Study on Heat Transfer and Flow Characteristics of a Bank of Tubes with Tube-to-Baffle Leakage Z 29 < Z < 55 R 0.4 < R < 0.75 RANS This study investigated pressure drop characteristics of a bank of tubes with tube-to-baffle leakage and that of baffle-to-tube spacing itself by conducting experiments on various orifice shape factors Z and leakage ratios R. The results show that the two pressure drop factors depend neither on the orifice shape factor for Z = 29-55 nor on the leakage ratio for R = 0.4-0.75. Also, the pressure drop factor when the leakage flows into the bank of tubes is lower than the factor when the leakage flows out. This result is obtained not only experimentally, but also numerically by RANS simulation. 1. 緒言 Kays and London ( 1 ) Zukauskas ( 2 ) Zukauskas and Ulinskas ( 3 ) ( 4 ) Bell and Bergelin ( 5 ) D d t Z = 2t/(D - d) 0.1 < Z < 33 Sullivan and Bergelin ( 6 ) Bergelin et al. ( 7 ) Z < 33 1 Z > 30 LES ( 8 ) ( 9 ) ( 10 ) ( 13 ) ( RANS ) Z > 30 2. 実験 2. 1 バッフルリーク実験第 1 図 第 2 図 64 IHI Vol.55 No.4 ( 2015 )
バッフルリーク供試体 差圧計 DP ブースタポンプ 流量計 Q 2 セクタ供試体 DP 流量計 Q 1 差圧計 タンク ポンプ 水 第 1 図 Fig. 1 Overall experimental system Q 2 Q 2 N=14 ( 189 mm 105 mm ) 第 2 図 1 Q 1 Q 1 Q 1 189 第 2 図 mm Fig. 2 Test section with tube-to-baffle leakage ( unit : mm ) 105 105 15 N = 14 5 p = 1.26 d = 29.95 mm t = 15 mm D = 30.5 30.6 30.7 31.0 mm Z = 55 48 40 29 0.4 < R < 0.75 2. 2 セクタ実験第 3 図 d = 10 mm p = 1.26 A ( 48 mm 105 mm ) B ( 240 mm 105 mm ) 30 f 2.0 23 B A Q 2 R = (Q 1 - Q 2 ) / Q 1 13 f 2.0 7 f 2.0 拡大流れ A 第 3 図 Fig. 3 Sectorial test section B 縮小流れ IHI Vol.55 No.4 ( 2015 ) 65
3. 実験結果と考察 3. 1 バッフルリークを伴う管群直交流 2. 1 項 f Re max 第 4 図 第 5 図 (Q 1 + Q 2 )/2 U max Re max = U max d/v d ( m ) v ( m 2 /s ) f ( 1 ) 主流の損失係数 f 主流の損失係数 f :f 31.0 ( Z=29 ) :f 30.7 ( Z=40 ) :f 30.6 ( Z=48 ) :f 30.5 ( Z=55 ) : リークなし 第 4 図 Fig. 4 Re max vs. f in lower section :f 31.0 ( Z=29 ) :f 30.7 ( Z=40 ) :f 30.6 ( Z=48 ) :f 30.5 ( Z=55 ) : リークなし 第 5 図 Fig. 5 Re max vs. f in upper section 1 2 DP = 4 f U N r max ( 1 ) 2 DP ( Pa ) f r ( kg/m 3 ) U max ( m/s ) N Z Z Z Zukauskas and Ulinskas ( 3 ) Z Z Z Zukauskas and Ulinskas ( 3 ) f 0.4 < R < 0.75 ( 14 ) R 第 4 図 第 5 図 R 第 6 図 z Re L Q 1 -Q 2 U L D eq. Re L = U L D eq. /v z ( 2 ) 66 IHI Vol.55 No.4 ( 2015 )
リーク流れの損失係数 z 100 10 1 :Kukral & Stephan ( 15 ) ( Z =29 ) :O ( 1/Re ) ( Z =67 ) :f 31.0 ( Z=29 ) :f 30.7 ( Z=40 ) :f 30.6 ( Z=48 ) :f 30.5 ( Z=55 ) 損失係数 f :Jacob ( 16 ) :CFD( 二次元 ) : 実験 ( 拡大流れ ) : 実験 ( 縮小流れ ) 0.1 100 1 000 10 000 レイノルズ数 Re L 第 6 図 Fig. 6 Re L vs. z of tube-to-baffle leakage 第 7 図 Fig. 7 Re max vs. f of a bank with expansion or contraction 1 DP = z r 2 U L 2 ( 2 ) DP ( Pa ) z r ( kg/m 3 ) U L ( m/s ) DP ( Pa ) 29 < Z < 55 Z Kukral and Stephan ( 15 ) ( 0.1 < Z < 30 ) Z = 29 ( 1/Re ) z R ( 14 ) 第 6 図 R 3. 2 流路の拡大 縮小を伴う管群直交流第 7 図 2. 2 項 f Re max r m = (r in + r out )/2 U max d Re max = U max d/v r in r out Jacob ( 16 ) Zukauskas and Ulinskas ( 3 ) Re max k-e CFD ANSYS FLUENT 6.3 第 8 図 - ( a ) - ( b ) Re max = 1.5 10 4 ( 4 ) 4. 数値解析 4. 1 解析モデルと手法 2. 1 項 第 9 図 N = 14 1 ( p = 1.26 ) ( y = ±W/2 ) IHI Vol.55 No.4 ( 2015 ) 67
速度 ( m/s ) 4.00 3.80 3.60 3.40 3.20 3.00 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 0.80 0.60 0.40 0.20 0.00 ( a ) 拡大流れ ( b ) 縮小流れ速度 ( m/s ) 4.00 3.80 3.60 3.40 3.20 3.00 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20 0.80 0.60 0.40 0.20 0.00 ( 注 ) 解析条件 Re max ( レイノルズ数 )=1.5 10 4 第 8 図 Fig. 8 Velocity magnitude obtained by CFD H t H W ( = 1.26d ) Y Z 0 X X 2d N=14 2d 3d 5d 5d d Wsin(π/6) 対称境界 出口 入口 1 2 3 対称境界 13 14 流路の側面境界 流路の側面境界 多孔質ゾーン 第 9 図 Fig. 9 Top and cross-sectional views of numerical domain k-e Enhanced Wall Treatment ( EWT ) ANSYS FLUENT 14.0 RANS 250 y + 1 QUICK SIMPLE 4. 2 解析結果と考察 ( 8 ) ( 13 ) Simonin and Barcouda ( S&B ) ( 17 ) ( U 0 = 1.06 m/s Re = 18 000 d = 21.7 mm ) 第 10 図 X x = 11 mm U/U 0 S&B EWT k-e 第 9 図 第 1 表 68 IHI Vol.55 No.4 ( 2015 )
22.5 U 0 *1 ( a ) 評価領域 ( b ) 速度分布 R 10.85 2.0 1.5 :S&B ( 17 ) :RANS Y 軸座標 y ( mm ) 10.85 R 10.85 速度分布 U/U 0 1.0 0.5 0.0 0 10.85 X 軸座標 x ( mm ) 22.5 0.5 0 5 10 15 20 25 主流と直角方向の Y 軸座標 y ( mm ) ( 注 ) *1:U 0 ( 入口平均流速 )= 1.06 m/s 第 10 図 Fig. 10 Comparison with S&B s experimental data 第 1 表 Table 1 Analytical Conditions Z ( m/s ) Re max 1 0.08 8.08 10 3 :CFD( 上段 )Z=29 :CFD( 上段 )Z=67 : 実験 ( 上段 ) 2 10 4 29 3 0.15 1.48 10 4 4 0.20 1.98 10 4 5 0.08 8.97 10 3 6 1.12 10 4 67 7 0.15 1.70 10 4 主流の損失係数 f 8 0.20 2.28 10 4 Z = 29 67 4 第 11 図 第 12 図 f 第 4 図 第 5 図 主流の損失係数 f :CFD( 下段 )Z=29 :CFD( 下段 )Z=67 : 実験 ( 下段 ) 第 11 図 Fig. 11 Re max vs. f in lower section 第 13 図 2 円柱後流の速度分布 u x /u i 2.50 2.00 1.50 0.50 0.00 : 上段第 8 円柱 : 下段第 7 円柱 第 12 図 Fig. 12 Re max vs. f in upper section 0.50 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 主流と直角方向の座標 y/d ( 注 ) 解析条件 : ケース 2 第 13 図 Fig. 13 x-velocity distribution behind a tube IHI Vol.55 No.4 ( 2015 ) 69
7 8 u i Y 5. 結言 (1) f Zukauskas and Ulinskas ( 3 ) f (2) z 29 < Z < 55 Z (3) Re max 参考文献 ( 1 ) W.M. Kays and A.L. London : Compact Heat Exchangers McGraw-Hill 2nd Edition ( 1964 ) ( 2 ) A. Zukauskas : Advances in Heat Transfer Academic Press Vol. 8 ( 1972. 10 ) pp. 93 160 ( 3 ) A. Zukauskas and R. Ulinskas : Heat Transfer Design Handbook Hemisphere Publishing ( 1983 ) Sec. 2. 2. 4 (4) FBR T90058 1991 6 pp. 1 31 ( 5 ) K. J. Bell and O. P. Bergelin : Flow Through Annular Orifices Transaction of the ASME Vol. 79 ( 1957. 4 ) pp. 593 601 ( 6 ) F. W. Sullivan and O. P. Bergelin : AIChE Chemical Engineering Progress Symposium Series Vol. 52 No. 18 ( 1956 ) pp. 85 94 ( 7 ) O. P. Bergelin, K. J. Bell and M. D. Leighton : Heat Transfer and Fluid Friction During Flow Across Banks of Tubes - VI The Effect of Internal Leakages Within Segmentally Baffled Exchangers Transaction ASME Vol. 80 ( 1958. 1 ) pp. 53 60 ( 8 ) S. Benhamadouche and D. Laurance : LES, coarse LES, and transient RANS comparisons on the flow across a tube bundle International Journal of Heat and Fluid Flow Vol. 24 ( 2003. 10 ) pp. 470 479 ( 9 ) P. Rollet-Miet, D. Laurance and J. Ferziger : LES and RANS of turbulent flow in tube bundles International Journal of Heat and Fluid Flow Vol. 20 ( 1999. 6 ) pp. 241 254 ( 10 ) R. W. Johnson : Modeling strategies for unsteady turbulent flows in the lower plenum of the VHTR Nuclear Engineering and Design Vol. 238 ( 2008. 3 ) pp. 482 491 ( 11 ) R. Artit and T. Akira : Benchamark Simulation of Turbulent Flow through a Staggered Tube Bundle to Support CFD as a Reactor Design Tool Part I: SRANS CFD Simulation Journal of Nuclear Science and Technology Vol. 45 No. 12 ( 2008 ) pp. 1 293 1 304 ( 12 ) R. Artit and T. Akira : Benchamark Simulation of Turbulent Flow through a Staggered Tube Bundle to Support CFD as a Reactor Design Tool Part II: URANS CFD Simulation Journal of Nuclear Science and Technology Vol. 45 No. 12 ( 2008 ) pp. 1 305 1 315 ( 13 ) L. Xiaowei, W. Xinxin and H. Shuyan : Numerical 70 IHI Vol.55 No.4 ( 2015 )
Investigation of the Turbulent Cross Flow and Heat Transfer in a Wall Bounded Tube Bundle International Journal of Thermal Sciences Vol. 75 ( 2014 ) pp. 127 139 ( 14 ) 51 CD-ROM 2014 5 H213 ( 15 ) R. Kukral and K. Stephan : The Effect of Internal Leakage on Steady State and Transient Behaviour of Shell-and-Tube Heat Exchangers Proceedings of the 10 th International Heat Transfer Conference ( 1994. 8 ) pp. 393 398 ( 16 ) J. P. Holman : Heat Transfer McGraw-Hill 8th Edition ( 1997 ) p. 313 ( 17 ) O. Simonin and M. Barcouda : Measurements and prediction of turbulent flow entering a staggered tube bundle Proceedings of the 4th International Symposium on Applications of Laser Anemometry to Fluid Mechanics ( 1988 ) < http: //cfd.mace.manchester.ac.uk/ > 2015-10-06 IHI Vol.55 No.4 ( 2015 ) 71