Abstract
<jats:p>Для использования закона Пуазейля при описании медленного движения вязкой несжимаемой жидкости в трещинах горных пород и трещинах гидроразрыва необходимо введение корректирующего коэффициента, зависящего от шероховатости их берегов. С целью уточнения возможного вида такой зависимости в работе на основе программного комплекса CADRUN проведено численное моделирование ламинарных течений в каналах с периодическими стенками. В результате для ряда популярных зависимостей выделена область параметров (частоты шероховатости, ее амплитуды и формы), в которой они неприменимы. Также показано, что ряд параметров шероховатости (например, среднее и среднеквадратичное отклонения поверхности), несмотря на свою популярность, не могут быть основой для построения таких зависимостей в общем случае.</jats:p> <jats:p>Poiseuille’s law, which determines the pressure drop in laminar flow of an incompressible viscous fluid in a planar channel, is derived from the Navier – Stokes equations under the assumptions of constant channel width and straight parallel walls. Due to its simplicity, it is widely used to describe fluid flow in rock fractures and hydraulic fractures, even though these assumptions are not satisfied in such cases. Although the introduction of a correction factor accounting for fracture wall roughness extends the applicability of Poiseuille’s law to a broader class of flows, a comprehensive theory determining the form of this factor and the spectrum of roughness parameters affecting it has not yet been established. In this study, we employ the CADRUN numerical method to perform numerical simulations of laminar flows in channels with rough walls to evaluate the accuracy of both Poiseuille’s law itself and several correction factor formulas available in the literature. The channel wall surfaces were defined using periodic functions, which allowed us to assess assessing and minimizeminimizing computational errors by performing calculations within a single periodic element of the channel. While the use of a relatively narrow class of surfaces does not permit the derivation of a universal correction factor formula, our numerical results have identified a range of roughness parameters (frequency, amplitude, and shape) where the existing formulas become inapplicable. Furthermore, we demonstrate that common roughness parameters such as mean and root-mean-square deviation of the surface profile, despite their widespread use, cannot serve as a basis for constructing general correction formulas for arbitrary channel geometries.</jats:p>