Working principle of steam turbines

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　　This includes the working principle of the turbine stages and the working principle of the entire turbine unit. The working principle of a turbine involves the flow of steam, the generation of forces on the blades and the formation of losses, as well as the methods used to enable the turbine to adapt to changes in external load. 　　Working principle of turbine stages Based on the way in which the energy contained in the steam is converted into mechanical work within a turbine stage, turbine stages can be divided into three types: impulse stages, reaction stages, and velocity stages. 　　Impulse stage Figure 2 shows a schematic diagram of the working principle of the impulse stage. The steam expands in the nozzle, with the pressure dropping from p0 at the inlet to p1 at the outlet (Figure 2a). As the cross-sectional area of the nozzle flow channel gradually decreases (Figure 2b), the velocity of the steam within the nozzle increases accordingly. The energy contained in the steam is converted into the kinetic energy of the steam jet; its absolute velocity at the exit of the nozzle is c1, and the angle of the steam jet is α1. Since the circumferential velocity of the moving blade is u, the relative velocity of the steam entering the moving blade is w1, and the steam flow angle is β1. The pressure does not change as the steam passes through the moving blades; that is, the pressure at the exit of the moving blades, p2, is equal to the pressure at the inlet, p1. The relative velocity at the outlet of the moving blade is w2, the steam flow angle is β2, the absolute velocity is c2, and the steam flow angle is α2 (Figure 2c). As the steam flow passes through the moving blades, its direction changes, and its momentum also changes; as a result, a force is exerted on the moving blades, driving the rotor to rotate and perform work. The blade profile of the impulse stage blades is nearly symmetrical left and right. At the inlets and outlets of the nozzle and moving blades, the magnitude and direction of the steam flow velocity can be represented in a proportional manner by the magnitude and direction of vector segments; these vector segments form what is known as a velocity triangle. 　　On the H-S diagram (Figure 2d), with enthalpy H on the vertical axis and entropy S on the horizontal axis, an isentropic line is drawn from the steam state point at the nozzle inlet to the static pressure p2 after the stage. The enthalpy value at the starting point of this line is H0, and the enthalpy value at the ending point is H2; the difference H0-H2=I0 is known as the isentropic enthalpy drop. The unit is kilojoules per kilogram. After the isentropic enthalpy drop is converted into the kinetic energy of the steam flow, it represents the ideal velocity of the steam stream at the nozzle exit. However, there are losses in the flow within the nozzle; therefore, the actual steam velocity at the outlet is c1 = κc1t, where κ is known as the nozzle velocity coefficient, and it generally ranges from 0.96 to 0.98. Similarly, due to flow losses, the relative velocity w2 of the steam stream at the exit of the moving blade is equal to w1; this is known as the moving blade velocity coefficient, which generally ranges from 0.92 to 0.95. Due to the change in the velocity and direction of the steam flow, the circumferential force generated when a steam stream with a mass flow rate of 1 kilogram per second passes through the moving blades is Fu = c1cosα1 + c2cosα2 newtons. The corresponding power is referred to as the circumferential power Pu, or it can be expressed in terms of the enthalpy drop Hu: Pu = Hu = Fu·u = u(c1cosα1 + c2cosα2). In this way, the quantitative calculation of the conversion of steam energy into work can be accomplished using H-S diagrams and velocity triangle diagrams. 　　The efficiency of peripheral energy conversion can be expressed as the ratio of Hu to I0, known as the peripheral efficiency; it is related to factors such as blade height and can reach over 90%. The ratio of the peripheral velocity u of the moving blades to the steam flow velocity c1 at the nozzle exit is called the speed ratio; it has a decisive influence on the circumferential efficiency of the turbine stage. When the speed ratio is zero, the torque exerted by the steam on the main shaft is at its maximum; however, since the circumferential speed is zero, the power of the stage is zero, and so is the peripheral efficiency. When the speed ratio is close to 1, the blade movement speed is similar to the steam flow speed; the force exerted by the steam on the blades and the torque on the main shaft are both zero. Therefore, the power of the stage and its peripheral efficiency are also zero. Theoretically, the peripheral efficiency and power reach their maximum values at a speed ratio of cosα1/2 (Figure 1). At this point, the residual kinetic energy (velocity loss) of the exhaust gas stream is minimal. 　　Reaction stage Figure 3 shows a schematic diagram of the working principle of the reaction stage. Compared to the impulse stage, the reaction stage is characterized by steam expanding in both the stator and rotor passages, resulting in p0＞p1＞p2. On the H-S diagram in Figure 3d, the isentropic enthalpy drop of the moving blade is denoted as Hb, while the isentropic enthalpy drop of the stationary blade (nozzle) is denoted as Hu. The ratio of Hb to I0 is called the reactivity. The reaction degree of the reactive stage is generally 50%. The presence of reaction degree accelerates the steam in the flow channels of the moving blades, improving the flow properties. Therefore, modern impulse stages also often have a small amount of reaction degree (=0.05–0.10). The profile of the moving and stationary vanes in the reaction stage is essentially the same (Figure 3b). Theoretically, the peripheral efficiency is highest when the velocity ratio of the reaction stage, u/c1, is cosα1. Under the same conditions of diameter and rotational speed, at the theoretically optimal speed ratio, the isentropic enthalpy drop of a reaction stage is half that of an impulse stage. Therefore, in a turbine with similar conditions, the number of reaction stages is greater than that of impulse stages. The impulse stage and the reaction stage, as two basic types of stages, are widely used in various types of steam turbines. 　　Speed stage Figure 4 shows a schematic diagram of the working principle of the speed stage. The velocity stage utilizes the kinetic energy generated by steam expansion in the nozzle in several stages, and generally consists of two rows of moving vanes. Theoretically, the optimal speed ratio for a two-row speed stage is cosα1/4; under the same conditions, its working capacity is equivalent to that of 3–4 impulse stages or 6–8 reaction stages. When the isentropic enthalpy drop of the steam exceeds the limit that can be effectively utilized by ordinary impulse or reaction stages, and a multi-stage turbine is not desired, using a single speed stage is often the most advantageous solution. However, the peripheral efficiency at high speeds is relatively low, generally not exceeding 80%. Speed stages are mostly used in single-stage steam turbines, or as the first stage (regulating stage) in medium and small multi-stage impulse steam turbines and multi-stage reaction steam turbines. To improve flow performance, the rotor blades and guide vanes in modern speed classes also have a small degree of reaction (Figure 4a). 　　In some speed and impulse stages, nozzles are installed only on a portion of the entire circumference, with no steam passing through the remaining part of the circumference; such stages are called partially fed stages. For stages with a low steam flow rate, it can increase the blade height to reduce losses. 　　Intra-stage loss: Intra-stage loss mainly includes three components: flow loss in the nozzles (stator blades), flow loss in the rotor blades, and residual velocity loss. Intra-stage loss is the reason that makes the peripheral efficiency of the stage less than 1. There are also a series of additional losses, such as wheel friction loss, steam leakage loss, wet steam loss, and partial steam inlet loss, etc. The presence of these additional losses reduces the efficiency of the turbine stage compared to the peripheral efficiency; this efficiency is referred to as the internal efficiency of the stage. Since the additional loss is related to the speed ratio, the actual optimal speed ratio for the stage is slightly lower than the theoretical value. 　　Two-dimensional flow theory and three-dimensional flow theory: In the principle of operation of steam turbines, in addition to the one-dimensional flow theory, which assumes that the velocity of the steam changes only along the streamlines, there are also two-dimensional and three-dimensional flow theories. The two-dimensional theory suggests that the velocity of the vapor flow surrounding the blade is uneven not only along the streamlines but also in the direction perpendicular to them. Along the convex surface of each blade, the average velocity of the steam flow is higher and the average pressure is lower; the opposite is true along the concave surface of the blade. As a result, the steam flow exerts a force on the blade directed from the high-pressure side to the low-pressure side (Figure 5). It is this force that causes the rotor to rotate. 　　When the ratio of blade height to average diameter is large, it is insufficient to rely solely on a two-dimensional flow perspective for analysis, as the flow at different blade heights varies. The design of the low-pressure stages in modern steam turbines generally employs three-dimensional flow theory to take into account the three velocity components of the steam flow; as a result, the cross-sectional profiles of the moving and stationary blades change continuously along the blade height. The root of the moving blade is close to the impulse type, while its upper part is close to the reaction type; such blades are known as twisted blades, and they are widely used in large-scale power plants. 　　Principles of multi-stage turbines The isentropic enthalpy drop that can be effectively utilized by a single-stage turbine is limited; to take advantage of a larger isentropic enthalpy drop, multi-stage turbines must be used. On the H-S diagram, the thermodynamic process of steam expanding stage by stage in a multi-stage turbine is shown by the line segment ABCDE in Figure 6. Compared to a single stage, it features the following: ① The residual velocity loss from the previous stage can be utilized in the subsequent stage under certain conditions ； ②The sum of the isentropic enthalpy drops at all levels is greater than the isentropic enthalpy drop H0 of the entire turbine, and the ratio of the two is greater than 1. Therefore, the overall internal efficiency of a multi-stage turbine is greater than the average internal efficiency of each stage. In Figure 6, segment AB represents the steam admission process of the turbine, that is, the throttling process as the steam passes through the main steam valve and the control valve. Section BC represents the thermodynamic process when steam passes through 1 double-row speed stage and 8 impulse stages. The CD segment represents the final residual velocity loss process, and the enthalpy difference between points C and D indicates the magnitude of the residual velocity loss. The DE section represents the steam throttling process from the outlet of the last stage of the turbine to the inlet of the condenser. Hi represents the effective enthalpy drop of the entire turbine, that is, the work done per unit volume of steam as it passes through the various stages of the turbine. When the mass flow rate is qm, then the power of the turbine N = qmHi. 　　Regulation of steam inflow to the turbine To adapt to changes in external load, it is necessary to adjust the amount of steam entering the turbine. The main methods for regulating steam inflow include throttling control, nozzle control, bypass control, and slide pressure control. 　　Throttling control: The steam supply volume is adjusted by changing the opening degree of the control valve. When the control valve is partially open, the throttling loss during the steam admission process of the turbine increases; this is shown in Figure 6 as point B moving to the right along a horizontal line, resulting in a decrease in the turbine’s efficiency. The advantage of throttle control is that the turbine has a simple structure and low manufacturing costs, while the disadvantage is its poor thermal efficiency at low loads. 　　Nozzle adjustment: The nozzles in the adjustment stage are divided into several groups, with each group controlled by a separate control valve; by turning these control valves on and off in sequence, the amount of steam supplied can be adjusted. Figure 7a shows a cross-section of the steam inlet chamber of a turbine equipped with 4 control valves. When 1 or 2 valves are opened, the turbine generates power below the rated level. When all 3 valves are fully open, the total steam flow rate G0 allows the turbine to generate its rated power. When the new steam parameters decrease or the back pressure increases, all 4 valves open to ensure that the turbine can still generate its rated power. Figure 7b shows the operating curve of nozzle adjustment. The pressure line p1 shows how the steam pressure after the regulation stage changes with the turbine flow rate (i.e., power). The pΙ, pⅡ, pⅢ, and p curves show how the pressure in front of each group of nozzles changes as the steam flow rate varies, from when the control valves are closed to when they are fully open. When this control method is used, usually only the throttle of the last valve to be opened is large. Therefore, the throttling loss under partial load with this method is much smaller than that using throttling control. The disadvantage of this control method is that when the first control valve is fully open, the pressure difference before and after the control stage is very large, and partial steam admission occurs, which is highly detrimental to the strength and vibration characteristics of the blades in the control stage. 　　Bypass regulation: At high loads, the steam in the turbine bypasses the high-pressure stages and enters the low-pressure stages directly, so that a larger amount of steam can pass through. This type of regulation is still used only in marine steam turbines. 　　Sliding pressure control: Keeping the opening of the turbine control valve constant, this method relies on sliding pressure (by changing the steam supply pressure from the boiler) to regulate the amount of steam entering the turbine. The main advantage of this control method is that the temperature change after the control stage is minimal, thereby avoiding the risk of significant thermal stress being generated within the cylinder. Another approach involves a combination of slide pressure and nozzle regulation: nozzle regulation is used between full load and half load, while slide pressure of the boiler is utilized for regulation below half load.