Piping is an integral element in steam turbine power plants, transporting steam from boilers to turbine inlets and redirecting it from outlets to re-heaters, condensers and other equipment. These pipes exert significant forces and moments on the turbine casing in 3 principal directions. It is the turbine designer’s responsibility to define allowable limits for these forces and moments, ensuring they do not cause excessive distortion and stress to the casing and joints.
When piping systems are outsourced to third- party contractors, these limits must be clearly communicated. Forces and moments imposed on turbine casing by external piping systems are constrained by turbine distortion limits, and in some cases, stress thresholds. Distortions in the casing can misalign the rotor, both during cold and operational conditions. The shell distortion has to be maintained within the specific limits by limiting the piping forces. Appropriate analysis can help maximize these limits, enabling third- party suppliers to design compliant piping systems without compromising turbine performance.
The principle of superposition, a foundational concept in mechanics, states that the resultant deflection from multiple simultaneous loads can be determined by summing the deflections caused by each load individually. This principle applies to linear systems where deflections and rotations remain small, ensuring that Hooke’s law holds and the load-deflection relationship remains linear.
In the context of piping load analysis, the principle allows for the decomposition of complex loading scenarios into simpler cases. These individual deflections are calculated and then superimposed to obtain the total deflection. For example, in a cantilever beam subjected to multiple loads, the resultant deflection is the algebraic sum of the deflections caused by each load, provided the loads and their effects remain within the linear elastic range. The illustration below further sheds light on the use of the principle of superposition for calculating the deflections of beams. For instance, let us assume a beam subjected to loads P1 and P2 simultaneously as shown below figure (1)
Figure 1: A simple cantilever beam with two-point loads
From the principle of superposition, we can split the combined load on beam into two individual loads as shown below figure (2).
Figure 2: Deflections due to individual loading
We can then calculate the deflection at the free end of the beam due to load P1 alone as
And deflection at free end due to load P2 alone as
And the method of superposition says that the resultant deflection from these two individual loads is simply the algebraic sum of individual loads, as shown in below figure (3). Resultant deflection due to combined loads is given below
Figure 3: Deflection due to combined loading
To analyze the turbine casing, unit forces and unit moments were applied independently on each pipe. The total number of unit load cases equals 6 (Number of pipes), representing three forces and three moments for each pipe in the principal directions. The following values were used for unit loading:
The following figure (4) shows a typical casing with pipe and the application of unit loading on a casing with the help of rigid links created at the center of the pipe.
Figure 4: Casing with a pipe and application of load on a pipe
The casing was analyzed under these unit loads, and the resulting axial, vertical and transverse deflections were measured at predefined points using FEA. Assuming linear elastic behavior, these results were used to construct a load / deflection transfer function in the spreadsheet. This transfer function enables rapid calculation of casing deflections for any combination of forces and moments.
The following equation shows the load/ deflection transfer function at any point “A” for one pipe.
Number of terms in the load/deflection transfer function depends on the number of nozzles the turbine has i.e. 6 Number of nozzles.
Validation runs confirmed that the spreadsheet's predictions aligned closely with FEA results, typically showing errors of less than 1%. This accuracy ensures that the spreadsheet tool is a reliable and efficient method for calculating deflections under complex loading scenarios.
Figure 5: Input and output for a typical Spreadsheet tool.
Monte Carlo simulations were employed to address uncertainties in force and moment ranges, providing a robust statistical framework for optimization. Unlike deterministic analysis, which evaluates a single scenario, Monte Carlo simulations generate thousands of random scenarios to assess the impact of uncertain variables on the system.
Monte Carlo simulation derives its name from Monte Carlo, Monaco, famed for its casinos and games of chance. Games such as roulette wheels, dice, and slot machines exhibit random behavior. This randomness mirrors how Monte Carlo simulation selects values for variables at random to simulate a model. For example, when rolling a die, the outcome is always one of six possibilities, but the specific result is unpredictable. Similarly, variables with defined ranges but uncertain exact values behave in a comparable way in the simulation.
Crystal Ball:
Crystal Ball Standard is an intuitive simulation program that helps analyze risks and uncertainties in Microsoft Excel spreadsheet models. Excel models are inherently deterministic, meaning inputs are fixed to single values per cell, allowing only one solution to be viewed at a time. For alternative results, manual changes to inputs are required.
Crystal Ball extends Excel’s capabilities by enabling rapid simulations of numerous potential outcomes. While Excel cannot run on simulations without extensive macro coding, Crystal Ball provides an efficient alternative. It allows for hundreds or even thousands of simulation trials to be conducted in minutes.
During a single trial, Crystal Ball randomly selects values for uncertain variables – such as forces and moments - based on their defined range and probability distribution. The spreadsheet then recalculates results for the chosen scenario, providing a comprehensive analysis of potential outcomes.
Defining Assumptions:
The first step in using Crystal Ball is identifying uncertain model inputs and assigning profitability distributions to them. For each uncertain variable, such as forces or moments, the possible range (of values is defined.. The type of probability distribution is selected based on the variable’s conditions.
Distribution types include:
Figure 6: Types of distributions for uncertain variables
In this analysis, a uniform distribution was chosen, where all values between the minimum and maximum are equally likely to occur.
Uniform distribution, assumes the following:
This assumption simplifies the modeling process while ensuring accurate representation of input variability.
Defining Target Forecasts:
A forecast is a formula cell in the spreadsheet representing the output to be analyzed – such as the deflection at a specific point of interest. The coded load / deflection transfer function in spreadsheet calculates these values dynamically.
Multiple assumptions (uncertain inputs) and forecasts (outputs) can be defined. Once these parameters are set, the number of simulation trials is chosen, ranging from hundreds to several thousand, depending on the required accuracy and computational resources.
The simulation was run for 50,000 trials; resulting in 50,000 forecasts. Results were displayed in the form of interactive histograms(frequency charts), providing a clear visualization of deflection distributions. The below figure shows the results of 50,000 trials of our piping analysis at one of the targets forecast.
Figure 7: Simulation results after 50000 trails
Figure 7 showed a deflection range of–2.10 mils to 2.11 mils, based on the assumed forces and moment ranges. This range of distortion can be fine-tuned by adjusting input assumptions. To do so, sensitivity analysis identifies the most influential forces and moments affecting deflections.
The sensitivity chart ranks input variables based on their impact, providing insight into which forces or moments require tighter controls. Figure 8 demonstrates a typical sensitivity chart from the analysis.
Figure 8: Sensitivity chart for one of the targets forecast
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Sadasiva Reddy Challa holds a Master’s degree in Mechanical Engineering with a specialization in Solid Mechanics and Design from IIT Kanpur. With over 25 years of experience in Finite Element Analysis and Engineering Design, he has developed expertise in design optimizations, data-matched simulations, and hand calculations. His extensive experience spans multiple industries including automotive, heavy engineering, white goods, HVAC, aerospace, oil & gas, and rail. Sadashiva possesses a comprehensive understanding of various engineering service quality standards, ensuring excellence in all his professional endeavors.
Upon receipt of a De Novo request, the FDA will conduct an acceptance review. The acceptance review is an administrative review to assess the completeness of the application and whether it meets the minimum threshold of acceptability. If any of the acceptance elements are not included, a justification has to be provided for the omission.
To aid in the acceptance review, it is recommended to submit an Acceptance Checklist as per the guidance document with the De Novo request that identifies the location of supporting information for each checklist element.
The De Novo request will not be accepted and will receive a Refuse to Accept (RTA) designation if one or more of the elements noted as RTA items in the Acceptance Checklist are not present and no explanation is provided for the omission(s). However, during the RTA review, the FDA staff has the discretion to determine whether the missing checklist elements are needed to ensure the De Novo request is administratively complete to allow the De Novo request to be accepted.
Within 15 calendar days of the Document Control Center receiving the De Novo request, the FDA will notify the requester electronically of the acceptance review result as one of the following:
Once the De Novo request is accepted for substantive review, the FDA conducts a classification review of legally marketed device types and analyzes whether an existing legally marketed device of the same type exists. This information is used to confirm that the device is eligible for De Novo classification.
During the substantive review of a De Novo request, the FDA may identify deficiencies that can be adequately addressed through interactive review and not require a formal request for additional information.
If the issues and deficiencies cannot be addressed through interactive review, an Additional Information letter will be sent to the requester. If an Additional Information letter is sent, then the De Novo request will be placed on hold. The requester has 180 calendar days from the date of the Additional Information letter to submit a complete response to each item in the Additional Information letter.
Note: The response must be sent to the DCC within 180 calendar days of the date of the Additional Information letter. No extensions beyond 180 days are granted. If the FDA does not receive a complete response to all deficiencies in the Additional Information letter within 180 days of the date of the letter, the request will be considered withdrawn and deleted from the FDA's review system. If the De Novo request is deleted, the De Novo requester will need to submit a new request to pursue the FDA's marketing authorization for that device.
The requester must submit their response to an Additional Information letter in electronic format (eCopy), to the DCC of the appropriate center. The response should—
The final step is the De Novo request decision. Under MDUFA IV, the FDA's goal is to decide about a De Novo request in 150 review days. Review days are calculated as the number of calendar days between the date the De Novo request was received by the FDA and the date of the FDA's decision, excluding the days a request was on hold for an Additional Information request.
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