Numerical simulation of laminar flow past a circular cylinder

The present paper focuses on the analysis of two- and three-dimensional flow past a circular cylinder in different laminar flow regimes. In this simulation, an implicit pressure-based finite volume method is used for time-accurate computation of incompressible flow using second order accurate convective flux discretisation schemes. The computation results are validated against measurement data for mean surface pressure, skin friction coefficients, the size and strength of the recirculating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding and the mean and RMS amplitude of the fluctuating aerodynamic coefficients for the unsteady periodic flow regime. The complex three dimensional flow structure of the cylinder wake is also reasonably captured by the present prediction procedure.     

Numerical study on bacterial flagellar bundling and tumbling in a viscous fluid using an immersed boundary method

The bundling and tumbling behavior of bacterial flagella in a viscous fluid has got immense significance in the field of biological fluid dynamics. In this paper we investigate the hydrodynamic interaction among two and more than two flagella in a viscous fluid based on an immersed boundary method. We model each helical flagellum by a number of triangular cross-sections with three immersed boundary (IB) points on each cross-section. Three types of elastic links are generated from each IB point to create an elastic network model of the flagellum and the first cross-section is modeled as the flagellar motor. The elastic forces are computed based on the elastic energy approach and the motor forces are obtained from the applied angular frequency of rotation of the motor. The Stokes equations governing the flow are solved on a staggered Cartesian grid system using a fractional-step based finite-volume method. It is observed that when two left-handed helical flagella rotate in the counter-clockwise direction, the resulting hydrodynamic interaction leads to bundling. When one of the flagella reverses the direction of rotation to clockwise the hydrodynamic interaction results in tumbling. During the bundling, the flagella wrap and intertwine each other, whereas during the tumbling they separate in an erratic way. There exists an exact combination of the handedness and rotational direction of the flagella to achieve the bundling. The bundling-to-tumbling behavior of the flagella is studied and it is concluded that the tumbling occurs faster than the bundling. Further, the hydrodynamic interaction among three flagella in a viscous fluid is studied for the cases of rotation in the same direction and in different directions. The bundling and tumbling behavior is well captured even for the case of multiple (more than two) flagella using the developed model.     

Numerical modeling of unsteady flow in steam turbine stage

This work deals with numerical solution of unsteady flow in turbine stage. We use models of compressible single-phase flow of air and two-phase flow of wet steam. Presented numerical methods are based on different stator-rotor matching algorithms, as well as different numerical schemes. Numerical results achieved by both methods and flow models are discussed.     

Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid–structure interaction by differential quadrature method

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier–Stokes (N–S) equations by firstly taking fluid–structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow’s Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.     

Optimal control of non-isothermal viscous fluid flow

For flow inside a four-to-one contraction domain, we minimize the vortex that occurs in the corner region by controlling the heat flux along the corner boundary. The problem of matching a desired temperature along the outflow boundary is also considered. The energy equation is coupled with the mass, momentum, and constitutive equations through the assumption that viscosity depends on temperature. The latter three equations are a non-isothermal version of the three-field Stokes–Oldroyd model, formulated to have the same dependent variable set as the equations governing viscoelastic flow. The state and adjoint equations are solved using the finite element method. Previous efforts in optimal control of fluid flows assume a temperature-dependent Newtonian viscosity when describing the model equations, but make the simplifying assumption of a constant Newtonian viscosity when carrying out computations. This assumption is not made in the current work.     

Application of lattice Boltzmann method for incompressible viscous flows

Because of the presence of corner eddies that change in number and pattern the lid-driven cavity problem has been found suitable to study various aspects of the performance of solution algorithms for incompressible viscous flows. It retains all the difficult flow physics and is characterized by a large primary eddy at the centre and secondary eddies located near the cavity corners. In this work, lid-driven cavity flow is simulated by lattice Boltzmann method with single-relaxation-time and it is compared with those by lattice Boltzmann method with multi-relaxation-time and finite difference method. The effects of the Reynolds number on the size, centre position and number of vortices are studied in detail together with the flow pattern in the cavity. The close agreement of the results bears testimony to the validity of this relatively new approach. However lattice Boltzmann method with multi-relaxation-time model is seen to remove the difficulties faces by the lattice Boltzmann method with single-relaxation-time at higher Reynolds numbers.     

Existence of viscous compressible barotropic flow in a moving domain with free upper surface,via Galerkin method

The previous results on a global in time existence or stability have based on the local time existence in anisotropic Sobolev-Slobodetski spacesW ₂ ^{2+r, 1+r/2}, which are obtained by energy method for weak norm estimates, and by linear theory for higher norm estimates. On the other hand, in the paper of B.J. Jin and M. Padula [2], the global in time existence and stability have been obtained by purely Energy method, where the regularity class is different from anisotropic Sobolev-Slobodetski spacesW ₂ ^{2+r, 1+r/2}. We construct solution local in time of viscous compressible Navier-Stokes equations in a moving domain with free surface, via Galerkin method for the solution of linearized problem and, via iterative procedure for the solution of the nonlinear problem. With this method we obtain local in time solution whose regularity class is the same as the one in [2].

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Sunto I risultati noti sull'esistenza globale o la stabilità sono basati su esistenza locale nel tempo in spazi anisotropici di Sobolev-SlobodetskiW ₂ ^{2+r, 1+r/2}, essi sono ottenuti con il metodo dell'energia per il calcolo di stime di norme deboli, e con la teoria lineare per stime in norme più regolari. D'altra parte, nel lavoro di B.J. Jin e M. Padula [2], esistenza globale int e stabilità sono state ottenute unicamente col metodo dell'energia, in classi di regolarità diverse da quelle degli spazi di Sobolev-Slobodevski. In questa nota costruiamo soluzioni locali int per le equazioni di fluidi di Navier-Stokes viscosi comprimibili in domini con frontiera libera, con il metodo di Galerkin per le soluzioni del problema linearizzato e con una procedura iterativa per le soluzioni del problema nonlineare. Con questo metodo otteniamo soluzioni locali nel tempo avente la stessa classe di regolarità richiesta in [2].

     

Numerical simulation of solitary blood waves in an elastic tube subjected to a localised deformation

In order to well apprehend what really happens in a locally deformed elastic tube, a numerical analysis of the liquid flow in such a media has been undertaken. A cylindrical tube with constant rigidity subjected to a localised dilatation is first considered and results obtained help to understand the behaviour and the developing process of aneurysm. The analysis of the effects of stenoses on blood flow is also done.     

Numerical simulation of pressure-driven startup laminar flows through a planar T-junction channel

A start-up flow of a viscous incompressible fluid in a T-junction channel is studied numerically. The flow starting from rest is driven by a constant pressure drops suddenly applied between the entries and exits of a planar T-junction channel. The Navier-Stokes equations in primitive variables are solved numerically using finite-volume techniques. Predicted variations with time of the volume flow rates and the flow patterns are presented for several values of pressure drops. It has been shown that a start-up flow can pass through different regimes (or different flow direction) before asymptotically reaching steady state distribution.