Single-dimension CFD simulation based on an instationary friction model enables precise dimensioning of pump piping systems

Single-dimension CFD simulation based on an instationary friction model enables precise dimensioning of pump piping systems

Pump manufacturer Lewa is installing a test center for validation of simulation results obtained from their new proprietary software module

A technical animation that visualizes the synchronization of three Triplex process diaphragm pumps in different operating states was one of the highlights at Lewa's booth at this year's ACHEMA show. The objective of this kind of simulation is to reduce pressure-induced pulsation and to prevent formation of pipe vibrations that are harmful to the system. Having a detailed pulsation study is essential for optimizing a complex piping system. Lewa of southwestern Germany is the only pump manufacturer in the world to have an internally-developed software program for performing numeric simulations and examining API-674 criteria during the system dimensioning process. Lewa recently added a powerful one-dimensional model for Computational Fluid Dynamics (CFD) in order to obtain precise statements about dynamic processes or pressure amplitudes, such as when pumps are running in parallel.

Particularly with reciprocating positive-displacement pumps, interactions between connected pipelines and other parts of the system are an important factor. Especially when large pumps with high hydraulic output are used, the designer must be sure in advance that the entire structure of the system is properly balanced. By performing pulsation studies early in the planning phase, Lewa can ensure that the entire system will run reliably and more safely.

The studies incorporate not only the complexity of the system, but also the kinematics, the number of cylinders of the pump, and the stroke frequency range. The properties of the fluid, such as viscosity, compressibility, vapor pressure, and sound velocity also play important roles during dimensioning. During the planning phase, all analyses are performed in the form of computer simulations that run on Lewa's own software, known as PumpDesign. During simulation, pressure pulsations and their frequency spectrum are examined in detail in order to uncover and avoid the potential for cavitation and overloads in advance.

Testing friction models

These calculations are used to optimize pulsation damping and piping dimensions in order to prevent the appearance of typical problems such as fatigue damage on pipelines and other components. For these needs, one-dimensional CFD simulation is usually the best compromise between precision and calculation time. The Navier-Stokes equations, which fully describe fluid dynamics, require too much calculation time to be solved directly for large and complex systems. Therefore, a few assumptions and simplifications are needed in order to obtain equations that describe the physical processes in pump pipeline systems with a good degree of accuracy. In addition, even very long and complex piping systems must be solved quickly with a computer. In this simplified process, information about internal friction in the fluid, which was originally contained in the complete physical equations, is lost and must be "artificially" added back in at the end. Several approaches to modeling are available for this purpose. Recently Lewa has focused on researching, testing, and validating the various friction models so they can be used in their one-dimensional CFD software. Lewa engineers have designed and constructed a complex pulsation test center for use as a validation tool that lets them compare simulations and measurements in real time. This serves as a yardstick for assessing the accuracy of the numerical forecast of each approach to modeling. "We installed a Lewa LDC-M910S metering pump in a Triplex configuration in the test system. The stroke length can be varied within a range of 0 to 15 mm. The maximum stroke frequency of the pumps is 420 spm," according to Marco Klinkigt, physicist at LEWA´s Technical Product Management department. Absolute discharge pressure can be adjusted within the range of 1 to 146 bar. The pressure/time curve can be measured at many different positions during operation. The length of the line between the pump and the vessel can be adjusted from 20 to 80 m. The path of the piping can be modified by opening or closing valves; resonators and damping devices can also be installed in various locations.

No commercial CFD calculation program based on the discrete friction model is known

In general, there are two distinct classes of friction models that can be used in one-dimensional CFD calculations. Instationary models incorporate a flow profile that changes over time. Stationary models, by contrast, do not. In many applications, flow rate does not change at all or changes only very slowly, such as systems with centrifugal pumps. Stationary friction models are suitable for these situations. "But when reciprocating positive displacement pumps are used, flow rate typically changes very rapidly and very significantly, so a fully developed flow profile never arises in the pipeline, according to Marco Klinkigt. "In these cases, it is essential that we take the rapid changes to the flow profile into consideration," he continues. However, implementing the model requires a much greater effort and significantly longer calculation times. "To the best of our knowledge, there are no commercially available one-dimensional CFD software programs that implement a comparable model."

Lewa has validated the new CFD module with both stationary and instationary friction models. The stationary model was additionally checked against a commercial software solution. The results of the Lewa software matched the results of the third-party software. Then both fiction models were put onto the experimental test center to show how well they can reproduce the actual measurement results.

Excessive "peak to peak" pressure pulsation and false fading behavior

The comparison between the measurement series clearly shows that the instationary friction model has quantitatively and qualitatively better congruence with the measurement results, whereby two things are most apparent: When the stationary friction model was used, the value of the peak-to-peak pressure pulsation (pmax[t] - pmin[t]) was too large in virtually every observed case. In some cases, a deviation of greater than 200 percent was observed. "Using this kind of model during the design phase can sometimes lead to the selection of inefficiently large dampers or resonators and the installation of unnecessary orifices in the pipes,“ says Marco Klinkigt.

Another significant difference between the simulation results is the fade behavior of the initial pressure peaks during connection. Due to the compressibility of the fluid, the valves at the pump head open with a certain delay. And once the valves are finally open, the piston is already in movement. As result, the connection between the fluid in the line and the fluid in the pump head can be very hard and lead to initial pressure peaks. The simulation with the instationary friction model reproduces virtually the same fade behavior as the measurement results. The stationary friction model exhibits fade behavior that is much too slow.

While the stationary friction model exhibited much poorer congruence in many test measurements, the simulation results with the instationary friction model corresponded very well with the measurement values. So Klinkigt's opinion can be summed up as follows: "Instationary friction models in one-dimensional CFD calculations exhibit very good congruence with the measurement results and help avoid the use of unnecessary, inefficient, or redundant measures intended to reduce pressure pulsation."

Next steps in the planning

Stefan Glasmeyer, Managing Director of Lewa GmbH, feels that the most recent results confirm the company's strategic alignment: "Our mission is to continually advance in the interests of our customers, which is why we not only use cutting-edge tools and processes, but also make every effort to continually improve our equipment and methods." In the near future, we will focus on optimizing simulation models of various damper devices like bladder accumulators, air chambers, and resonators. In a second step, the simulation of the mechanical reaction of the piping elements and fittings due to pressure pulsations will be examined and optimized. Based on the simulation results, Lewa will then have the ability to additionally optimize the mechanical mounting aspect of the pipeline system. Proper dimensioning and positioning of piping fasteners reduces investment costs and contributes to the overall system's longevity and reliability.

Lewa has published a whitepaper with additional information about pulsation studies and the latest findings in the field of Downstream Processing in the Downloads section of its website.