Showing papers on "Incompressible flow published in 2018"

Empirical Wall-Pressure Spectral Modeling for Zero and Adverse Pressure Gradient Flows

Abstract: This paper presents a new empirical model for turbulent boundary-layer wall pressure spectrum and validates the new model against measurement data for zero pressure gradient flat plate flows and ad...

Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

Abstract: The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important open problems in these fields are discussed. The exposition concentrates on $$H^1$$ -conforming finite elements.

Exponential self-similar mixing by incompressible flows

Abstract: We study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions. The scalar solves the continuity equation with a divergence-free velocity field, which satisfies a bound in the Sobolev space Ws,p, where s ≥ 0 and 1 ≤ p ≤ ∞. The mixing properties are given in terms of a characteristic length scale, called the mixing scale. We consider two notions of mixing scale, one functional, expressed in terms of the homogeneous Sobolev norm H−1, the other geometric, related to rearrangements of sets. We study rates of decay in time of both scales under self-similar mixing. For the case s = 1 and 1 ≤ p ≤ ∞ (including the case of Lipschitz continuous velocities, and the case of physical interest of enstrophy-constrained flows), we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound, established in previous works, on the time decay of both scales. We also present several consequences for the geometry of regular Lagrangian flows associated to Sobolev velocity fields.

An explicit power-law-based wall model for lattice Boltzmann method–Reynolds-averaged numerical simulations of the flow around airfoils

Abstract: In this paper, an explicit wall model based on a power-law velocity profile is proposed for the simulation of the incompressible flow around airfoils at high Reynolds numbers. This wall model is particularly suited for the wall treatment involved in Cartesian grids. Moreover, it does not require an iterative procedure for the friction velocity determination. The validation of this power-law wall model is assessed for Reynolds-averaged Navier-Stokes simulations of the flow around a two-dimensional airfoil using the lattice Boltzmann approach along with the Spalart-Allmaras turbulence model. Good results are obtained for the prediction of the aerodynamic coefficients and the pressure profiles at two Reynolds numbers and several angles of attack. The explicit power-law is thus well suited for a simplified near-wall treatment at high Reynolds numbers using Cartesian grids.

Analysis of the Aerodynamic Benefit from Boundary Layer Ingestion for Transport Aircraft

Abstract: Propulsors with boundary layer ingestion (BLI) generate a propulsive force with lower flow power input than conventional engines. This aerodynamic benefit can be traced back to its sources: reducti...

A cell-based smoothed finite element method with semi-implicit CBS procedures for incompressible laminar viscous flows

Abstract: Summary In this paper, the cell-based Smoothed Finite Element Method (CS-FEM) with the semi-implicit Characteristic-Based Split (CBS) scheme (CBS/CS-FEM) is proposed for computational fluid dynamics (CFD). The 3-node triangular (T3) element and 4-node quadrilateral (Q4) element are employed for present CBS/CS-FEM for two-dimensional flows. The 8-node hexahedral element (H8) is used for three-dimensional flows. Two types of CS-FEM are implemented in this paper. One is standard CS-FEM with quadrilateral gradient smoothing cells for Q4 element and hexahedron cells for H8 element. Another is called as n-sided CS-FEM (nCS-FEM) whose gradient smoothing cells are triangles for Q4 element and pyramids for H8 element. To verify the proposed methods, benchmarking problems are tested for two-dimensional and three-dimensional flows. The benchmarks show that CBS/CS-FEM and CBS/nCS-FEM are capable to solve incompressible laminar flow, and can produce reliable results for both steady and unsteady flows. The proposed CBS/CS-FEM method has merits on better robustness against distorted mesh with only slight more computation time and without losing accuracy, which is important for problems with heavy mesh distortion. The blood flow in carotid bifurcation is also simulated to show capabilities of proposed methods for realistic and complicated flow problems.

Excitation of Free Shear-Layer Instabilities for High-Speed Flow Control

Abstract: Free shear layers are building blocks of many flows of interest in applications, including jets, cavity flows, and separated flows. It was found several decades ago that free shear layers are unsta...

Recent Developments in Variational Multiscale Methods for Large-Eddy Simulation of Turbulent Flow

Abstract: The variational multiscale method is reviewed as a framework for developing computational methods for large-eddy simulation of turbulent flow. In contrast to other articles reviewing this topic, which focused on large-eddy simulation of turbulent incompressible flow, this study covers further aspects of numerically simulating turbulent flow as well as applications beyond incompressible single-phase flow. The various concepts for subgrid-scale modeling within the variational multiscale method for large-eddy simulation proposed by researchers in this field to date are illustrated. These conceptions comprise (i) implicit large-eddy simulation, represented by residual-based and stabilized methods, (ii) functional subgrid-scale modeling via small-scale subgrid-viscosity models and (iii) structural subgrid-scale modeling via the introduction of multifractal subgrid scales. An overview on exemplary numerical test cases to which the reviewed methods have been applied in the past years is provided, including explicit computational results obtained from turbulent channel flow. Wall-layer modeling, passive and active scalar transport as well as developments for large-eddy simulation of turbulent two-phase flow and combustion are discussed to complete this exposition.

Shape Holomorphy of the stationary Navier-Stokes Equations *

Abstract: We consider the stationary Stokes and Navier--Stokes equations for viscous, incompressible flow in parameter dependent bounded domains $\mathrm{D}_T$, subject to homogeneous Dirichlet (``no-slip'')...

Compression Ramp Induced Shock Wave/Turbulent Boundary Layer Interactions on a Compliant Material.

Abstract: PHA. M, HARRY TOÀN. Compression Ramp Induced Shock Wave/Turbulent Boundary Layer Interactions on a Compliant Material. (Under the direction of Dr. Venkateswaran Narayanaswamy.). An investigation into the potential use of soft compliant materials towards unsteady shock load mitigation is made. Compression ramps with different angles are used to generate shock waves impinging on the surface of the compliant layer embedded on a rigid flat plate in a Mach 2.5 flow. A urethane rubber material is chosen as the candidate compliant material for its well characterized material properties and ease of fabrication. Shock boundary layer interactions and fluid structure interactions are analyzed through oil-pigment surface streakline visualization and high-speed pressure transducer measurements. Reductions in the mean separation size are observed by embedding the compliant layer compared to without it. Furthermore, significant reduction in the energy content of the low frequency shock oscillations over the intermittent region was also observed by embedding a compliant layer on the rigid plate. © Copyright 2018 by Harry Toàn Pha.m

Mass-conserving advection-diffusion Lattice Boltzmann model for multi-species reacting flows

Abstract: Given the complex geometries usually found in practical applications, the Lattice Boltzmann (LB) method is becoming increasingly attractive. In addition to the simple treatment of intricate geometrical configurations, LB solvers can be implemented on very large parallel clusters with excellent scalability. However, reacting flows and especially combustion lead to additional challenges and have seldom been studied by LB methods. Indeed, overall mass conservation is a pressing issue in modeling multi-component flows. The classical advection–diffusion LB model recovers the species transport equations with the generalized Fick approximation under the assumption of an incompressible flow. However, for flows involving multiple species with different diffusion coefficients and density fluctuations – as is the case with weakly compressible solvers like Lattice Boltzmann –, this approximation is known not to conserve overall mass. In classical CFD, as the Fick approximation does not satisfy the overall mass conservation constraint a diffusion correction velocity is usually introduced. In the present work, a local expression is first derived for this correction velocity in a LB framework. In a second step, the error due to the incompressibility assumption is also accounted for through a modified equilibrium distribution function. Theoretical analyses and simulations show that the proposed scheme performs much better than the conventional advection–diffusion Lattice Boltzmann model in terms of overall mass conservation.

Odd surface waves in two-dimensional incompressible fluids

Abstract: We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the {\it chiral} Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to the case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.

Vortex Sheet Intensity Computation in Incompressible Flow Simulation Around an Airfoil by Using Vortex Methods

Abstract: A numerical scheme is developed to simulate a flow around airfoils by using vortex methods. For this scheme, a numerical algorithm is constructed and exact analytical expressions are obtained for the coefficients of a system of linear algebraic equations. For some test problems, it is shown that the developed scheme allows us to solve a wider class of problems and provides much more accurate results in comparison with the known approaches.

Far-wake meandering induced by atmospheric eddies in flow past a wind turbine

Abstract: A novel algorithm is developed to calculate the nonlinear optimal boundary perturbations in three-dimensional incompressible flow. An optimal step length in the optimisation loop is calculated without any additional calls to the Navier-Stokes equations. The algorithm is applied to compute the optimal in flow eddies for the flow around a wind turbine to clarify the mechanisms behind wake meandering, a phenomenon usually observed in wind farms. The turbine is modelled as an actuator disc using an immersed boundary method with the loading prescribed as a body force. At Reynolds number (based on free-stream velocity and turbine radius) Re = 1000, the most energetic inflow perturbation has a frequency ω = 0:8 ~ 2, and is in the form of an azimuthal wave with wavenumber m = 1 and the same radius as the actuator disc. The inflow perturbation is amplified by the strong shear downstream of the edge of the disc and then tilts the rolling-up vortex rings to induce wake meandering. This mechanism is verified by studying randomly perturbed flow at Re ≤ 8000. At five turbine diameters downstream of the disc, the axial velocity oscillates at a magnitude of more than 60% of the free-stream velocity when the magnitude of the inflow perturbation is 6% of the free-stream wind speed. The dominant Strouhal number of the wake oscillation is 0.16 at Re = 3000 and keeps approximately constant at higher Re. This Strouhal number agrees well with previous experimental findings. Overall the observations indicate that the well observed stochastic wake meandering phenomenon appearing far downstream of wind turbines is induced by large-scale (the same order as the turbine rotor) and low-frequency free-stream eddies.

Phase field simulation of Rayleigh–Taylor instability with a meshless method

Abstract: The purpose of this paper is a numerical study of Rayleigh–Taylor instability problem in two dimensions, based on phase-field (PF) formulation and diffuse approximate method (DAM) meshless solution procedure, enabling single-domain fixed-node approach for coping with moving boundary problems. The problem is formulated based on three physically different models that reduce to solving Cahn–Hilliard equation in addition to the Navier–Stokes equations for incompressible fluids. The governing equations are solved by using explicit time discretization. DAM is structured with second order polynomial basis, Gaussian weighting, upwinding and local domain support. The pressure–velocity coupling is performed by the fractional step method. The assessment of the method is carried out based on different node density, weighting, and the size of the local domain support. The novel approach is verified by reproducing the boundary dynamics, consistent with the previously published results. A detailed comparison with the volume of fluid finite volume approach is presented. The combination of PF and DAM provides a valuable numerical tool for solving immiscible convective hydrodynamics problems. The paper represents a pioneering attempt in solution of Rayleigh–Taylor instability problem by a meshless solution of the phase-field formulation of the problem.

Flow Physics and Frequency Scaling of Sweeping Jet Fluidic Oscillators

Abstract: Incompressible flow simulations are employed to investigate the internal fluid dynamics of a sweeping jet fluidic oscillator with a focus on the mechanisms and scaling laws that underpin the jet os...

Analytical approach to entropy generation and heat transfer in CNT-nanofluid dynamics through a ciliated porous medium

Abstract: The transportation of biological and industrial nanofluids by natural propulsion like cilia movement and self-generated contraction-relaxation of flexible walls has significant applications in numerous emerging technologies. Inspired by multi-disciplinary progress and innovation in this direction, a thermo-fluid mechanical model is proposed to study the entropy generation and convective heat transfer of nanofluids fabricated by the dispersion of single-wall carbon nanotubes (SWCNT) nanoparticles in water as the base fluid. The regime studied comprises heat transfer and steady, viscous, incompressible flow, induced by metachronal wave propulsion due to beating cilia, through a cylindrical tube containing a sparse (i.e. high permeability) homogenous porous medium. The flow is of the creeping type and is restricted under the low Reynolds number and long wavelength approximations. Slip effects at the wall are incorporated and the generalized Darcy drag-force model is utilized to mimic porous media effects. Cilia boundary conditions for velocity components are employed to determine analytical solutions to the resulting non-dimensionalized boundary value problem. The influence of pertinent physical parameters on temperature, axial velocity, pressure rise and pressure gradient, entropy generation function, Bejan number and stream-line distributions are computed numerically. A comparative study between SWCNT nanofluids and pure water is also computed. The computations demonstrate that axial flow is accelerated with increasing slip parameter and Darcy number and is greater for SWCNT- nanofluids than for pure water. Furthermore the size of the bolus for SWCNT-nanofluids is larger than that of the pure water. The study is applicable in designing and fabricating nanoscale and microfluidics devices, artificial cilia and biomimetic micro-pumps

A particle distribution function approach to the equations of continuum mechanics in Cartesian, cylindrical and spherical coordinates: Newtonian and non-Newtonian fluids

Abstract: The evolution equations for the particle distribution functions are written in a divergence form applicable in three dimensions. From this set, it is shown that the continuity equation and the equations of motion are satisfied in Cartesian, cylindrical and spherical coordinates for all fluids when additional source terms are added to the equations of evolution in the latter two coordinate systems. If the body forces are present, a new set of source functions is required in each coordinate system and these are described as well. Next, the energy equation is derived by using a separate set of particle distribution functions. Modifications of the relevant equations to be applicable to incompressible fluids is described. The incorporation of boundary conditions and the description of the numerical scheme for the simulation of the flows employing the new approach is given. Validation results obtained through the modelling of a mixed convection flow of a Bingham fluid in a lid-driven square cavity, and the steady flow of a Bingham fluid in a pipe of square cross-section are presented. Next, using the cylindrical coordinate version of the evolution equations, numerical modelling of the steady flow of a Bingham fluid and the Herschel–Bulkley fluid in a pipe of circular cross-section have been performed and compared with the simulation results using the augmented Lagrangian method as well as the analytical solutions for the velocity field and the flow rate. Finally, some comments on the theoretical differences between the present approach and the existing formulations regarding Lattice Boltzmann Equations are offered.

An enstrophy-based linear and nonlinear receptivity theory

Abstract: In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations

Abstract: This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It systematically extends work previously made for incompressible fluids to the compressible case. We consider in detail the numerical scheme on 2D irregular simplicial meshes and evaluate the scheme numerically for the rotating shallow water equations. In particular, we investigate whether the scheme conserves stationary solutions, represents well the nonlinear dynamics, and approximates well the frequency relations of the continuous equations, while preserving conservation laws such as mass and total energy.