A Proposed Guideline For Applying Waterhammer Predictions Under Transient Cavitation Conditions
AFT Impulse™ Technical Paper
Authors: Matthew Stewart P.E., AECOM Management Services; Trey Walters, P.E., Applied Flow Technology; Greg Wunderlich P.E., AECOM Management Services; Erin A. Onat Applied Flow Technology
Presented at the 2018 ASME PVP Conference July 16, 2018
Abstract Part 1: Pressures
Part 1 of this paper describes the various safety factors already provided by ASME B31.3 for pressure containment, provides criteria for accepting the results of HTA calculations that show the presence of transient cavitation, and makes recommendations where the user should include additional safety factors based on the transient cavitation results.
Situations are discussed where waterhammer abatement is recommended to reduce hydraulic transient pressures and forces, and for increasing confidence in HTA results in specific cases. The result is a proposed comprehensive and pragmatic guideline which practicing engineers can use to perform waterhammer analysis and apply pressure predictions to pipe stress analysis.
To this end, various issues are discussed here that result in the calculation of pressures greater than those predicted by the Joukowsky equation. These conditions include reflected waves at tees, changes in piping diameter, and changes in pipe wall material, as well as frictional effects referred to as line pack, and the effects due to the collapse of vapor pockets.
In short, the fundamental goal here is to alert practicing engineers of the cautions that should be applied when using the Joukowsky equation as a first approximation of fluid transient pressures.
Abstract Part 2: Imbalanced Forces
This Part 2 discusses methods of accounting for uncertainty in HTA imbalanced force predictions due to cavitation. The criteria in this paper assume that cavitation in the HTA has been assessed and accepted per the criteria in Part 1 of this paper.
A guideline is proposed for accepting and applying such results and, in particular, makes recommendations on safety factors to use in pipe stress analysis for different cases. The specific recommendations depend on numerous factors including:
- Presence or absence of cavitation in hydraulically connected or isolated parts of the system
- If cavitation occurs, whether the peak forces occur before or after cavitation first occurs
- Size of the cavitation vapor volumes with respect to the computing volumes
- Use of point forces as a conservative substitute in place of potentially less certain elbow pair forces or the manual assessment of maximum envelope values for the force.
Situations are discussed where waterhammer abatement is recommended to reduce hydraulic transient forces, and for increasing confidence in HTA results in specific cases. The result is a proposed comprehensive and pragmatic guideline which practicing engineers can use to perform waterhammer analysis and apply imbalanced force predictions to pipe stress analysis.
Part 1: Pressures
Waterhammer analysis (herein referred to as Hydraulic Transient Analysis or simply “HTA”) becomes more complicated when transient cavitation occurs (also known as liquid column separation). While standard HTA transient cavitation models used with analysis based on the Method of Characteristics show good correlation when compared to known test/field data, the great majority of test/field data are for simple systems experiencing a single transient. Transient cavitation in more complicated systems or from two or more independently initiated transients have not been validated against data.
Part 2: Imbalanced Forces
This complication is exacerbated when trying to predict imbalanced forces as this often involves comparing pressure times area (“PxA”) forces at two locations (for example at elbow pairs). Whereas the pressure at each elbow location has increased uncertainty because of transient cavitation, the difference in PxA forces at elbow pairs involves subtracting one potentially uncertain pressure from another uncertain pressure. Exacerbating this uncertainty yet further, the existence of vapor in a liquid system can dramatically affect the fluid wavespeed and, hence, the timing of the pressure wave travel between two locations such as elbow pairs; so the pressure calculated at each location would not actually occur at exactly the same time.
Below is an excerpt. Use the links above to view the full paper.
Part 1 Introduction
An essential purpose of HTA is to provide guidance so the effects of transients can be accounted for in the piping system’s structural design. It is frequently the case that HTA Engineers and Pipe Mechanical Design Engineers (or Pipe Stress Engineers) work in separate departments and, to some degree, speak a different “engineering language.”
Among the things that HTA Engineers are concerned with is the prediction of fluid pressures and assessing their confidence level in those predicted pressures. Pipe Mechanical Design Engineers need to translate the HTA predicted pressures and their understanding of HTA confidence levels into pipe loads and safety factors used in pipe stress analysis.
A recent project at a nuclear facility in the USA led to a collaboration between the authors. While ASME piping codes provide guidance on safety factors, very little guidance exists for applying them to waterhammer conditions. Safety and piping integrity was a significant concern for this project as the fluids were radioactive.
The collaboration involved bringing together HTA Engineers and Pipe Stress Engineers to create criteria for accepting HTA results. The HTA Engineers documented these criteria in a software validation report. One of the unique aspects of the collaboration was that it involved not only the engineering design firm but also the developer of the HTA software.
The engineering design firm needed pragmatic guidance on how to interpret and apply HTA predictions. One issue that is especially challenging in HTA is modeling transient cavitation (frequently called liquid column separation).
Part 2 Introduction
A byproduct of HTA is the generation of essential parameters to predict imbalanced forces due to waterhammer. The occurrence of transient cavitation (frequently called liquid column separation) greatly complicates the task of determining maximum forces. If one wants to calculate imbalanced forces from waterhammer with increased confidence, it is best to avoid transient cavitation altogether. However, that is not always possible. As a result, increased safety factors are recommended as discussed in this guideline.
As discussed in Part 1 of this paper (Stewart, Walters, Wunderlich and Onat [1]), the authors collaborated on a project involving radioactive fluid transport. The collaboration involved bringing together HTA Engineers and Pipe Stress Engineers to create criteria for accepting HTA results and imbalanced force predictions. The HTA Engineers documented these criteria in a software validation report. The collaboration was unique in that it involved not only the engineering design firm but also the developer of the HTA software.
The authors are not aware of any previously published guidelines for accepting predictions of imbalanced forces from waterhammer. The engineering design firm from the first and third author needed pragmatic guidance on how to interpret and apply HTA pressure and imbalanced force predictions.
The traditional approach for predicting imbalanced forces at, for example, elbow pairs, uses differences in pressure multiplied by area at the elbows. A more complete force balance includes friction and fluid momentum which can result in substantially different predictions. See Wilcox and Walters [2]. Whichever method is used, the presence of transient cavitation is a complicating factor.