Numerical Simulation of Transient Flow Friction of Compressed Pipes

Numerical Simulation of Transient Flow Friction of People's Yangtze River Pressure Pipeline Li Jinping 1 Li Xiushu 2 (1. Department of Hydropower, Wuhan University of Hydraulic and Electric Engineering, Wuhan 43007, China; 2. Design Institute of Yangtze River Water Resources Commission, Wuhan 430010, Hubei, China) A non-constant friction term was introduced.

Numerical Simulation of Transient Flow Friction of People's Yangtze River Pressure Pipeline Li Jinping 1 Li Xiushu 2 (1. Department of Hydropower, Wuhan University of Hydraulic and Electric Engineering, Wuhan 43007, China; 2. Design Institute of Yangtze River Water Resources Commission, Wuhan 430010, Hubei, China) A non-constant friction term was introduced. Using this model for non-constant laminar flow calculations, reasonable results are obtained, which can reflect the distortion of the pressure waveform and the reverse flow in the near-wall region, confirming the feasibility of the model.

1 Overview of any hydropower station's waterway system, due to changes in the operating conditions of the hydro-generator set and load changes and the turbine adjustment caused by it, will produce a hydraulic phenomenon of non-constant flow, that is, hydraulic transition process, such as non-pressure pipe Constant flow, unsteady flow in open channels, water level fluctuations in surge tanks, and transitions in clear and full flow. From the physical point of view, the unsteady flow of a pressurized pipeline is caused by the change of inertia of the water flow in the pipeline, accompanied by obvious pressure rise and fall, and propagates along the pipeline in the form of elastic waves. This phenomenon of non-constant water flow, also known as water hammer or water hammer, has an important influence on the layout of the pipeline and the structural design of the pipeline. In addition, in the turbine adjustment, the effect of the water hammer pressure on the turbine output is always opposite to that of the governor. For example, in order to reduce the output of the turbine, the governor is required to close the small vane opening to reduce the overcurrent of the unit. However, the water hammer pressure generated by the reduction of the flow rate causes an increase in the output force, thereby deteriorating the adjustment conditions of the unit output, directly affecting the adjustment quality of the unit and the power station.

However, in the actual analysis of the project, in order to make the calculation simple, the transient effect is not neglected or approximated in the frictional term, such as the current calculation procedure of the hydraulic transition process and the analysis software of various pipeline fluid transport transient processes. The frictional resistance in the middle adopts the quasi-constant current friction term, which inevitably causes a large error in some cases. In many hydraulic systems and engineering practices, non-constant transient flow phenomena are common, whether laminar or turbulent, when pressure waves propagate along a pipe to a section, not as imagined by the classic water hammer theory. That way the flow rate at each spatial point on the section is zero. Therefore, even if the average flow velocity of the section at this moment is zero, due to the existence of the radial flow gradient, the frictional stress of the pipe wall is not zero, and even at some time, the value is much larger than the frictional stress at the initial constant flow, which is Why use the constant current friction term as the reason for the near calculation to produce a large error. Whether the treatment of non-constant current friction loss is appropriate or not directly affects the correctness of the result. It can be seen that the research on the non-constant tube flow friction term is very large, both in theory and in engineering practice. The theoretical and practical significance.

Based on the previous research work, this paper establishes a concentric cylindrical ring model, which describes the quasi-two-dimensional analysis of the unsteady flow considering the instantaneous change of the shear stress of the pipe wall. The prediction results can reflect the true of the transient flow well. Physical phenomena, this analysis can be used to evaluate the importance of non-constant friction terms. At the same time, this analysis method will be very useful because it requires less computer memory than true two-dimensional analysis.

2 Mathematical model The basis of the cylindrical ring model is to divide the fluid in the pipe into many concentric cylindrical rings, and then establish a one-dimensional continuous equation and momentum equation for the discrete elements, and then use the characteristic line method and the finite difference method for analysis. In the preliminary study, this paper used the frictional force described by Newton's viscosity.

The force balance of a typical cylindrical ring describes a typical cylindrical ring of the unit length. J assumes that the cylindrical ring extends along the entire length of the tube, and the local axial flow velocity component is u. Generally, there is a lateral flow in and out of the adjacent cylindrical ring. The flow rates Vj* and Vj may be such that m = 2nrfp, which represents the lateral mass flow per unit length, aj is the cross-sectional area of ​​the cylinder, H is the local pressure head (assuming constant over the entire section), and c is the pressure wave propagation velocity, P For fluid density, F=2nrr represents the local shear force per unit length, then the governing equation for the transient flow of the pressurized pipeline is: N) Equations (1) and (2) can form a set of characteristic line equations by linear transformation. , the characteristic line method describing the phase (except for the expression of the shear force is different) and does not consider the lateral fluctuation of the velocity of the fluid at the speed of the c.

These equations are valid only in the direction of each characteristic line.

Taking the pipe diameter D as the characteristic length and the constant flow average velocity Um as the characteristic velocity, the following dimensionless quantity x0u0 flow rate component is selected. When there are several cylindrical rings, the thickness of each cylindrical ring can still be freely selected. This paper uses the equal-area cylindrical ring division, which means that as the radius increases, the thickness of the cylindrical ring gradually decreases, that is, the unit of the side wall area is finer, which is very advantageous because the radial disturbance is made of smooth side walls. Conditions are caused, and the dissipation process is much slower than the wave propagation process in the case of low Mach numbers. The following is the division of the cross section of the circular tube as the unit 1, that is, the division of the cylindrical ring of equal cross-sectional area made by the dimensionless circle.

In addition to the relative thickness of various cylindrical rings, the total number of cylinder rings must be selected. As with the number of grids along the length of the pipe, the more the number of cylinders, the more convenient it is to write, omitting the superscript of the dimensionless number. Thereby a dimensionless form of the system of ordinary differential equations is obtained.

The change process of the shear stress of the pipe wall is described, and the shear stress of the pipe wall is also transient. Under the same average flow rate, the shear stress of the pipe wall is heavier than that of the constant flow state. In the previous derivation process, the different cylinders are The size is not limited, in the People's Yangtze River only newsletter* Yangtze River, Rhine flood disaster and land use conflict seminar will be held in Germany by the German Research Council (DFG), the National Natural Science Foundation of China (NSFC), the German horse Jointly funded by the General Institute of Science and Technology (MPG) and the Chinese Academy of Sciences (CAS), the German Center for International Environment and Development Studies (ZEl/CIDER), the German Institute of Geography, Giessen University, and the Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences. The seminar will be held at the conference center in Whlbeiberg (near Bonn, Germany) from August 28 to 31, 2000. After the meeting, the Rhine River will be visited for one week.

The theme of the seminar is: China's Yangtze River and the German Rhine River Basin flood disasters and land use conflicts sustainable watershed risk management countermeasures. The seminar will invite 20 Chinese and German scholars engaged in scientific research and management of the Yangtze River and Rhine Basin to participate in the conference and make academic reports. The seminar will focus on the possibility of international cooperation research in the Yangtze River Basin. The homepage of the seminar is Http//*giesse.de/yangtze.(Jiangyan) The Yangtze River Committee hydrologists went to Tibet to monitor hydrology. On May 17, 2000, the hydrological science and technology rescue work consisted of 5 experts from the Yangtze River Committee Hydrology Bureau. Group, carrying advanced flow measuring instrument Doppler profile speedometer, went to Tibet Yigong disaster area to guide the rescue.

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Because it is difficult to accurately and quickly provide the inflow of landslide sections using conventional instruments, the Tibet Yigong Emergency and Disaster Relief Headquarters and the Hydrology Bureau of the Ministry of Water Resources have decided to send the Yangtze River Committee Hydrology Bureau to assist in the hydrological surveying and reporting of the Yigong disaster area. After receiving the notice, the Yangtze River Committee Hydrology Bureau mobilized the Doppler profile velocimeter, which was used to measure the flow of the Longkou in the Three Gorges River, and the technical experts of the Three Gorges Hydrology Bureau, which is more skilled in using the instrument, formed the Hydrological Science and Technology Rescue Working Group. .

The reservoir resettlement engineering research and development needs to adapt to the 4th academic discussion meeting of the Hubei Provincial Water Conservancy Society Reservoir Resettlement Engineering Committee held on May 19~21, 2000. The participants suggested that the reservoir resettlement engineering research should meet the requirements of the market economy. Expand the study of the jaw region and strengthen theoretical research.

The meeting summarized the development and engineering practice of reservoir immigration engineering research in China over the past years and conducted academic exchanges. The academic papers exchanged at the conference involved various aspects such as resettlement environmental capacity, resettlement supervision, cultural relics protection, immigrant family culture, and reservoir flooding. The research topics are broader and deeper than before. The delegates held a heated discussion on the engineering practice and theoretical research of the current immigration work. Everyone believes that with the development of the market economy, new situations and new problems that are constantly encountered in the practice of reservoir resettlement engineering require that this research should be actively adapted. The requirements of the market economy, broaden the study of the jaw domain, and strengthen theoretical research to better guide the practice of immigration engineering.

want. This is unpredictable in the expression of the quasi-constant friction term.

The shear stress variation of the pipe wall at 1/8 of the valve end 4 Conclusion The purpose of this paper is to study the frictional characteristics of the unsteady flow of the pipe. The theoretical part starts from Newton's law and assumes that the tube flow is axisymmetric. The circular tube is divided into cylindrical rings of equal section, and the basic governing equation of the unsteady flow of the circular tube is established. This is compared with the Navier-Stokes equation. Consistent, only slightly different in the handling of convection items. The numerical calculation is based on the characteristic line method suitable for hydraulic transient flow calculation. Finally, the model is validated by the laminar flow condition of high viscous fluid, and the feasibility of the model is illustrated.

The frictional term of the non-constant flow is introduced into the non-constant flow concentric cylindrical ring model of the pressurized pipeline, which can correctly reflect the pressure rise and fall during the hydraulic transition of the pressurized pipeline, and provides more for the layout of the pipeline and the structural design of the pipeline. Reasonable basis. The model also shows that the quasi-constant friction term can predict the maximum pressure rise or decrease in the transient flow, but it does not reflect the pressure wave attenuation and distortion. In addition, the model provides a useful theoretical basis for improving the friction term expression of transient turbulence.

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