arXiv subjects

Surya Pratap Vanka

Publications and source records attributed to Surya Pratap Vanka.

15 recordsLinked to original sources

arXiv2024

High-order meshless global stability analysis of Taylor-Couette flows in complex domains

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical solver is developed employing the meshless framework to efficiently compute the hydrodynamic stability of fluid flows in complex geometries. The developed method is tested on two cases of Taylor-Couette flows. The concentric case represents the parallel flow assumption incorporated in the Orr-Sommerfeld model and the eccentric Taylor-Couette flow incorporates a non-parallel base flow with separation bubbles. The method was validated against earlier works by Marcus [1], Oikawa et al. [2], Leclercq et al. [3], and Mittal et al. [4]. The results for the two cases and the effectiveness of the method are discussed in detail. The method is then applied to Taylor-Couette flow in an elliptical enclosure and the stability of the flow is investigated.

physics.flu-dyn↗

arXiv2023

Dynamics of two air bubbles rising in a shear-thinning fluid

In this paper, we have studied the three-dimensional dynamics of two equally sized air bubbles rising in a shear-thinning fluid. We have used the combined level set and volume of fluid (CLSVOF) method to track interface, maintain mass balance and estimate the interface curvature. Additionally, we have incorporated a Sharp Surface Force Method (SSF) for surface tension forces. This method significantly suppressed the spurious velocities commonly observed with the conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in an in-house code called CUFLOW and runs on multiple GPUs platform. We have explored the effects of fluid rheology on the three-dimensional dynamics of two in-line bubbles. Two power-law indices (0.5 and 1) are investigated to highlight differences in shear-thinning and Newtonian fluids. For a range of parameters examined here, bubbles motion in a shear-thinning fluid is seen to be unsteady with significant shape oscillations. Further, we have examined the rise velocity, droplets rise path, transient shapes and found that modification of viscosity by the motion of the leading bubble changes the dynamics of the trailing bubble.

physics.flu-dyn↗

arXiv2023

Dynamics of Argon Gas Bubbles Rising in Liquid Steel in the Presence of Transverse Magnetic Field

Bubbly flows are present in various industrial processes including metallurgical processes in which gas bubbles are injected at the bottom of bulk liquid metal to stir the liquid metal and homogenize the metal. Understanding the motion of such bubbles is essential, as it has been shown that bubble flotation can remove inclusions. In this work, we have numerically studied three-dimensional dynamics of a pair of inline Argon bubbles rising in molten steel under the influence of a transverse magnetic field. We have explored the effects of two transverse magnetic field strengths (Bx = 0 and 0.2 T). The bubbles' motion and transient rise velocities are compared under different magnetic fields. The shape deformations and path of the bubbles are discussed. The flow structures behind the bubbles are analyzed. We found that structures are more organized and elongated under a magnetic field, whereas it is complex and intertwined when the magnetic field is not included. We have used a geometry construction-based volume of fluid (VOF) method to track interface, maintain mass balance and estimate the interface curvature. Additionally, we have incorporated a Sharp Surface Force Method (SSF) for surface tension forces. The algorithm is able to minimize the spurious velocities.

physics.flu-dyn↗

arXiv2022

Large Scale GPU Based Simulations of Turbulent Bubbly Flow in a Square Duct

In this paper, we present the results of a numerical study of air-water turbulent bubbly flow in a periodic vertical square duct. The study is conducted using a novel numerical technique which leverages Volume of Fluid method for interface capturing and Sharp Surface Force method for accurate representation of the surface tension forces. A three-dimensional geometry construction method is employed during solution of interface equation which gives absolute conservation of mass and sharp interface between gas and liquid phases. The entire algorithm has been implemented on a data parallel mode on multiple graphics processing units (GPU) taking advantage of the large number of available cores. We have studied the dynamics of a swarm of spherical bubbles co-flowing with the upward turbulent flow and compared results with an unladen turbulent flow. The frictional Reynolds number of the unladen $Re_τ$ is 360, which is sufficient to sustain a turbulent flow. We observe the turbulence-driven secondary flows in the mean flow, with complex instantaneous turbulent vortical structures. The interaction of these secondary flows with the upwards rising bubbles is very complex and leads to significant changes in the instantaneous and time-averaged flow field. We present the results of mean void fraction distribution, mean velocities, longitudinal and transverse turbulence intensities along the wall, corner bisector, and wall bisector. A peak in the void fraction distribution near the walls is observed representing the migration of bubbles to a preferred section of the duct. The effects of turbulence-driven secondary flows and instantaneous large eddies on preferential concentration of the bubbles are discussed. The dispersed bubbles are seen to break the long elongated turbulent structures commonly observed in the unladen turbulent flow.

physics.flu-dyn↗

arXiv2022

Simulation of Heat Conduction in Complex Domains of Multi-material Composites using a Meshless Method

Several engineering applications involve complex materials with significant and discontinuous variations in thermophysical properties. These include materials for thermal storage, biological tissues with blood capillaries, etc. For such applications, numerical simulations must exercise care in not smearing the interfaces by interpolating variables across the interfaces of the subdomains. In this paper, we describe a high accuracy meshless method that uses domain decomposition and cloud-based interpolation of scattered data to solve the heat conduction equation in such situations. The polyharmonic spline (PHS) function with appended polynomial of prescribed degree is used for discretization. A flux balance condition is satisfied at the interface points and the clouds of interpolation points are restricted to be within respective domains. Compared with previously proposed meshless algorithms with domain decomposition, the cloud-based interpolations are numerically better conditioned, and achieve high accuracy through the appended polynomial. The accuracy of the algorithm is demonstrated in several two and three dimensional problems using manufactured solutions to the heat conduction equation with sharp discontinuity in thermal conductivity. Subsequently, we demonstrate the applicability of the algorithm to solve heat conduction in complex domains with practical boundary conditions and internal heat generation. Systematic computations with varying conductivity ratios, interpoint spacing and degree of appended polynomial are performed to investigate the accuracy of the algorithm.

math.NA↗

arXiv2022

Consistency and Convergence of a High Order Accurate Meshless Method for Solution of Incompressible Fluid Flows

Computations of incompressible flows with velocity boundary conditions require solution of a Poisson equation for pressure with all Neumann boundary conditions. Discretization of such a Poisson equation results in a rank-deficient matrix of coefficients. When a non-conservative discretization method such as finite difference, finite element, or spectral scheme is used, such a matrix also generates an inconsistency which makes the residuals in the iterative solution to saturate at a threshold level that depends on the spatial resolution and order of the discretization scheme. In this paper, we examine inconsistency for a high-order meshless discretization scheme suitable for solving the equations on a complex domain. The high order meshless method uses polyharmonic spline radial basis functions (PHS-RBF) with appended polynomials to interpolate scattered data and constructs the discrete equations by collocation. The PHS-RBF provides the flexibility to vary the order of discretization by increasing the degree of the appended polynomial. In this study, we examine the convergence of the inconsistency for different spatial resolutions and for different degrees of the appended polynomials by solving the Poisson equation for a manufactured solution as well as the Navier-Stokes equations for several fluid flows. We observe that the inconsistency decreases faster than the error in the final solution, and eventually becomes vanishing small at sufficient spatial resolution. The rate of convergence of the inconsistency is observed to be similar or better than the rate of convergence of the discretization errors. This beneficial observation makes it unnecessary to regularize the Poisson equation by fixing either the mean pressure or pressure at an arbitrary point. A simple point solver such as the SOR is seen to be well-convergent, although it can be further accelerated using multilevel methods.

math.NA↗

arXiv2022

Shear-Driven Flow in an Elliptical Enclosure Generated by an Inner Rotating Circular Cylinder

Shear-driven flow between a rotating cylinder and a stationary elliptical enclosure is studied in this paper. Two-dimensional time-dependent Navier Stokes equations are solved using a meshless method where interpolations are done with Polyharmonic Spline Radial Basis Functions. The fluid flow is analyzed for various aspect ratios of the ellipse and eccentric placements of the inner cylinder. Contour plots of vorticity with streamlines, plots of non-dimensional torque, and the angle of eye of the primary vortex are presented in the paper for Reynolds numbers between 200 and 2000. Formation of Moffatt like vortices in the wide-gap region of the model is observed and some benchmark data are provided for various cases that are simulated.

physics.flu-dyn↗

arXiv2021

Sensitivity Analysis of Lift and Drag Coefficients for Flow over Elliptical Cylinders of Arbitrary Aspect Ratio and Angle of Attack using Neural Network

Flow over bluff bodies has multiple engineering applications and thus, has been studied for decades. The lift and drag coefficients are practically important in the design of many components such as automobiles, aircrafts, buildings etc. These coefficients vary significantly with Reynolds number and geometric parameters of the bluff body. In this study, we have analyzed the sensitivity of lift and drag coefficients on single and tandem elliptic cylinders to cylinder aspect ratios, angles of attack, cylinder separation, and flow Reynolds number. Sensitivity analysis with Monte-Carlo algorithm requires several function evaluations, which is infeasible with high-fidelity computational simulations. We have therefore trained multilayer perceptron neural networks (MLPNN) using computational fluid dynamics data to estimate the lift and drag coefficients efficiently. Line plots of the variations in lift and drag as functions of the governing parameters are also presented. The present approach is applicable to study of various other bluff body configurations.

physics.flu-dyn↗

arXiv2021

A High-Order Accurate Meshless Method for Solution of Incompressible Fluid Flow Problems

Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or elements, issues such as grid skewness that adversely impact accuracy are eliminated. Gaussian, Multiquadrics and inverse Multiquadrics are some of the most popular RBFs used for the solutions of fluid flow and heat transfer problems. But they have additional shape parameters that have to be fine tuned for accuracy and stability. Moreover, they also face stagnation error when the point density is increased for accuracy. Recently, Polyharmonic splines (PHS) with appended polynomials have been shown to solve the above issues and give rapid convergence of discretization errors with the degree of appended polynomials. In this research, we extend the PHS-RBF method for the solution of incompressible Navier-Stokes equations. A fractional step method with explicit convection and explicit diffusion terms is combined with a pressure Poisson equation to satisfy the momentum and continuity equations. Systematic convergence tests have been performed for five model problems with two of them having analytical solutions. We demonstrate fast convergence both with refinement of number of points and degree of appended polynomials. The method is further applied to solve problems such as lid-driven cavity and vortex shedding over circular cylinder. We have also analyzed the performance of this approach for solution of Euler equations. The proposed method shows promise to solve fluid flow and heat transfer problems in complex domains with high accuracy.

math.NA↗

arXiv2021

Application of a High Order Accurate Meshless Method to Solution of Heat Conduction in Complex Geometries

In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial basis functions (RBFs) have been popularly used as high accuracy interpolants of function values at scattered locations. In this paper, we apply the polyharmonic splines (PHS) as the RBF together with appended polynomial and solve the heat conduction equation in several geometries using a collocation procedure. We demonstrate the expected exponential convergence of the numerical solution as the degree of the appended polynomial is increased. The method holds promise to solve several different governing equations in thermal sciences.

math.NA↗

arXiv2021

A Semi-Implicit Meshless Method for Incompressible Flows in Complex Geometries

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as interpolants. Higher-order polynomials are appended to polyharmonic splines (PHS-RBF) and a collocation method is used to derive the interpolation coefficients. The interpolating kernels are then differentiated and the partial-differential equations are satisfied by collocation at the scattered points. The PHS-RBF interpolation is shown to be exponentially convergent with discretization errors decreasing as a high power of a representative distance between points. We present here a semi-implicit algorithm for time-dependent and steady state fluid flows in complex domains. At each time step, several iterations are performed to converge the momentum and continuity equations. A Poisson equation for pressure corrections is formulated by imposing divergence free condition on the iterated velocity field. At each time step, the momentum and pressure correction equations are repeatedly solved until the velocities and pressure converge to a pre-specified tolerance. We have demonstrated the convergence and discretization accuracy of the algorithm for two model problems and simulated three other complex problems. In all cases, the algorithm is stable for Courant numbers in excess of ten. The algorithm has the potential to accurately and efficiently solve many fluid flow and heat transfer problems in complex domains. An open source code Meshless Multi-Physics Software (MeMPhyS) is available for interested users of the algorithm.

math.NA↗

arXiv2021

A Non-Nested Multilevel Method for Meshless Solution of the Poisson Equation in Heat Transfer and Fluid Flow

We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve exponential convergence of discretization errors. The interpolations are performed over local clouds of points and the Poisson equation is collocated at each of the scattered points, resulting in a sparse set of discrete equations for the unkown variables. To solve this set of equations, we have developed a non-nested multilevel algorithm utilizing multiple independently generated coarse sets of points. The restriction and prolongation operators are also constructed with the same RBF interpolations procedure. The performance of the algorithm for Dirichlet and all-Neumann boundary conditions is evaluated in three model geometries using a manufactured solution. For Dirichlet boundary conditions, rapid convergence is observed using SOR point solver as the relaxation scheme. For cases of all-Neumann boundary conditions, convergence is seen to slow down with the degree of the appended polynomial. However, when the multilevel procedure is combined with a GMRES algorithm, the convergence is seen to significantly improve. The GMRES accelerated multilevel algorithm is included in a fractional step method to solve incompressible Navier-Stokes equations.

math.NA↗

arXiv2020

Optimization of Solidification in Die Casting using Numerical Simulations and Machine Learning

In this paper, we demonstrate the combination of machine learning and three dimensional numerical simulations for multi-objective optimization of low pressure die casting. The cooling of molten metal inside the mold is achieved typically by passing water through the cooling lines in the die. Depending on the cooling line location, coolant flow rate and die geometry, nonuniform temperatures are imposed on the molten metal at the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. A finite volume based numerical solver is used to determine the temperature-time history and correlate the inputs to outputs. The objective of this research is to develop and demonstrate a procedure to obtain the initial and wall temperatures so as to optimize the product quality. The non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization in this work. The number of function evaluations required for NSGA-II can be of the order of millions and hence, the finite volume solver cannot be used directly for optimization. Therefore, a multilayer perceptron feed-forward neural network is first trained using the results from the numerical solution of the fluid flow and energy equations and is subsequently used as a surrogate model. As an assessment, simplified versions of the actual problem are designed to first verify results of the genetic algorithm. An innovative local sensitivity based approach is then used to rank the final Pareto optimal solutions and select a single best design.

cs.CE↗

arXiv2019

Uncertainty Quantification in Three Dimensional Natural Convection using Polynomial Chaos Expansion and Deep Neural Networks

This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation and global sensitivity analysis. In case A, stochastic variation is introduced in the two non-dimensional parameters (Rayleigh and Prandtl numbers) with an assumption that the boundary temperature is uniform. Being a two dimensional stochastic problem, the polynomial chaos expansion (PCE) method is used as a surrogate model. Case B deals with non-uniform stochasticity in the boundary temperature. Instead of the traditional Gaussian process model with the Karhunen-Lo$\grave{e}$ve expansion, a novel approach is successfully implemented to model uncertainty in the boundary condition. The boundary is divided into multiple domains and the temperature imposed on each domain is assumed to be an independent and identically distributed (i.i.d) random variable. Deep neural networks are trained with the boundary temperatures as inputs and Nusselt number, internal temperature or velocities as outputs. The number of domains which is essentially the stochastic dimension is 4, 8, 16 or 32. Rigorous training and testing process shows that the neural network is able to approximate the outputs to a reasonable accuracy. For a high stochastic dimension such as 32, it is computationally expensive to fit the PCE. This paper demonstrates a novel way of using the deep neural network as a surrogate modeling method for uncertainty quantification with the number of simulations much fewer than that required for fitting the PCE, thus, saving the computational cost.

math.NA↗

arXiv2018

Finite Volume Simulation Framework for Die Casting with Uncertainty Quantification

The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. State of the art uncertainty quantification technique is included in the framework to incorporate the effects of stochastic variations in the input parameters. Rigorous validation is presented using published experimental results of a solidification problem.

math.NA↗