Roger Grundmann

Electromagnetic control of seawater flow around circular cylinders

We investigate numerically the electromagnetic control of seawater flows over an infinitely long circular cylinder. Stripes of electrodes and magnets, wrapped around the cylinder surface, produce a tangential body force (Lorentz force) that stabilizes the flow. This mechanism delays flow separation, reduces drag and lift, and finally suppresses the von Karman vortex street. Results from two-dimensional simulations of the Navier–Stokes equations in a range 10<Re<300 and Lorentz force calculations are presented. Emphasis is placed on the disclosure of physical phenomena as well as a quantitative detection of the flow field and forces. It is shown that the drag strongly depends on the geometry of the electromagnetic actuator and on its location at the cylinder surface. The effect of flow control increases with larger Reynolds numbers, since the boundary layer thickness and the penetration depth of the Lorentz force are closely connected.

Spin-up of a liquid metal flow driven by a rotating magnetic field in a finite cylinder: A numerical and an analytical study

This paper presents a combined numerical and analytical study of the impulsive axisymmetric spin-up from rest of an isothermal liquid metal in a closed cylinder. The motion of the liquid is caused by the action of a low-frequency, low-induction rotating magnetic field, whose magnetic Taylor number is in the range (0.01–0.9) Tacr3D with Tacr3D given by Grants and Gerbeth [“Linear three-dimensional instability of a magnetically driven rotating flow,” J. Fluid Mech. 463, 229 (2002)]. The computations were performed for cylindrical containers of aspect ratios (diameter/height) R equal to 0.5, 1, and 2. The numerical simulations are compared with the predictions of an analytical model, valid for small Ekman numbers E extending a former work by Ungarish [“The spin-up of liquid metal driven by a rotating magnetic field,” J. Fluid Mech. 347, 105 (1997)]. The first phase of the motion from rest is an initial adjustment: the inviscid fluid begins to rotate due to the externally forced azimuthal acceleration, and co...

On the stability of the boundary layer subject to a wall-parallel Lorentz force

The stability of a transitional boundary layer influenced by a wall-parallel, streamwise oriented Lorentz force is investigated by means of direct numerical simulation. Damping of Tollmien-Schlichting waves is observed already at weak force amplitudes. For a particular amplitude, similar to homogeneous suction, the initial Blasius layer evolves towards an exponential velocity profile of strongly enhanced stability. Here, intermediate velocity profiles are found to have linear stability properties superior to that of the asymptotic exponential profile. Additional three-dimensional simulations support the two-dimensional results as Lorentz forcing clearly damps the coherent structures of the transitional flow.

Numerical investigations of Lorentz force influenced Marangoni convection relevant to aluminum surface alloying

Abstract This work deals with the numerical investigation of the development of a laser molten aluminum pool under the influence of static magnetic fields with different strengths. Special attention has been paid to laser surface alloying by means of nickel. It was observed that thermocapillary forces drive two counter-rotating vortices which by themselves induce two secondary vortices at the free surface. This scenario yields an alloyed layer with an extension of about half the maximum pool depth. In the presence of a static magnetic field applied perpendicular to the plane of interest, the system of vortices is suppressed. This damped flow situation in the melt results in a variation of the solute distribution in the solid and in shallower alloyed layers depending upon the applied magnetic induction.

Taylor-Görtler Vortices in the Flow Driven by a Rotating Magnetic Field in a Cylindrical Container

Taylor-Görtler vortices play an important role in the flow driven by rotating magnetic field in a closed cylindrical container. The visualization of these structures is essential to understand their physics and their impact on the dynamics of the flow. We present a study of various methods for identifying vortex cores, including the so-called λ2 andQriteria. While λ2 is, probably, the better indicator it is more sensitive to numerical noise and thus less effective in devising 3D vortex structures. Here, the Q criterion proved particularly useful when applied to the fluctuation velocity field.

Linear and nonlinear instability in a cylindrical enclosure caused by a rotating magnetic field

Rotating magnetic fields generate a swirling motion in electrically conductive fluids. In previous theoretical and experimental studies this flow was found to be susceptible to non-normal nonlinear transition mechanisms, which are triggered by small perturbations. In this Brief Communication we present a numerical investigation of the transition in a closed cylindrical container. Depending on the magnetic Taylor number, three different scenarios have been identified: a single subcritical burst, a series of supercritical bursts and, at higher Taylor numbers, a sustained unsteady regime. In all three cases, the unsteady stages are governed by Taylor-Gortler vortices.

STABILIZED DISCONTINUOUS GALERKIN METHODS FOR FLOW–SOUND INTERACTION

The wave propagation in musical instruments is considered. A high-order discontinuous Galerkin method for solving the Euler equations is presented, and an alternative concept for supplying local non-reflecting boundary conditions is introduced. This concept is based on local extrapolation in conjunction with a stabilizing slope limiting. The practicability of this method is discussed via numerical tests, and the results are compared with classical characteristic boundary treatment. Investigations of wave propagation phenomena in musical instruments like the bassoon are performed, and the results are presented.

A Parallel PSPG Finite Element Method for Direct Simulation of Incompressible Flow

We describe a consistent splitting approach to the pressure-stabilized Petrov-Galerkin finite element method for incompressible flow. The splitting leads to (almost) explicit predictor and corrector steps linked by an implicit pressure equation which can be solved very efficiently. The overall second-order convergence is proved in numerical experiments. Furthermore, the parallel implementation of the method is discussed and its scalability for up to 120 processors of a SGI Origin 3800 system is demonstrated. A significant superlinear speedup is observed and can be attributed to cache effects. First applications to large-scale fluid dynamic problems are reported.

Stabilized High-Order Discontinuous Galerkin Methods for Aeroacoustic Investigations

Solving the compressible, unsteady Navier-Stokes equations is a powerful method to investigate the acoustic phenomena in technical systems with superimposed meanflow. This includes pipes, bends, but also musical woodwind instruments. Often the acoustics of these systems is treated as an linearacoustic problem and investigated by solving the Helmholtz equation. This approach neglects interactions between mean flow and acoustic wave, flow phenomena and also nonlinear phenomena like wave steepening. The pressure related to the flow field and the acoustic pressure perturbations that are radiated can vary about four or five order of magnitude. Resolving these effects requires the solution as accurate as possible to avoid numerical dissipation and dispersion errors. We use an explicit, high-order discontinuous Galerkin formulation to minimize these errors.

Electromagnetic Control of Separation at Hydrofoils

Lorentz forces originating from surface-mounted actuators of permanent magnets and electrodes in weakly conducting fluids like seawater provide a convenient tool for separation control at hydrofoils. A well-known actuator design is considered which creates a mainly streamwise Lorentz force that is exponentially decaying in wall-normal direction. Separation control by steady forcing at the suction side and by oscillatory forcing near the leading edge of a symmetric foil is investigated numerically, mostly in the post-stall regime. Direct numerical simulations are performed in the laminar flow regime in order to reveal basic control phenomena as well as simulations using turbulence modelling at higher Reynolds numbers which are closer to possible naval applications. Strong enough steady control s capable of suppressing separation completely, and the scaling behaviour of the maximum lift gain \(\Delta C_L^{max}\) in the turbulent regime is found to agree nicely with experimental results. As oscillatory forcing always has to compete with natural shedding, lock-in behavior is detected, and lift-optimum control at strong control is found in a frequency band around the natural shedding frequency. In terms of the momentum coefficient describing the control effort, appropriate excitation allows for a more effective lift control than steady forcing for small lift gains; for large lift enhancement the effort seems to approach the level of steady control.