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Pressure Transients in Liquid-Gas Lines - Part 2

This is the second in a series of articles on fluid transients in piping systems.

A trapped gas pocket in a liquid system can occur in several configurations, as illustrated in Figure 1. Consider the first case where the gas pocket is trapped in-line at a dead-end, at an initial pressure Pg0. As the pump starts, the gas pocket is compressed, causing an oscillatory pressure in the gas.

The gas pressure can be calculated by closed-form solution based on mass conservation and momentum principles, with gas state equations. A closed-form solution to the differential equations (DE) is plotted in Figure 2, labeled “DE Model”.

A more realistic pressure can be calculated by computational fluid dynamics, taking into consideration the compressibility of the liquid. Figure 2 shows a comparison of the computational fluid dynamics numerical solution with liquid compressibility (labeled “Numerical”) to the rigid column differential equation closed-form solution (labeled “DE Model”). The CFD method goes one step further than just modeling compressibility; it also models the propagation of pressure waves; this is why smaller precursor pressure spikes representing the pump start-up pressure can be found before the main pressure peak.

The second consideration that can be added to these equations is the pump startup characteristics, which may be represented by an exponential ramp up function, where the time constant is pump-specific:

P(t) = Pop exp [-1 / (t + 0.1)s]

The differential equations can then be solved by a numerical stepping method. Figure 3 shows a comparison of an instantaneous pressure increase (pump pressure as step function, labeled “Numerical”) to a pump ramp up without liquid compressibility (labeled “DE Model W/Startup”) and with liquid compressibility (labeled “Numerical Model W/Startup”). These solutions are still bounding as they do not account for the liquid velocity, which is limited by the pump capacity.





Becht Nuclear Projects

  • CFD Analysis
  • Analysis of Buried Tanks
  • Pump Trips/Chk Valve Closure

Computational Fluid Dynamic (CFD) Analysis Resolves Deaerator Cracking

Becht Engineering recently reviewed a utility company's deaerators which experienced a through-wall, circumferential crack at the toe of the fillet weld attaching the saddle to the shell and a through-wall crack was found at the head-to-shell junction at the steam inlet end of the drum.

The saddle to shell cracking was attributed to restrained axial thermal expansion of the shell at a tightly bolted sliding saddle support. The crack was ground out, welded and the support modified to permit sliding.

The head to shell crack cause was attributed to corrosion fatigue, a common occurrence in deaerators. The crack was most likely initiated at a weld surface defect on the I.D. of the drum and grew with time. The daily operating cycles of the drum during periods of reduced steam demand and thermal stresses which we attributed to a poorly designed steam inlet nozzle were the main contributors to the crack growth.

A large diameter superheated steam inlet nozzle extended through the head of the drum terminating 18” into the vessel. The steam exited through a rectangular shaped slot opening on the underside of the pipe which directed the flow of superheated steam directly into the condensate on the bottom of the drum near the shell-to-head weld.

Becht’s computational fluid dynamics model (CFD) indicated that there was little dispersion of the steam exiting the nozzle and that the velocity of the steam mixing with the condensate was relatively high. The superheated steam contact with the cooler condensate resulted in a violent reaction with localized heating and cooling of the vessel shell. This cycling can cause thermal stresses which can result fatigue cracking. Generally, fatigue cracking occurs at welds and heat affected zones adjacent to the weld. Notably no such weld cracking occurred at

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Soil-Structure Interaction Analysis of Buried Tanks

Becht Engineering is performing a seismic analysis to assess the structural integrity of the tanks subjected to a postulated earthquake. The motivation for performing the soil-structure interaction (SSI) analysis in the time domain is to capture the behavior of several contact interfaces present in the tanks including the interface between the tank concrete and the surrounding soil. The presence of this contact interface helps to establish a realistic initial geostatic stress state under gravity loading.

Before the SSI analysis was conducted, a site-response analysis was performed to determine the strain-compatible soil properties. Boundary conditions on the model were prescribed to enforce shear beam behavior of the soil column surrounding and supporting the tank. The seismic input was applied at the base of the SSI model as a force time series corresponding to the known acceleration record.

The model includes the tank waste and the effects of concrete degradation as illustrated below. The soil and concrete are modeled using linear elastic material properties with concrete degradation simulated through the use of equivalent degraded elastic properties. When linear elastic material properties are used to model soils, there is potential for developing artificial soil arching. Excessive arching behavior will result in underestimating the vertical loads on the concrete dome and tank sidewalls. To mitigate the potential for soil arching above the dome, vertical contact surfaces are inserted into the soil above the dome to create annular rings of soil that are free to displace vertically consistent with the tank dome, but allow the load to be transferred laterally during horizontal motion. This effectively creates a nonlinear yield mechanism that acts in the vertical direction only and allows for horizontal load transfer from one ring to the other ring. A low coefficient of friction is used, thereby ensuring

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Pump Trips/Check Valve Closure

pump tripSystems running multiple pumps in parallel can undergo serious equipment and piping damage during a pump trip caused by a power outage or pump mechanical failure. Uncontrolled reverse flow in the system can occur and if improperly selected check valves are used it can result in pumps running backwards or transient pressure spikes in the system, i.e., water hammer.

Water hammer will occur if reverse flow occurs prior closure of the check valve and the effect increases with higher reverse flow velocity. Becht has worked with clients on analysis of the design of their systems, e.g., a water treating facility running multiple 52,000 gpm pumps in parallel, a seawater pump station pumping cooling water through a several mile pipeline to an inland facility and a boiler feed water circulation system for a 3000 psig forced circulation boiler.

In a three pump system (two operating and one spare), one and two pump trips were analyzed to determine the response of the system, i.e., fluid deceleration, time at the occurrence of reverse flow vs. time of check valve closure, pressure transients and unbalanced forces that are imposed on the piping and pumps. The figure shows the forward fluid velocity vs. time as the speed of the pump(s) slows, the point of reverse flow, the time at check valve closure and pressure spikes in the system.

Based on the analysis, the required performance of the check valve to minimize reverse flow can be determined and a valve selected. No valve will close precisely at "zero" fluid velocity; however, certain type valves perform significantly better than others.

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Becht Nuclear - Articles

  • Fluid Transients in Piping Systems 1 +

    Part 1 – Waterhammer in Liquid Lines This is the first in a series of articles on fluid transients in piping systems. Four Broad Categories. From a practical point of view, fluid transients in piping systems can be divided into four Read More
  • Fluid Transients in Piping Systems 2 +

    Pressure Transients in Liquid-Gas Lines - Part 2 This is the second in a series of articles on fluid transients in piping systems. A trapped gas pocket in a liquid system can occur in several configurations, as illustrated in Figure 1. Read More
  • Fluid Transients in Piping Systems 3 +

    Fluid Transients in Piping Systems - Part 3 Liquid-Gas Transients Modeling water hammer due to trapped gas can involve complicated equations while requiring potentially overly conservative assumptions.  In an effort to better show the effects of different modeling methods, this paper will Read More
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Becht Nuclear Lunch & Learn

becht nuclear training

Becht Nuclear Services offers free, 1-hour overview sessions on a variety of topics such as:

  • Wall Thinning Corrosion or Erosion in Piping Systems using ASME XI CC N-513 and N-597
  • Operability of Piping Systems using ASME III Div.1 Appendix F
  • Crack-Like Flaws using ASME XI Failure Assessment Diagram
  • Wall Thinning Corrosion or Erosion in Buried Piping Systems using ASME XI CC N-806
  • Plus much, much more...

Each seminar is followed by a question period for participants.

47 georgeablogInstructor:  George Antaki, PE, fellow ASME, is chairman of ASME III Working Group Piping Design, chairman of ASME B31 Mechanical design Committee, and member of ASME O&M Subgroup Piping.  George is the Division Manager for Becht Nuclear and has over 40 years of hands-on experience.

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