通用流体管网数值计算
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摘要
通过分析流体网络内流体一维流动特点,结合管路流动损失理论,采取节点、支路的建模思想,建立了适合不可压流与可压流管网水力计算的流体管网数学模型。并提出了“局部平衡,整体收敛”计算方法,克服了Hardy cross法、牛顿迭代法等传统管网计算方法存在的初场给定难以及网络拓扑关系难确定的问题。
研究了不同状态下流体网络内液体和气体的密度、粘度以及比热容的计算方法,并采用摩尔体积混合法对混合流体的上述属性进行计算。在管网水力计算过程中同步求解流体属性参数,解决了管网计算过程中由于流动参数变化造成的计算不准确问题。
采用插值方法开发了一套流体阻力系数数据库,含有直管道、突扩管、突缩管、汇流管、分流管以及各种阀门等十多种管路元件与管路附件的流阻系数,为管网计算技术的实际应用提供方便。
以某型航空发动机减速器滑油系统为例,结合所建立的管网计算数学模型,对三种不同状态下滑油系统供油情况进行分析,数值计算得到的总供油量与经验公式的计算结果差别约为3.1%,吻合较好。并且,与传统经验公式相比,数值计算结果体现出了各喷嘴喷油量的差别,表明在齿轮啮合处以及高速轴承处需要大量的滑油,符合减速器供油系统实际工作情况。
This paper analyzed the characteristics of one-dimension flow in fluid network. Relating flow loss theory of pipe network, a general mathematical model, which was available for deal with incompressible and compressible flow problem, was set up by separating pipe network into nodes and branches for numeric simulation. A new numeric simulation method named“Local balance, Whole convergence”was used to calculate the model, which analyze the topological structure and initial data expediently. The method overcame the disadvantages of the traditional methods, such as Hardy cross method and Newton iterative method.
The different methods for calculating physical property parameters of liquid and gas were researched, and the density, viscosity and specific heat capacity of the mixture were calculated by using molar volume mixing method. Getting the fluid attributes synchronously in hydraulic calculation process of the pipe network, which ensured that the numeric result of the model could compute accurate. Also, using interpolation methods developed a fluid resistance coefficient database, more than ten different resistance options were provided for modeling momentum sources or sinks in the branches. The available floe resistance options included: pipe flow, floe through a restriction, pipe flow with entrance and exit loss, thin sharp orifice, square expansion, and so on.
Taking the oil system of certain aero-engine reducer as a study object, the model was used in simulating the characteristics of the system on three diverse work states. The numeric results nearly in agreement with the data given by the experiential expressions which was used extensive in practical project, shows that the employed model and arithmetic is valid.
研究了不同状态下流体网络内液体和气体的密度、粘度以及比热容的计算方法,并采用摩尔体积混合法对混合流体的上述属性进行计算。在管网水力计算过程中同步求解流体属性参数,解决了管网计算过程中由于流动参数变化造成的计算不准确问题。
采用插值方法开发了一套流体阻力系数数据库,含有直管道、突扩管、突缩管、汇流管、分流管以及各种阀门等十多种管路元件与管路附件的流阻系数,为管网计算技术的实际应用提供方便。
以某型航空发动机减速器滑油系统为例,结合所建立的管网计算数学模型,对三种不同状态下滑油系统供油情况进行分析,数值计算得到的总供油量与经验公式的计算结果差别约为3.1%,吻合较好。并且,与传统经验公式相比,数值计算结果体现出了各喷嘴喷油量的差别,表明在齿轮啮合处以及高速轴承处需要大量的滑油,符合减速器供油系统实际工作情况。
This paper analyzed the characteristics of one-dimension flow in fluid network. Relating flow loss theory of pipe network, a general mathematical model, which was available for deal with incompressible and compressible flow problem, was set up by separating pipe network into nodes and branches for numeric simulation. A new numeric simulation method named“Local balance, Whole convergence”was used to calculate the model, which analyze the topological structure and initial data expediently. The method overcame the disadvantages of the traditional methods, such as Hardy cross method and Newton iterative method.
The different methods for calculating physical property parameters of liquid and gas were researched, and the density, viscosity and specific heat capacity of the mixture were calculated by using molar volume mixing method. Getting the fluid attributes synchronously in hydraulic calculation process of the pipe network, which ensured that the numeric result of the model could compute accurate. Also, using interpolation methods developed a fluid resistance coefficient database, more than ten different resistance options were provided for modeling momentum sources or sinks in the branches. The available floe resistance options included: pipe flow, floe through a restriction, pipe flow with entrance and exit loss, thin sharp orifice, square expansion, and so on.
Taking the oil system of certain aero-engine reducer as a study object, the model was used in simulating the characteristics of the system on three diverse work states. The numeric results nearly in agreement with the data given by the experiential expressions which was used extensive in practical project, shows that the employed model and arithmetic is valid.
引文
[1] Don J. Wood & Lindel E Ormsbee. Supply Identification For water Distribution System. Journal AWWA, july, 1989:74-80.
[2] B.Coulbeck & M.J.H.Stering. Modeling Techiques in Dynamic Control of water Distribution System. Measurement and Control. Vol.11, October.1978.385-389.
[3] Bending M.J, Hutchison H.P, The Calulation of Steadystate Incompressible Flow in Large Networks of Pipe. Chem. Eng. Sci, 1973, Vol.28.pp. 1857-1864.
[4] K.Sridharan.R. S. N. Datta and K. R. Narayan_Iyengar. Role of calibration in Rehabilitation of a Water Transmission Main-A case Study. Integrated computer application in Water Supply and distribution. 1993:357-367.
[5] Majumdar,A.K. : “A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks”, Sverdrup Technology Report #331-201-96-003, Contract Number Nas8-40836,Oct 1996.
[6] Majumdar,A.K. and Van Hooser,K.P.,“A General Fluid System Simulation Program to Model Secondary Flows in Turbomachinery ” ,Paper No.AIAA 95-2969, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference,July 10-12,1995,San Diego,California.
[7] Howell,G.W.and Weather,T.M.“,Aerospace Fluid Component Designers Handbook”,Volume 1,Revision D,TRW Systems Group,RPL-TDR-64-25 February,1970.
[8] Majumdar,A.K.,Bailey,J.W.,Holt,K.A.and Turner,S.G.,“Mathematical Modeling of Free Convective Flows for Evaluating Propellant Conditioning Concepts ” ,Paper No. AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 1-3,1996,Lake Buema Vista,Florida.
[9] Schallhorn,P.A.and Majumdar,A.K.,“Numerical Prediction of Pressure Distribution Along the Front and Back Face of a Rotating Disc with or Without Blades”Paper No.97-3098, AIAA 97-3098, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference,July 6-9,1997,Seattle,WA.
[10] Cleary, N.L., Holt, K. A, and Flachbart,R.H.,“Simplified Liquid Oxygen Propellant conditioning Concepts”,NASA Technical Memorandum 108482,March 1995.
[11] Bates R.and Majumdar,A.K,“Status Report on a Conjugate Computational Fluid Dynamic and Thermal Model of the Passive Recirculation Test Rig”,Sverdrup Technology,Report No.321-207-95-002, June 1995.
[12] Majumdar,A.K., “3rd Workshop on General Fulid System Simulation Program” Sverdrup Technology,Report No.321-201-95-306,October 1995.
[13] Majumdar,A.K.,“Generalized Fluid System Simulation Program(GFSSP) Version 3.0”, Sverdrup Technology,Report No.MG-99-290,Contract No.NAS8-40836,November 1999.
[14] Majumdar,A.K.,and Steadman,T.,“Numerical Modelin of Pressurization of a Propellant Tank”,Paper No.AIAA 99-0879,37th AIAA Aerospace Sciences Meeting Conference and Exhibit,January 11-14,1999,Reno,Nevada.
[15] Epstein,M.,and Anderson,R.E.,“An Equation for the Prediction of Cryogenic Pressurant Requirements for Axisymmetric Propellant Tanks ” , advances in cryogenic Engineering,plenum,New York,Vol.13,No.6,pp.207-214,1968.
[16] Schallhorn,P.A.,Majumdar,A.K.,Van Hooser,K. and Marsh,M., “ Flow Simulation in secondary Flow Passages of a Rocket Engine Turbopump ” ,Paper No. AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 13-15,1998, Cleveland, Ohio.
[17] Jung,S.Y.;San Andres,L.A.;Vance,J.M.:“Measurements of Pressure Distributions and Force Coefficients in a Squeeze Film Damper Part I:Fully Open Ended Configuration”,Tribology Transactions,Volume 34,No. 3,pp.375-382,1991.
[18] Jung,S.Y.;San Andres,L.A.;Vance,J.M.:“Measurements of Pressure Distributions and Force Coefficients in a Squeeze Film Damper Part Ⅱ:Fully Open Ended Configuration”,Tribology Transactions,Volume 34,No. 3,pp.383-388,1991.
[19] Crane company,“Flow of Fluids through Valves,Fittings and Pipe”,Technical Paper No.410,1988.
[20] 付林,江亿,承担冷负荷的热水水力工况模拟计算及应用[J],热能动力工程,1999年9月,第14卷
[21] 秦绪忠,江亿,基于遗传算法的环形供热网可及性分析[J],清华大学学报(自然科学版),1999年第39卷,第6期
[22] 秦绪忠,江亿,集中供热网的可及性分析[J],暖通空调,1999年第29卷第1期
[23] 江亿,管网可调性和稳定性的定量分析[J],暖通空调,1997年第27卷第3期
[24] 王兰,供热管网模拟调节[J],石家庄铁道学院学报,2001年12月,第14卷,第4期
[25] 纪昊鹏,陈海荣,白志伟,卢焱,给水管网优化模型求解方法综述[J],河北建筑工程学院学报,2002年10月,第20卷,第4期
[26] 孙震平,王兰,基于Matlab的流体网络模拟调节[J],节能技术,2001年5月,第19卷,第3期
[27] 季海波,热工管网的迭代算法及其应用[J],中国科技大学学报,2000年12月,第30卷第6期
[28] 刘波,程礼.航空发动机滑油系统稳态压力模型研究[J].航空动力学报,2004,18(6)
[29] 刘波,周强、程礼.构建航空发动机滑油系统稳态模型[J].推进技术,2005,26(6)
[30] 许维德著,流体力学[M],国防工业出版社,1979
[31] 童秉纲等著,气体动力学[M],高等教育出版社,1990
[32] 华志强等著,工程热力学[M],高等教育出版社,1986
[33] (美)赛埃(Saleh,J,M.)编;邓敦夏译,流体流动手册[M],北京:中国石化出版社,2004
[34] (美)乔佩(Chopey, N.P.),(美)希克思(Hicks, T.G.)著,化工计算手册[M],化学工业出版社,1988.12
[35] (美)乔佩(Chopey, N.P.)主编,化学工程计算手册[M],大连工学院出版社,1986
[36] 童景山编著,流体的热物理性质[M],中国石化出版社,1996
[37] 童景山、李敬编著,流体热物理性质的计算[M],清华大学出版社,1982
[38] 华绍曾,杨学宁等编译,实用流体阻力手册[M],国防工业出版社,1985
[2] B.Coulbeck & M.J.H.Stering. Modeling Techiques in Dynamic Control of water Distribution System. Measurement and Control. Vol.11, October.1978.385-389.
[3] Bending M.J, Hutchison H.P, The Calulation of Steadystate Incompressible Flow in Large Networks of Pipe. Chem. Eng. Sci, 1973, Vol.28.pp. 1857-1864.
[4] K.Sridharan.R. S. N. Datta and K. R. Narayan_Iyengar. Role of calibration in Rehabilitation of a Water Transmission Main-A case Study. Integrated computer application in Water Supply and distribution. 1993:357-367.
[5] Majumdar,A.K. : “A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks”, Sverdrup Technology Report #331-201-96-003, Contract Number Nas8-40836,Oct 1996.
[6] Majumdar,A.K. and Van Hooser,K.P.,“A General Fluid System Simulation Program to Model Secondary Flows in Turbomachinery ” ,Paper No.AIAA 95-2969, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference,July 10-12,1995,San Diego,California.
[7] Howell,G.W.and Weather,T.M.“,Aerospace Fluid Component Designers Handbook”,Volume 1,Revision D,TRW Systems Group,RPL-TDR-64-25 February,1970.
[8] Majumdar,A.K.,Bailey,J.W.,Holt,K.A.and Turner,S.G.,“Mathematical Modeling of Free Convective Flows for Evaluating Propellant Conditioning Concepts ” ,Paper No. AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 1-3,1996,Lake Buema Vista,Florida.
[9] Schallhorn,P.A.and Majumdar,A.K.,“Numerical Prediction of Pressure Distribution Along the Front and Back Face of a Rotating Disc with or Without Blades”Paper No.97-3098, AIAA 97-3098, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference,July 6-9,1997,Seattle,WA.
[10] Cleary, N.L., Holt, K. A, and Flachbart,R.H.,“Simplified Liquid Oxygen Propellant conditioning Concepts”,NASA Technical Memorandum 108482,March 1995.
[11] Bates R.and Majumdar,A.K,“Status Report on a Conjugate Computational Fluid Dynamic and Thermal Model of the Passive Recirculation Test Rig”,Sverdrup Technology,Report No.321-207-95-002, June 1995.
[12] Majumdar,A.K., “3rd Workshop on General Fulid System Simulation Program” Sverdrup Technology,Report No.321-201-95-306,October 1995.
[13] Majumdar,A.K.,“Generalized Fluid System Simulation Program(GFSSP) Version 3.0”, Sverdrup Technology,Report No.MG-99-290,Contract No.NAS8-40836,November 1999.
[14] Majumdar,A.K.,and Steadman,T.,“Numerical Modelin of Pressurization of a Propellant Tank”,Paper No.AIAA 99-0879,37th AIAA Aerospace Sciences Meeting Conference and Exhibit,January 11-14,1999,Reno,Nevada.
[15] Epstein,M.,and Anderson,R.E.,“An Equation for the Prediction of Cryogenic Pressurant Requirements for Axisymmetric Propellant Tanks ” , advances in cryogenic Engineering,plenum,New York,Vol.13,No.6,pp.207-214,1968.
[16] Schallhorn,P.A.,Majumdar,A.K.,Van Hooser,K. and Marsh,M., “ Flow Simulation in secondary Flow Passages of a Rocket Engine Turbopump ” ,Paper No. AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 13-15,1998, Cleveland, Ohio.
[17] Jung,S.Y.;San Andres,L.A.;Vance,J.M.:“Measurements of Pressure Distributions and Force Coefficients in a Squeeze Film Damper Part I:Fully Open Ended Configuration”,Tribology Transactions,Volume 34,No. 3,pp.375-382,1991.
[18] Jung,S.Y.;San Andres,L.A.;Vance,J.M.:“Measurements of Pressure Distributions and Force Coefficients in a Squeeze Film Damper Part Ⅱ:Fully Open Ended Configuration”,Tribology Transactions,Volume 34,No. 3,pp.383-388,1991.
[19] Crane company,“Flow of Fluids through Valves,Fittings and Pipe”,Technical Paper No.410,1988.
[20] 付林,江亿,承担冷负荷的热水水力工况模拟计算及应用[J],热能动力工程,1999年9月,第14卷
[21] 秦绪忠,江亿,基于遗传算法的环形供热网可及性分析[J],清华大学学报(自然科学版),1999年第39卷,第6期
[22] 秦绪忠,江亿,集中供热网的可及性分析[J],暖通空调,1999年第29卷第1期
[23] 江亿,管网可调性和稳定性的定量分析[J],暖通空调,1997年第27卷第3期
[24] 王兰,供热管网模拟调节[J],石家庄铁道学院学报,2001年12月,第14卷,第4期
[25] 纪昊鹏,陈海荣,白志伟,卢焱,给水管网优化模型求解方法综述[J],河北建筑工程学院学报,2002年10月,第20卷,第4期
[26] 孙震平,王兰,基于Matlab的流体网络模拟调节[J],节能技术,2001年5月,第19卷,第3期
[27] 季海波,热工管网的迭代算法及其应用[J],中国科技大学学报,2000年12月,第30卷第6期
[28] 刘波,程礼.航空发动机滑油系统稳态压力模型研究[J].航空动力学报,2004,18(6)
[29] 刘波,周强、程礼.构建航空发动机滑油系统稳态模型[J].推进技术,2005,26(6)
[30] 许维德著,流体力学[M],国防工业出版社,1979
[31] 童秉纲等著,气体动力学[M],高等教育出版社,1990
[32] 华志强等著,工程热力学[M],高等教育出版社,1986
[33] (美)赛埃(Saleh,J,M.)编;邓敦夏译,流体流动手册[M],北京:中国石化出版社,2004
[34] (美)乔佩(Chopey, N.P.),(美)希克思(Hicks, T.G.)著,化工计算手册[M],化学工业出版社,1988.12
[35] (美)乔佩(Chopey, N.P.)主编,化学工程计算手册[M],大连工学院出版社,1986
[36] 童景山编著,流体的热物理性质[M],中国石化出版社,1996
[37] 童景山、李敬编著,流体热物理性质的计算[M],清华大学出版社,1982
[38] 华绍曾,杨学宁等编译,实用流体阻力手册[M],国防工业出版社,1985