US20160252311A1

US20160252311A1 - Wavy Fin Structure and Flat Tube Heat Exchanger Having the Same

Info

Publication number: US20160252311A1
Application number: US14/832,588
Authority: US
Inventors: Gwang Hoon Rhee; Gun Woo Kim; Young Bae Song
Original assignee: Industry Cooperation Foundation of University of Seoul
Current assignee: Industry Cooperation Foundation of University of Seoul
Priority date: 2014-12-09
Filing date: 2015-08-21
Publication date: 2016-09-01
Also published as: KR20160069822A; KR101675553B1

Abstract

Disclosed are a wavy fin structure, in which a cross-cut having a designated length is formed at a designated position of a wavy fin, and a flat tube heat exchanger having the same. The cross-cut is formed around at least one valley or peak of the fin. One cross-cut is formed at a valley or a peak at the central portion of the fin or a plurality of cross-cuts is formed at designated periods in the length direction of the fin. Further, the cross-cut is formed at a position at the rear of the peak and the length of the cross-cuts is

\frac{1}{5} C to \frac{4}{5} C .

The wavy fin structure generates flow disturbance due to a wavy-type dynamic flow, thus improving heat transfer performance.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This U.S. patent application claims the benefit of priority under 35 U.S.C. §119 of Korean Patent Application No. 10/2014/0175913, filed Dec. 9, 2014, the entire content of which is hereby incorporated herein by reference for all purposes.

TECHNOLOGICAL FIELD

The present disclosure relates to a wavy fin structure and a flat tube heat exchanger having the same, and more particularly to a wavy fin structure which may further improve heat exchange performance of a fluid and a flat tube heat exchanger having the same.

BACKGROUND

In general, a heat exchanger is an apparatus which executes heat exchange between two different fluids separated from each other by a solid wall and is widely used in industrial fields, such as heating, air conditioning, power generation, waste heat recovery, chemical processes and the like. There are various types of heat exchangers and, thereamong, a fin-type heat exchanger having an expanded heat transfer surface, which has a simple structure and is easily manufactured, is widely used now. In order to improve heat transfer performance of the fin-type heat exchanger, research on change of the shape of fins at an operating fluid side has been carried out and, as kinds of compact heat exchangers having a small size and a light weight which have been developed, there are a louvered fin-type heat exchanger, an offset strip fin-type heat exchanger, a wavy fin-type heat exchanger and the like.
There among, a wavy fin is easily manufactured, as compared to other high-performance fins, and is easily applied to a fin-flat tube heat exchanger. The wavy fin is formed by modifying a general plain fin into a wavy type in a flow direction and thus increases a heat transfer area, and dynamically forms a flow and thus increases heat transfer performance. Further, a wavy fin-type heat exchanger is advantageous in that it has high heat transfer performance and is less influenced by dust, thus being usable in a wide variety of environments. FIG. 1 is a view illustrating surfaces of a wavy fin structure which is applied to a flat tube and FIGS. 2(a) and 2(b) are photographs of a general wavy fin structure.
Research on a wavy fin-type heat exchanger was executed by many investigators through experimentation and numerical analysis. In the case of a wavy fin, it is known that a flow of the wavy fin is dynamically formed in the wavy shape of the fin and divided into a laminar flow region, an abnormal region in which a longitudinal vortice is formed, and a turbulent flow region, and important shape parameters influencing wavy fin performance include a wavelength, a warpage angle, a fin pitch and the like. Further, Korean Patent Laid-open Publication No. 10-2013-0059784 (Publication Date: Jun. 7, 2013) discloses a wavy fin structure which partially structurally changes fins so as to promote turbulence of a fluid and to improve heat exchange efficiency of the fluid.
Cross-Cutting means a technique in which a fin is cut into a designated length in a direction vertical to the flow direction of a fluid so as to improve heat transfer performance. In ‘Fluid flow and heat transfer characteristics of cross-cut heat sinks (Tae Young Kim and Sung Jin Kim, International Journal of Heat and Mass Transfer 52, pp. 5358-5370, 2009)’, heat transfer performance improvement effects, through an experiment in which cross-cuts are applied to a plain fin, were confirmed. In general, it is known that, if cross-cuts are applied to a fin, a thermal boundary layer collapses, heat transfer in the length direction is blocked and, thus, heat transfer performance is improved.

SUMMARY OF THE DISCLOSURE

Therefore, the present disclosure has been made in view of the above problems, and it is an object of the presently described embodiments to provide a wavy fin structure, which may further improve heat exchange performance of a fluid by applying cross-cuts to wavy fins, and a flat tube heat exchanger having the same.
In accordance with an aspect of the presently described embodiments, the above and other objects can be accomplished by the provision of a wavy fin structure in which fins are periodically arranged in a plurality of rows and each fin is periodically waved to form repeated valleys and peaks in the length direction of the fin, wherein a cross-cut having a designated length is formed around at least one valley or peak of the fin.
Here, one cross-cut may be formed at a valley or a peak of the central portion of the fin in the length direction of the fin or a plurality of cross-cuts may be formed at designated periods in the length direction of the fin.
The cross-cut may be formed at a position at the rear of the peak.
The length of the cross-cut may be
$\frac{1}{5} C to \frac{4}{5} C,$

C may be

$\frac{b}{2 \sin (α)},$
α may be a warpage angle of the fin, and b may be a fin pitch.
In accordance with another aspect of the presently described embodiments, there is provided a flat tube heat exchanger having the wavy fin structure.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and other advantages of the presently described embodiments will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a conceptual view illustrating a general flat tube and wavy fins applied thereto;

FIGS. 2(a) and 2(b) are photographs illustrating perspective and plan views of a general wavy fin structure;

FIGS. 3 and 4 are views illustrating the geometric structure of a wavy fin with cross-cuts applied to embodiment 1 of the present disclosure;

FIG. 5 is a view illustrating distributions of temperature contour lines of a wavy fin without cross-cuts (da=0 m) and wavy fins with cross-cuts in accordance with embodiment 1 (da=0.001 m, 0.003 m);

FIGS. 6(a) and 6(b) are views illustrating the geometric structure of a wavy fin applied to tests of embodiment 2 and embodiment 3 and FIG. 6(c) is a view illustrating a non-uniform grid state of the wavy fin;

FIG. 7 is a view illustrating graphs representing validation results of f (upper) −Nu_lm(low) of the wavy fin of FIG. 6 under the condition of 100≦Re≦400;

FIG. 8 is a view illustrating the geometric structure of the wavy fin in accordance with embodiment 2 in which cross-cuts are applied to positions in front of and at the rear of peaks;

FIG. 9 is a view illustrating graphs representing results of Nu/Nu_nocut(upper) and f/f_nocut(lower) when cross-cuts are applied to positions in front of and at the rear of peaks of the wavy fin in accordance with embodiment 2;

FIGS. 10(a) to 10(c) are views illustrating distributions of non-dimensionalized velocity (upper)—temperature contour lines of a wavy fin without cross-cuts ((a) Nocut) and wavy fins with cross-cuts in accordance with embodiment 2 ((b) Front cut) ((c) Back cut) under an Re of 400;

FIG. 11 is a view illustrating the geometric structure of the wavy fin in accordance with embodiment 3 to which cross-cuts having various lengths are applied to a region at the back of a peak of the wavy fin;

FIG. 12 is a view illustrating graphs representing results of Nu/Nu_nocut(upper) and f/f_nocut(lower) when cross-cuts having various lengths are applied to positions in front of peaks of the wavy fin in accordance with embodiment 3;

FIG. 13 is a view illustrating distributions of non-dimensionalized velocity (upper)—temperature contour lines of the wavy fin in accordance with embodiment 3 when cross-cuts having various lengths are applied to positions in front of peaks of the wavy fin;

FIG. 14 is a graph illustrating results of Nu distributions when no cross-cuts are present and in case 3 and case 4 of embodiment 3 under an Re of 400;

FIG. 15 is a view illustrating a velocity streamline distribution (upper) and a pressure contour line distribution (lower) under an Re of 400 in part 6 of case 3 of embodiment 3;

FIG. 16 is a graph illustrating a result of j/f values when no cross-cuts are present and in case 3 of embodiment 3 under the condition of 100≦Re≦400; and

FIG. 17 is a view illustrating graphs representing results of levels of usefulness (c) and Nu values when no cross-cuts are present (0) and in the respective cases of embodiment 3 under an Re of 400.

DETAILED DESCRIPTION

Now, a wavy fin structure and a flat tube heat exchanger having the same in accordance with preferred embodiments in accordance with the present disclosure will be described in detail with reference to the annexed drawings.
As described above, a wavy fin-type heat exchanger has a flat tube through which a fluid may pass and a wavy fin structure to induce turbulence of the fluid to improve heat exchange efficiency is installed within the flat tube. The flat tube heat exchanger is well known to those skilled in the art and a detailed description thereof will thus be omitted.
In the wavy fin structure, as exemplarily shown in FIG. 2, fins are periodically arranged in a plurality of rows in the width direction of the wavy fin structure and upper and lower ends of the respective fins are bonded to a flat tube. The wavy fin structure is configured such that the fins are periodically waved to form a plurality of peaks and valleys in the length direction thereof, i.e., the flow direction of a fluid and, thus, a plurality of fluid passages are formed within the wavy fin structure so as to be divided from each other. Therefore, the fluid passing through the fluid passages of the wavy fins flows through the wavy structure, thus inducing turbulence and stirring.
In accordance with the presently described embodiments, cross-cuts which are cut vertically to the length direction of the fins, i.e., the flow direction of the fluid, are formed on the wavy fin structure. The cross-cut may be formed around at least one valley or peak of the wavy fin. One cross-cut may be formed at the valley or peak of the central portion of the wavy fin or a plurality of cross-cuts may be formed at valleys or peaks of the fin periodically.
Cross-Cuts are applied to various positions of wavy fins in accordance with various embodiments, which will be described later, or heat transfer performances acquired by applying cross-cuts having various lengths are confirmed through experimentation. If cross-cuts are applied to wavy fins, flow disturbance may be generated due to a dynamic flow of a wave type and heat transfer performance may be further increased.
Hereinafter, various embodiments will be described.

Embodiment 1—Formation of Cross-Cuts at Valleys or Peals of Wavy Fins

In this embodiment, a cross-cut having a designated size is formed around a valley or a peak around the central portion of a wavy fin and has a basic shape, as exemplarily shown in FIGS. 3 and 4. Here, it may be interpreted that a valley or a peak means the lowest point (lowest position) and the highest point (highest position) and ‘a region around a valley or a peak’ means a peripheral region including the valley or the peak. Further, in the embodiment, the wall of the wavy fin has a planar surface (a linear cross-section).
As exemplarily shown in FIGS. 3 and 4, in this embodiment, performance experimentation is executed using a 5 wave wavy channel, a cross-cut is formed at the central portion (the third wave), the length of one cycle of a fin is 10.8 mm, and a fin pitch is 2.5 mm. Further, the thickness of the fin is 0.2 mm, the height of the fin is 8 mm, and the fin is formed of aluminum.
An analysis region for numerical analysis is configured so as to completely represent the wavy fin and the channel of air. The flat tube to which the wavy fins are applied has a completely symmetrical shape in the height direction and thus, in order to reduce the analysis region, only the half of the flat tube in the height direction is modeled, and a symmetry boundary condition is input to the upper surface of the analysis region. Further, since the wavy fins are periodically arranged, modeling is executed over only one row not the entire model and a periodic boundary condition is given. Air flows along the surfaces of the fins from right to left. The velocity profile of air is not uniform at the inlet of the channel including the surfaces of the fins and the flat wall of the fins due to the thickness of the fins. For this reason, the analysis region has clearances having designated distances at the inlet and the outlet (inlet: 10.8 mm corresponding to the length of one cycle of the wavy fin, outlet: 21.6 mm corresponding to the length of two cycles of the wavy fin).
FIG. 5 illustrates temperature distributions if a cross-cut is formed at the centers of wavy fins. In FIG. 5, the first graph illustrates a temperature distribution if no cross-cut is formed at a wavy fin (no cut, d_a=0 m) and the second and third graphs illustrate temperature distributions if cross-cuts having different lengths are formed at wavy fins (d_a=0.001 m, d_a=0.003 m). As exemplarily shown in FIG. 5, it may be confirmed that temperatures at the cross-cuts are lowered. It may be understood that, if a cross-cut is formed, a flow boundary layer is destroyed and regenerated and such a process disturbs a stagnant thermal flow.

Embodiment 2—Research on Optimal Position of Cross-Cut

In accordance with embodiment 1, it may be understood that, if a cross-cut is formed around the valley or the peak of the center of a wavy fin, heat transfer performance is improved.
Further, embodiment 2 and embodiment 3 represent test examples to find the optimal position and length of a cross-cut.
In embodiment 2 and embodiment 3, all computational fluid dynamics (CFD) analysis is two-dimensionally carried out. With reference to FIGS. 6(a) to 6(c), a type of a 5 wave wavy channel (b/Lc=0.15) having a fin pitch (b) of 6.9 mm, a 1 cycle of wavy fins (Lc) of 45.7 mm, and a warpage angle of 20°, and used in a flow visualization test of Ali and Ramadhyani (W. M. Kays., A. L. London, Compact Heat Exchangers, 3rd edition, McCraw-Hill, New York, 1984.), which is non-dimensionalized into a hydraulic diameter, is used in analysis. The hydraulic diameter and an Re value are calculated by Equation 1 below. All equations refer to those given in Viscous Fluid Flow (Third edition, McGraw-Hill, New York, 2006) of Frank M. White.
$\begin{matrix} Dh = \lim_{w \to \infty} \frac{2 wb}{(w + b)} = 2 b Re = \frac{U_{in} D_{h}}{v} & [Equation 1] \end{matrix}$
As exemplarily shown in FIG. 6(b), information regarding the analyzed shape has b of 0.5 D_hand L_cof 3.312 D_has a non-dimensionalized result of a length dimension. Further, in the same manner as the shape used in the Ali and Ramadhyani test, clearances having designated distances are given to the inlet and the outlet (inlet: 1.036 5 D_h, outlet: 1.267 D_h).
A designated temperature condition is given to the wall surface as the boundary condition, a designated velocity condition is used as an inlet velocity, and a pressure condition is used as an outlet condition. An operating flow region is fixed to a region satisfying 100≦Re≦400, which is reported as a normal laminar flow in the Ali and Ramadhyani paper.
FIG. 6(c) illustrates the state of a grid which is used. A structured grid is used in a direction parallel with a fin wall and an unstructured grid which is more densely formed around the wall is used in a direction vertical to the fin wall. A grid dependency test is carried out using a Nu value and an f value of a flow having an Re of 400 in a wavy shape to which no cuts are applied. The Nu value and the f value are calculated by Equation 2 below.
$\begin{matrix} f = \frac{Δ p^{*}}{2 L *} Nu = | \frac{\partial θ}{\partial n^{*}} | = \frac{Q_{w}}{A_{s} (T_{w} - T_{in})} \frac{D_{h}}{k} & [Equation 2] \end{matrix}$
In Equation 2 above, L* is a non-dimensionalized value of the total length of a wavy fin. N* means a direction vertical to the fin wall. A_smeans the total heat transfer area.
Table 1 below represents results of an f-Nu grid dependency test to analyze an Re 400 wavy fin.

TABLE 1

Mesh	Friction factor	Nu
Number	(% deviation)	(% deviation)

7600	0.106173101	10.86369
13250	0.103713962 (2.32)	10.20564 (6.05)
20400	0.102659318 (1.02)	9.829024 (3.70)
29050	0.102136701 (0.51)	9.609202 (2.24)
39200	0.101836291 (0.29)	9.476781 (1.38)
50850	0.101622992 (0.21)	9.395578 (0.86)
64000	0.101465841 (0.15)	9.344464 (0.54)

A result of the grid dependency test, a grid of a mesh number of 29050 having a fraction factor and a Nu value, deviations of which are less than 1.5%, is used to execute analysis.
Validation of such analysis is carried out by comparing f-Nu analysis results to test result values proposed by the Ali and Ramadhyani test. A method for calculating an f value is the same as in the previous grid dependency test. However, as a Nu value, a Nu_lmvalue used in the Ali and Ramadhyani research is calculated and compared using Equation 3 below. A difference between T_wand T_inis calculated as 10° C.
$\begin{matrix} {Nu}_{lm} = \frac{Q_{w}}{{A_{s} (Δ T)}_{Lm}} \frac{D_{h}}{k} Δ T_{lm} = \frac{(T_{w} - T_{in}) - (T_{w} - T_{out})}{\ln [(T_{w} - T_{in}) - (T_{w} - T_{out})]} & [Equation 3] \end{matrix}$
FIG. 7 illustrates validation results and it is judged that analysis follows tendency of test results well. It may be understood that, as an Re value increases, both heat transfer performance and pressure loss increase. As results of the All and Ramadhyani test, an increase gradient of the Nu value is changed within the range of 100≦Re≦400, and it is reported that it is caused by effects of longitudinal (Goertler) vortices. In such research, analysis is carried out only within the range of 100≦Re≦400 and, thus, effects of longitudinal (Goertler) vortices are not confirmed.
In order to find the optimal position of a cross-cut, a cut having a size of 0.145 D_his applied to a position in front of a peak and a position at the rear of a peak of the center of an analysis model (the third wave), as exemplarily shown in FIG. 8, and thus heat transfer performance and pressure loss are compared. In terms of the inner flow of a wavy fin, a recirculation section is generated around a peak and heat transfer performance is relatively low. Therefore, a cross-cut is applied to a region around the peak.
As exemplarily shown in FIG. 8, cross-cuts are implemented by cutting a part of a fin wall by 0.145 D_hunder a periodic condition. Heat transfer performance and pressure loss are estimated using f and Nu which are used in the grid dependency test.
FIG. 9 illustrates results of the above test. If a cross-cut is applied to a position in front of a peak (front position), a Nu value increases by up to 5.71% at an Re of 400, as compared to the shape to which no cross-cut is applied. In this case, an f value increases by up to 4.56% at an Re of 400. If a cross-cut is applied to a position at the rear of a peak (back position), a Nu value increases by up to 14.14% at an Re of 400 and an f value increases by up to 5.10% at an Re of 400. In general, as an Re value increases, heat transfer performance and pressure loss increase. It is known that, if a cross-cut is applied, collapse of a thermal boundary layer of a flow at the applied part and blocking of heat transfer in the length direction due to a temperature difference between front and rear parts of a fin are simultaneously achieved and, thus, heat transfer performance is improved. However, in the case of this test, since two-dimensional analysis is carried out, blocking of heat transfer in the length direction may not be confirmed. Therefore, actual heat transfer improvement effects may be further increased, as compared to heat transfer improvement represented in this test.
Now, performances according to application positions of cross-cuts will be compared. It may be confirmed that heat transfer performance if a cross-cut is applied to a back position is about 3 times heat transfer performance if a cross-cut is applied to a front position. On the other hand, it may be confirmed that pressure loss is increased only by 1% and, thus, application of a cross-cut to a back position is more effective. The reason for this is that, if a cross-cut is applied to a front position, the cut is horizontal with the flow direction and flow disturbance effects are few, and if a cross-cut is applied to a back position, flow collides with the fin at the rear of the cut and oblique impinging-type flow disturbance is actively generated. This may be effectively confirmed through FIGS. 10(a) to 10(c). FIG. 10(a) represents results if no cross-cut is formed (no cut), FIG. 10(b) represents results if a cross-cut is formed at a position in front of a peak (front cut), and FIG. 10(c) represents if a cross-cut is formed at a position at the rear of a peak (back cut). Consequently, it may be confirmed that application of a cross-cut to a position at the rear of a peak is more effective.
As described above, it is confirmed that heat transfer performance if a cross-cut is applied to a position at the rear of a wave peak is about 3 times heat transfer performance if a cross-cut is applied to a position in front of a wave peak. The reason for this is that, if a cross-cut is applied to a position in the front of a wave peak, the cross-cut is horizontal with the flow direction and flow disturbance effects are few, and if a cross-cut is applied to a position at the rear of a wave peak, the cross-cut is not horizontal with the flow direction and flow disturbance effects are great. Additionally, due to active flow disturbance, pressure loss if a cross-cut is applied to a position at the rear of a wave peak is relatively great but a difference between pressure losses at the front position and the back position is not great.

Embodiment 3—Research on Optimal Length of Cross-Cut

In the previous embodiment, it is confirmed that heat transfer effects are great if a cross-cut is formed at a position at the rear of a peak. In this embodiment, research to find the optimal length of a cross-cut when the cross-cut is located at a position at the rear of a peak is carried out.
This research is carried out using C=b/(2 sin(α)) which is influenced by a fin pitch (b) and a warpage angle (α), as exemplarily shown in FIG. 11. Total 5 cut lengths of 0.145 P_h, 0.292 D_h(2/5 C), 0.365 D_h(1/2 C), 0.585 D_h(4/5 C), and 0.731 D_h(C) are implemented and compared and FIGS. 12 and 13 illustrate results of comparison between these lengths.
First, as compared to a shape to which no cross-cut is applied, case 2 (2/5 C) exhibits heat transfer performance which is increased by up to 22.9% and causes maximum performance improvement. It is confirmed that, in case 2, maximum flow disturbance is generated. When a flow occurs between fins, a thermal boundary layer is formed from the fin wall and the temperature of the central portion of the flow is lower than the temperature of the wall. Here, if a cross-cut having the length of case 2 is applied, impinging-type flow disturbance is formed at the central portion of the flow having the relatively low temperature and heat transfer performance is rapidly increased.
On the contrary, case 4 (4/5 C) does not effectively cause disturbance of the central portion of a flow due to an excessively long length of the cross-cut and forms the flow, the entirety of which passes through the cross-cut. Oblique impinging effects playing an important role in improvement of heat transfer performance are acquired by the flow of a relatively high temperature around the fin wall and, thus, heat transfer performance is improved by 3.26% at most. In case 5 (C) having a more increased length of the cross-cut, it is judged that a flow rising from the bottom through the cross-cut causes impinging effects and heat transfer performance is more improved, as compared to case 4.
As results of pressure loss, as compared to the shape to which no cross-cut is applied, the case 2 (2/5 C) exhibits pressure loss which is most highly increased by up to 6.16%. Since the central portion of a flow having large quantity of motion collides with the fin wall at the rear of the cross-cut, such a result is expected. Next, case 3 exhibits pressure loss which is increased by up to 5.80%. Further, it is confirmed that case 4, which causes the fewest flow disturbance, exhibits minimum pressure loss. A difference of heat transfer performance improvement degrees between case 2 and case 3 is only 0.05% but the pressure loss of case 3 is lower than that of case 2 by up to 1%. Therefore, it may be understood that the optimal length of a cross-cut is 0.365 D_h(1/2 C) of case 3. Further, the interesting thing is that, in case 5 (c) at an Re 100, a heat transfer area is decreased in proportion to increase of the length of the cross-cut and thus pressure loss becomes less than that of the case in which no cross-cut is applied.
As described above, as a result of research on the optimal length of a cross-cut, it is confirmed that heat transfer performance has maximum efficiency when the cross-cut has a size of 1/2 C=b/(2 sin(α)). If a cross-cut having the optimal length within the range of 100≦Re≦400 is applied, heat transfer performance is increased by up to 22.9% and pressure loss is increased by up to 5.80%. Such heat transfer performance improvement is acquired by collision of the central portion of a flow having a relatively low temperature with the fin at the rear of the cross-cut due to flow disturbance formed by the cross-cut. On the other hand, it is confirmed that, if a cross-cut having a size of 4/5 C is applied, heat transfer performance improvement is minimal.
Hereinafter, results of cross-cut analysis in accordance with embodiment 2 and embodiment 3 will be analyzed from various points of view.
First, FIG. 14 illustrates partial Nu values when a wavy fin having no cut and the wavy fins of case 3 and case 4 are respectively divided into 10 parts in the flow direction. As a result, it may be confirmed that heat transfer at part 6, in which a cross-cut is applied to a position at the rear of a peak, is greatly increased as in embodiment 2. Further, it may be confirmed that the Nu value of part 6 of case 3 having the optimal length of a cross-cut in embodiment 3 is 3.02 times the Nu value of the wavy fin having no cut and the Nu value of part 6 of case 4 exhibiting the minimum performance improvement is 1.34 times the Nu value of the wavy fin having no cut. Further, it may be confirmed that flow disturbance influence of the cross-cut is transmitted to a position after the cross-cut at the third wave and increases heat transfer performance of parts 7 to 10. However, it may be confirmed that, as a boundary layer is formed again, flow disturbance effects are reduced and heat transfer performance improvement at part 10 is not great.
FIG. 15 is a view illustrating a velocity streamline distribution and a pressure contour line distribution under an Re of 400 in part 6 of case 3 of embodiment 3. It may be confirmed that a recirculation section is formed just at the rear of the cross-cut and positive and negative pressure regions are formed due to oblique impinging. In general, if a recirculation section is formed, heat transfer performance of the corresponding section is lowered. However, it is judged, as a result of flow disturbance in sections except for the corresponding section, heat transfer performance is greatly improved and offsets influence of the recirculation section.
Nest, j/f values of the wavy fin having no cut and the wavy fin of case 3 of embodiment 3 within the range of 100≦Re≦400 are calculated and compared, and FIG. 16 illustrates a result of comparison of these values. Here, water is set as an operating fluid. Consequently, after application of cross-cuts, a j/f value is increased by 3.02% at an Re of 100, a j/f value is increased by 6.28% at an Re of 200, a j/f value is increased by 7.91% at an Re of 300, and a j/f value is increased by 8.60% at an Re of 400. This result may confirm that, if cross-cuts are applied, improvement of heat transfer performance is greater than increase of pressure loss and the cross-cuts are effective in a wavy fin-type heat exchanger. Further, it may be confirmed that, as an Re value increases, increase of j/f is high and, thus, as a flow becomes rapid, effects are increased.
Finally, in analysis of case 3 at an Re of 400, usefulness ε is calculated and compared to a result of Nu analysis. Usefulness ε is calculated by Equation 4 below and water is set as an operating fluid. A difference between T_wand T_inis calculated as 10° C. in the same manner as in validation. The usefulness equation refers to that given in Heat Transfer: A Practical Approach [23] of Yunus A. Cengel.
$\begin{matrix} ɛ = \frac{Q_{w}}{\dot{m} c_{p} (T_{w} - T_{in})} & [Equation 4] \end{matrix}$
FIG. 17 illustrates comparison results of usefulness ε and Nu. The Nu value of case 2 (2/5 C) and the Nu value of case 3 (1/2 C) are similar, with only a small difference of 0.05% therebetween, but the ε value of case 2 (2/5 C) is greater than the ε value of case 3 (1/2 C) by 0.38%. Further, as a cut length increases, a difference between ε and Nu values increases. Such a difference is generated because the ε value means a total heat transfer amount but the Nu value means a heat transfer amount per unit area, i.e., a heat flux. If the cross-cut technique is applied to wavy fins, the cross-cut technique raises heat transfer performance per unit area but reduces a heat transfer area. Since the heat transfer performances per unit area of case 2 and case 3 are not greatly different but the heat transfer area of case 2 is greater than the heat transfer area of case 3, the total heat transfer amount of case 2 is greater than the total heat transfer amount of case 3. It may be understood that, owing to the influence of the heat transfer area, as a cut length increases, a difference between ε and Nu values increases.
As described above, if cross-cuts having the optimal length are applied to the optimal position, a generated flow and heat transfer characteristics are confirmed. As a result of calculation of partial Nu values in the flow direction, it is confirmed that heat transfer performance at the cross-cut application position is increased up to 3.02 times, and influence of flow disturbance due to the cross-cut is transmitted to a position after the third wave and thus, heat transfer performance at the fin at the rear of the cut is also improved. In terms of characteristics of formation of a flow, if cross-cuts are applied, a recirculation section is generated at a position just at the rear of the cut and thus heat transfer performance of the corresponding section is relatively low, but flow disturbance in sections except for the corresponding section is active and thus heat transfer performance is improved. Further, it may be confirmed through j/f values that improvement of heat transfer performance is greater than increase of pressure and application of cross-cuts is effective. Finally, the total heat transfer amount and heat transfer performance per unit area are compared by comparing usefulness c and Nu values. As a result, it may be confirmed that the optimal cut length is 2/5 C in terms of the total heat transfer amount, and the optimal cut length is 1/2 C in terms of heat transfer performance per unit area.
As apparent from the above description, the presently described embodiments provide a wavy fin structure in which a cross-cut having a designated length is formed at a designated position of a wavy fin and thus generates flow disturbance due to a wavy-type dynamic flow so as to greatly improve heat transfer performance.
Although the preferred embodiments have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the disclosure as recited in the accompanying claims.

Claims

What is claimed is:

1. A wavy fin structure in which fins are periodically arranged in a plurality of rows and each fin is periodically waved to form repeated valleys and peaks in the length direction of the fin,

wherein a cross-cut having a designated length is formed around at least one valley or peak of the fin.

2. The wavy fin structure according to claim 1, wherein the cross-cut is formed at a valley or a peak of the central portion of the fin in the length direction of the fin.

3. The wavy fin structure according to claim 2, wherein the cross-cut is formed at a position at the rear of the peak.

4. The wavy fin structure according to claim 3, wherein the length of the cross-cut is

\frac{1}{5} C to \frac{4}{5} C,

wherein C is

\frac{b}{2 \sin (α)},

α is a warpage angle of the fin, and b is a fin pitch.

5. The wavy fin structure according to claim 1, wherein a plurality of cross-cuts is formed at designated periods in the length direction of the fin.

6. The wavy fin structure according to claim 5, wherein the cross-cuts are formed at positions at the rear of peaks.

7. The wavy fin structure according to claim 6, wherein the length of the cross-cuts is

\frac{1}{5} C to \frac{4}{5} C,

wherein C is

\frac{b}{2 \sin (α)},

α is a warpage angle of the fin, and b is a fin pitch.

8. The wavy fin structure according to claim 1, wherein the wall of the fin connecting the valleys and the peaks has a planar surface structure.

9. A flat tube heat exchanger having the wavy fin structure according to claim 1.

10. A flat tube heat exchanger having the wavy fin structure according to claim 2.