3D Incompressible Flow Research Articles

On the high-accuracy approach to flow simulation aroundthe airfoils by using vortex method

Some problems connected to vortex methods development for 2D incompressible flow simulation around airfoils are discussed. In the numerical schemes and algorithms which are normally used in the vortex methods, the airfoil is approximated by a polygon consists of rectilinear panels, and the the vortex sheet intensity, which is placed on the airfoil surface line and simulates the airfoil’s influence the flow, is assumed to be piecewise-constant or piecewise-linear function. The most accurate mathematical models and numerical algorithms, based on such approaches, provide the estimation for the order of the error between O(h) and O(h2) for the average vortex sheet intensity over the panels (h is the maximal panel length). In the present research a new approach is developed, where the vortex sheet intensity is assumed to be discontinuous piecewise-linear or piecewise-quadratic function and the curvature of the panels is taken into account. In order to compute the coefficients of the main system of the algebraic equations, the least squares method is used instead of commonly used no-through or no-slip conditions at separate control points or over the panels in the average. It is shown, that the developed approach is much more accurate in comparison with previously known ones: for some test problems (flows around a circular airfoil, an elliptical airfoil and Zhukovsky airfoil) it permits to obtain numerical solution which has error of order O(h4).

Numerical and experimental investigation of an airfoil design for a Martian micro rotorcraft

The present paper aims at investigating the impact of an airfoil design on the propulsion system for a Martian rotary wing micro air vehicle. The main challenge for flying on Mars is the atmosphere’s density and speed of sound that are significantly lower than on Earth. It leads to compressible ultra-low Reynolds number ([Formula: see text]) flows for a coaxial rotorcraft with a 30 cm diameter . Since those flows are unknown in the biosphere, numerical tools have not been validated yet. Therefore, the test section from a known depressurized experiment is simulated in 3D for solver assessment. XFoil, a program for the analysis of subsonic airfoil, is also evaluated in the Martian flow conditions for evaluating its ability to be used in an optimization process. Based on the XFoil’s performance evaluations, both the camber line and thickness distribution are optimized in 2D incompressible and compressible flows. Optimal shape is a highly cambered airfoil shifting the boundary layer separation downstream. For optimization assessment, airfoils from each optimization step are numerically evaluated with the validated solver showing that small variations in the airfoil design has little impact on the 2D aerodynamic performance. A compressible optimal airfoil is also proven to be more aerodynamically effective than the experimentally effective airfoils from literature. Finally, the impact of airfoil shapes on the 3D rotor performance is evaluated with a depressurized experimental campaign recreating the Martian atmosphere in terms of kinematic viscosity. The impact of gas composition is also assessed in subsonic flows.

Channel flow of viscoplastic fluids with pressure-dependent rheological parameters

We consider the 2D incompressible flow of a Herschel-Bulkley fluid with pressure-dependent rheological moduli in a symmetric channel of non-uniform width and small aspect ratio. Following Fusi et al. [“Pressure-driven lubrication flow of a Bingham fluid in a channel: A novel approach” J. Non-Newtonian Fluid Mech. 221, 66–75 (2015)] and Panaseti et al. [“Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters,” Phys. Fluids 30, 030701 (2018)], we write the momentum equation of the unyielded domain in an integral form and we focus on the leading order approximation of the lubrication expansion. The use of the integral formulation allows one to overcome the “lubrication paradox,” a well-known inconsistency consisting in a plug speed that is not uniform. Different from the aforementioned papers, here we assume that the flow is driven by a prescribed inlet flux and not by a given pressure drop. As we shall see, this difference is of crucial importance when solving the problem at the leading order of the lubrication expansion. Indeed, when the pressure drop is given, the mathematical problem reduces to a nonlinear integro-differential equation for the pressure, while in the case where the inlet flux is prescribed the mathematical problem reduces to a full nonlinear algebraic equation for the plug speed, a numerical problem which can be far simpler than the determination of the solution of the integro-differential equation. The approach, based on the knowledge of the inlet discharge, can be used even when the pressure gradient is prescribed. Indeed, we determine a relation that links the pressure drop to the flow discharge so that when the pressure drop is assigned we can find the flow discharge and apply the method presented here. To prove the validity of our approach, we finally show that the solutions obtained with the method proposed here are equal to the ones obtained in Panaseti et al. [“Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters,” Phys. Fluids 30, 030701 (2018)]. This proves that one can determine the same solutions of Fusi et al. [“Pressure-driven lubrication flow of a Bingham fluid in a channel: A novel approach,” J. Non-Newtonian Fluid Mech. 221, 66 (2015)] and Panaseti et al. [“Pressure-driven flow of a Herschel-Bulkley fluid with pressure-dependent rheological parameters,” Phys. Fluids 30, 030701 (2018)] without solving any integro-differential equation.

Comparative DEM-CFD study of binary interaction and acoustic agglomeration of aerosol microparticles at low frequencies

The paper concerns the problem of acoustic agglomeration due to the acoustic wake in diluted aerosols and addresses the development of the time-accurate discrete element method (DEM) simulation technique. The case of weak entrainment of heavier mono-sized microparticles at low-frequency sound waves is considered. The agglomerative motion of two identical micron-sized spherical particles is simulated numerically, and contribution of the particles boundary layer in transition from the diluted to the dense phase is investigated. A comparative study of the DEM approach against more accurate computational fluid dynamics (CFD) computations is performed. The 3D incompressible viscous flow of aerosol medium described by Navier–Stokes equations is considered regarding the fine scale of particles. The numerical results regarding the agglomeration rate, drag coefficient, and perturbation velocities are discussed. Moreover, the correction to the fluid–particle interaction force is proposed to increase the accuracy of the DEM model.

Global regularity to the 3D incompressible nematic liquid crystal flows with vacuum

This paper is concerned with the 3D incompressible nematic liquid crystal equations in smooth bounded domains, where the velocity u and macroscopic molecular orientation d admit the Dirichlet and Neumann boundary condition respectively. Global-in-time strong solution is proved to exist when the basic energy is suitably small. The initial vacuum is allowed.

A numerical study of transient flow around a cylinder and aerodynamic sound radiation

The fully 3D turbulent incompressible flow around a cylinder and in its wake at a Reynolds number Re = = 9×104 based on the cylinder diameter and Mach number M = 0.1 is calculated using Large Eddy Simulations (LES). Encouraging results are found in comparison to experimental data for the fluctuating lift and drag forces. The acoustic pressure in far-field is commutated through the surface integral formulation of the Ffowcs Williams and Hawkings (FWH) equation in acoustic analogy. Five different sound sources, the cylinder wall and four permeable surfaces in the flow fields, are employed. The spectra of the sound pressure are generally in quantitative agreement with the measured one though the acoustic sources are pseudo-sound regarding the incompressible flow simulation. The acoustic component at the Strouhal number related to vortex shedding has been predicted accurately. For the broad band sound, the permeable surfaces in the near wake region give qualitative enough accuracy level of predictions, while the cylinder wall surface shows a noticeable under-prediction. The sound radiation of the volumetric sources based on Lighthill tensors at vortex shedding is also studied. Its far-field directivity is of lateral quadrupoles with the weak radiations in the flow and cross-flow directions.

Tree representations of streamline topologies of structurally stable 2D incompressible flows

Tree representations of streamline topologies of structurally stable 2D incompressible flows

Numerical Study on Heat Transfer to an Arc Absorber Designed for a Waste Heat Recovery System around a Cement Kiln

A numerical study on combined free convection, forced convection, and radiation heat transfers from an industrial isothermal rotating cylinder (cement kiln) is carried out in this work. The investigation is done by the study of two-dimensional (2D) incompressible turbulent flow around the kiln under steady- and unsteady-state solutions. The results of this study show that the average Reynolds and Rayleigh numbers around the cylindrical kiln are 647,812.1 and 1.75986 × 1011, respectively. A heat absorber is specifically designed around the kiln, according to the available space around the kiln, in a sample cement factory. The study investigates the effect of an added absorber on the heat transfer features, for both constant heat flux and constant temperature, on the kiln. The temperature distribution along the absorber circumference is obtained for designing an efficient thermoelectric waste heat recovery system as a future study. It is observed that the contribution of the radiative heat transfer is significant in the total heat transferred from the kiln to the absorber.

A variational projection scheme for nonmatching surface-to-line coupling between 3D flexible multibody system and incompressible turbulent flow

This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D) incompressible turbulent flow solver, a nonlinear monolithic elastic structural solver for constrained flexible multibody system and the nonlinear iterative force correction scheme for coupling of the turbulent fluid-flexible multibody system with nonmatching interface meshes. While the fluid equations are discretized using a stabilized Petrov–Galerkin formulation in space and the generalized-α updates in time, the multibody system utilizes a discontinuous space-time Galerkin finite element method. We address two key challenges in the present formulation. Firstly, the coupling of the incompressible turbulent flow with a system of nonlinear elastic bodies described in a co-rotated frame. Secondly, the projection of the tractions and displacements across the nonmatching 3D fluid surface elements and the one-dimensional line elements for the flexible multibody system in a conservative manner. Through the nonlinear iterative correction and the conservative projection, the developed fluid-flexible multibody interaction solver is stable for problems involving strong inertial effects between the fluid-flexible multibody system and the coupled interactions among each multibody component. The accuracy of the proposed coupled finite element framework is validated against the available experimental data for a long flexible cylinder undergoing vortex-induced vibration in a uniform current flow condition. Finally, a practical application of the proposed framework is demonstrated by simulating the flow-induced vibration of a realistic offshore floating platform connected to a long riser and an elastic mooring system.

An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties

An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties

Effect of inlet turbulence on compressible flow through the tip-section turbine blade cascade with supersonic inlet

The contribution deals with the numerical simulation of 2D compressible flow though the tip-section turbine blade cascade with the supersonic inlet boundary conditions. The simulation was carried out by the in-house numerical code using the explicit algebraic Reynolds stress model completed by the bypass transition model with the algebraic equation for the intermittency coefficient. The γ-Re model implemented in the commercial code Fluent was used for the comparison. Predictions carried out for the nominal conditions were focused on the effect of inlet free-stream turbulence on the flow structure in the blade cascade under supersonic inlet conditions. Numerical results were compared with experimental data.

Existence of the uniform trajectory attractor for a 3D incompressible non-Newtonian fluid flow

This paper studies the trajectory asymptotic behavior of a non-autonomous incompressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

A simple gas kinetic scheme for simulation of 3D incompressible thermal flows

ABSTRACTIn this work, a simple gas kinetic scheme is presented for solving the 3D incompressible thermal flow problems. In the scheme, the macroscopic-governing equations are discretized by finite volume method, and the numerical fluxes at cell interface are reconstructed by the local solution of the Boltzmann equation. To compute the numerical fluxes, two equilibrium distribution functions are introduced. One is the sphere function for calculating the fluxes of mass and momentum equations, and the other is the D3Q6 discrete velocity model for evaluating the flux of energy equation. Using the difference of equilibrium distribution functions at the cell interface and its surrounding points to approximate the nonequilibrium distribution function, and at the same time considering the incompressible limit, the numerical fluxes of macroscopic governing equations at the cell interface can be given explicitly and concisely. Numerical results showed that the present scheme can predict accurately the thermal flow properties at a wide range of the Rayleigh numbers.

An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows

In this work, an implicit simplified sphere function-based gas kinetic scheme (SGKS) is presented for simulation of 3D incompressible isothermal flows. At first, the numerical fluxes of governing equations are reconstructed by the local solution of Boltzmann equation with sphere function distribution. Due to incompressible limit, the sphere at cell interface can be approximately considered to be symmetric as shown in the work. Besides that, the energy equation is usually not needed for simulation of incompressible isothermal flows. With all these simplifications, the formulations of the simplified SGKS can be expressed concisely and explicitly. Secondly, the commonly-used implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method is adopted to further improve the computational efficiency and numerical stability of present scheme. In LU-SGS method, only a forward and a backward sweep are needed for marching the conservative variables in time. As a result, the simplified SGKS with the LU-SGS method can be implemented easily. Numerical experiments, including the 3D lid-driven cavity flow and flow over a backward-facing step, showed that the incompressible isothermal flows can be well simulated by the developed scheme and its computational efficiency is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS). In addition, it was found that the present scheme with the LU-SGS method is more efficient than that with the explicit Euler method, and the speedup ratio is about 2 to 5.

An immersed boundary-simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible flows

In this work, an immersed boundary-simplified sphere function-based gas kinetic scheme (SGKS) is presented for the simulation of 3D incompressible flows with curved and moving boundaries. At first, the SGKS [Yang et al., “A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows,” J. Comput. Phys. 295, 322 (2015) and Yang et al., “Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows,” J. Comput. Phys. 319, 129 (2016)], which is often applied for the simulation of compressible flows, is simplified to improve the computational efficiency for the simulation of incompressible flows. In the original SGKS, the integral domain along the spherical surface for computing conservative variables and numerical fluxes is usually not symmetric at the cell interface. This leads the expression of numerical fluxes at the cell interface to be relatively complicated. For incompressible flows, the sphere at the cell interface can be approximately considered to be symmetric as shown in this work. Besides that, the energy equation is usually not needed for the simulation of incompressible isothermal flows. With all these simplifications, the simple and explicit formulations for the conservative variables and numerical fluxes at the cell interface can be obtained. Second, to effectively implement the no-slip boundary condition for fluid flow problems with complex geometry as well as moving boundary, the implicit boundary condition-enforced immersed boundary method [Wu and Shu, “Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications,” J. Comput. Phys. 228, 1963 (2009)] is introduced into the simplified SGKS. That is, the flow field is solved by the simplified SGKS without considering the presence of an immersed body and the no-slip boundary condition is implemented by the immersed boundary method. The accuracy and efficiency of the present scheme are validated by simulating the decaying vortex flow, flow past a stationary and rotating sphere, flow past a stationary torus, and flows over dragonfly flight.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier–Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad–div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ=180 as well as 590.

Turbulent clustering of initially well-mixed buoyant particles on a free-surface by Lagrangian coherent structures

Particles that float on the surface of a 3D incompressible turbulent flow are exposed to non-divergence-free properties that result in clustering and unmixing, a reversal of how turbulence normally acts to mix and dilute scalars. Particle clustering is dominated by Lagrangian processes that depend on the time history of the flow; this suggests that Lagrangian coherent structures (LCS) might serve as templates for cluster formation. In this study, non-divergence-free clustering is examined both experimentally and numerically to elucidate the role of LCS in the formation of particle clusters and voids. Experiments are performed on the free-surface of a water-filled tank with turbulence driven by the random pulsing of centrifugal pumps on the tank bottom. Clustering is quantified by imaging fluorescent, buoyant particles that are placed in an initially random distribution on the free-surface. Within clusters, concentrations are observed to increase by an order of magnitude, with the likelihood of observing enhanced concentrations increasing by two orders of magnitude. LCS, obtained from velocity fields utilizing particle image velocimetry, are shown to act as templates for cluster formation. In addition, LCS are shown to possess a dilatation component in non-divergence-free flows that is responsible for unmixing. Numerically, a non-divergence-free chaotic model consisting of interacting Taylor vortices is utilized to investigate processes responsible for cluster formation seen in the experiments. The model results support the experimental finding that LCS act as templates for particle clusters, with scalar unmixing driven by the dilatation component.

Experimental and Numerical Investigation of the Performance of a Centrifugal Pump When Pumping Water and Light Crude Oil

In the oil and gas industry, crude oil is frequently transported and centrifugal pumps are used extensively. The pump impeller works under both design and off-design conditions in the applications, and the flow pattern deviates from the ideal case because of viscosity and density changes. An experimental as well as a numerical study was conducted to study the performance of a pump delivering water and light crude oil under design and off-design conditions. A 3D steady incompressible flow in the centrifugal pump was simulated by solving the Reynolds-averaged Navier–Stokes equations and SST turbulence model. At a low flow rate, extensive reverse flow occurs at the inlet of the impeller in the case of water, whereas the opposite was found for light crude oil. Recirculation was observed in the impeller flow passage for both water and the crude oil, but this diminished at higher flow rates.

A combined method for solving 2D incompressible flow and heat transfer by spectral collocation method and artificial compressibility method

A combined method is developed for solving 2D steady incompressible flow and heat transfer by spectral collocation method (SCM) and artificial compressibility method (ACM). Instead of the steady governing equations, the unsteady artificial compressibility equations are introduced and solved. The steady results can be obtained by solving the unsteady equations when the pressure, velocity and temperature time derivatives approach to zero. The partial differential equations are discretized by SCM with Chebyshev polynomial and the spatial domain is discretized by the Chebyshev-Gauss-Lobbatto (CGL) collocation points. The artificial compressibility parameter c is investigated and determined firstly. Then, the accuracy of the SCM-ACM is tested by solving an exact solution with three time schemes (explicit scheme, implicit scheme and fourth order explicit Runge-Kutta scheme). Lastly, two classical cases (the lid-driven cavity flow and natural convection in a square cavity) are solved by the SCM-ACM with explicit scheme. The results show that the SCM-ACM can be used for the solving of incompressible flow and heat transfer, and high accuracy can be achieved after some calculation steps by the SCM-ACM especially with the fourth order explicit Runge-Kutta scheme. The SCM-ACM inherits the characteristics of exponential convergence and high accuracy from spectral method, and it is simplified, efficient and easy to implement which derives from the ACM. The SCM-ACM provides a new selection for the solution of incompressible flow and heat transfer.

A three-dimensional numerical approach on water entry of a horizontal circular cylinder using the volume of fluid technique

In this paper, complicated hydrodynamics of a horizontal circular cylinder entering water is investigated numerically for low Froude numbers. A numerical approach is used to model the solid-liquid interactions in presence of a free-surface. The governing equations for the 3D incompressible fluid flow are continuity and Navier-Stokes equations along with an equation for the free surface advection. To track the free-surface motion, the fast-fictitious-domain method is integrated into the volume-of-fluid (VOF) technique. The governing equations are solved everywhere in the computational domain including the horizontal cylinder. A rigid body motion is applied to the region occupied by the circular cylinder. The no-slip boundary condition on the solid-liquid interface is exerted implicitly via increasing the viscosity of the region occupied by the solid. To validate the numerical scheme, the results are compared with those of the experiments available in the literature. The effects of cylinder diameter, length, impact velocity, and cylinder-water density ratio on the non-dimensional depth are also investigated.