The immersed boundary method has attracted considerable interest in the last few years. The method is a computational cheap alternative to represent the boundaries of a geometrically complex body, while using a cartesian mesh, by adding a force term in the momentum equation. The advantage of this is that bodies of any arbitrary shape can be added without grid restructuring, a procedure which is often time-consuming. Furthermore, multiple bodies may be simulated, and relative motion of those bodies may be accomplished at reasonable computational cost. The numerical platform in development has a parallel distributed-memory implementation to solve the Navier-Stokes equations. The Finite Volume Method is used in the spatial discretization where the diffusive terms are approximated by the central difference method. The temporal discretization is accomplished using the Adams-Bashforth method. Both temporal and spatial discretizations are second-order accurate. The Velocity-pressure coupling is done using the fractional-step method of two steps. The present work applies the immersed boundary method to simulate a Newtonian laminar flow through a three-dimensional sudden contraction. Results are compared to published literature. Flow patterns upstream and downstream of the contraction region are analysed at various Reynolds number in the range 44 ≤ R e D ≤ 993 for the large tube and 87 ≤ R e D ≤ 1956 for the small tube, considerating a contraction ratio of β = 1 . 97 . Comparison between numerical and experimental velocity profiles has shown good agreement.
The present paper concerns large-eddy simulations of turbulent downhole flow for six Reynolds numbers and five Taylor numbers. Swirl parameter within the range (0-0.98), which compares the effects of the rotation and the flow rates, was evaluated. In this work, the fluid is injected through the drill pipe and then accelerated by the nozzle. As the fluid discharges from the nozzle, a high speed jet is generated in the downhole region, the fluid then impinges the bottomhole surface and finally flows out the downhole region through the annulus. The nozzle is represented by a sudden contraction. The dynamic subgrid scale model has been used to calculate the turbulent viscosity. The immersed boundary method is employed to represent the solid walls of the proposed geometry. Coherent structures appear as spiral rolls into the nozzle and their inclination angles depend on the rotational speed. When the rotational speed increases, these structures are more aligned with the tangential direction. Due to the geometry of the problem, a toroidal vortex takes place and it grows as the Reynolds number increases. The magnitude of the velocity fluctuations increase in the jet region and near the sidewall with increasing flow rate; it also increased in the jet region with increasing rotational speeds.The impact force and the peak pressure on the impacted surface increases with increasing flow rates. Good agreement of the impact force with other works supports the present work methodology.
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