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This post was last edited by GavinLiang on 2019-11-5 03:48. Calculation of load during turbine tripping (air hammer calculation). Turbine tripping refers to the process in which the main steam valve and control valves of the unit close as a result of the activation of the unit’s main protection systems, thereby cutting off the supply of air and stopping the operation of the unit. The main reasons for turbine tripping include electrical-related tripping, for which there should be an alarm ； Protection malfunction and tripping can be caused by grounding issues as well as external signal interference ； Malfunctions and the main protection of electrical generators ； Over-speeding caused by external power grid issues, etc. During normal startup and shutdown processes, the increase or decrease in load occurs gradually, which helps to avoid sudden changes in steam in the piping system or in the electrical circuits. However, when the circuit trips for some reason and the load disappears instantly, the main inlet valve of the turbine shuts off immediately; otherwise, the turbine would operate at high speed, which is quite dangerous. Even the residual steam in the steam box and intake pipes has enough power to drive the turbine to dangerous speeds. At the moment the main steam valve closes, the steam flow slows down or even stops, and pressure waves are generated at this time. This is actually the basic principle behind water hammer; in the case of steam pipelines, we *usually refer to this phenomenon as air hammer. Pressure waves travel throughout the pipeline system, generating shock forces while the pressure inside the pipes increases. The impact force causes the steam pipes to vibrate and generate loud noise. Because steam is highly compressible, the impact force generated by closing a steam turbine valve is not as severe as that in liquid pipelines. It was not until 1960 that the phenomenon of steam pipeline supports being damaged by air hammers occurred, and it was then that air hammers began to attract attention. The first theoretical study on air hammers was published in 1966, and since then, air hammer analysis has been formally included in pipeline design. According to the water hammer theory, a sudden decrease in the fluid velocity within a pipe causes a sudden increase in pressure due to inertia. This increase in pressure generates pressure waves, which travel upstream through the pipe at the speed of sound. There is a relationship between the decrease in speed and the increase in pressure, as follows: is the density of the medium, and a is the sound speed of the medium within the pipe. Although the fluid velocity decreases significantly, this does not happen in an instant; the speed of the change depends on the time it takes to close the valve. Therefore, as shown in Figure 12.21, throughout the valve closing process, the changes in velocity and pressure can be divided into a series of time intervals, corresponding to one another, and so on. The total pressure change occurs at the moment when the valve is completely closed: the typical pressure increase due to a turbine trip is between 10% and 15% of the operating pressure. The pressure increase rate of the high-pressure main steam is low, and the proportion of low-pressure reheat steam is high. Although the pressure still shows a tendency to increase after the valve is fully closed, as indicated by the dashed line in the figure. But this part is usually ignored in calculations. Because the value for this part is difficult to obtain without detailed hydraulic calculations. One more thing to mention is that pressure waves propagate through the pipe at the speed of sound. When pressure increases, the density and temperature of the fluid also rise, which in turn increases the speed of sound in the fluid, ultimately leading to the accumulation of pressure wave fronts. In any case, these changes are very small; ignoring the changes in density and temperature, the sound speed is taken as the normal value for that fluid. In the analysis of steam pipelines, the effect of momentum changes caused by variations in flow velocity is also usually neglected. Therefore, the impact force purely originates from the change in pressure. In this way, the calculation of the impact force is very simple; it’s just PA. Density can be determined from pressure and temperature; flow velocity is calculated from mass flow rate and density. The speed of sound was discussed earlier, and it can be found using the specific heat ratio k=1.28. The time history of the impact force is consistent with the time history of the pressure change. Similar to the exhaust reaction force of a safety valve, the difference is that in the case of a steam hammer, it’s related to the closing of a valve, while in the case of a safety valve, it’s related to the opening of a valve. The effective valve closing time can be taken as 75% of the time provided by the valve manufacturer. The reasons were explained in the article on safety valves. Since the valve closing time determines the net impact force on each pipe segment, an accurate valve closing time is essential for accurately estimating the impact force on those segments. To calculate the impact force of a pneumatic hammer, we need to determine the impact force at each end of each section of pipe, and then obtain the unbalanced load by subtracting the impact forces at these two ends; this is similar to the calculation method used for exhaust systems in closed safety valves. The difference is that the impact force of a safety valve is generated by the impact of the actual fluid, whereas the air hammer force is produced by pressure waves. The characteristic of pressure waves is that as they move forward and encounter an obstacle, they are reflected. With each reflection, their energy decreases and their impact force weakens, until they have attenuated to zero after multiple reflections back and forth. In our analysis, we only consider the pressure wave from the first rebound, ignoring all others. We still use the ideal impact curve for calculation, as shown in Figure 12.22. The figure shows the time-history curves of the pressure wave at each point. Taking point 1 as an example, the pressure increases linearly until the valve is completely closed; it reaches its maximum value at that point, and this maximum value persists until the pressure wave that rebounds reaches point 1. The time it takes for the pressure wave to reach the boiler is. Then a reflected wave is generated; due to friction and exit losses, this reflected wave bounces back as a negative pressure of slightly less magnitude than the original wave, before reaching point 1 again. Then the pressure at point 1 began to decrease, and ultimately the impact force time history curve at point 1 is shown as a solid line. Of course, the further back a point is, the later in time the shock wave acts. As at 4 o’clock, the forward shock wave has not yet reached its maximum intensity, while the reflected wave has already returned; as these waves cancel each other out, the impact force at 4 o’clock never reaches its maximum value. Next, we need to find the difference in impact forces at the two endpoints of the same pipe segment; this is the shaded area in the figure, and it represents the unbalanced force we are looking for. It causes the pipeline to vibrate. The maximum unbalanced force still depends on the length of the pipe segment; if the length is such that the time it takes for sound to travel is greater than the time required to close the valve, then the maximum impact force is as follows. If the length of the pipe segment is less than the product of the speed of sound and the valve closing time, the maximum unbalanced force is calculated as follows: it refers to the pipe segment between i and j. It’s the same as valve calculation. As can be seen from the equation above, the value of depends on the value of . If the pipe segment is very short, the unbalanced impact force is small, and it may be omitted in the analysis. With the unbalanced force obtained, we can choose two methods to analyze the pipeline. First, a static analysis method is used to identify DLF for analysis; however, it must be noted that choosing this static analysis method implies assuming that the unbalanced impact loads on all pipe sections occur simultaneously. It is also possible to use the time-history analysis method by incorporating the actual impact force time histories at each point for analysis; the specific methods for this analysis will be explained in detail later. Feel free to follow the WeChat official account “The World of Pipelines” to discuss with me. Previous articles: Stress analysis of pressure pipelines, Calculation of the exhaust reaction force of safety valves – Stress analysis of pressure pipelines in closed discharge systems, Calculation of the exhaust reaction force of safety valves – Open discharge systems. Chapter 5: Methods for calculating fluid impact loads on pressure pipelines. Material categories in CAESARII and creation of material libraries. Detailed explanation of the types, functions, and simulation of supports and hangers for pressure pipelines. Relationship between stress and strength theories in pipeline standards. Chapter 1: Single-degree-of-freedom systems. Adding entries to a grade database is that simple! Methods for adding to the PLANT4D database (video). Useful tips for using CAESARII – model positioning. 5. Handling pipeline vibration problems: knowledge you must have. 4. Handling pipeline vibration problems: knowledge you must have. Handling pipeline vibration problems: knowledge you must have. 3. Single-degree-of-freedom systems (SDOF) – two methods. Simulation applications for sleeve compensators. Simulation applications for sleeve compensators. Basics of dynamic analysis – DLF. CAESARII methods for dynamic load analysis 3. CAESARII methods for dynamic load analysis 2. The relationship between stress and strength theories in pressure pipeline design. Methods for modeling long-span arch pipes – CAESARII. CAESARII methods for dynamic load analysis – static equivalence method