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Allie Yuxin Lin
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In my first year of university, I became enamored with science fiction novels, particularly those dealing with the subgenre of time travel. During one of my literary pursuits, I came across the story of a 20th century nurse who manages to save the lives of many 16th century soldiers because she engineered a modern syringe from a viper’s hollow fang. While the modern hypodermic needle was not invented until the 1850s, the first syringe (not necessarily hypodermic) was created in 1650 based on Pascal’s Law, which states that a pressure applied at any point in a confined fluid will be directly transmitted throughout the fluid. I would later learn of another indispensable part of modern civilization that is also based on Pascal’s Law, and, you could say, transforming lives in its own way.
A piston pump is a type of reciprocating pump in which the reciprocating motion of a piston forms a chamber. When the pump expands, the chamber draws in fluid through a valve; when the pump contracts, the chamber expels fluid through a separate valve. A syringe’s plunger works by the same mechanism, as do hand soap dispensers, well pumps, bicycle pumps, and more. These machines have a simple design, which has allowed them to become a critical part of the oil and gas industry, where they are primarily used to transfer fluids at high pressures during extraction and processing operations. Their function as a positive displacement device, as well as their ability to generate high pressures and handle a wide range of fluid types, make piston pumps particularly attractive for the oil and gas industry. In particular, they are used in tasks such as well stimulation (including hydraulic fracturing and acidizing), mud pumping during drilling, chemical injection for corrosion inhibition, flow assurance, wellhead service, and high-pressure fluid transfer in pipelines and processing facilities.
Given their importance in industry, finding the right tools to model piston pumps can offer valuable insights into the design and application of these ubiquitous tools. However, piston pumps often involve complex moving boundaries, as well as intricate piston motion and valve dynamics, which may pose a challenge for simulation. These apparatuses are also prone to cavitation, which refers to the formation and collapse of vapor bubbles in the pump’s fluid. This happens when the working pressure inside the pump falls below the fluid’s vapor pressure, causing localized vaporization. When these bubbles collapse, they create shock waves that may lead to undesired vibrations, machinery damage, and reduced efficiency over time.
CONVERGE is a useful tool for piston pump simulations because it can efficiently overcome many of the challenges associated with these devices. Our solver automatically generates the computational mesh at each time-step, eliminating the need for complex re-meshing strategies. Adaptive Mesh Refinement (AMR) ensures high resolution where it is needed without incurring extensive computational costs. Fluid-structure interaction (FSI) modeling can accurately track the interaction between the piston, the valves, and surrounding fluid to predict pressure and flow behavior. Furthermore, CONVERGE includes several built-in cavitation models and multi-phase capabilities that help predict vapor formation, bubble collapse, and pressure spikes.
In this CONVERGE case study, we simulated a piston pump with plate valves to regulate the pressure and suction sides and compared our results to experimental data.1 In this geometry,2 the fluid (water) is induced by an oscillatory movement of the plunger. As the plunger reaches its minimum displacement, the pump begins its suction stroke; similarly, as the plunger reaches its maximum displacement, the pump begins its discharge stroke.
CONVERGE’s FSI modeling captured the dynamic relationship between the fluid and the plate valves, the pump chamber, and the suction and pressure pipes. The two-way coupled FSI approach predicted the rigid-body motion of the plate valves resulting from the balance between the fluid load and suction pressure on one side and the spring loads on the other. In this study, both forces were set up as 1DOF FSI objects, i.e., they could only move translationally, along the x-axis. The FSI spring feature models spring forces between a fixed object and a rigid FSI object (valve). The model approximates the force of a linear coil spring, with specified parameters for stiffness, damping constant, length, and pre-load.
Other CONVERGE features that aided in this simulation include the RNG k-epsilon model, which accounted for the turbulent flow in the pump. The phase change between the liquid and vapor phases was captured using cavitation modeling, specifically, the homogenous relaxation model (HRM). HRM predicts the mass exchange between the liquid and vapor and describes the rate at which the liquid-vapor mass interchange approaches equilibrium. In this case, we used time scale coefficients for the condensation and evaporation of water to predict mass flow rate and discharge.
For a more accurate simulation, velocity- and void fraction-based AMR were applied to refine and coarsen the mesh depending on the resolution requirements. In addition, fixed embedding was employed around the valves and the piston crown to maintain a fine resolution while keeping the rest of the grid coarse. Pressure-velocity coupling was captured with the Pressure Implicit Splitting of Operators (PISO) scheme, which performs the PISO algorithm in a loop until it reaches a user-specified PISO tolerance value.
Overall, there was good agreement between the experimental values and CONVERGE data, as measured by the valve lift. In addition to accurately capturing the amount of displaced volume in the pump, our simulation effectively predicted compressibility effects.
Much like the inventive syringe, piston pumps—which are rooted in the same scientific principles—are an indispensable part of modern industry. Their simple yet powerful design, based on Pascal’s Law, allows them to perform critical tasks in the oil and gas sector, in spite of challenges such as multi-phase dynamics and cavitation. In this case study, we leveraged CONVERGE’s innovative tools, including FSI and multi-phase flow modeling, to simulate two-phase flow in a reciprocating displacement pump incorporating fluid-actuated valve movement. Advanced simulations such as the one outlined in this blog help refine our understanding of piston pumps, ensuring they continue to function efficiently and effectively under all circumstances.
[1] Anciger, D., “Numerische Simulation der Fluid-Struktur-Interaktion fluidgesteuerter Ventile in oszillierenden Verdrängerpumpen.” Ph.D. thesis, Technische Universität München, Munich, Germany, 2012.
[2] Deimel, C., et al. “Numerical 3D Simulation of the Fluid-Actuated Valve Motion in a Positive Displacement Pump with Resolution of the Cavitation-Induced Shock Dynamics.” Eighth International Conference on Computational Fluid Dynamics (ICCFD8), ICCFD8-2014-0433, Chengdu, China, July 14-18, 2014. DOI: 10.13140/2.1.3443.2326
