AUGMENTATION OF HEAT TRANSFER IN CORRUGATED TUBE USING FOUR-START SPIRAL WALL

: This article dealt with an important heat transfer field, which is passive heat transfer technique represented by corrugated tube. The study conducted numerically by ANSYS Fluent 14. The motivation behind the current study was to clarify the characteristics and merits of such tube geometry in terms of heat transfer and pressure drop. The obtained results reported under constant heat flux, temperature-dependent thermo-physical properties and Reynolds number range of 300-1500. Results show good heat transfer enhancement of 6.15-33.24% in spite of an increase in friction factor of 1.80-2.93 times the smooth values. The corrugated tube with φ =4.76×10 -2 has the top thermal 1.16-1.25 for all Reynolds number. The most important finding is that the gained heat transfer is much more than the increase in pressure loss until a certain threshold of Reynolds number about 900, later, the pressure loss increase and dominates over the heat gained. The effect of Prandtl number on the heat transfer for three types of fluids produced too. A criterion correlation equation of Nusselt number developed to describe the cases of four starts spirally corrugated tubes by deviation ±3% compared with the simulation results.


INTRODUCTION
Different types of the heat exchangers have been used in the electrical, chemical, automotive and industrial applications. One of the important types in a co-axial heat exchanger is the spirally corrugated tube, which can improve the overall heat transfer performance of the heat exchangers [1]. Corrugated tubes have been developed from single start to multiple starts. Corrugation augments the heat transfer due to the mix of fluid, which produced during the flow separation and then re-attaches stages [2].
It is imperative to find out a way for sharing resources and saving energy due to horrible energy exhausting. Axiomatically, energy resources are running short with, and the globe on the verge of imminent lack [1]. Heat transfer field holds the promises; it is the most important field that could be helpful in such issue. It can reduce the wasted energy significantly in the case of employing an effective and well functional technique in many applications, such as electronic device cooling, heat exchangers, and nuclear reactor cooling [3][4][5][6][7]. In general, the desired magnification of gained heat could be achieved by primarily two techniques. First one; produces a good outcome, but it needs external power and it is called "active technique" [8]. The second one; does not need any external power and it could be achieved by adding something to the fluid or modify the surface, this method is called "passive technique" [9]. There is another method which called ''compound technique '' which involves the two previous types (active and passive) like using an electrostatic field or vibrated flow which is active types in addition to use the nanofluid or vortex

MATHEMATIC MODEL
First of all, one smooth and five corrugated tubes were created by utilizing SolidWorks software package. The tubes material was selected to be steel of 2 mm thickness and 2 m length. The bore diameter D b of all tubes remain constant at 10mm, on the other hand, the envelope diameter D e is varying from 12 to 14 mm with increment step of 0.5mm. The primary parameters that usually used to describe the rippled tube are the corrugation height e, corrugation pitch p, nominal diameter D n and the severity index φ as shown in Figure  1 .

Figure 1: Corrugated Tube Geometry
Instead of discussing the effect of both corrugation height e and corrugation pitch p individually, the expression of "severity index φ" proposed which include the effect of both corrugation height and pitch. The severity index simply indicates how corrugation is severe and calculates from the following equation [2]: Where, D n represents the nominal diameter and it often used in the corrugation tubes in order to denote to the "hydraulic diameter" due to irregular tube geometry. The nominal diameter could be calculated from the following equation [10]: The tubes characteristic and dimensions that employed in the current simulations described in the Table 1 and the corresponding cross sections for the cases appear clearly in Figure 2.

GOVERNING EQUATIONS
The discretization of the governing equations should be made prior to simulation. For the flow of fluid in the tube, the following three equations are the main governing equations [8].
-Continuity Equation: (3) -Momentum Equation in z-direction (axial direction): -Energy Equation: The other important heat transfer parameter can be compute by using analytical equation, such as local heat transfer coefficient (h), which can be computed as below:- where, both T w (z) and T b (z) represent local wall and bulk temperatures respectively. While q s (z) is the locally applied heat flux, which can be determined by:- On the other hand, both of local and average Nusselt number determined from the following equations:- Eventually, Reynolds number was determined from the following expression (11)

NUMERICAL PROCEDURE AND BOUNDARY CONDITIONS
ANSYS MESHING ICEM CFD 14 is the tool that employed for this purpose. Mesh process acting as an essential character in accuracy and reliability of the results. Tetrahedral elements of constant stress element owning four nodes were applied. For each node, the elements were represented in 3-Dim space possessing three degrees of freedom in X, Y and Z, directions with take care about the meshing qualities like mesh skewness, aspect ratios and mesh smooth that collected to be 0.75%, 1% and 20% respectively.

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For consistency in the discretization scheme, the density of the grid plays an important parameter to get the right solution [20]. It is known that any increases in the density about the spatial grids will minimize the errors. Element number has an important parameter to get mesh dependence results as shown in Figure  3. In the current study, the grid density limits were 2763566-3094583 tetrahedral cells.
Grid Convergence Index (GCI) was performed to verify the meshing quality [21]. Mesh spaces were tested for each case 0.1, 0.2, 0.3, 0.4 and 0.5 mm respectively, where the GCI's were 0.107, 0.131, 0.169 and 0.205 mm respectively. Therefore, the mesh spacing of 0.1 mm was selected for the whole cases as shown in Figure 4. Moreover, the reduction in mesh spacing gives more stability and accurate outcome values, where the bulk fluid temperature becomes reasonable and has precise value, as the mesh space gets finer as shown in both Figures 3 and 4

.
A commercial code of ANSYS FLUENT 14.0 [22] used to construct the fluid flow model of smooth and corrugated pipes. Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm produced to solve the Navier Stokes equations by coupling the pressure and velocity. In discrete arrangement, second order upwind chosen for computing momentum and energy while standard format chosen for pressure. Convergence conditions absolute value of energy residual is setting less than 1×10 -9 , beside the value of other quality residuals are less than 1×10 -6 . For all cases, the simulations conducted the stainless steel pipe under constant heat flux of 10 KW/m 2 , with steady state and temperature-dependent thermo-physical properties. The working fluid is Newtonian fluid as pure water enters at temperature 300K with Reynolds number range was 300-1500.

VALIDATIONS
Firstly, validation was made to confirm the results of smooth tube; this verification will give a confidence for the final numerical results of the corrugated tubes. The validation was present numerically for fluid flow in the smooth tube of stainless steel tube has 2 mm thickness, nominal diameter Dn of 10 mm and 2 m length.
Nusselt number for the smooth pipe compared with both Churchil and Ozoe equation [9] beside Shah and London equation [23]. Churchil and Ozoe [9] prescribed an equation that covers the entrance and fully develops region confirmed for Pr about 0.7 to 10, and has reliable intimate of small Gz and large Pr, as: Where: Moreover, Shah and London equation [23] was:

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Vol. 10, No. 4 ISSN: 1998-4456 Figure 5 shows a good agreement with the current outcomes with acceptable deviations of ±4.7% and 3.8% with the data reported by [9] and [23] respectively. This deviation came from both assumption approximations and numerical error.
On the other hand, the friction factor is habitually used for the validation of pressure drop, where the validation achieved by comparing the numerical results of smooth tube with the Darcy friction factor as in the following Figure 6 and equation (15) with maximum deviations of ±5.87% occurs at Re=1500.

HEAT TRANSFER RESULTS
The reasonable matching of both Nusselt number and friction factor validation for both the current numerical results give an indication and corroboration about the fidelity of the current study. For further reliability of the ANSYS simulation, the calculated Nusselt number of Severity Index φ=1.98×10 -  As it was expected, the severity index helps to mix the fluid layers next to the tube wall while keeping the core flow intact. This behavior has two merits. First, enhancing the heat transfer by the disturbance near the wall; second; it keeps the flow laminar in the core zone, which minimizes the pressure loss. The mentioned contours figure strongly indicate that the coefficient of the heat transfer gets enhances through the growth of severity index due to the decrease of the overall wall temperature with increase of severity index. This attributes to the turbulence in the secondary flow region that helps to mix the fluid layers and lead to increase the rate of heat transferred from the wall toward the fluid.
The differences of the water properties in this study and the ethylene glycol properties in Barba et al [25] beside their fixed parameters like e=1.5mm and p=11.5mm are the reasons of the dissimilar values of Nusselt number. Moreover the variations in helical corrugation angles were the reasons of the difference between the values of this study compared with Abdel-Kariem and Fletcher [26]. Srinivasan and Christensen [24] obtained the maximum divergence was ±4.91% so the numerical study for the corrugated tubes in different values of severity index can be acceptable.

4.76×10
-2 at Reynolds Number of 300 to 1500 for the corrugated tubes. For the same Reynolds number, and once the severity index increases, the mixing of the fluid develops according to eddies generated due to the increase of the twisted wall compared with low severity index. Although of the figures declared that, the highest temperature increases with rising of the severity index, this is because of a miniature amount of fluid compared with the main flow encloses near the corners which has a high local temperature compared with the mean fluid flow temperature through the pipe. As the inlet velocity increases, Reynolds number increases, and mass flow rate will enlarge, therefore the overall heat transfer will enhance too thus the surface temperature of the tube decreases.

2.3.FRICTION FACTOR RESULTS
As it commonly known, when the inlet velocity increases, means Reynolds number increase and the mass flow rate increase too so the velocity contour increases as it clear shown in the Figure 9, for the corrugate tubes at Re=300,900 and 1500. As the severity index rises, eddies will generated gradually, the local velocity will decrease, and the local pressure will increase which is satisfied the Bernoulli Equation.
While Figure 10 shows the pressure contours of the integer corrugation height at Re= 300,900 and 1500. It clearly indicates the actual case of losing energy (pressure loss) as both of corrugation height and Re increase. Pressure loss reaches the maximum value at the highest value of φ =4.76×10 -2 and Re=1500. This figure also shows that the maximum pressure occurring at the corrugation gap region due to the induced turbulence caused by the corrugation and there was an increase in pressure loss of range 20.6-39.1%. Copyright @ 2017 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. at Re=300 to1500 As it commonly known, the energy dissipation increases as the flow rate increase. Analogously, the increase in Reynolds number causes an increase in the pressure loss as shown in Figure 11. The desired heat gained is accompanied with appreciable pressure loss and pumping power. The figure shows the of increasing Reynolds number on the friction factor of the numerical study values at the severity index φ=1.98×10 -2 and compared with another previous correlation equations. Srinivasan (20) Meng et al [27] presented correlation equation for oil flow in circular and elliptical tubes by p/D=2-3 for 500≤Re≤50000 as: The deviation of Barba [25] and Meng et al [27] equations were as the different of the thermo physics properties between the water for this study and the other types of the work fluids. Srinivasan and Christensen equation obtained a maximum divergence of ±3.1% so that it can be conclude that the other values of the Severity Index are acceptable.

2.4.THERMAL PERFORMANCE FACTOR
Figure12 shows Nusselt number ratio Nu c /Nu s between the corrugated tubes with the smooth tube against Reynolds number. The Nu ratio indicates that the corrugated pipe is better than the smooth pipe that means that the heat transfer performance of the corrugated pipe is more efficient and the largest value in Nu c /Nu s was reach 1.560. In additional the resistance coefficient ratio; f c /f s through the corrugated tube increases directly with booth the Reynolds number and Severity Index along with maximum value 1.80-2.93 times the smooth tube for Reynolds number from 300-1500 respectively as shown in Figure 13.   This factor was proposed to describe the overall performance of an enhanced tube or tube with the promoter. The gained heat transfer ratio to the gained pressure loss simply represents the thermal performance factor as in the following equation [20].
The thermal performance of the current cases shows in Figure 14. The figure shows the tube of highest severity index is the best one in term of overall thermal performance, while the tube of lowest severity index is the worst one and the maximum enhancement was in the range of Reynolds numbers 900.

ANALYSIS OF DIFFERENT FLUID TYPES
Air, water and engine oil investigated to explore the effects of the medium properties on the overall characteristics of the heat transfer for smooth and corrugated tube. By varying the medium type, the fluid properties change and the relation between fluid property like Pr and Nu could be produced by the numerical method. Physical characteristics of the fluids at temperature 350 K exposed in Table 2 [28]. As it concluded in the water cases study, the best corrugation type to enhance the heat transfer depends on the Severity Indexes occurs at φ=4.76×10 -2 , so that this severity index will used to get the evaluations for the other fluid mediums. The distribution of augmentation ratio of the heat transfer Nu c /Nu s that evaluated for the three fluids through the smooth and corrugated tube as shown in Figure 15. It can be conclude that the Nusselt number Nu of four start corrugate pipe is better than the smooth pipe and for the greater Prandtl number working fluid like engine oil, Nusselt number will be better than the lower Prandtl number working fluid like in air. so that It can be establishing that the progression of Nusselt number ratio Nu c /Nu s from low to high as: air, water, engine oil. Largest ratio of Nusselt number Nu c /Nu s could be reach 5.778, which points to that for the engine oil medium with a high Pr cause a higher value in the augmentation of the heat transfer.  Figure 16 shows the friction factor ratio for the different working mediums (air, water and engine oil) at Severity Index φ=4.76×10 -2 with all range of Reynolds numbers. It can be shown the curves act as the same behavior of the water and the effect of the fluid properties on the resistance of the fluid inside the pipe is not large so that the curves of the friction factor ratio f c /f s is similar. It's clear that the friction factor for all fluid mediums for the corrugated tube is higher than the smooth tube. The curve of the engine oil medium is higher the others as the high viscosity compared with the other working fluids so the pumping power will be more than the other fluids.  Figure 17 shows the thermal performance factor against the Reynolds number for the corrugated tube with Severity Index φ=4.76×10 -2 for the air, water and engine oil. It can be noted that the engine oil has a higher thermal performance than the other fluids as the high values of the Nusselt number ratio Nu c /Nu s that acts in significant outcome more than the effect of its friction factor ratio f c /f s . The maximum values of the Thermal performance ratio was not in the same Reynolds number but its change in the range of Re=800-1200 from the low Prandtl number to the high Prandtl number as the fluid properties are changed.  As shown before, there are many parameters effects on the heat transfer phenomena as the geometry factors (corrugation depth e and pitch p), the properties of the fluid flow and Reynolds number Re, so that the non dimensional factors like e/dn, p/dn, Re and Pr are confirmed by Zhi-Jiang Jin [1] as parameters of the correlation criteria. The general form can expressed as: Nu=F(e/d n ,p/d n , Re,Pr) Zhi-Jiang Jin [1] mentions that the correlation equation could be adjust in power function as: The statistic program SPSS was used to interpret the output results and get the correlation equation using Multiple Regression Analysis. The criteria of the analysis of multiple regression results were; the Multiple R is 0.999949, R Square is 0.999899, Adjusted R Square is 0.952265 and the Standard Error is 0.021933. The criterion correlation of the heat transfer through five cases of four-start spirally corrugated pipes is: This criterion correlation is satisfied for water flow inside corrugated tube with 0.1818≤e/d n ≤0.333, 2.333≤p/d n ≤2.545, 300≤Re≤1500, 500≤L/e≤1000 and 166.667≤L/d n ≤181.82. Then a comparison of Nu between simulation and calculation results is shows in Figure 18. The deviation between these results is inside ±3%, so that the correlation for the calculations of heat transfer through the corrugated tube is reliable.