1、4730 Numerical Study of the Similarity Law for the Cross-Flow Fan of a Split-Type Air Conditioner Yang-Cheng Shih, Ph.D. Member ASHRAE ABSTRACT Hung-Chi Hou Hsucheng Chiang, Ph.D. Member ASHRAE Cross-flow fans (CFF) have been used in many industrial applications. The split-type air conditioner is on
2、e of them. Up to date, no complete similarity laws of CFFs were available for designing split-type air conditioners. This paper adopted the CFD method to simulate the internalflowfields of a split-type air conditioner The efect of the rotational speed on the simi- larity law for CFF inside the air c
3、onditioner was investigated, and the factors injluencing the movement and the strength of eccentric vortex were addressed. From the numerical results, a linear relation of similarity law between the total pressure of the center of eccentric vortex and the rotational speed of CFF was concluded. Moreo
4、ver, the impact of the existence of evap- orator and air-return grille on the newly derived similarity law was also examined. INTRODUCTION With the rapid development of modern scientific technol- ogy and the progress in the standard of living, the demands of domestic high-performance air conditioner
5、s increase rapidly. A high-quality air conditioner not only needs to consider the factors of good outlook, low noise, and reasonable price, but it also needs to meet the requirements of creating comfortable and healthy environments. In Taiwan, window-type and split- type air conditioners are two of
6、the most popular domestic air conditioners. Owing to the merits of low noise, compact size, easy installation, and high cooling capacity, etc., the split-type air conditioner has gradually replaced the window-type air conditioner to become the mainstream in the market of domes- tic electrical produc
7、ts. Unlike axial and centrifugal fans, there are still no universal theories to design the cross-flow fan (CFF) inside the split-type air conditioner, mainly because of the complex internal flow fields resulting from the eccentric vortex generated inside the CFF. To promote the design tech- nology o
8、f CFF, a numerical method will be used to study the internal flow fields of the split-type air conditioner in this paper, and the simulated results will be incorporated into the similarity law of CFF. Figure 1 shows the internal construction of a conventional split-ype air conditioner. It is mainly
9、made of four parts: rotor (i.e., CFF), rear wall, tongue, and evaporator. According to previous studies (Eck 1952; Mazur 1984; Murta andNishihara Figure 1 Internal construction of a conventional split-type air conditionev. Yang-Cheng Shih is an assistant professor and Hung-Chi Hou is a graduate stud
10、ent in the Department of Air-conditioning and Refrigerating Engineering, National Taipei University of Technology, Taiwan, ROC. Hsucheng Chiang is a researcher at Energy Takushima et al. 1990; Murta and Tanaka 1994, 1995; Tsuruski et al. 1997; Lazzarotto et al. 2001). Understanding the development o
11、f internal flow of CFF is helpful in improv- ing the CFF performance. As shown in Figure 2a, when a CFF rotates alone, there is a vortex forming inside the center of the CFF, and the flow field is almost symmetrical. If a rear wall is added, as displayed in Figure 2b, the vortex is pushed away from
12、the rear wall, and the flow field becomes asymmetrical. When a tongue is put near the CFF, as shown in Figure 2c, the vortex moves toward the tongue, and it is usually called “eccentric vortex“; as a result, the internal flow of CFF is divided into two regions: eccentric vortex flow and transverse f
13、low, as depicted in Figure 1. The center of the eccentric vortex has the lowest static pressure (negative pressure) within the whole flow field and is almost stagnant. It functions like a sink to induce the outer flow to move toward it and pass around it, resulting in the so-called transverse flow.
14、Hence, the air- supplying performance of the split-type air conditioner essen- tially depends on the control of the position and the total pres- sure of the center of eccentric vortex. Usually, the closer to the tongue the center of the eccentric vortex is and the lower its total pressure, the bette
15、r the air-supplying performance for the air conditioner. Current literature of studies for CFFs was limited, and most belonged to pattern documents. Because the fan perfor- mance depended upon several complicated parameters, the designers usually used trial-and-error methods to find the opti- mal de
16、sign of CFF. Until now, there were no complete theories to predict the internal flow fields of CFF successfully. To investigate the internal flow fields of CFF, many researchers used the methods of flow visualization and adopted pitot tubes to observe the position and to measure the total pressure o
17、f the center of the eccentric vortex, respectively. They believed that the performance of CFFs depended primarily upon the posi- tion and the total pressure of the vortex center. Matsuki et al. (1988) designed a three-dimensional movable platform for installing a cylindrical pitot tube and inserted
18、it into the inter- nal air conditioner to measure the pressure distribution around the rotor and to estimate the position of the vortex center. Moreover, they converted the measured pressure field into the velocity field. In their studies, they investigated various parameters, including the gap betw
19、een CFF and tongue, tongue shape, and inclined angles of evaporator, that influence the position and total pressure of the vortex center in order to find the optimal rules to design the air conditioner. Because inserting apitot tube into a CFF could destroy the internal flow structure, Takushima et
20、al. (1990) used laser Doppler veloci- meter (LDV) to measure both the velocity and turbulence data inside the air conditioner. Their study focused on the effect of the position of tongue, the gap between tongue and impeller, and the shape of the suction region on the variation of internal flow field
21、s and vortex movement. To avoid destroying the internal flow structure, the optical technique seems to be a better choice. Recently, Tsurusaki et al. (1997) utilized parti- cle-tracking velocimetry (PTV) to observe the internal flow of CFF. Instead of using air, they adopted water as working fluid b
22、ecause water is easy to observe by means of flow visualiza- tion. The most serious criticism for the design of CFF is that there are no universal laws to follow. To find the universal form for CFF performance, Murta and Tanaka (1995) measured both internal velocity and pressure distributions of seve
23、ral CFFs with geometrical similarity but different dimensions. By analyzing the measured data, they proposed a universal form of CFF performance based upon the relation of the reduced flow coefficient and the reduced total pressure rise coefficient. Lazzarotto et al. (2001) tested the performance of
24、 five impel- lers with similar shape but different dimensions operating at various rotational speeds. They found that there existed simi- larity laws for the CFF Performance when the operating Reynolds number was above the critical Reynolds number, ranging from 4,000 to 15,000, depending upon geomet
25、rical characteristics of the casing. From the literature review, it is found that most previous studies adopted experimental methods to investigate CFF performance, and finding the similarity laws for CFF perfor- mance was one of the most important issues for the designers in this field. However, ex
26、perimental measurement is a time- consuming work and there is a lot of cost in building the exper- imental apparatus. Therefore, the technology of airflow simu- lation by using computers becomes one of the most cost- effective methods. In the past, a few numerical studies (Fukano et al. 1995; Bert e
27、t al. 1996; Moon et al. 2003) on predicting the internal flow fields of CFF have been performed successfully. In this paper, the CFD (computational fluid dynamics) method will be utilized to simulate the intemal flow ASHRAE Transactions: Research 379 fields of CFF, and the objective is to find the s
28、imilarity law of a CFF within a split-type air conditioner operating at different rotational speeds. Moreover, the effect of the existence of both air-return grille and evaporator on the similarity law will be examined. NUMERICAL METHODOLOGY In this study, the CFD software FLUENT (1998) was utilized
29、 to simulate the internal airflow distribution of the split-type air conditioner. The numerical model is based upon the finite volume method. The governing equations, including continuity, momentum, and turbulence equations, obey the principle of conservation and can be expressed in the follow- ing
30、general form: + where p is the air density, (2) where ap and anb are discretized coefficients, and b is the discretized source term. In Equation 2, subscript p represents the grid point under consideration, and nb is the neighbor of grid pointp. To account for the movement of the rotor, sliding mesh
31、es were applied to both inner and outer impeller inter- faces, which separate the rotor and the airflow regions. By employing the iterative scheme of a point implicit (Gauss-Seide1)linear equation solver in conjunction with an algebraic multigrid (AMG) method, the pressure, velocity, and turbulence
32、fields can be solved from Equation 2. During the iterative procedure, the SIMPLEC (semi-implicit method for pressure-linked equations-consistent) algorithm was employed to solve the pressure-velocity coupling equations. Regarding the boundary conditions, no-slip condition was used at the wall, such
33、as for the blades of the impeller, and the standard wall functions were adopted to link the solution variables at the near-wall cells and the corresponding quanti- ties near the wall. Moreover, turbulence kinetic energy k and turbulence kinetic energy dissipation rate E employed in the airflow inlet
34、 were calculated by the following equations: 3 *_ ;k2 E=C- I”I (3) (4) I = 0.070, (5) where uaVg is the mean flow velocity, I is turbulence intensity, Dh is hydraulic diameter of inlet, and C,= 0.09. RESULTS AND DISCUSSION In this paper, the sample split-type air conditioner, as shown in Figure 3a,
35、was adopted as a simulated sample. The CFF specifications are listed in Table 2. Figure 3b shows the grid system under consideration. Two-dimensional geometry was assumed for the numerical simulation, and the whole domain was chosen as a semicircle area, with its diameter 20 Table 1. Terms, Coeficie
36、nts, and Constants Used in Equation 1 p wff % Momentum V bff -VP Equation Continuity 1 O O + Turbulence kinetic energy k as a result, the grid-independence study of this case was verified. Therefore, the grid number of 48 179 was utilized in this study in general. Figure 6 shows both velocity field
37、and total pressure distribution predicted by FLUENT. It can be seen that the eccentric vortex was close to the position of the tongue. To estimate the vortex center, its position was measuring from the x-axis, as shown in Figure 7. For this case, the position of the vortex center was approxi- mately
38、 at 8 = 242“. In addition, the vortex center was observed to have the lowest total pressure and to be almost stagnant. 382 ASHRAE Transactions: Research The Effect of Rotational Speed on CFF Performance According to the paper of Lazzarotto et al. (2000), it was 2nN Di ut = -.- 60 2 (7) known that mo
39、st practical of CFF Operated at the where Q is the volume flow rate, L is the impeller axial length, condition Offlow Coefficient equal to 0.2-0.3. The flow Cod- ficient is defined as follows: D, is the diameter ofimpeller, andNis the rotational speed. The value of flow coefficient was decided by gi
40、ving different volume flow rates at the velocity inlet and various rotational speeds of CFF. If the flow coefficient is too low, such as equal to O. 1, an unstable flow condition occurs and the ($22- LDl Ut (6) 8.8 - - 8 8.6 - 3 j- j 8.4 - 3 - 82 - - Y t X 6=180 _ 0=270i I 4(1000 8Cl 12om 1mmo 81a I
41、 ciri however, the absolute value of the total pressure of vortex center increased, representing the intensification of the vortex strength. In fact, in analyzing the vortex movement, should be considered, two factors, including the inertial force resulting from the rotation of the impeller and the
42、system resistance, composed of the combining effect of CFF, internal flow duct, evaporator and air-return grille, etc. At constant flow Coefficients, as displayed in the 20 - 18 - - 16 - 14 - - 12- e- - ; 10- ; 8- E- 8- - 4- - 2- - 2 4 6 8 10 12 14 16 FirnRate (W) Figure8 The effect of rotational sp
43、eeds on CFF performance. 384 ASHRAE Transactions: Research Ok, , , , , , a, , , , , , , , , , , , ,3 Figure 9 The predicted distribution of total pressure near the inner circle of rotov. dashed lines of Figure 8, the total pressure rise grew with the increase of rotational speeds, which indicated th
44、at the increase of inertial force was accompanied with the rise of system resistance. When both terms were balanced, the position of the eccentric vortex center stayed at the appropriate position near the tongue. If the inerial term overcame the system resistance, the vortex center can move closer t
45、o the tongue. Otherwise, it will be at the position far away from the tongue-even worse, the unstable oscillating movement of vortex could occur. Therefore, by checking the results of constant flow coeffi- cients shown in Table 4, the reason the vortex center can keep at almost the same position sho
46、uld be due to the balance of inertial force and system resistance. However, the magnitude of the total pressure of vortex center was raised with the increase of the rotational speed at constant flow coefficients; as a result, the lower the total pressure of the vortex center was, the larger the volu
47、me flow rate was. Figures 9a to 9e display the effect of various rotational speeds on the total pres- sure distributions near the inner circle of the rotor. Those results confirmed that the strength of the eccentric vortex was enhanced with the increase of the speeds of rotation as the flow coeffici
48、ent remained constant. From Figure 8, it can be found that at constant rotational speeds, the total pressure rise decreased as volume flow rates were raised, which revealed that the excess of inertial force over system resistance became larger as the flow coefficient increased, resulting in the move
49、ment of the vortex center closer to the tongue, as shown in Table 4. Moreover, it is known that the strength of the vortex center intensified with the rise of volume flow rate at constant rotational speeds. Similarity Law Between the Total Pressure of Eccentric Vortex Center and the Rotational Speed of CFF According to previous discussions, it is known that the total pressure of the eccentric vortex center had very important impact on CFF performance and it had close relation with the rotational speed of CFF. From the dimensional analysis, it is known that pressure is proportion
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