Two-dimensional treesph simulations of choked flow systems
J. Klapp a,1, L. Di G. Sigalotti b,2, S. Galindo a,3, and E. Sira b,4
a Departamento de Física, Instituto Nacional de Investigaciones Nucleares, Km. 36.5 Carretera México-Toluca, 52045 Estado de México, México.
b Centro de Física, Instituto Venezolano de Investigaciones Científicas, Apartado Postal 21827, Caracas 1020A, Venezuela. e-mail: 1 klapp@nuclear.inin.mx,2 lsigalot@cassini.ivic.ve,3 sgu@nuclear.inin.mx,4 esira@hubble.ivic.ve.
]]> Recibido el 1 de septiembre de 2004.
Abstract
It is well-known that the flow of gas, liquid, and their mixtures through restrictors installed in pipeline systems is of great practical importance in many industrial processes. In spite of its significance, numerical hydrodynamics simulations of such flows are almost non-existent in the literature. Here we present exploratory two-dimensional calculations of the flow of a viscous, single-phase fluid through a wellhead choke of real dimensions, using the method of Smoothed Particle Hydrodynamics (SPH) coupled with a simple isothermal equation of state for description of the flow. The results indicate that an approximately stationary mean flow pattern is rapidly established across the entire tube, with the density and pressure dropping and the flow velocity rising within the choke throat. If the downstream flow is inhibited at the outlet end of the tube, a pressure drop of about 12% occurs across the choke when the mean flow reaches an approximate steady state. If, on the other hand, the flow is not inhibited downstream, the pressure drop is reduced to about 8% or less. The flow across the choke throat remains subsonic with typical velocities of ~ 0.1c, where c denotes the sound speed. In contrast, the flow velocities in the upstream and downstream sections of the pipe are on the average factors of ~ 6 and ~ 3.5 times lower, respectively. Correlation studies based on experimental data indicate that the pressure drop is only 3% or even less for gas flow through wellhead chokes at a speed of 0.1c. This discrepancy reflects the inadequacy of the isothermal equation of state to describe realistic gas flows.
Keywords: SPH; numerical particle metnods; choked flow; compressible flow.
Resumen
Es bien conocido que el flujo de gas, líquido y sus mezclas a través de restrictores instalados en sistemas de tuberías es de gran importancia práctica en muchos procesos industriales. A pesar de su importancia, simulaciones hidrodinámicas numéricas de este tipo de flujos son casi inexistentes en la literatura. Aquí presentamos cálculos exploratorios bidimensionales de flujo viscoso de una sola fase a través de un estrangulador de dimensiones reales, utilizando el Método de Hidrodinámica de Partículas Suavizadas (SPH) acoplado con una ecuación sencilla isotérmica de estado para la descripción del flujo. Los resultados indican que un patrón de flujo medio aproximadamente estacionario se establece rápidamente a través de todo el tubo, con la densidad y presión cayendo y el flujo de velocidad aumentando dentro del estrangulador. Si el flujo aguas abajo es inhibido a la salida del tubo, una caída de presión de alrededor de 12% ocurre a través del estrangulador cuando el flujo medio alcanza un estado aproximadamente estacionario. Si, por otro lado, el flujo no es inhibido aguas abajo, la caída de presión se reduce a 8% o menos. El flujo a través del estrangulador se mantiene subsónico con velocidades típicas de ~ 0.1c, donde c denota la velocidad del sonido. En contraste, la velocidad del flujo en las secciones aguas arriba y abajo del tubo son en promedio factores de ~ 6 y ~ 3.5 veces menores, respectivamente. Estudios de correlación basados en datos experimentales indican que la caída de presión es de solo 3% o inclusive menos para flujo de gas a través del estrangulador de la cabeza de un pozo a una velocidad de 0.1c. Esta discrepancia refleja que la ecuación isotérmica de estado no es adecuada para describir flujos realistas de gas.
Descriptores: SPH; métodos numéricos de partículas; flujo estrangulado; flujo compresible.
]]>PACS: 47.11.+j;47.27.-i;47.85.Dh
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Acknowledgments
We thank an anonymous referee for suggestions that improved the final version of the manuscript. One of us (J.K.) is grateful to Federico Gonzalez Tamez of PEMEX, who introduced me to the interesting problem of flow through wellhead chokes. The calculations in this paper were performed using the Silicon Graphics Altix 350 computer system of the Instituto Nacional de Investigaciones Nucleares (ININ) of Mexico. This work is partially supported by the Mexican Consejo Nacional de Ciencia y Tecnología (CONACyT) under contracts U43534-R and J200.476/2004, the Fondo Nacional de Ciencia, Tecnología e Innovation (Fonacit) of Venezuela, the German Deutsche Forshungsgemainshaft (DFG) and the German Deutscher Akademischer Austauschdienst (DAAD).
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