Recent research has shown that a commonly used method to estimate transient pipe forces does not reliably yield conservative predictions. As the topic of transient compressible flow is quite complex, engineers should be very cautious in applying simple algebraic formulas to estimate loads for design use. With that caution in mind, some engineers would still like to have a simple method available.

This paper develops a new method that offers an improved way of estimating transient pipe loads. Comparisons are made against numerical simulations for a realistic power station piping example using real gas models for the steam properties and pipe friction. The comparisons are surprisingly good for this example. The improved method provides better estimates than methods commonly used today and is recommended as a replacement for such methods. Engineers should consider using the new, improved method as a preliminary design tool and for screening purposes. Engineers should take extra care in using the new method for detailed design purposes.

Author: Trey W. Walters, PE, Applied Flow Technology, USA; Presented at the ASME PVP Pressure Vessels & Piping Conference, July 2022

An Improved Method of estimating steam hammer loads is detailed. To be used, it requires only a quality steady -state solution. Comparisons against simulation results show surprisingly good agreement. 

Systems designed using the Goodling Method are likely not as safe as previously believed. This includes nuclear power station piping in recent decades. 

The method makes many assumptions and may be best used as a screening tool or for preliminary design purposes. Many existing pipe systems in operating power stations have been designed using the Goodling Method which has been shown to be potentially unconservative. This Improved Method can help evaluate which of these pipe systems should be re -evaluated for safety reasons.

The Improved Method offers significant advantages over the Goodling Method and should
be considered by the engineering community as a replacement for Goodling.

Below is an excerpt. Use the links above to view the full papers. 

INTRODUCTION

Walters [1] and Walters and Lang [2] showed that the Goodling Method [3-4] for estimating steam hammer loads is not reliably conservative. Walters [1] recommended that the Goodling Method should not be trusted by engineers. What then should engineers do? A Recommendation in [1] was that “engineers should consider using a capable simulation tool to determine peak loads and load profiles.” The simulation tool used in [1-2] to elucidate the Goodling Method shortcomings is a commercially available tool [5]. The advantage of such a tool is that it properly handles all important aspect of steam hammer simulation using accurate ASME Steam Tables. Further, it includes a complete force balance on the piping [6] and can therefore generate more accurate peak forces and force-time profiles. As a result, engineers will get the best answer possible while reducing uncertainty and the resulting need to overdesign.

A question arises from this line of thought. If one should not rely on the Goodling Method, are there any quick analytical short cuts that can be used to estimate steam hammer loads that provide more trustworthy predictions? This paper attempts to provide such a short cut method based on the findings in [1-2]. By necessity, engineers are pragmatic. In the Recommendations section of this paper some pragmatic advice will be given on when and when not to use the short cut method in this paper. It will be recommended to use the short cut method in this paper as a preliminary design tool and for screening purposes. Use of a “capable simulation tool” [1] is recommended to finalize design loads.

This paper relies heavily on the findings in [1-2]. One who wishes to understand the details behind this paper should consult those references. Here the relevant findings from [1-2] that explain this new method will be collected, reiterated and applied.

SUMMARY OF STEAM FLOW WAVE BEHAVIOR

Here a brief summary is given of some of the main points detailed in [1-2]. When a valve closes in a steam line (or any gas line) where there is positive forward flow, a compression wave is generated upstream of the valve. The wave travels in the opposite direction of the bulk fluid flow. When the valve closes over some finite time (as all real valves do), a family of compression waves is generated. For a perfect gas in frictionless, adiabatic flow, closed-form analytical relationships can be developed to predict movement and behavior of this family of waves over time and space [2]. For real systems which include real gas behavior and friction, a capable simulation tool is needed to accurately predict this [1]. Fig. 1 shows an example system from [1]. Here the steam flow is from left to right. The TSV (Turbine Stop Valve) at the right closes over some time, tc. This generates a family of waves which moves to the left, backward into the oncoming flow of steam.

Read the full paper for detailed examples, equations, and reference index.