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In the last two decades, the lattice Boltzmann method (LBM) has emerged as a promising tool for simulating complex fluid flows. The method uses a uniform mesh spacing throughout the domain. Near solid boundaries, the resolution required to capture steeper gradients in flow variables can cause massive computational load due to the same mesh resolution being used everywhere else in the domain. This limitation is circumvented by using multi-block LBM in which finer mesh is used near the solid-fluid interface, whereas coarser mesh is used away from the solid boundaries. Consequently, multi-block approach requires exchange of data between the coarse and the fine grid at the interface at each time step. For two-dimensional flow problems like flow past a cylinder and flow in a lid driven cavity, the transfer of data between coarse and fine grid by using univariate splines has already been developed successfully. However, an efficient and accurate interpolation scheme in three-dimensional fluid flow simulation using multi-block LBM has not been demonstrated so far. This work employs a bivariate version of splines and devises an efficient algorithm for the solution of unknown coefficients. At the interface of the coarse and fine grid blocks, bicubic splines are constructed using the data on the coarse grid. The bicubic splines are subject to appropriate continuity conditions across adjacent splines and suitable boundary conditions. The resulting coupled equations in terms of the unknown coefficients are solved using a direct method without matrix inversion. The validation of the use of bicubic splines is done by solving flows around a three-dimensional cylinder and sphere with the help of multi-block LBM. Subsequently, the bicubic spline interpolation is employed for moving boundary simulation of a three-dimensional rigid hovering wing. The coefficients of drag and lift computed using multiblock LBM based on bicubic spline interpolation shows considerable reduction in noise compared to available results that use uniform mesh. © 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

World University root node

Department of Mechanical Engineering

AIAA Scitech 2020 Forum

Improving resolution of three-dimensional lattice boltzmann simulations using bicubic spline interpolation for moving boundaries

We mimic a flapping wing through a fluid-structure interaction (FSI) framework based upon a generalized lumped-torsional flexibility model. The developed fluid and structural solvers together determine the aerodynamic forces, wing deformation and self-propelled motion. A phenomenological solution to the linear single-spring structural dynamics equation is established to help offer insight and validate the computations under the limit of small deformation. The cruising velocity and power requirements are evaluated by varying the flapping Reynolds number (20 ≤ Ref ≤ 100), stiffness (represented by frequency ratio, 1 ≲ w∗ ≤ 10) and the ratio of aerodynamic to structural inertia forces (represented by a dimensionless parameter Ψ (0.1 ≤ Ψ ≤ 3). For structural inertia dominated flows (Ψ ≤ 3), pitching and plunging are shown to always remain in phase (φ ≈ 0) with the maximum wing deformation occurring at the end of the stroke. When aerodynamics dominates (Ψ &gt; 1), a large phase difference is induced (φ ≈ π/2) and the maximum deformation occurs at mid-stroke. Lattice Boltzmann simulations show that there is an optimal w∗ at which cruising velocity is maximized and the location of optimum shifts away from unit frequency ratio (w∗ = 1) as Ψincreases. Furthermore, aerodynamics administered deformations exhibit better performance than those governed by structural inertia, quantified in terms of distance travelled per unit work input. Closer examination reveals that although maximum thrust transpires at unit frequency ratio, it is not transformed into the highest cruising velocity. Rather, the maximum velocity occurs at the condition when the relative tip displacemen. © 2018 Cambridge University Press.

Journal of Fluid Mechanics

Analysis of passive flexion in propelling a plunging plate using a torsion spring model

A novel numerical framework for conducting linear stability analysis of two-dimensional steady laminar flows is presented. Using two case studies involving analysis of thermal and laminar flows, stability of laminar flows in the numerical sense is addressed. The two-dimensional base flow is computed by using the lattice Boltzmann method for various values of the controlling parameter (Reynolds number for flow past a square cylinder and Rayleigh number for double-glazing problem). Subsequently, the perturbed equations with two-dimensional disturbances are linearized and form a set of partial differential equations that govern the evolution of these perturbations. Using normal mode analysis, the eigenvalues of the resultant equation are used to determine the stablilty of the base flow. © 2018 by the authors of the abstracts.

International Conference on Computational Methods for Thermal Problems

A numerical framework for linear stability analysis of two-dimensional steady flows

The aim of the present study is to characterize the flow patterns, propulsion efficiency and power requirements associated with a self-propelled-heaving thin flat plate in a quiescent medium. In this regard, a numerical model using a shifting discontinuous-grid and based upon multi-relaxation-time lattice Boltzmann method is developed to probe the resulting aerodynamics. The influence of kinematic parameters namely flapping Reynolds number Ref (20−100) and plunging amplitude β (0.2–1), and the density ratio ρ* (101−102) on forward flight is pursued. Depending on the kinematics, various periodic vortex shedding characteristics of the plunging plate are observed that lead to modification of the angle of attack as a result of wing-wake interaction and downward jet. The presence of strong vortex dipole at the trailing edge with an attached leading edge vortex are factors responsible for maximum thrust generation. A wing-wake interaction which occurs at low β and high Ref due to weak vortex dissipation and presence of vortex dipole at the trailing edge acting in tandem can lead to achieving high propulsion efficiency. Through surrogate modelling, a set of Pareto-optimal solutions that describe the tradeoff between efficiency and input power for forward flight is presented and offers insight into the design and development of next generation flapping wing micro-air vehicles. © 2016 Elsevier Ltd

Journal of Fluids and Structures

Flow patterns and efficiency-power characteristics of a self-propelled, heaving rigid flat plate

A translating discontinuous-grid-block model for moving boundaries of finite thickness based on multi-relaxation time version of lattice Boltzmann method has been developed. The implementation of this model to simulate moving boundary flows has been demonstrated for the cases of a cylinder in simple shear flow, a single rigid wing executing 'clap and fling' motion, and the propulsion of a plunging flat plate. A number of interpolation schemes of linear, quadratic and cubic natures are assessed around the discontinuous grid interface. It is shown that the implementation of a body-fitted refined mesh that moves along with the object reduces the spurious oscillations registered in the force and velocity measurements compared to a single coarse grid block. Moreover, use of multiple relaxation times helps overcome stability issues at high Reynolds number, normally encountered in the single-relaxation time model. Significantly, in the former model the same base grid could handle flows with good accuracy for 10 ≤ Re ≤ 1000. The proposed technique offers significant advantage in terms of capturing flow around moving solids at lower computational cost and simulation time as compared to the stationary discontinuous-grid-block method. © 2015 Elsevier Ltd.

Computers and Fluids

A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations

A translating discontinuous-grid-block model for moving boundaries of finite thickness based on multi relaxation time version of LBM has been developed. In this regard, the execution of this model to simulate moving boundary flows has been demonstrated for the cases of a cylinder in simple shear flow, a single rigid wing executing ‘clap and fling’ motion, and the propulsion of a plunging flat plate. It is shown that the implementation of a body fitted refined mesh that moves along with the object improves its resolution and reduces the spurious oscillations registered in the force and velocity measurements compared to a single grid block. A number of interpolation schemes of linear, quadratic and cubic natures are assessed around the discontinuous grid interface. This method is highly suitable for problems that (a) involve large domain sizes in which the moving solid keeps traversing indefinitely in one direction, and (b) a high resolution around the body is demanded without the expenditure of additional computational power and memory as with the stationary discontinuous-grid-block. © 2015, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

22nd AIAA Computational Fluid Dynamics Conference

The aim of the present study is to understand the mechanism of propulsion in biological flyers, initially starting from rest, towards development of micro-air vehicles employing the same concept using a computational analysis of the plunging motion of a rigid wing. A two-dimensional numerical model has been developed to probe the fluid mechanics associated with the vertical plunging motion of a flat plate analogous to the biological flight of birds and insects. Recent experiments have shown that propulsion can be achieved in still air by a rigid wing if it is flapped above a critical Reynolds number (based on the flapping frequency). The influence of parameters such as density ratio ρ* and flapping Reynolds number Ref on the propulsion of a vertically heaving wing unconstrained to move in horizontal direction has been investigated. Flow fields generated at different time instants indicate that the interaction with the previous shed vortices creates asymmetry that pushes the wing into locomotion. The vortical wake patterns are scrutinized at steady translation which varied depending upon the Strouhal number. In addition, the behavior of input/output power and efficiency has been quantified.

32nd AIAA Applied Aerodynamics Conference

Forward propulsion of a rigid plunging airfoil

The present study focuses on the analysis of the fluid dynamics associated with the flapping motion of finite-thickness wings. A two-dimensional numerical model for one and two-winged "clap and fling" stroke has been developed to probe the aerodynamics of insect flight. The influence of kinematic parameters such as the percentage overlap between translational and rotational phase ξ, the separation between two wings δ and Reynolds numbers Re on the evolvement of lift and drag has been investigated. In addition, the roles of the leading and trailing edge vortices on lift and drag in clap and fling type kinematics are highlighted. Based on a surrogate analysis, the overlap ratio ξ is identified as the most influential parameter in enhancing lift. On the other hand, with increase in separation δ, the reduction in drag is far more dominant than the decrease in lift. With an increase in Re (which ranges between 8 and 128), the mean drag coefficient decreases monotonously, whereas the mean lift coefficient decreases to a minimum and increases thereafter. This behavior of lift generation at higher Re was characterized by the "wing-wake interaction" mechanism which was absent at low Re. © 2014 AIP Publishing LLC.

Fulltext

Physics of Fluids

Lift-drag and flow structures associated with the "clap and fling" motion

In the past two decades, the lattice Boltzmann method (LBM) has offered itself as an alternative framework compared to the Navier Stokes simulations. However, the applicability of this method to simulate moving boundary problems has not received sufficient attention. The present study primarily focuses on developing and employing the halfway bounceback LBM to analyse the flow dynamics associated with the flapping motion of finite-thickness wings. A two-dimensional numerical model for one and two-winged 'clap and fling' stroke has been developed to study the aerodynamic performance of insect flight. The influence of kinematic parameters such as the percentage overlap between translational and rotational phase ξ, the separation between two wings δ and different Reynolds numbers Re on lift generation has been studied and presented here. In addition, the time-dependent behaviour of the leading and trailing edge vortices and their role on lift generation in clap and fling type kinematics has been identified. Based on simulation data, regression analysis was carried out to express the mean lift coefficient as a function of the varied parameters. Results show that overlap ratio ξ is the most influential parameter in enhancing lift. With increase in separation δ, the reduction in drag is far more dominant than the decrease in lift. With an increase in Re (which ranges between 8 and 128), the mean drag coefficient decreases monotonously, whereas the mean lift coefficient decreases to a minimum and increases thereafter. This behaviour of lift generation at higher Re was characterised by the 'wing-wake interaction' mechanism which was absent at low Re.

31st AIAA Applied Aerodynamics Conference

A lattice Boltzmann framework for analysis of 'clap and fling' motion of finite thickness membranes

The present study focuses on deciphering various aerodynamic phenomena and flow structures that explains the principles of lift generation in tiny insects. Simulations are performed on three-dimensional elliptical wings performing “clap and fling” motion based on the flight of Encasia Formosa. In this regard, a numerical fluid solver based on D3Q19 multiple relaxation time (MRT) model of lattice Boltzmann method (LBM) is developed. To justify the applicability of LBM on the moving boundaries, validations have been performed for the cases of hovering flat plate and sedimentation of a sphere in a fluid tank at different Reynolds numbers. The influence of the kinematic parameters such as rotational-translational overlap ξ (0% - 100%) and Reynolds number (Re = 10 and Re = 50) on the behaviour of lift and drag is examined. It is observed that overlap is the most influential parameter as lift to drag ratio at ξ = 100% is almost an order of magnitude higher than at ξ = 0% and is attributed to the attachment of a strong leading-edge vortex (LEV) during the clap phase in the former. Only a slight variation in lift to drag ratio is witnessed with Reynolds number for the small range considered in this work.