arXiv subjects

Kamran Mohseni

Publications and source records attributed to Kamran Mohseni.

At least 19 recordsLinked to original sources

arXiv2023

Capturing the kinematics and dynamics of fluid fronts

Gibbs was the first person to represent a phase interface by a dividing surface. He defined the dividing surface as a mathematical surface that has its own material properties and internal dynamics. In this paper, an alternative derivation to this mathematical surface is provided that generalizes the concept of dividing surface to fluid fronts beyond that of just a phase or material interface. Other fluid fronts being a vortex sheet, shock front, moving contact line, and gravity wavefront, to name a few. Here, this extended definition of dividing surface is referred to as the extended dividing hypersurface (EDH), as it is not just applicable to a surface front but also to a line and a point front. This hypersurface is a continuum approximation of a diffused region with fluid properties and flow parameters varying sharply but continuously across it. This paper shows that the properties and equations describing an EDH can be derived from the equations describing the diffused region by integrating it in the directions normal to the hypersurface. This is equivalent to collapsing the diffused region in the normal direction. Hence, ensuring that the EDH is both kinematically and dynamically equivalent to that of the diffused region. Various canonical problems are examined to demonstrate the ability of the EDH to accurately represent different types of fluid and flow fronts, including static and dynamic interfaces, shock fronts, and vortex sheets. These examples emphasize the EDH's capability to represent various functionalities within a front, the relationship between the flux of quantities and hypersurface quantities, and the importance of considering the mass of front and associated dynamics.

physics.flu-dyn↗

arXiv2020

On the maintenance of an attached leading-edge vortex via model bird alula

Researchers have hypothesized that the post-stall lift benefit of bird's alular feathers, or alula, stems from the maintenance of an attached leading-edge vortex (LEV) over their thin-profiled, outer hand-wing. Here, we investigate the connection between the alula and LEV attachment via flow measurements in a wind tunnel. We show that a model alula, whose wetted area is 1% that of the wing, stabilizes a recirculatory aft-tilted LEV on a steadily-translating unswept wing inclined at post-stall incidences. The attached vortex is the result of the alula's ability to smoothly merge otherwise separate leading- and side-edge vortical flows. We identify two key processes that facilitate this merging: i) the steering of spanwise vorticity generated at the wing's leading edge back to the wing plane and ii) an aft-located wall-jet of high-magnitude root-to-tip spanwise flow (>80% that of the freestream velocity). The latter feature induces LEV roll-up while the former feature tilts LEV vorticity aft and evacuates this flow toward the wing tip via an outboard vorticity flux. We identify the alula's streamwise position (relative to the leading-edge of the thin wing) as important for vortex steering and the alula's cant angle as important for high-magnitude spanwise flow generation. These findings advance our understanding of the likely ways bird's leverage LEVs to augment slow flight.

physics.flu-dyn↗

arXiv2019

Concurrent Flow-Based Localization and Mapping in Time-Invariant Flow Fields

We present the concept of concurrent flow-based localization and mapping (FLAM) for autonomous field robots navigating within background flows. Different from the classical simultaneous localization and mapping (SLAM) problem, where the robot interacts with discrete features, FLAM utilizes the continuous flow fields as navigation references for mobile robots and provides flow field mapping capability with in-situ flow velocity observations. This approach is of importance to underwater vehicles in mid-depth oceans or aerial vehicles in GPS-denied atmospheric circulations. This article introduces the formulation of FLAM as a full SLAM solution motivated by the feature-based GraphSLAM framework. The performance of FLAM was demonstrated through simulation within artificial flow fields that represent typical geophysical circulation phenomena: a steady single-gyre flow field and a double-gyre flow field with unsteady turbulent perturbations. The results indicate that FLAM provides significant improvements in the robots' localization accuracy and a consistent approximation of the background flow field. It is also shown that FLAM leads to smooth robot trajectory estimates.

cs.RO↗

arXiv2019

Analytic solutions to two quaternion attitude estimation problems

This paper presents solutions to the following two common quaternion attitude estimation problems: (i) estimation of attitude using measurement of two reference vectors, and (ii) estimation of attitude using rate measurement and measurement of a single reference vector. Both these problems yield to a direct geometric analysis and solution. The former problem already has a well established analytic solution in literature using linear algebraic methods. This note shows how the solution may also be obtained using geometric methods, which are not only more intuitive, but also amenable to unconventional extensions. With respect to the latter problem, existing solutions typically involve filters and observers and use a mix of differential-geometric and control systems methods. However, no analytic solution has yet been reported to this problem. In this note, both the problems are formulated as optimization problems, which can be solved analytically to obtain a unique closed-form solution. The analytic attitude estimates are (i) instantaneous with respect to the measurements, thus overcoming the latency inherent in solutions based upon negative feedback upon an error, which can at best show asymptotic convergence, (ii) exact, thus overcoming errors in solutions based upon linear methods, and (iii) geometry-based, thus enabling imposition of geometric inequality constraints.

eess.SY↗

arXiv2018

Numerical simulation of compressible flows using two-phase observable Euler equations

Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous generation of high wavenumber modes, which we term the '$k_\infty$ irregularity.' In this work, an inviscid regularization technique called 'observable regularization' is proposed for the simulation of two-phase compressible flows. The proposed approach regularizes the equations at the level of the partial differential equation and as a result, any numerical method can be used to solve the system of equations. The regularization is accomplished by introducing an 'observability limit' that represents the length scale below which one cannot properly model or continue to resolve flow structures. An observable volume fraction equation is derived for capturing the material interface, which satisfies the pressure equilibrium at the interface. The efficacy of the observable regularization method is demonstrated using several test cases, including a one-dimensional material interface tracking, one-dimensional shock-tube and shock-bubble problems, and two-dimensional simulations of a shock interacting with a cylindrical bubble. The results show favorable agreement, both qualitatively and quantitatively, with available exact solutions or numerical and experimental data from the literature. The computational saving by using the current method is estimated to be about one order of magnitude in two-dimensional computations and significantly higher in three-dimensional computations. Lastly, the effect of the observability limit and best practices to choose its value are discussed.

physics.flu-dyn↗

arXiv2018

Theoretical model of a finite force at the moving contact line

In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is integrable and results in a finite force at the moving contact line if the contact line is treated as a one-dimensional manifold and all three interfaces that make up the moving contact line are taken into consideration. This is due to the dipole nature of the vorticity and pressure distribution around the moving contact line. Mathematically, this finite force is determined by summing all the forces that act over an infinitesimally small cylindrical control volume that encloses the entire moving contact line. With this finite force, we propose a new dynamic Young's equation for microscopic dynamic contact angle that is a function of known parameters only, specifically the interface velocity, surface tension, and fluid viscosity. We combine our model with Cox's model for apparent dynamic contact angle and find good agreement with published dynamic contact angle measurements.

physics.flu-dyn↗

arXiv2018

The role of surface tension gradient in determining microscopic dynamic contact angle

Following Gibb's interpretation of an interface as a dividing surface, we derive a model for the microscopic dynamic contact angle by writing a force balance for a control volume encompassing the interfaces and the contact line. In doing so we identify that, in addition to the surface tension of respective interfaces, the gradient of surface tension plays an important role in determining the dynamic contact angle. This is because not only does it contribute towards an additional force, but it also accounts for the deviation of local surface tension from its static equilibrium value. It is shown that this gradient in surface tension can be attributed to the convective acceleration in the vicinity of the contact line, which in turn is a direct result of varying degree of slip in that region. In addition, we provide evidence that this gradient in surface tension is one of the key factors responsible for the difference in contact angle at the leading and trailing edge, of a steadily moving contact line. These findings are validated using molecular dynamics simulations.

physics.flu-dyn↗

arXiv2017

Long-Term Inertial Navigation Aided by Dynamics of Flow Field Features

A current-aided inertial navigation framework is proposed for small autonomous underwater vehicles in long-duration operations (> 1 hour), where neither frequent surfacing nor consistent bottom-tracking are available. We instantiate this concept through mid-depth, underwater navigation. This strategy mitigates dead-reckoning uncertainty of a traditional inertial navigation system by comparing the estimate of local, ambient flow velocity with preloaded ocean current maps. The proposed navigation system is implemented through a marginalized particle filter where the vehicle's states are sequentially tracked along with sensor bias and local turbulence that is not resolved by general flow prediction. The performance of the proposed approach is first analyzed through Monte Carlo simulations in two artificial background flow fields, resembling real-world ocean circulation patterns, superposed with smaller-scale, turbulent components with Kolmogorov energy spectrum. The current-aided navigation scheme significantly improves the dead-reckoning performance of the vehicle even when unresolved, small-scale flow perturbations are present. For a 6-hour navigation with an automotive-grade inertial navigation system, the current-aided navigation scheme results in positioning estimates with under 3% uncertainty per distance traveled (UDT) in a turbulent, double-gyre flow field, and under 7.3% UDT in a turbulent, meandering jet flow field. Further evaluation with field test data and actual ocean simulation analysis demonstrates consistent performance for a 6-hour mission, positioning result with under 25% UDT for a 24-hour navigation when provided direct heading measurements, and terminal positioning estimate with 16% UDT at the cost of increased uncertainty at an early stage of the navigation.

cs.RO↗

arXiv2016

Unsteady Aerodynamics and Vortex-sheet Formation of A Two-dimensional Airfoil

Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modeling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical Kutta condition can be extended to unsteady situations by realizing that a flow cannot turn abruptly around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a finite-angle trailing edge, or in the case of flow separation away from a sharp corner, the direction of the forming vortex sheet is ambiguous. To remove any ad-hoc implementation, the unsteady Kutta condition, the conservation of circulation, as well as the conservation laws of mass and momentum are coupled to analytically solve for the angle, strength, and relative velocity of the trailing-edge vortex sheet. The two-dimensional aerodynamic model together with the proposed vortex-sheet formation condition is verified by comparing flow structures and force calculations with experimental results for airfoils in steady and unsteady background flows.

physics.flu-dyn↗

arXiv2016

Structure-Preserving Model Reduction of Forced Hamiltonian Systems

This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to fit empirical data. Our aim is two-fold. First, to achieve computational savings for large-scale Hamiltonian systems with external forces. Second, to simultaneously preserve the symplectic structure and the forced structure of the original system. We first reformulate d'Alembert's principle in the Hamiltonian form. Corresponding to the integral and local forms of d'Alembert's principle, we propose two different structure-preserving model reduction approaches to reconstruct low-dimensional systems, based on the variational principle and on the structure-preserving projection, respectively. These two approaches are proven to yield the same reduced system. Moreover, by incorporating the vector field into the data ensemble, we provided several algorithms for energy preservation. In a special case when the external force is described by the Rayleigh dissipative function, the proposed method automatically preserves the dissipativity, boundedness, and stability of the original system. The stability, accuracy, and efficiency of the proposed method are illustrated through numerical simulations of a dissipative wave equation.

math.NA↗

arXiv2015

A unified slip boundary condition for flow over a surface

Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the widely used no-slip and the Navier and Maxwell slip boundary conditions do not capture the complete physics associated with complex problems, such as spreading of liquids or corner flows. Hence, we present a unified boundary condition that is applicable to a wide-range of flow problems.

physics.flu-dyn↗

arXiv2015

Symplectic Model Reduction of Hamiltonian Systems

In this paper, a symplectic model reduction technique, proper symplectic decomposition (PSD) with symplectic Galerkin projection, is proposed to save the computational cost for the simplification of large-scale Hamiltonian systems while preserving the symplectic structure. As an analogy to the classical proper orthogonal decomposition (POD)-Galerkin approach, PSD is designed to build a symplectic subspace to fit empirical data, while the symplectic Galerkin projection constructs a reduced Hamiltonian system on the symplectic subspace. For practical use, we introduce three algorithms for PSD, which are based upon: the cotangent lift, complex singular value decomposition, and nonlinear programming. The proposed technique has been proven to preserve system energy and stability. Moreover, PSD can be combined with the discrete empirical interpolation method to reduce the computational cost for nonlinear Hamiltonian systems. Owing to these properties, the proposed technique is better suited than the classical POD-Galerkin approach for model reduction of Hamiltonian systems, especially when long-time integration is required. The stability, accuracy, and efficiency of the proposed technique are illustrated through numerical simulations of linear and nonlinear wave equations.

math.NA↗

arXiv2014

Nonlinear Model Reduction via an Adaptive Weighting of Snapshots

In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear systems characterized by parameter variations. Instead of using a global basis to construct a global reduced model, the proposed method approximates the original system by multiple lower-dimensional subspaces. Each localized reduced basis is generated by the SVD of a weighted snapshot ensemble; here, each weighting coefficient is a function of the input parameter. Compared with a global model reduction method, such as the classical POD, the adaptive model reduction method could yield a more accurate solution with a fixed subspace dimension. Moreover, we combine the adaptive reduced model with the chord iteration to solve elliptic PDEs in a computationally efficient fashion. The potential of the method for achieving large speedups, while maintaining good accuracy, is demonstrated for both elliptic and parabolic PDEs in a few numerical examples.

math.NA↗

arXiv2014

An Online Manifold Learning Approach for Model Reduction of Dynamical Systems

This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a model reduction procedure. Specifically, starting with a test solution, the method solves a reduced model to obtain a more precise solution, and it repeats this process until sufficient accuracy is achieved. The reduced model is obtained by projecting the full model onto a subspace that is spanned by the dominant modes of an extended data ensemble. The learning procedure is computed in the online stage, as opposed to being computed offline, which is used in many projection-based model reduction techniques that require prior calculations or experiments. After providing an error bound of the classical POD-Galerkin method in terms of the projection error and the initial condition error, we prove that the sequence of approximate solutions converge to the actual solution of the original system as long as the vector field of the full model is locally Lipschitz on an open set that contains the solution trajectory. Good accuracy of the proposed method has been demonstrated in two numerical examples, from a linear advection-diffusion equation to a nonlinear Burgers equation. In order to save computational cost, the SIRM method is extended to a local model reduction approach by partitioning the entire time domain into several subintervals and obtaining a series of local reduced models of much lower dimensionality. The accuracy and efficiency of the local SIRM are shown through the numerical simulation of the Navier--Stokes equation in a lid-driven cavity flow problem.

math.DS↗

arXiv2013

Effect of slip on circulation inside a droplet

Internal recirculation in a moving droplet plays an important role in several droplet-based microfluidic devices as it enhances mixing, chemical reaction and heat transfer. The occurrence of fluid slip at the wall, which becomes prominent at high shear rates and lower length scales, results in a significant change in droplet circulation. Using molecular dynamics (MD) simulations, the presence of circulation in droplets is demonstrated and quantified. Circulation is shown to vary inversely with slip length, which is a measure of interface wettability. A simple circulation model is established that captures the effect of slip on droplet circulation. Scaling parameters for circulation and slip length are identified from the circulation model which leads to the collapse of data for droplets with varying aspect ratio (AR) and slip length. The model is validated using continuum and MD simulations and is shown to be accurate for droplets with high AR.

physics.flu-dyn↗

arXiv2013

Observations on the flow structures and transport in a warm-core ring in the Gulf of Mexico

This study presents several new observations from the study of a warm-core ring (WCR) in the Gulf of Mexico based on the ECCO2 global ocean simulation. Using Lagrangian coherent structures (LCS) techniques to investigate this flow reveals a pattern of transversely intersecting LCS in the mixed layer of the WCR which experiences consistent stretching behavior over a large region of space and time. A detailed analysis of this flow region leads to an analytical model velocity field which captures the essential elements that generate the transversely intersecting LCS. The model parameters are determined from the WCR and the resulting LCS show excellent agreement with those observed in the WCR. The three-dimensional transport behavior which creates these structures relies on the small radial outflow which is present in the mixed layer and is not seen below the pycnocline, leading to a sharp change in the character of the LCS at the bottom of the mixed layer. The flow behavior revealed by the LCS limits fluid exchange between the WCR and the surrounding ocean, contributing to the long life of WCRs. Further study of these structures and their associated transport behavior may lead to further insights into the development and persistence of such geophysical vortices as well as their transport behavior.

physics.ao-ph↗

arXiv2012

Lift Evaluation of a 2D Flapping Flat Plate

Several previous experimental and theoretical studies have shown that a leading edge vortex (LEV) on an airfoil or wing can provide lift enhancement. In this paper, unsteady 2D potential flow theory is employed to model the flow field of a flapping flat plate wing. A multi-vortices model is developed to model both the leading edge and trailing edge vortices (TEVs), which offers improved accuracy compared with using only single vortex at each separation location. The lift is obtained by integrating the unsteady Blasius equation. It is found that the motion of vortices contributes significantly to the overall aerodynamic force on the flat plate. The shedding of TEVs and the stabilization of LEVs explicitly contributes to lift enhancement. A Kutta-like condition is used to determine the vortex intensity and location at the leading edge for large angle of attack cases; however, it is proposed to relax this condition for small angle of attack cases and apply a 2D shear layer model to calculate the circulation of the new added vortex. The results of the simulation are then compared with classical numerical, modeled and experimental data for canonical unsteady flat plat problems. Good agreement with these data is observed. Moreover, these results suggested that the leading edge vortex shedding for small angles of attack should be modeled differently than that for large angles of attack. Finally, the results of vortex motion vs. lift indicate that both a motion against the streamwise direction of the LEV and a streamwise motion of the TEV contributes positive lift. This also provides the insights for future active flow control of MAVs that the formation and shedding process of LEVs and TEVs can be manipulated to provide lift enhancement.

physics.flu-dyn↗

arXiv2012

Analysis of Boundary Slip in a Flow with an Oscillating Wall

Molecular dynamic (MD) simulation is used to study slip at the fluid-solid boundary in an unsteady flow based on the Stokes second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical shear rate of the corresponding steady flow. This increased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteady mathematical model for slip is established, which estimates the increment in slip at the boundary. The model shows that slip is also dependent on acceleration in addition to the shear rate of fluid at the wall. By writing acceleration in terms of shear rate, it is shown that slip at the wall in unsteady flows is governed by the gradient of shear rate and shear rate of the fluid. Non-dimensionalizing the model gives a universal curve which can be used to find the slip boundary condition at the fluid-solid interface based on the information of shear rate and gradient of shear rate of the fluid. A governing non-dimensional number, defined as the ratio of phase speed to speed of sound, is identified to help in explaining the mechanism responsible for the transition of slip boundary condition from finite to a perfect slip and determining when this would occur. Phase lag in fluid velocity relative to wall is observed. The lag increases with decreasing time period of wall oscillation and increasing wall hydrophobicity. The phenomenon of hysteresis is seen when looking into the variation of slip velocity as a function of wall velocity and slip velocity as a function of fluid shear rate. The cause for hysteresis is attributed to the unsteady inertial forces of the fluid.

physics.flu-dyn↗