Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session R31: General Fluid Dynamics: General II 
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Chair: Ivan Christov, Purdue University Room: 156 
Monday, November 20, 2023 1:50PM  2:03PM 
R31.00001: Numerical study of the dynamics of a particle in a microchannel with cylindrical obstacles in inertial microfluidics Thota Krishnaveni, Timm Krueger Inertial microfluidics is an emerging technology for the passive manipulation, focusing and sorting of particles. The presence of secondary flow due to flowwise changes in the channel geometry can modify the number and location of the focusing positions. In this work, we numerically investigate the effect of secondary flow, generated by the presence of an array of cylindrical obstacles, on particle migration in a straight rectangular duct under mild inertia. We employ a combination of the latticeBoltzmann, finiteelement, and immersedboundary methods to simulate the fully coupled system. For channels without obstacles, the particle first migrates along the shorter edge, before moving along the longer edge. However, we find the opposite behavior for the channel with larger obstacles. For mediumsized obstacles, we observe the emergence of a new stable focusing position near the centre of the channel. Moreover, as the interobstacle distance decreases, the particle tends to migrate to the focusing position near the channel centre for a wider range of initial positions. Our work opens the door for a better understanding of the focusing mechanisms in bespoke geometries, vital for designing and optimizing channel geometries for inertial microfluidic applications.

Monday, November 20, 2023 2:03PM  2:16PM 
R31.00002: High Reynolds number incompressible crossflow on a rectangular cylinder near a plane wall boundary Daniel Sanchez, Karan Venayagamoorthy Classical literature on different types of cylinders (rectangular or circular) in crossflow have well established the relationship between the drag coefficient versus the Reynolds number; where in the drag coefficient is generally independent of viscous effects beyond a critical Reynolds number. 
Monday, November 20, 2023 2:16PM  2:29PM 
R31.00003: Abstract Withdrawn

Monday, November 20, 2023 2:29PM  2:42PM 
R31.00004: Eigenfunction expansions for sixthorder boundary value problems arising in elasticplated thinfilm dynamics Ivan C Christov, Nectarios C Papanicolaou Thinfilm flows with a surface that has elastic bending resistance are governed by a sixthorder parabolic longwave equation for the film height. Linearizing for small deflections about the equilibrium film height leads to a sixthorder boundary value problem (BVP). We discuss the boundary conditions (BCs) under which such sixthorder BVPs relevant to thinfilm dynamics are selfadjoint. For a particular set of BCs, corresponding to an elasticplated thin film in a closed trough, we explicitly derive a complete set of odd and even orthonormal eigenfunctions, which resemble trigonometric sines and cosines, as well as the socalled ``beam'' functions. Further, we derive explicitly the formulae for expressing derivatives of these eigenfunctions back into the same basis. Based on these novel, explicitlyconstructed eigenfunctions and their derivative expansions, we propose a Galerkin spectral method for sixthorder BVPs relevant to thinfilm dynamics. Importantly, due to the higherorder nature of the BVP, the coefficients of the spectral series decay rapidly in an algebraic manner, making the proposed expansions a highlyefficient computational tool. The proposed Galerkin spectral method and its convergence are demonstrated by solving model sixthorder problems. 
Monday, November 20, 2023 2:42PM  2:55PM 
R31.00005: A Minimization Principle for Incompressible Fluid Mechanics Haithem E Taha, Cody Gonzalez, Mohamed Shorbagy Fluid mechanics is a branch of mechanics concerned with the motion of fluid flows. Mechanics is typically classified into Newtonian and variational mechanics. The great victories in mechanics achieved by physicists in the past century were mainly enabled by variational approaches. While classical mechanics fails at small scales (e.g., atoms) and large scales (e.g., planets), variational mechanics has provided a fundamental approach in both Einstein’s general relativity and quantum mechanics. On the other hand, when we focus our attention on the mechanics of fluids, we find little success has been achieved beyond the Newtonian approach which was culminated in the NavierStokes equations of motion. Certainly, the distribution of research efforts between Newtonian and variational formulations in fluid mechanics is exorbitantly uneven; the overwhelming majority of research efforts are concerned with the Newtonianmechanics formulation of NavierStokes' equations, which may be stalling. Indeed, there is a real need to seriously consider other branches in mehcanics and what they may offer to the motions of fluids. 
Monday, November 20, 2023 2:55PM  3:08PM 
R31.00006: Magnus Force Estimation using the principle of minimum pressure gradient Mohamed A Mohamed, Haithem E Taha The flow around a rotating cylinder is one of the fundamental problems that piqued the interests of many venerable aerodynamicists and fluid mechanicians since the time of Lord Rayleigh. The force caused by the rotation of the cylinder has always been considered as an immediate consequence of viscosity, since the potential flow model failed entirely to predict the value of the circulation, due to the lack of a Kuttalike condition. On the other hand, Glauert modeled the flow outside the boundary layer of a rotating cylinder as a potential flow with an unknown circulation. He then obtained an approximate solution of Prandtl’s boundary layer equations and applied the noslip condition to estimate the circulation in the outer flow. Interestingly, for rapidly rotating cylinders (α = ωR/U >> 1), up to fourthorder in the small parameter ϵ = 1/α, the obtained circulation is independent of viscosity. In this work, we use Glauert’s model of the outer flow over a rotating cylinder (i.e., a potential flow with an unknown circulation). However, instead of the tedious boundary layer calculations, we rely on the recently developed Principle of Minimum Pressure Gradient to obtain the unknown circulation. Perfect matching with Glauert’s solution is found. Moreover, our solution, in contrast to Glauerts’, points to the existence of different physics at small rotational speeds. The obtained results, given their perfect matching with Glauert’s solution (relying on the noslip condition), points to a potential equivalence between the noslip condition and fluid body forces. 
Monday, November 20, 2023 3:08PM  3:21PM 
R31.00007: Pressure Unit Conversion in Lattice Boltzmann Method Matthew Blubaugh, Xiaoyu Zhang, Duan Z Zhang, Dongke Sun, Huidan Yu The lattice Boltzmann method (LBM) is a class of computational fluid dynamics techniques that operates on mesoscale to simulate complex flows. It is a special discrete representation of the Boltzmann equation on lattice nodes/cells, solving the time evolution of particle distribution functions through a set of collision and propagation operations. The fluid particles propagate from one lattice node/cell to another and collide with each other at each time step, resulting in the redistribution of particle distribution functions according to local fluid properties. The macroscopic variables such as density and velocity are calculated through the zeroth and 1^{st} order moments of the particle distribution functions. One challenge in LBM is that pressure values are typically represented on the mesoscopic level, which may not directly correspond to macroscopic units like Pascals or atmospheres used in realworld flow systems. Therefore, it is crucial to establish an appropriate conversion between lattice units (mesoscale) and physical units (macroscale) to ensure the accuracy and relevance of computed pressure. In this study, we systematically explore pressure unit conversion in two specific scenarios: Stokes flow and laminar or turbulent pipe flow, considering viscous and inertial effects, respectively, to characterize the pressure field. The simulated pressure fields are rigorously validated against analytical solutions and experimental measurements. We also address pertinent issues concerning the influence of lattice models and LBM models on the accuracy of pressure quantification, providing practical recommendations to enhance the precision of pressure computations. 
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