循环射流混合槽内瞬态压力波动非线性标度特性
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摘要
在湍流状态下(Re=3660～32940)利用动态数据采集系统对新型循环射流混合槽射流混合区内不同轴向、径向和周向位置的瞬态脉动压力进行测量,研究了压力波动的湍动能量及其时间结构函数的扩展自相似标度律.基于压力波动信号的递归率和能量分布特点,确定瞬态压力波动分析的初始优化参数.结果表明,数据长度n≥80000时,时间序列的波动能量趋于稳定且相对变化率低于0.3%,其对数值与雷诺数存在线性关系;瞬态压力波动的q阶与3阶时间结构函数的双对数存在线性关系,同时波动信号的q阶时间结构函数的标度指数ξ(q)小于同阶时间结构函数相对标度指数ξ(q,3),相对标度指数ξ(1,3)和ξ(5,3)[或ξ(2,3)和ξ(4,3)]关于ξ(3,3)对称分布,q≥4时相对标度指数ξ(q,3)随极角θ增加而增大;q<3的相对标度指数ξ(p,3)随r/R和θm的变化与q≥4时的相对标度指数分布相反.
In order to reveal the nonlinearity of fluid system in the mixing zones of a circulating jet tank, a high-speed acquisition system was employed to measure the instantaneous pressure fluctuation signals at different axial, radial and circumferential positions in turbulent flow region with a range of Re between 3 660 and 32 940. Both the amplitudes of fluctuation energy and scaling law of extended self-similarity for the structure function of pressure signals were evaluated. The initial parameters on sampling frequency and data length of pressure time series were optimized based on the recurrence rate and amplitudes of fluctuation energy. The experimental results indicated that the relative increasing ratios of amplitude of fluctuation energy were below 0.3% and a linear relationship between logarithm values of amplitude of fluctuation energy and Re existed when the date length was not less than 80 000. The logarithm values between the qth- and third-order time structure functions of pressure signals were in accordance with a linear relationship. The scaling exponent ξ(q) of time structure function was smaller than relative scaling exponent ξ(q, 3). The profiles of relative scaling exponents ξ(1, 3) and ξ(5, 3) [or ξ(2, 3) and ξ(4, 3)] were symmetrically distributed about the profile of ξ(3, 3). The relative scaling exponent ξ(q, 3) was enlarged with the increase of θ m when the order value of q was equal or greater than 4. But the distribution of ξ(q, 3) was contrary with the increase of polar angle θ or r/R when the order value of q was less than 3.
In order to reveal the nonlinearity of fluid system in the mixing zones of a circulating jet tank, a high-speed acquisition system was employed to measure the instantaneous pressure fluctuation signals at different axial, radial and circumferential positions in turbulent flow region with a range of Re between 3 660 and 32 940. Both the amplitudes of fluctuation energy and scaling law of extended self-similarity for the structure function of pressure signals were evaluated. The initial parameters on sampling frequency and data length of pressure time series were optimized based on the recurrence rate and amplitudes of fluctuation energy. The experimental results indicated that the relative increasing ratios of amplitude of fluctuation energy were below 0.3% and a linear relationship between logarithm values of amplitude of fluctuation energy and Re existed when the date length was not less than 80 000. The logarithm values between the qth- and third-order time structure functions of pressure signals were in accordance with a linear relationship. The scaling exponent ξ(q) of time structure function was smaller than relative scaling exponent ξ(q, 3). The profiles of relative scaling exponents ξ(1, 3) and ξ(5, 3) [or ξ(2, 3) and ξ(4, 3)] were symmetrically distributed about the profile of ξ(3, 3). The relative scaling exponent ξ(q, 3) was enlarged with the increase of θ m when the order value of q was equal or greater than 4. But the distribution of ξ(q, 3) was contrary with the increase of polar angle θ or r/R when the order value of q was less than 3.
引文
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[2]Li Z P,Bao Y Y,Gao Z M.Piv Experiments and Large Eddy Simulations of Single-loop Flow Fields in Rushton Turbine Stirred Tanks[J].Chem.Eng.Sci.,2011,66(6):1219-1231.
[3]Takahashi K,Motoda M.Chaotic Mixing Created by Object Inserted in a Vessel Agitated by an Impeller[J].Chem.Eng.Res.Des.,2009,87(4):386-390.
[4]Zhang Q H,Yong Y M,Mao Z S,et al.Experimental Determination and Numerical Simulation of Mixing Time in a Gas-Liquid Stirred Tank[J].Chem.Eng.Sci.,2009,64(12):2926-2933.
[5]Douroumis D,Fahr A.Enhanced Dissolution of OxcarbazepineMicrocrystals Using a Static Mixer Process[J].Colloids Surf.B,2007,59(2):208-214.
[6]鲁占军,杨春苹,高美蓉,等.浆料罐搅拌器改造总结[J].聚氯乙烯,2003,31(3):44-45.
[7]禹言芳,吴剑华,孟辉波.新型循环射流混合器湍流特性分析[J].过程工程学报,2011,11(1):1-8.
[8]Yu Y F,Wu J H,Meng H B.Numerical Simulation Process Aspects of the Novel Static Circulating Jet Mixer[J].Can.J.Chem.Eng.,2011,89(3):460-468.
[9]Yu Y F,Liu X R,Wu J H,et al.Comparison among Turbulence Models for a Novel Static Circulating Jet Mixer[J].Applied Mechanics and Materials,2010,26/28:382-385.
[10]Luo P C,Cheng Y,Jin Y,et al.Fast Liquid Mixing by Cross-flow Impingement in Millimeter Channels[J].Chem.Eng.Sci.,2007,62(22):6178-6190.
[11]骆培成,程易,汪展文,等.液-液快速混合设备研究进展[J].化工进展,2005,24(12):1319-1326.
[12]Bai Z S,Wang H L,Tu S T.Study of Air-Liquid Flow Patterns in Hydrocyclone Enhanced by Air Bubbles[J].Chem.Eng.Technol.,2009,32(1):55-63.
[13]Fossett H,Prosser L E.The Application of Free Jets to the Mixing of Fluids in Bulk[J].Proc.Inst.Mech.Eng.,1949,160(1):224-232.
[14]Patwardhan A W,Thatte A R.Process Design Aspects of Jet Mixers[J].Can.J.Chem.Eng.,2004,82(1):198-205.
[15]Patkar V C,Patwardhan A W.Effect of Jet Angle and Orifice Shape in Gas-Gas Mixer Using CFD[J].Chem.Eng.Res.Des.,2011,89(7):904-920.
[16]Zughbi H D,Rakib M A.Mixing in a Fluid Jet Agitated Tank:Effects of Jet Angle and Elevation and Number of Jets[J].Chem.Eng.Sci.,2004,59(4):829-842.
[17]Zughbi H D,Ahmad I.Mixing in Liquid-jet-agitated Tanks:Effects of Jet Asymmetry[J].Ind.Eng.Chem.Res.,2005,44(4):1052-1066.
[18]Zughbi H D,Rakib M A.Investigations of Mixing in a Fluid Jet Agitated Tank[J].Chem.Eng.Commun.,2002,189(8):1038-1056.
[19]Kalaichelvi P,Swarnalatha Y,Raja T.Mixing Time Estimation and Analysis in a Jet Mixer[J].J.Eng.Appl.Sci.,2007,2(5):35-43.
[20]伍沅.撞击流-原理、性质、应用[M].北京:化学工业出版社,2005.135-163.
[21]伍沅,周玉新,郭嘉,等.液体连续相撞击流强化过程特性及相关技术装备的研发和应用[J].化工进展,2011,30(3):463-472.
[22]Zhang J W,Wang X W,Wang C Y.Multi-scale and Multi-fractal Characteristics of Instantaneous Velocity Signals in Impinging Stream Mixer[J].Can.J.Chem.Eng.,2010,88(2):172-178.
[23]张建伟,焦丽.基于撞击流混合器压力波动信号的小波多重分形奇异谱[J].过程工程学报,2006,6(4):627-632.
[24]Sun H Y,Wu Y,Xu C H.Pressure Fluctuation in the Submerged Circulative Impinging Stream Reactor[J].Chin.J.Chem.Eng.,2006,14(4):428-434.
[25]孙志刚,李伟锋,刘海峰.大间距两不对称喷嘴对置撞击流驻点偏移规律[J].高校化学工程学报,2009,23(6):990-994.
[26]李伟锋,孙志刚,刘海峰,等.两喷嘴对置撞击流径向射流流动特征[J].化工学报,2009,60(10):2453-2459.
[27]刘建华,姜楠,王振东,等.用局部平均速度结构函数检测湍流边界层多尺度相干结构[J].应用数学与力学,2005,26(4):456-464.
[28]She Z S,Leveque E.Universal Scaling Laws in Fully Developed Turbulence[J].Phys.Rev.Lett.,1994,72(3):336-339.
[29]Benzi R,Ciliberto S,Tripiccione R,et al.Extended Self-similarity in Turbulent Flows[J].Phys.Rev.E,1993,48(1):29-32.
[30]Marwan N,Wessel N,Kurths J.Recurrence Plot Based Measures of Complexity and Its Application to Heart Rate Variability Data[J].Phys.Rev.E,2002,66(2):026702.