**By Denis Bruno**, Wesley Bauver, Haiyang Qian and Scott Herman, General Electric

The need for fast start up and cycling of combined cycle power plants in response to the growth of renewables is well understood in the power industry. Both trends have been widely discussed. This need is supported with the Rapid Response combined cycle system employing the new 7HA and 9HA gas turbines and others with hot start times around 30 minutes and operational efficiencies as high as 62 percent.

The need for both high efficiency and cycling puts conflicting requirements on Heat Recovery Steam Generation (HRSG) pressure parts. Application of new or higher-grade materials is an option. However, considering the long industry experience and cost of the plant, exploring the capacity of the existing materials, with improved design and analysis, is desired to meet the current challenge. For existing materials to endure higher pressure and temperature, thicker components are needed. The thicker components result in higher through wall temperatures and thermal stress, which is further increased due to faster cycling.

Heat Recovery Steam Generators must be designed to accommodate fast and increased cycling over the life of a power plant. This should include a design life assessment that accounts for fatigue caused by cycling and creep from long term operation at high temperature and pressure. |

Critical to designing HRSG pressure parts is a life assessment analysis that takes into account all aspects of imposed steady state and transient thermal and pressure loads along with material and geometry of components. Both the EN and ASME codes provide guidance on life assessment approaches, however the simplified methods provided can result in either over or anticonservative predictions of component life. GE uses an approach generally based on EN 12952-3 and 12952-4 for fatigue and creep assessment along with robust transient modeling to define transient operating conditions. This article outlines the approach used by GE for HRSG life assessment.

## Transient Analysis

It is necessary to define the transient operating conditions that the HRSG pressure parts must endure. For units that are not yet in operation, this requires a dynamic model to predict steam/water flow pressure and temperature in the pressure parts as a function of time. Additionally, the heat transfer to the pressure parts must be determined as a function of the flow conditions as this defines the thermal transient that the component is subjected to. The primary inputs to the dynamic model are the gas turbine flow and temperature curves as these provide the energy into the HRSG. If the HRSG has a duct burner the ramp rate of that heat input must also be included. The dynamic model must include the operational logic and constraints for the various control valves, bypasses and attemperators. Figure 1 shows typical transients for an operating cycle.

It is noted that a complete transient should be defined as a combination of a ramp up (startup) and ramp down (shutdown) progress, not a single ramp. As will be discussed later, Finite Element Analysis (FEA) is required for determination of component stresses that affect lifetime. The required transient inputs for the FEA include the local heat transfer coefficients on the component. It is important to evaluate these with Computational Fluid Dynamics (CFD) and to validate with field measurements. Figure 2 shows a CFD analysis of local heat transfer coefficients inside a superheater manifold. Use of a simplified calculation on heat transfer based on uniform conditions can result in significant under prediction on local stresses and hence life usage.

## Component Selection

EN12952-3, 5.5 provides a method of screening components for fatigue but this is based strictly on component material, dimensions and operating pressure and does not consider the operational transient that the component would be subjected to. The operating temperature/pressure and the rates of temperature/pressure change based on the dynamic model or operating data must be used to select the components subjected to the most severe operating transients. These factors must be considered as well as the component design. Typically, it can be assumed that the final superheater or reheater and the high pressure drum will be subjected to fast temperature increases at startup. Components directly downstream of attemperators can also be subject to fast transients. These can occur multiple times over a single start stop cycle so the anticipated load change scenarios must be considered as well as the numbers of startups and shutdowns. In this study, a manifold of the final stage superheater, as shown in Figure 3, is selected to show the fatigue evaluation of cyclic load.

## Fatigue Evaluation Methods

ASME BPVP Code Section I does not provide specific rules or procedures to evaluate the fatigue usage of an HRSG. The general philosophy is stated in the Forward of ASME BPVP Code Section I, “to afford reasonable protection of life and property and to provide a margin for deterioration in service so as to give a reasonably long safe period of usefulness.” The increasing number of cyclic operations on HRSGs requires a better understanding of the fatigue evaluation methods and the margins associated with them. The American Boiler Manufacturers Association (ABMA) has discussed the different methods to calculate fatigue usage for HRSGs and compared the results. The ABMA paper also discussed the strengths and weaknesses of each method. As EN 12952-3 provides detailed procedures specifically focused on water tube boiler fatigue, in this analysis, EN 12952-3 is chosen to be the calculation method to show the effect of input parameters of the fatigue analysis.

EN 12952-3 provides a procedure for fatigue calculation of boiler pressure parts of boilers in Section 13 and associated Annexes, which can be completed by hand in the form of a table calculation as shown in the sample problems in Annex C of EN 12952-3. The code also allows using more complicated methods such as FEA to get more exact life predictions to reduce the conservatism, “Due to the simplicity of this analysis, the results may be conservative with respect to life prediction. More complex methods, e.g. finite element analysis, may be applied to obtain more exact life predictions.” Regardless of the methods used in the analysis, the key inputs include geometry, material properties and transient load boundary conditions. The assumptions in selecting these input parameters can make the results different even if the calculations are following the same code methodology.

## Effect of Ramp Rate Selection

EN 12952-3 provides two sample calculations in Annex C, illustrating the fatigue calculation procedure described in Section 13 (hereinafter referred to as “sample method”). The samples show the procedures of calculation of the admissible number of load cycles and calculation of the admissible temperature gradient. Due to the simplicity of the method, the calculation assumes a constant fluid (steam or water) temperature ramp rate for the start-up and shutdown transient. This constant fluid temperature ramp rate is used as the metal temperature ramp rate on the inside surface of the component. The effect of heat transfer coefficient (HTC) is included in the thermal stress concentration factor (αt) in the sample method. The HTC values are also simplified to two constant values for steam and water. Then the thermal stress is combined with the stress due to internal pressure to obtain the stress range. This simplified method does not reflect the nonlinearity and combination of the internal fluid conditions, e.g., fluid temperature ramp rate, pressure and flow rate.

The determination of the transient temperature ramp rate can be subjective. The Ramp Rates 1, 2 and 3 in Figure 1 illustrate different selections of the simplified linear transient steam ramp rates. Ramp Rate 1 assumes a detailed transient analysis has been performed and uses the actual steam ramp rate of startup and shutdown as the constant ramp rate. Ramp Rate 2 assumes the transient starts when the pressure starts to increase, ends when the steam temperature reaches the operating temperature. For the shutdown, the transient is assumed to start and end with the change of the flow and pressure. Ramp Rate 3 assumes the startup transient starts with pressure increase and ends when pressure, flow and temperature all reach the operating conditions. The ramp rates can be significantly different and result in errors of the fatigue assessment, as shown in Table 1. Ramp Rate 1 considers the most conservative steam ramp rate only, in the entire startup and shutdown transients, resulting in a very high stress range and low allowable number of cycles on fatigue. However, this information is not available unless a detailed transient analysis is performed from a complete dynamic model simulation. In many cases, the ramp rates will be calculated a straight line connecting two steady states, which is closer to the Ramp Rate 3 case. It can be seen that the difference in allowable number of cycles are two orders of magnitude between Ramp Rates 1 and 3, in Table 1.

The effect of transient ramp rate selection might not be as sensitive for long transients with slow ramp rates. With safety factors, this simplified sample method using constant ramp rate can be reasonably conservative. However, the design requirement of today’s HRSGs is for faster response time and more cycles. The selection of transient ramp rates is critical in fatigue life assessment. As suggested in ERPI report, a detailed transient analysis is needed for HRSG fatigue life assessment.

## Effect of Discrete Time Steps and HTC

To take advantage of the time history of the transient details, one improvement over the sample method can be separating the transient by discrete time steps (hereinafter referred to as “discrete method”). At each time step, the through wall temperature difference can be calculated to reflect the conditions provided by the advanced transient analysis. The resultant stresses due to thermal and internal pressure will be combined at each time step instead of only maximum and minimum values in the sample method. The discrete method fully represents the results from transient analysis and better calculates the through-wall temperature distribution.

The stress calculation is still based on the equations and parameters presented in EN 12952-3, assuming one dimensional through-wall heat transfer with corresponding stress concentration factors.

EN 12952-3 suggests the heat-transfer coefficient (HTC) values as follows:

Heat-transfer coefficient:

These HTC values reasonably represent a general average value during a relatively long transient. However, it does not fully represent the heat transfer conditions during the thermal transient. For example, if the constant HTC value for steam is used, then the enhanced thermal transfer due to condensation will be neglected in the analysis. The market is requiring faster response and the HRSG start-up period becomes shorter. A more detailed HTC estimation is needed with respect to the associated transient. Correlations such as Dittus Boelter [5] can be used as the basis for calculating the convective inside HTC assuming well-developed turbulent flow. Direct application of the Dittus Boelter correlation on HTC considers the effect the fluid conditions, e.g., temperature, flow rate, etc. It is a significant improvement on HTC estimation comparing to a constant average value during the entire transient. However, flow in a typical HRSG critical component, e.g., a manifold or a header, does not have the same heat transfer coefficient characteristics as a well developed flow in a pipe.

Typically, flow enters from a pipe in a fully developed turbulent state, which is then decelerated by the expansion into the cavity or by impinging onto the walls of the manifold. In addition to the deceleration, the flow changes direction to follow the path required to reach the exit from the cavity. Then at the exit of the cavity the flow is accelerated through a contraction and begins to redevelop a turbulent boundary layer. These flow patterns typically increase turbulence levels and enhance local heat transfer. All of these flow characteristics need to be accounted for in the thermal boundary conditions. It was found that these characteristics enhance heat transfer to the metal and therefore simple correlations need a multiplier to account for the increased heat transfer. This heater transfer coefficient correction factor (HTCCF) is determined by comparing the heat transfer coefficient determined from CFD to that from the simple correlation as shown in Figure 2.

The stress ranges and corresponding fatigue allowable number of cycles are presented in Table 2, using discrete method with different HTC values and the transient shown in Figure 1. For the default constant HTC values from EN 12952-3 assuming the fluid is all steam during the startup and shutdown process, the stress range and fatigue allowable number of cycles is in between the ones of Ramp Rate 1 and 3, smaller than the ones of Ramp Rate 2. Using Dittus Boelter correlation to calculate HTC, without correction factors from CFD analysis, the stress range is smaller and the allowable number of cycles is higher. Using Dittus Boelter correlation with HTCCF, the stress range is the highest among the three cases, and the allowable number of cycles is the lowest. It can be noted that, comparing the case of Ramp Rate 2, the 520 Mpa stress range is lower than 574 MPa, but the allowable number of cycles are 6235, lower than the 7494 Ramp Rate 2 allowable number of cycles. It is because, using the discrete method, the reference temperature is calculated using the temperatures at the maximum and minimum stress time points, while in the simple method, the reference temperature is calculated from the maximum and minimum temperature of the transient.

Generally, the discrete method provides results closer to Ramp Rate 2 using the simplified sample method. The results from discrete methods shows much smaller difference based on different assumptions of HTC values. It represents more details of the transient and is more robust compared to the sample method.

## Application of FEa Effect of 3D Geometry

Both the sample method and discrete method are based on the equations and parameters presented in EN 12952-3, assuming one dimensional through-wall heat transfer with corresponding stress concentration factors. There are no 3D effects or interactions between non-isolated penetrations considered in the calculation. For example, due to fluid impingement, the component can be heated up much faster on one side and bows to create additional bending moment. If the penetrations are close to each other, the area around the penetrations can be heated up or cooled down faster, such that a hot/cold spot is formed and resulting in additional stresses. This could lead to an anticonservative estimation of the stress and thus an anticonservative fatigue life prediction. The application of 3D finite element analysis (FEA) better represents the actual condition and provides more accurate stress and fatigue results.

Figure 4 plots a color contour of the stress range distribution over a sample manifold in HRSG. The manifold has 3 tube penetrations marked as Tube A, B and C, and a larger nozzle penetration. They are numbered as Position 1, 2, 3 and 4 at 12, 3, 6 and 9 o’clock position, for each of the penetrations, respectively. Table 4 lists the stress ranges at different positions around the penetration for the tubes and the nozzle. It can be seen that the stress ranges at the tube locations are generally higher than the ones at the nozzle locations. This is consistent with the trend shown in the results from the sample method and discrete method. The stress ranges at the nozzle of all 4 positions and the stress ranges at the tube of Positions 2 and 4 are reasonably close to the stress ranges calculated from discrete method with HTCCF. For the nozzle location, the stress range values do not vary, while the stress range values at Positions 2 and 4 are significantly higher than the ones at Positions 1 and 3, for the tube locations. Due to design limitation, the tubes are located on one side of the manifold and heat up or cool down the manifold on one side of the manifold faster than the other side. The interaction between the tube connections produces more thermal stress during the transient and leads to higher stress ranges at Positions 1 and 3, while the stress range values at Positions 2 and 4 are less affected. The nozzle penetration is isolated, and hence, shows less difference in stress range around the penetration edge.

## Inelastic FEA

For cases with stress range fully exceeding the elastic range, a plastic correction is provided in Annex B of EN 12952-3.

This correction is essentially Neuber’s rule correction. When plastic strains are small, it provides a reasonable correction to the results calculated from elastic analysis. For cases with larger plastic strains, the Neuber’s rule correction will be too conservative or under conservative, depending on the type of loads. EN 12952-3 allows using total strain range to calculate the virtual stress range as:

The total strain range can be calculated using inelastic FEA. After obtaining the virtual stress range, following the same procedure, the fatigue life can be calculated.

Table 4 presents the stress ranges and allowable number of cycles calculated from discrete method, elastic FEA and inelastic FEA.

It can be seen the results from linear elastic FEA is most conservative, while results from discrete method and inelastic FEA are closer. It should be noted that it does not mean the discrete method always provides results close to the inelastic FEA.

The stress range value from discrete method is lower than elastic FEA is because it does not consider the interaction between the tube penetrations. The inelastic FEA leads to lower stress range and higher allowable than elastic FEA, because of the redistribution of local high stress in elastic FEA and the more accurate strain range.

## Conclusions and Recommendations

- The HRSG design needs to accommodate higher efficiency and more cycling over the life. Higher efficiency requires higher pressures and temperatures, resulting in thicker components. Both thicker components and faster cycling bring challenge to the fatigue life of the components. The results from simplified methodology can be over or anticonservative. An understanding of the true fatigue life of the critical components is needed. The following are required to achieve this.
- Transient analysis is critical to the fatigue evaluation of cyclic loading, although it is not required by the codes. For new designs, this requires a dynamic model. It provides the detailed history of fluid conditions, including pressure, temperature and flow rate of each of the critical components, while the simplified method generally determines a constant transient ramp of all the fluid conditions by linearly connecting two steady states. With the more cycling and shorter startup time, the results from the simplified method can be misleading. The difference between the predicted fatigue lives can be 1 to 2 orders of magnitudes, depending on the different assumptions, as shown in Table 1. The transient analysis results provide the basis of the detailed analysis on stress and fatigue life.
- Fatigue can be calculated for simple geometries using the discrete method taking advantage of the time history of the fluid conditions, based on the transient analysis results. The discrete method is based on the same equations and stress concentration factors in the sample method. One factor that can contribute to the difference in fatigue life prediction is the selection of heat transfer coefficient. However, the difference is small compared to the difference due to more arbitrary ramp rate selection in the sample method. The Dittus Boelter correlation with correction factors from CFD is recommended for the discrete method.
- FEA is strongly recommended especially for the fatigue assessment of the critical components. It is a GE requirement on HRSGs. The 3D FEA model can not only appreciate the detailed fluid conditions from transient analysis, but also includes the actual geometry effect, e.g., non-uniform heat up and the interaction between the penetrations. Neglecting these effects can lead to anticonservative fatigue life prediction in the design stage. For cases with large strain/stress ranges, inelastic FEA is recommended to reduce the error produced when using general plastic correction equations. It should be noted that using FEA is allowed in most of the design codes as an option for detailed analysis, when the code calculation is too conservative. This study shows that due to the wide range of possible assumptions where the codes are not specifically written, results calculated from code equations are not always conservative.
- An online monitoring system is highly recommended for the HRSGs.

The life assessment at design stage can only be based on limited operating conditions obtained from the dynamic models. The plants can be operated differently from the analyzed conditions. With a monitoring system, the life assessment can be done based on the field measured data. The plant life management will be improved based on more information and better analysis. GE provides “HRSG Life Monitor” as the online life monitoring tool for HRSGs.