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Effect of the rectangular exit-port geometry of a distribution manifold on the flow performance
Applied Thermal Engineering 117 (2017) 481–486
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Effect of the rectangular exit-port geometry of a distribution manifold on the flow performance Honggang Yang a,b, Yi Wang a,⇑, Meitao Ren a, Xiaoni Yang a,c a
School of Environmental and Municipal Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, PR China College of Materials and Mineral Resources, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, PR China c Huaqing College, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710043, PR China b
h i g h l i g h t s Effect of the inlet Reynolds number on the flow distribution uniformity was studied. Effect of the aspect ratio (AR) of the rectangle exit-port on the flow distribution uniformity was studied. The flow pressure drop of the distribution manifold was investigated. Design variables that affect the flow performance were suggested.
a r t i c l e
i n f o
Article history: Received 24 November 2016 Revised 9 February 2017 Accepted 11 February 2017 Available online 14 February 2017 Keywords: Computational fluid dynamics Distribution manifold Aspect ratio Flow distribution Pressure drops
a b s t r a c t Flow distribution performance of the distribution manifold is the most important index to evaluate its design rationality. To date, many published literatures have extensively investigated the effect of the manifold geometry on its flow distribution performance; however, there is no related study regarding the effect of the aspect ratio (AR) of the rectangle exit-port. In this paper, the effect of the AR on the flow distribution performance in the turbulent-flow regime is numerically simulated and analyzed. The research results are as follows: (i) With constant AR, the variation of the inlet Reynolds number (Re, 1.0 105–1.0 106) has little effect on the flow distribution uniformity in the obvious turbulent-flow regime. (ii) With a constant inlet Reynolds number, the corresponding uniformity coefficient decreases from 89.81% to 82.60% when the AR increases from 0.2 to 4.0, which indicates that the flow distribution becomes less uniform with the increase in AR. (iii) With the same inlet Reynolds number, the flow pressure drop of the distribution manifold maintains a decelerated increasing trend with increased AR, which becomes stable after the AR reaches 2.0. The research results can provide a reference for the geometrical optimization of distribution manifolds. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Distribution manifolds are widely used in industry applications, such as perforated ventilation ducts, [1–3], various micro-channel devices [4–8], heat exchangers [9–12], and flow distribution systems. In these engineering applications, a uniform flow distribution requirement is critical because it significantly affects the performance of a distribution manifold. Therefore, for most applications, the goal of distribution manifold design is to achieve a uniform flow distribution through all exit-ports. Many factors affect the flow distribution uniformity of the manifold, such as the manifold structure, hole spacing, manifold length, aperture ratio (which ⇑ Corresponding author. E-mail address: [email protected] (Y. Wang). http://dx.doi.org/10.1016/j.applthermaleng.2017.02.046 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
is defined as the ratio of the total discharge area to the crosssectional area of the manifold), Re, and roughness. Among these factors, Reynolds number is related to the operating conditions, and the roughness of the distribution manifold is related to the material. The remaining factors are related to the geometrical structure of the manifold. Many researchers have experimentally, analytically and numerically studied the effect of the manifold geometry on the flow distribution uniformity. Jimmy C.K. Tong et al. [13] studied the effect of the cross-sectional geometry of the distribution manifold on the uniformity of the flow distribution in a laminar-flow regime. They obtained the geometry of the distribution manifold in favor of uniformity, which is to increase the sectional area of the distribution manifolds or use the tapered distribution manifold. The results of the study also show that the flow distribution uniformity of the
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Nomenclature AR L n a b l W H Re
aspect ratio of the rectangle (b/a) Total length of manifold (m) numbers of exit-ports length of each rectangle exit-port (m) width of each rectangle exit-port (m) exit-port spacing (m) width of manifold cross-section (m) height of manifold cross-section (m) Reynolds number
distribution manifold significantly increases with increasing flow Reynolds number regardless of the geometric configuration. Hassan et al. [14] conducted a comparative study of the uniformity of the flow distribution of the longitudinal and cross-sectional distribution manifolds in the turbulent-flow regime using experimental and numerical simulations. These researchers show that (Re > 10 104) has no effect on the uniformity of the flow distribution, and the cross-sectional distribution manifolds have better distribution uniformity than the longitudinal distribution manifolds. Cloud and Morey [15] find that the hole spacing has an effect on the uniformity. Air follows the path of least resistance. The path of least resistance in ventilation ducts is the straight section from the beginning to the end of the duct. In rough-wall ducts, there is generally more open area near the front of the duct than the distal end to obtain a uniform distribution. Carpenter [16] tested 3 m, 5 m, 10 m, 20 m, and 90 m polyethylene perforated ducts and found that the duct length of 20 m and less had similar performance. The discharge of air steadily increased from the entrance to the distal end. The 90 m duct discharged more uniformly over its entire length because of the increased friction loss in longer ducts. Lee et al. [17] numerically investigated the effects of the blockage ratio via the changes in number of orifices on the flow distribution performance in a multi-perforated tubes. Their result indicates that a larger increase in blockage ratio of multiperforated tubes corresponds to a more uniform flow distribution among the orifices. The effect of the exit-port geometry of distribution manifolds on the flow distribution performance is clearly of practical relevance but appears rarely investigated in the published literature. An in-depth literature search shows only one reference that attempted to investigate the effect of the shape of the exit-ports on the flow distribution uniformity. In that paper, Chen and Sparrow [18] investigated the effect of three candidate exit-port geometries on the flow distribution characteristics of manifolds using a numerical simulation method. The numerical results indicate that the single continuous slot provides the optimal flow distribution with end-to-end mass flow variations of less than ±5%, the discrete array of rectangular orifices provides a uniformity of ±10%, and the discrete circular orifices provide a uniformity of ±15%. However, in practical engineering, in many cases, the design of exit-ports of the single continuous slot is not permitted. It is currently common to design the exit-ports of distribution manifolds as discrete rectangles. To date, the effect of the AR of rectangular exit-port on the flow distribution uniformity has not been studied. The literature review shows that previous studies on the flow characteristics of distribution manifolds mainly used the experimental method, and a recent study used the numerical simulation technology. Numerical simulation using computational fluid dynamics is the current method of choice to solve the flow distribution uniformity problem of distribution manifolds, which can be found in the published literature [4,13,14,17–20]. Chen and Sparrow [20] used the synergistic combination method of numerical
Q x Qaver Qi
p
volumetric flow (m3/s) distance from the entrance of manifold in the x-axis direction (m) averaged volumetric flow through all exit-ports (m3/s) volumetric flow through the ith exit-port (m3/s) uniformity coefficient, defined by Eq. (1)
simulation and laboratory experiments to investigate three turbulence models, which can be used in the distribution manifolds flow. The numerical predictions obtained from the application of these models were compared with the experimental results, and the realizable k-e model was found to provide the best representation of the data. Thus, this study investigates the effect of the changes in AR of exit-ports and inlet Reynolds number on the flow distribution performance using numerical simulation. The effect of the pressure drop was also investigated; ultimately, design variables that affect the flow distribution were pursued.
2. Geometric issues In this study, the studied distribution manifold is the airflow distribution channel of the large bag filter. For the airflow distribution channel into a large fabric bag house, uniform gas distribution and low pressure drop are desired, ensuring each individual bag house to receive gas flow from specific exit-port. The shape of the distribution manifolds for the work is illustrated in Fig. 1. Fig. 1 consists of a schematic of the distribution manifold and definitions of the geometric parameter. The longitudinal direction of the distribution manifold was set as an axial direction (flow direction, x axis direction). The end of the distribution manifold is blocked, and the interval between the starting and ending points is L. For the distribution manifold, the rectangular exit-ports were installed on the side of the rectangular distribution manifold with an AR of 0.86. The aperture ratio of the distribution manifolds was 1.0. The aperture ratio is defined as the ratio of the total discharge area to the cross-sectional area of the manifold. Here, the number of exit-ports was determined to be 10 (n = 10). The changes in AR of the rectangular exit-ports and other required data are shown in Table 1. As pointed by Chen and Sparrow [18] single slot with AR of 0.19 presented the best flow performance. However, since in our channel to the bag house, discrete exit-port must be adopted. Therefore, we chose AR = 0.2 as the lower limit of experimental conditions, to determine the flow uniformity and pressure drop, because it is quite close to 0.19.
3. Analysis methods 3.1. Numerical model A CFD model with the identical geometry and dimensions as the scaled distribution manifold model was created using the software Fluent (version 6.3.26) [21]. The solver used the finite-volume method and second-order upwind scheme. The SIMPLE algorithm, which was proposed by Patankar and Spalding [22], was used to achieve the pressure-velocity coupling.
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Detail of A a H b
z x
y o
L l
z o
x 1
A
2
n
Fig. 1. Schematics of the distribution manifolds and definitions of the geometric parameter.
Table 1 Analysis conditions. Case
a (m)
b (m)
AR
Aperture ratio
n
l (m)
W (m)
H (m)
L (m)
1 2 3 4 5 6 7
2.773 2.479 1.753 1.239 0.876 0.716 0.620
0.554 0.620 0.876 1.239 1.753 2.147 2.479
0.2 0.25 0.5 1.0 2.0 3.0 4.0
1
10
2.84
4.22
3.64
31.24
The effects of turbulence were frequently modeled using twoequation models: the standard k-e model [23], RNG k-e model [24] and realizable k-e model [25]. The realizable k-e model was used to simulate the distribution manifold flow because it was recommended in previous studies and demonstrated better simulations [20]. A non-slip condition was imposed on all wall boundaries.
3.3. Mesh sensitivity The mesh independence was investigated using meshes of 107,000, 226,000 and 907,000 cells. Fig. 2 shows the average veloc-
3.2. Boundary condition The analysis to investigate the flow distribution uniformity of the distribution manifolds was performed according to the changes in inlet Reynolds number, as shown in Table 2, with respect to the geometrical conditions in Table 1. The air density of a working fluid of 1.225 kg/m3 and a viscosity coefficient of 1.7894 105 kg/ms, were applied.
Table 2 Inlet boundary conditions. Number
Re (105)
Inlet velocity (m/s)
Q (m3/s)
1 2 3 4 5
1 2 4 8 10
1.49 2.99 5.98 11.96 14.95
22.96 45.93 91.85 183.70 229.63
Fig. 2. Variation of velocity for different meshes.
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ity of each exit-port from the mesh sensitivity study. The velocity profile shows a difference among all meshes, which indicates that the velocity is not sensitive to the mesh. This paper selects the number of grids to be 907,000 in the follow-up simulation study. 4. Results and discussion 4.1. Effect of the inlet Reynolds number on the flow distribution uniformity Fig. 3 illustrates the volumetric flow through each exit-port when the inlet Reynolds number changed from 1 105 to 1 106 at AR = 0.25. x/L = 0 on the graph represents to the inlet of a distribution manifold, and x/L = 1 represents its end. At the same inlet Reynolds number, the flow distribution between exitports increases with the longitudinal direction of the manifold. The flow through each exit-port increases with the increase in inlet Reynolds number. However, it is difficult to obtain the uniformity of the flow distribution in a manifold with different Reynolds number. To achieve a dimensionless form, each exit-port volume flow was normalized by the average volume flow through all exitports. The results are shown in Fig. 4. Q/Qaver in the graph represents the relative ratio of the volume flow to the average volumetric flow of the actual outflow through each exit-port. When Q/ Qaver = 1.0, the distribution manifold achieves a completely uniform distribution. The flow distribution between exit-ports in the longitudinal direction of the distribution manifold exhibits almost no change with the change in inlet Reynolds number. Hence, the inlet Reynolds number has little effect on the flow distribution of the manifold. To quantify the difference in flow distribution in the manifold, the flow distribution uniformity is determined according to the formula given by Davis et al. [26]. They defined the flow uniformity as the ratio of the change in flow from the single exit-port to the average flow. The parameter to determine the flow uniformity is the uniformity coefficient p, which is defined as:
p¼ 1
Pn
i¼1 jQ av er
Q ij
nQ av er
100
ð1Þ
where p is the coefficient of uniformity, Qaver is the average volumetric flow, Qi is the volumetric flow through the ith exit-port, and n is the number of exit-ports. The results are shown in Table 3.
Fig. 3. Volumetric flow through each exit-port when the inlet Reynolds number changed from 1 105 to 1 106 at AR = 0.25.
Fig. 4. Volumetric flow distribution along the manifold with respect to the inlet Reynolds number at AR = 0.25.
Table 3 Coefficient of uniformity for different values of inlet Re. AR
Re (105)
Inlet volumetric flow (m3/s)
Uniformity (%)
0.25
1 2 4 8 10
22.96 45.93 91.85 183.70 229.63
89.98 89.88 89.79 89.72 89.48
The results in Table 3 show that the distribution uniformity coefficient values of the distribution manifold at different inlet Reynolds numbers slightly differ. With the increase in inlet Reynolds number, the uniformity coefficient slightly decreases, but the magnitude of this decrease is notably small, and the variance of the coefficient of uniformity is 0.0358, which further shows the result in Fig. 3. The inlet Re has almost no effect on the flow distribution of the manifold. 4.2. Effect of the AR on the flow distribution uniformity Fig. 5 illustrates the flow distribution between exit-ports when the AR changed from 0.25 to 4.0 at Re = 8 105. The flow distribu-
Fig. 5. Volumetric flow distribution along the manifold with respect to the AR at Re = 8 105.
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tion between exit-ports exhibits an obvious difference in flow distribution between the entrance of the manifolds and the end. When AR = 0.25, the difference in flow distribution is the smallest; with the increase in AR, the difference also increases. To quantitatively analyze this flow distribution difference, we approximated the linear fitting of the flow distribution curves in Fig. 5 and obtained the linear slope values with the change in AR, as shown in Fig. 6. Fig. 6 displays the gradient of flow distribution with the AR. The inlet Reynolds number was maintained at 8 105. A larger increase in AR corresponds to a larger slope increase in the investigated inlet Reynolds number. It is worth emphasizing that a lower slope value corresponds to a more uniform flow distribution. This result implies a growing uniformity of the flow distribution between exit-ports as a consequence of a decrease in AR of the exit-ports. To obtain a quantitative result for the uniformity of the flow distribution in the distribution manifold, the uniformity coefficient for different ARs is calculated using the David flow uniformity calculation formula. Table 4 shows the uniformity coefficient of the distribution manifold for different ARs. The results show that the flow uniformity decreases with increasing AR. It is particularly noted that as the AR is less than 0.25, the change in flow uniformity is very minor as the AR decreases.
Fig. 7. Static pressure distribution along the centerline at AR = 0.25 and Re = 1 105.
AR=0.25 AR=0.5
4.3. Static pressure distribution
AR=1.0
Fig. 7 displays the static pressure distribution on the centerline of the distribution manifolds at AR = 0.25 and Re = 8 105. The static pressure increases with decreasing distance to the end of the manifolds, and a large pressure change occurs as a result of the loss
AR=2.0 AR=3.0 AR=4.0 Fig. 8. Static pressure contours on the inner side of the exit-ports of the distribution manifolds at Re = 8 105.
of momentum because the working fluid leaks among the rectangular exit-ports. Fig. 8 displays static pressure contours on the inner side of the exit-ports of the distribution manifolds. For rectangular exit-ports of different ARs, the static pressure distribution contours appear similar. However, the static pressure contours of different ARs show that a larger AR corresponds to a larger static pressure. When AR = 0.25, the static pressure is minimum, and the static pressure distribution on the inner side of the exit-ports of distribution manifolds increases with the increase in AR.
Fig. 6. Gradient of flow distribution with respect to the AR.
Table 4 Coefficient of uniformity for different ARs. Re (105)
AR
Uniformity (%)
8
0.2 0.25 0.5 1.0 2.0 3.0 4.0
89.81 89.72 88.51 86.58 85.19 83.45 82.60
4.4. Pressure drops Fig. 9 displays the variation of pressure drop according to the AR with respect to multiple inlet Reynolds numbers. When the inlet Reynolds number increases, the pressure drop tends to increase as expected because of the increase in flow velocity in the distribution manifold. For rectangular exit-ports of different ARs, the changes in the pressure drop curves with the inlet Reynolds number appear similar. When the inlet Reynolds number is constant, the pressure drop of the distribution manifold shows an increase in deceleration with the increase in AR. After AR = 2.0, the pressure drop does not significantly increase. It is important to note that when the aspect ratio is less than 0.25, the variation of the flow pressure drop is very minor as the AR decreases.
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To summarize, when the aspect ratio is equal to 0.25, the flow performance of the manifold is very close to the best performance when AR = 0.2. Therefore, 0.25 is the AR of the rectangular exitport recommended to apply in practice. This result can be useful for exit-ports geometry design of the distribution manifolds. Acknowledgments This research project is sponsored by the National Science Funds for Distinguished Young Scholar (Grant No. 51425803) and the Natural Science Foundation of China (Grant No. 51238010). References
Fig. 9. Variation of the pressure drop with the Reynolds number for different ARs.
5. Conclusions This study investigated the effect of the changes in AR of the rectangular exit-ports and inlet Reynolds number on the flow distribution uniformity of distribution manifolds. Through the numerical simulation, the following conclusions were obtained. First, with the increase in inlet Reynolds number, the uniformity coefficient slightly decreases, but the magnitude of this decrease is notably small. Furthermore, the variance of the coefficient of uniformity is 0.0358, which shows that the flow distribution among rectangular exit-ports in the longitudinal direction of manifolds has almost no difference with the change in inlet Reynolds number. Second, the flow distribution between exit-ports obviously changes between the entrance of manifolds and the end. When AR = 0.2, the difference of the flow distribution is the smallest; with the increase in AR, the difference also increases. The results show that the flow uniformity worsens with increasing AR. Third, the static pressure increases with decreasing distance to the end of the manifolds, and a large pressure change occurs as a result of the loss of momentum because the working fluid leaks between rectangular exit-ports. This phenomenon can be explained as a result of the increase in axial deceleration-based pressure along the manifold, which overcomes the resistance. For rectangular exit-ports of different ARs, the static pressure distribution contours appear similar. However, the static pressure contours of different ARs show that a larger AR corresponds to a larger static pressure. Finally, when the inlet Reynolds number increases, the pressure drop tends to increase as expected because of the increase in flow velocity in the distribution manifold. For rectangular exit-ports of different ARs, the changes in the pressure drop curves with the inlet Reynolds number appear similar. When the inlet Reynolds number is constant, the pressure drop of the distribution manifold shows an increase in deceleration with the increase in AR. After AR = 2.0, the pressure drop does not significantly increase.
[1] Ian R. Mackinnon, Air Distribution from Ventilation Ducts, Macdonald College of McGill University, Quebec, March 1, 1990, pp. 12–17. [2] K.E. Moueddeb, S.F. Barrington, N. Barthakur, Perforated ventilation ducts: Part 1. A model for air flow distribution, J. Agric. Eng. Res. 68 (1997) 21–27. [3] K.E. Moueddeb, S.F. Barrington, N. Barthakur, Perforated ventilation ducts: Part 2. Validation of an air distribution model, J. Agric. Eng. Res. 68 (1997) 29–37. [4] D. Kim, C.H. Yu, S.H. Yoon, J.S. Choiet, Effects of manifold geometries on flow distribution to parallel microchannels, J. Mech. Sci. Technol. 25 (12) (2012) 3069–3074. [5] S. Balaji, S. Lakshminarayanan, Improved design of microchannel plate geometry for uniform flow distribution, Can. J. Chem. Eng. 84 (2006) 715–721. [6] R. Chein, J. Chen, Numerical study of the inlet/outlet arrangement effect on microchannel heat sink performance, Int. J. Therm. Sci. 48 (2009) 1627–1638. [7] J.M. Commenge, L. Falk, J.P. Corriou, M. Matlosz, Optimal design for flow uniformity in microchannel reactors, AIChE J. 48 (2002) 345–358. [8] M. Pan, Y. Tang, L. Pan, L. Lu, Optimal design of complex manifold geometries for uniform flow distribution between microchannels, Chem. Eng. J. 137 (2008) 339–346. [9] M.K. Bassiouny, H. Martin, Flow distribution and pressure drop in plate heat exchangers-I U-type arrangement, Chem. Eng. Sci. 39 (4) (1984) 693–700. [10] M.K. Bassiouny, H. Martin, Flow distribution and pressure drop in plate heat exchangers-II Z-type arrangement, Chem. Eng. Sci. 39 (4) (1984) 701–704. [11] C.C. Wang, K.S. Yang, J.S. Tsai, I.Y. Chen, Characteristics of flow distribution in compact parallel flow heat exchangers, Part I: Typical inlet header, Appl. Therm. Eng. 31 (16) (2011) 3226–3234. [12] C.C. Wang, K.S. Yang, J.S. Tsai, I.Y. Chen, Characteristics of flow distribution in compact parallel flow heat exchangers, Part II: Modified inlet header, Appl. Therm. Eng. 31 (16) (2011) 3235–3242. [13] J.C.K. Tong, E.M. Sparrow, J.P. Abraham, Geometric strategies for attainment of identical outflows through all of the exit-ports of a distribution manifold in a manifold system, Appl. Therm. Eng. 29 (2009) 3552–3560. [14] J.M. Hassan, T.A. Mohamed, W.S. Mohammed, W.H. Alawee, Modeling the uniformity of manifold with various configurations, J. Fluids 2014 (2014) 1–8. [15] H.A. Cloud, R.V. Morey, Distribution duct performance for through ventilation of stored potatoes, Trans. ASAE (1980) 1213–1218. [16] G.A. Carpenter, The design of permeable ducts and their application to the ventilation of livestock buildings, J. Agric. Eng. Res. 17 (1972) 219–230. [17] S. Lee, N. Moon, J. Lee, A study on the exit flow characteristics determined by the orifice configuration of multi-perforated tubes, J. Mech. Sci. Technol. 26 (2012) 2751–2758. [18] A.W. Chen, E.M. Sparrow, Effect of exit-port geometry on the performance of a flow distribution manifold, Appl. Therm. Eng. 29 (2009) 2689–2692. [19] J. Wang, H. Wang, Discrete method for design of flow distribution in manifolds, Appl. Therm. Eng. 89 (2015) 927–945. [20] A.W. Chen, E.M. Sparrow, Turbulence modeling for flow in a distribution manifold, Int. J. Heat Mass Transf. 52 (2009) 1573–1581. [21] FLUENT User’s Guide, Fluent Inc., New Hampshire, USA, 2005. [22] S.V. Patankar, D.B. Spalding, A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows, Int. J. Heat Mass Transf. 15 (1972) 1787–1806. [23] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Methods Appl. Mech. Eng. 3 (1974) 269–289. [24] V. Yakhot, S.A. Orzag, Renormalization group analysis of turbulence. I. Basic theory, J. Sci. Comput. 1 (1986) 3–51. [25] T.H. Shih, W.W. Liou, A. habbir, Z.G. Yang, J. Zh, A new k-e eddy viscosity model for high Reynolds number turbulent flows, Comput. Fluids 24 (1995) 227–238. [26] D.C. Davis, J.S. Romberger, C.A. Pettibone, S.C. Andales, Perforated corrugated duct design for air distribution systems, ASAE (1978), No. 78-4060.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Effect of the rectangular exit-port geometry of a distribution manifold on the flow performance Honggang Yang a,b, Yi Wang a,⇑, Meitao Ren a, Xiaoni Yang a,c a
School of Environmental and Municipal Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, PR China College of Materials and Mineral Resources, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, PR China c Huaqing College, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710043, PR China b
h i g h l i g h t s Effect of the inlet Reynolds number on the flow distribution uniformity was studied. Effect of the aspect ratio (AR) of the rectangle exit-port on the flow distribution uniformity was studied. The flow pressure drop of the distribution manifold was investigated. Design variables that affect the flow performance were suggested.
a r t i c l e
i n f o
Article history: Received 24 November 2016 Revised 9 February 2017 Accepted 11 February 2017 Available online 14 February 2017 Keywords: Computational fluid dynamics Distribution manifold Aspect ratio Flow distribution Pressure drops
a b s t r a c t Flow distribution performance of the distribution manifold is the most important index to evaluate its design rationality. To date, many published literatures have extensively investigated the effect of the manifold geometry on its flow distribution performance; however, there is no related study regarding the effect of the aspect ratio (AR) of the rectangle exit-port. In this paper, the effect of the AR on the flow distribution performance in the turbulent-flow regime is numerically simulated and analyzed. The research results are as follows: (i) With constant AR, the variation of the inlet Reynolds number (Re, 1.0 105–1.0 106) has little effect on the flow distribution uniformity in the obvious turbulent-flow regime. (ii) With a constant inlet Reynolds number, the corresponding uniformity coefficient decreases from 89.81% to 82.60% when the AR increases from 0.2 to 4.0, which indicates that the flow distribution becomes less uniform with the increase in AR. (iii) With the same inlet Reynolds number, the flow pressure drop of the distribution manifold maintains a decelerated increasing trend with increased AR, which becomes stable after the AR reaches 2.0. The research results can provide a reference for the geometrical optimization of distribution manifolds. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Distribution manifolds are widely used in industry applications, such as perforated ventilation ducts, [1–3], various micro-channel devices [4–8], heat exchangers [9–12], and flow distribution systems. In these engineering applications, a uniform flow distribution requirement is critical because it significantly affects the performance of a distribution manifold. Therefore, for most applications, the goal of distribution manifold design is to achieve a uniform flow distribution through all exit-ports. Many factors affect the flow distribution uniformity of the manifold, such as the manifold structure, hole spacing, manifold length, aperture ratio (which ⇑ Corresponding author. E-mail address: [email protected] (Y. Wang). http://dx.doi.org/10.1016/j.applthermaleng.2017.02.046 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
is defined as the ratio of the total discharge area to the crosssectional area of the manifold), Re, and roughness. Among these factors, Reynolds number is related to the operating conditions, and the roughness of the distribution manifold is related to the material. The remaining factors are related to the geometrical structure of the manifold. Many researchers have experimentally, analytically and numerically studied the effect of the manifold geometry on the flow distribution uniformity. Jimmy C.K. Tong et al. [13] studied the effect of the cross-sectional geometry of the distribution manifold on the uniformity of the flow distribution in a laminar-flow regime. They obtained the geometry of the distribution manifold in favor of uniformity, which is to increase the sectional area of the distribution manifolds or use the tapered distribution manifold. The results of the study also show that the flow distribution uniformity of the
482
H. Yang et al. / Applied Thermal Engineering 117 (2017) 481–486
Nomenclature AR L n a b l W H Re
aspect ratio of the rectangle (b/a) Total length of manifold (m) numbers of exit-ports length of each rectangle exit-port (m) width of each rectangle exit-port (m) exit-port spacing (m) width of manifold cross-section (m) height of manifold cross-section (m) Reynolds number
distribution manifold significantly increases with increasing flow Reynolds number regardless of the geometric configuration. Hassan et al. [14] conducted a comparative study of the uniformity of the flow distribution of the longitudinal and cross-sectional distribution manifolds in the turbulent-flow regime using experimental and numerical simulations. These researchers show that (Re > 10 104) has no effect on the uniformity of the flow distribution, and the cross-sectional distribution manifolds have better distribution uniformity than the longitudinal distribution manifolds. Cloud and Morey [15] find that the hole spacing has an effect on the uniformity. Air follows the path of least resistance. The path of least resistance in ventilation ducts is the straight section from the beginning to the end of the duct. In rough-wall ducts, there is generally more open area near the front of the duct than the distal end to obtain a uniform distribution. Carpenter [16] tested 3 m, 5 m, 10 m, 20 m, and 90 m polyethylene perforated ducts and found that the duct length of 20 m and less had similar performance. The discharge of air steadily increased from the entrance to the distal end. The 90 m duct discharged more uniformly over its entire length because of the increased friction loss in longer ducts. Lee et al. [17] numerically investigated the effects of the blockage ratio via the changes in number of orifices on the flow distribution performance in a multi-perforated tubes. Their result indicates that a larger increase in blockage ratio of multiperforated tubes corresponds to a more uniform flow distribution among the orifices. The effect of the exit-port geometry of distribution manifolds on the flow distribution performance is clearly of practical relevance but appears rarely investigated in the published literature. An in-depth literature search shows only one reference that attempted to investigate the effect of the shape of the exit-ports on the flow distribution uniformity. In that paper, Chen and Sparrow [18] investigated the effect of three candidate exit-port geometries on the flow distribution characteristics of manifolds using a numerical simulation method. The numerical results indicate that the single continuous slot provides the optimal flow distribution with end-to-end mass flow variations of less than ±5%, the discrete array of rectangular orifices provides a uniformity of ±10%, and the discrete circular orifices provide a uniformity of ±15%. However, in practical engineering, in many cases, the design of exit-ports of the single continuous slot is not permitted. It is currently common to design the exit-ports of distribution manifolds as discrete rectangles. To date, the effect of the AR of rectangular exit-port on the flow distribution uniformity has not been studied. The literature review shows that previous studies on the flow characteristics of distribution manifolds mainly used the experimental method, and a recent study used the numerical simulation technology. Numerical simulation using computational fluid dynamics is the current method of choice to solve the flow distribution uniformity problem of distribution manifolds, which can be found in the published literature [4,13,14,17–20]. Chen and Sparrow [20] used the synergistic combination method of numerical
Q x Qaver Qi
p
volumetric flow (m3/s) distance from the entrance of manifold in the x-axis direction (m) averaged volumetric flow through all exit-ports (m3/s) volumetric flow through the ith exit-port (m3/s) uniformity coefficient, defined by Eq. (1)
simulation and laboratory experiments to investigate three turbulence models, which can be used in the distribution manifolds flow. The numerical predictions obtained from the application of these models were compared with the experimental results, and the realizable k-e model was found to provide the best representation of the data. Thus, this study investigates the effect of the changes in AR of exit-ports and inlet Reynolds number on the flow distribution performance using numerical simulation. The effect of the pressure drop was also investigated; ultimately, design variables that affect the flow distribution were pursued.
2. Geometric issues In this study, the studied distribution manifold is the airflow distribution channel of the large bag filter. For the airflow distribution channel into a large fabric bag house, uniform gas distribution and low pressure drop are desired, ensuring each individual bag house to receive gas flow from specific exit-port. The shape of the distribution manifolds for the work is illustrated in Fig. 1. Fig. 1 consists of a schematic of the distribution manifold and definitions of the geometric parameter. The longitudinal direction of the distribution manifold was set as an axial direction (flow direction, x axis direction). The end of the distribution manifold is blocked, and the interval between the starting and ending points is L. For the distribution manifold, the rectangular exit-ports were installed on the side of the rectangular distribution manifold with an AR of 0.86. The aperture ratio of the distribution manifolds was 1.0. The aperture ratio is defined as the ratio of the total discharge area to the cross-sectional area of the manifold. Here, the number of exit-ports was determined to be 10 (n = 10). The changes in AR of the rectangular exit-ports and other required data are shown in Table 1. As pointed by Chen and Sparrow [18] single slot with AR of 0.19 presented the best flow performance. However, since in our channel to the bag house, discrete exit-port must be adopted. Therefore, we chose AR = 0.2 as the lower limit of experimental conditions, to determine the flow uniformity and pressure drop, because it is quite close to 0.19.
3. Analysis methods 3.1. Numerical model A CFD model with the identical geometry and dimensions as the scaled distribution manifold model was created using the software Fluent (version 6.3.26) [21]. The solver used the finite-volume method and second-order upwind scheme. The SIMPLE algorithm, which was proposed by Patankar and Spalding [22], was used to achieve the pressure-velocity coupling.
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Detail of A a H b
z x
y o
L l
z o
x 1
A
2
n
Fig. 1. Schematics of the distribution manifolds and definitions of the geometric parameter.
Table 1 Analysis conditions. Case
a (m)
b (m)
AR
Aperture ratio
n
l (m)
W (m)
H (m)
L (m)
1 2 3 4 5 6 7
2.773 2.479 1.753 1.239 0.876 0.716 0.620
0.554 0.620 0.876 1.239 1.753 2.147 2.479
0.2 0.25 0.5 1.0 2.0 3.0 4.0
1
10
2.84
4.22
3.64
31.24
The effects of turbulence were frequently modeled using twoequation models: the standard k-e model [23], RNG k-e model [24] and realizable k-e model [25]. The realizable k-e model was used to simulate the distribution manifold flow because it was recommended in previous studies and demonstrated better simulations [20]. A non-slip condition was imposed on all wall boundaries.
3.3. Mesh sensitivity The mesh independence was investigated using meshes of 107,000, 226,000 and 907,000 cells. Fig. 2 shows the average veloc-
3.2. Boundary condition The analysis to investigate the flow distribution uniformity of the distribution manifolds was performed according to the changes in inlet Reynolds number, as shown in Table 2, with respect to the geometrical conditions in Table 1. The air density of a working fluid of 1.225 kg/m3 and a viscosity coefficient of 1.7894 105 kg/ms, were applied.
Table 2 Inlet boundary conditions. Number
Re (105)
Inlet velocity (m/s)
Q (m3/s)
1 2 3 4 5
1 2 4 8 10
1.49 2.99 5.98 11.96 14.95
22.96 45.93 91.85 183.70 229.63
Fig. 2. Variation of velocity for different meshes.
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ity of each exit-port from the mesh sensitivity study. The velocity profile shows a difference among all meshes, which indicates that the velocity is not sensitive to the mesh. This paper selects the number of grids to be 907,000 in the follow-up simulation study. 4. Results and discussion 4.1. Effect of the inlet Reynolds number on the flow distribution uniformity Fig. 3 illustrates the volumetric flow through each exit-port when the inlet Reynolds number changed from 1 105 to 1 106 at AR = 0.25. x/L = 0 on the graph represents to the inlet of a distribution manifold, and x/L = 1 represents its end. At the same inlet Reynolds number, the flow distribution between exitports increases with the longitudinal direction of the manifold. The flow through each exit-port increases with the increase in inlet Reynolds number. However, it is difficult to obtain the uniformity of the flow distribution in a manifold with different Reynolds number. To achieve a dimensionless form, each exit-port volume flow was normalized by the average volume flow through all exitports. The results are shown in Fig. 4. Q/Qaver in the graph represents the relative ratio of the volume flow to the average volumetric flow of the actual outflow through each exit-port. When Q/ Qaver = 1.0, the distribution manifold achieves a completely uniform distribution. The flow distribution between exit-ports in the longitudinal direction of the distribution manifold exhibits almost no change with the change in inlet Reynolds number. Hence, the inlet Reynolds number has little effect on the flow distribution of the manifold. To quantify the difference in flow distribution in the manifold, the flow distribution uniformity is determined according to the formula given by Davis et al. [26]. They defined the flow uniformity as the ratio of the change in flow from the single exit-port to the average flow. The parameter to determine the flow uniformity is the uniformity coefficient p, which is defined as:
p¼ 1
Pn
i¼1 jQ av er
Q ij
nQ av er
100
ð1Þ
where p is the coefficient of uniformity, Qaver is the average volumetric flow, Qi is the volumetric flow through the ith exit-port, and n is the number of exit-ports. The results are shown in Table 3.
Fig. 3. Volumetric flow through each exit-port when the inlet Reynolds number changed from 1 105 to 1 106 at AR = 0.25.
Fig. 4. Volumetric flow distribution along the manifold with respect to the inlet Reynolds number at AR = 0.25.
Table 3 Coefficient of uniformity for different values of inlet Re. AR
Re (105)
Inlet volumetric flow (m3/s)
Uniformity (%)
0.25
1 2 4 8 10
22.96 45.93 91.85 183.70 229.63
89.98 89.88 89.79 89.72 89.48
The results in Table 3 show that the distribution uniformity coefficient values of the distribution manifold at different inlet Reynolds numbers slightly differ. With the increase in inlet Reynolds number, the uniformity coefficient slightly decreases, but the magnitude of this decrease is notably small, and the variance of the coefficient of uniformity is 0.0358, which further shows the result in Fig. 3. The inlet Re has almost no effect on the flow distribution of the manifold. 4.2. Effect of the AR on the flow distribution uniformity Fig. 5 illustrates the flow distribution between exit-ports when the AR changed from 0.25 to 4.0 at Re = 8 105. The flow distribu-
Fig. 5. Volumetric flow distribution along the manifold with respect to the AR at Re = 8 105.
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tion between exit-ports exhibits an obvious difference in flow distribution between the entrance of the manifolds and the end. When AR = 0.25, the difference in flow distribution is the smallest; with the increase in AR, the difference also increases. To quantitatively analyze this flow distribution difference, we approximated the linear fitting of the flow distribution curves in Fig. 5 and obtained the linear slope values with the change in AR, as shown in Fig. 6. Fig. 6 displays the gradient of flow distribution with the AR. The inlet Reynolds number was maintained at 8 105. A larger increase in AR corresponds to a larger slope increase in the investigated inlet Reynolds number. It is worth emphasizing that a lower slope value corresponds to a more uniform flow distribution. This result implies a growing uniformity of the flow distribution between exit-ports as a consequence of a decrease in AR of the exit-ports. To obtain a quantitative result for the uniformity of the flow distribution in the distribution manifold, the uniformity coefficient for different ARs is calculated using the David flow uniformity calculation formula. Table 4 shows the uniformity coefficient of the distribution manifold for different ARs. The results show that the flow uniformity decreases with increasing AR. It is particularly noted that as the AR is less than 0.25, the change in flow uniformity is very minor as the AR decreases.
Fig. 7. Static pressure distribution along the centerline at AR = 0.25 and Re = 1 105.
AR=0.25 AR=0.5
4.3. Static pressure distribution
AR=1.0
Fig. 7 displays the static pressure distribution on the centerline of the distribution manifolds at AR = 0.25 and Re = 8 105. The static pressure increases with decreasing distance to the end of the manifolds, and a large pressure change occurs as a result of the loss
AR=2.0 AR=3.0 AR=4.0 Fig. 8. Static pressure contours on the inner side of the exit-ports of the distribution manifolds at Re = 8 105.
of momentum because the working fluid leaks among the rectangular exit-ports. Fig. 8 displays static pressure contours on the inner side of the exit-ports of the distribution manifolds. For rectangular exit-ports of different ARs, the static pressure distribution contours appear similar. However, the static pressure contours of different ARs show that a larger AR corresponds to a larger static pressure. When AR = 0.25, the static pressure is minimum, and the static pressure distribution on the inner side of the exit-ports of distribution manifolds increases with the increase in AR.
Fig. 6. Gradient of flow distribution with respect to the AR.
Table 4 Coefficient of uniformity for different ARs. Re (105)
AR
Uniformity (%)
8
0.2 0.25 0.5 1.0 2.0 3.0 4.0
89.81 89.72 88.51 86.58 85.19 83.45 82.60
4.4. Pressure drops Fig. 9 displays the variation of pressure drop according to the AR with respect to multiple inlet Reynolds numbers. When the inlet Reynolds number increases, the pressure drop tends to increase as expected because of the increase in flow velocity in the distribution manifold. For rectangular exit-ports of different ARs, the changes in the pressure drop curves with the inlet Reynolds number appear similar. When the inlet Reynolds number is constant, the pressure drop of the distribution manifold shows an increase in deceleration with the increase in AR. After AR = 2.0, the pressure drop does not significantly increase. It is important to note that when the aspect ratio is less than 0.25, the variation of the flow pressure drop is very minor as the AR decreases.
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To summarize, when the aspect ratio is equal to 0.25, the flow performance of the manifold is very close to the best performance when AR = 0.2. Therefore, 0.25 is the AR of the rectangular exitport recommended to apply in practice. This result can be useful for exit-ports geometry design of the distribution manifolds. Acknowledgments This research project is sponsored by the National Science Funds for Distinguished Young Scholar (Grant No. 51425803) and the Natural Science Foundation of China (Grant No. 51238010). References
Fig. 9. Variation of the pressure drop with the Reynolds number for different ARs.
5. Conclusions This study investigated the effect of the changes in AR of the rectangular exit-ports and inlet Reynolds number on the flow distribution uniformity of distribution manifolds. Through the numerical simulation, the following conclusions were obtained. First, with the increase in inlet Reynolds number, the uniformity coefficient slightly decreases, but the magnitude of this decrease is notably small. Furthermore, the variance of the coefficient of uniformity is 0.0358, which shows that the flow distribution among rectangular exit-ports in the longitudinal direction of manifolds has almost no difference with the change in inlet Reynolds number. Second, the flow distribution between exit-ports obviously changes between the entrance of manifolds and the end. When AR = 0.2, the difference of the flow distribution is the smallest; with the increase in AR, the difference also increases. The results show that the flow uniformity worsens with increasing AR. Third, the static pressure increases with decreasing distance to the end of the manifolds, and a large pressure change occurs as a result of the loss of momentum because the working fluid leaks between rectangular exit-ports. This phenomenon can be explained as a result of the increase in axial deceleration-based pressure along the manifold, which overcomes the resistance. For rectangular exit-ports of different ARs, the static pressure distribution contours appear similar. However, the static pressure contours of different ARs show that a larger AR corresponds to a larger static pressure. Finally, when the inlet Reynolds number increases, the pressure drop tends to increase as expected because of the increase in flow velocity in the distribution manifold. For rectangular exit-ports of different ARs, the changes in the pressure drop curves with the inlet Reynolds number appear similar. When the inlet Reynolds number is constant, the pressure drop of the distribution manifold shows an increase in deceleration with the increase in AR. After AR = 2.0, the pressure drop does not significantly increase.
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