Large-eddy simulation and streamline coordinate analysis of flow over an axisymmetric hull

Abstract

A new perspective on the analysis of turbulent boundary layers on streamlined bodies is provided by deriving the axisymmetric Reynolds-averaged Navier–Stokes equations in an orthogonal coordinate system aligned with streamlines, streamline-normal lines and the plane of symmetry. Wall-resolved large-eddy simulation using an unstructured overset method is performed to study flow about the axisymmetric DARPA SUBOFF hull at a Reynolds number of $Re_L = 1.1 \times 10^{6}$ based on the hull length and free-stream velocity. The streamline-normal coordinate is naturally normal to the wall at the hull surface and perpendicular to the free-stream velocity far from the body, which is critical for studying bodies with concave streamwise curvature. The momentum equations naturally reduce to the differential form of Bernoulli's equation and the $s$ – $n$ Euler equation for curved streamlines outside of the boundary layer. In the curved laminar boundary layer at the front of the hull, the streamline momentum equation represents a balance of the streamwise advection, streamwise pressure gradient and viscous stress, while the streamline-normal equation is a balance between the streamline-normal pressure gradient and centripetal acceleration. In the turbulent boundary layer on the mid-hull, the curvature terms and streamwise pressure gradient are negligible and the results conform to traditional analysis of flat-plate boundary layers. In the thick stern boundary layer, the curvature and streamwise pressure gradient terms reappear to balance the turbulent and viscous stresses. This balance explains the characteristic variation of static pressure observed for thick boundary layers at the tails of axisymmetric bodies.

Effect of tabs on the shear layer dynamics of a jet in cross-flow

“…The first issue was addressed by the novel parallel communication structure of Horne & Mahesh (2019a) and the second by the interpolation scheme of Horne & Mahesh (2019b). This overset method has been validated for a variety of flows (Horne & Mahesh 2019b) and has been applied to successfully perform large-eddy simulation of the turbulent boundary layer over an axisymmetric hull (Morse & Mahesh 2021) and a ducted propulsor in crashback (Kroll & Mahesh 2022), as well as DNS of a variety of resolved particle-laden flows (Horne & Mahesh 2019b). The solution is advanced in time using a implicit Crank-Nicolson time stepping with a predictor-corrector scheme, where the velocities are predicted using the momentum equation and subsequently corrected using the pressure Poisson equation to satisfy continuity.…”

“…The first issue was addressed by the novel parallel communication structure of Horne & Mahesh (2019 a ) and the second by the interpolation scheme of Horne & Mahesh (2019 b ). This overset method has been validated for a variety of flows (Horne & Mahesh 2019 b ) and has been applied to successfully perform large-eddy simulation of the turbulent boundary layer over an axisymmetric hull (Morse & Mahesh 2021) and a ducted propulsor in crashback (Kroll & Mahesh 2022), as well as DNS of a variety of resolved particle-laden flows (Horne & Mahesh 2019 b ).…”

Large-eddy simulation of tripping effects on the flow over a 6 : 1 prolate spheroid at angle of attack

“…Generally, P 11 , P 22 and P 33 are negligible compared to the shear production throughout the boundary layer, except at the edge, where the shear become small and the wall-normal and spanwise terms become larger. Finnigan (1983) and Morse & Mahesh (2021) derived the Navier-Stokes equations in streamline coordinates, which contain explicit centrifugal terms. The centrifugal terms and pressure gradient can be combined into a corrected pressure gradient as defined in…”

“…where k is the index corresponding to the direction orthogonal to the streamline vector and the i component (Morse & Mahesh 2021). Each term can be either positive or negative, i.e.…”

Flow Field Description and Simplification Based on Principal Component Analysis Downscaling and Clustering Algorithms

“…The streamline simulation is one of the most feasible methods for dominant flow characterization. In recent years, streamline simulation has attracted more and more attention (Mesbah et al, 2019;Wang et al, 2020;Morse and Mahesh, 2021;Namdari et al, 2021;Zhang et al, 2021). However, discrete streamline distribution cannot accurately represent the actual flow field, limiting its effective application to the oil field.…”