m/s, outlet pressure equals to atmospheric pressure, and no slip wall boundary conditions are used for the analysis.
Duct height (H) = 20 mm
Rib height (e) = 3 mm (square rib)
p/e = 13.3
Inlet length = 245 mm
Uniform heat at bottom surface = 1100 W/m2 (the surface below a rib is considered
insulated)
Aspect ratio (AR) = 5
Pitch p = 40 mm
Length of test section = 280 mm
Outlet length = 115 mm
Width of duct = 100 mm
Reynolds number = 8900.
3.2. Selection and validation of model
The selection of model is done as carried out by [19] by comparing the predictions of different low Reynolds number models with experimental results available in the literature [17]. The selected model is further validated, by comparing the heat transfer predictions within the inter-rib regions with the experimental results of Tanda [18]. Low-Reynolds number models are used for the near wall regions because high-Reynolds number models do not perform well in these regions [20,21]. For examples, standard k - ε model and Reynolds stress model (RSM) do not work well near wall region where k & ε approach to zero. Large numerical problems appear in the ε - equation, as k becomes zero. The destruction term in ε - equation includes ε2/ k, and this causes problem as k →0 even if ε also goes to zero; they must go to zero at an appropriate rate to avoid problem and this is often not the case. Similarly large eddy simulation (LES) model does not catch the small eddies near the wall [22]. Taking above difficulties into consideration low Reynolds number models have been developed. The k ―ω model replaces dissipation rate (ε) term by a specific dissipation rate (ω) term which transfers the k from the denominator to the numerator in the specific dissipation rate equation to avoid numerical difficulties. The renormalization group (RNG) k - ε model is developed using renormalization theory, to modify the k - ε model for near wall region, by including additional term in ε -equation [21]. The realizable k - ε model contains a new formulation for turbulent viscosity and new transport equations for ε, which is derived from an exact equation for the transport of the mean-square vorticity fluctuations. For the flow situations where core and wall bounded regions both are to be modeled with the same accuracies, the blending of both types of models can give satisfactory performance. The SST k ―ω model is developed using blending function between k - ε and
k ―ω models [20].
3.3. Governing Equations
A computer code has been developed [1] to perform numerical simulations of the steady incompressible turbulent flows. The SST k-ω turbulent model is used with enhanced wall functions for the near wall treatment.
Continuity equation:
Momentum equation:
Energy equation:
Where
and is the effective conductivity.
The Shear-Stress Transport (SST) k-ω Model:
In these equations, represents the generation of turbulence kinetic energy due to the mean velocity gradients. Gω represents the generation of ω. Γk and Γω are the effective diffusivity of
k and ω respectively. Yk and Yω represent the dissipation of k and ω due to turbulence, and Dω represents the cross-diffusion term.
4. Results and conclusion
x-velocity around the ribs indicates the existence of separation and reattachment of
flow over heated surface. Fig.4. shows the coutours of static temperature
Shows a plot of static temperature for the heated plate for a square ribs which clearly shows the gradual increase of the surface temperature. Although a maximum temperature is observed at the edges of the ribs in the region between the ribs, the temperature of the surface after the ribs is reduced compared to that when there are no ribs fig. 5. Whose temperature is observed to be on the increase. This shows the effect of the ribs on the cooling of the surface beyond the ribs.
shows the contours of turbulence intensity inside the duct. The peaks of turbulence intensity are found downstream in the vicinity of the ribs. The peaks of local surface heat transfer coefficient are also found at similar downstream locations, which describes the strong influence of turbulence intensity on heat transfer enhancement.
5. REFERENCES
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