Flow separation may occur in situations, where a boundary layer flow slowed down by wall friction is exposed to an adverse pressure gradient. It causes great energy losses and limits the performance of many fluid mechanical devices like airplanes, trucks, pumps and many other flow related machines. Flow separation imposes severe limitations on the design and operation of several fluid mechanic devices.
The two photographs below, taken by Ludwig Prandtl[1], show the flow around an airfoil in two qualitatively different situations. As usual, the flow comes from the left in both figures.
Attached flow around an airfoil at small angles of attack | Separated flow around an airfoil at high angles of attack (stall)[1] |
The photograph on the left hand side shows a fully attached flow. The streamlines formed by the particles indicate a flow field, which is approximately that of a potential flow. On the right hand side, the inclination angle of the airfoil is increased. Due to this, the pressure gradient for a hypothetical potential flow around this airfoil is larger than in the former case. The boundary layer fluid, which has lost some of its kinetic energy due to wall friction is no longer able to surmount the pressure hill and the motion of the near wall fluid is arrested. At some point, the surface streamline leaves the body contour and the boundary layer is said to separate. In consequence, a large region of separated flow forms behind the airfoil. The fluid motion inside this region is characterized by vortices and is usually turbulent.
Due to its shape, an airfoil is able to produce lift when it moves through a fluid. Simultaneously, the fluid exerts a drag force on the airfoil. The next figure shows the dependency of lift and drag of a RAF 34 airfoil with on its angle of attack.
Dependency of the coefficient of lift (C_{L}) and drag
(C_{D}) of a RAF 34 airfiol on the angle of attack (α) [2] |
For small angles of attack, the lift increases approximately linearly with the inclination as predicted by the potential flow theory. Simultaneously, the drag increases. The coefficients of lift (C_{L}) and drag (C_{D}) stand for the corresponding forces normalized by the area of the airfoil and the stagnation point pressure. At approximately 14° the lift starts to decrease with further increasing angle and the drag increase becomes much steeper. At this angle the flow separates and the airfoil is said to stall.
Many techniques have been developed to control flow separation. Suction, blowing and wall motion are known to work and many practical applications especially of the first two control mechanisms exist in aerodynamics.
If the fluid is electrically conducting, an additional possibility to control its flow is given by the Application of a Lorentz force f. This electromagnetic body force results from the vector product of the magnetic induction B and the current density j:
f=j × B.
The current density is given by Ohm´s law:j=σ(E+U × B),
where E denotes the electric field, U the velocity, and σ the electrical conductivity, respectively. Depending on the conductivity of the fluid, one can distinguish between two different types of magnetohydrodynamic (MHD) flow control. If the fluid has a high conductivity in the order of σ=10^{6}S/m like liquid metals or semiconductor melts, an external applied magnetic field alone can have a strong influence on the flow. As described by the right term of Ohm´s Law, the interaction of the flow with the magnetic field causes electrical currents in the liquid. These currents again interact with the external field and generate a Lorentz force field. Typical electrolytes like seawater possess a much lower electrical conductivity in the order of σ=10S/m. Therefore, electrical currents generated by the U×B term are too small to produce a noticeable Lorentz force. In order to obtain current densities large enough for flow control purposes in electrolytes, an additional external electric field has to be applied.
A stripwise arrangement of electrodes and permanent magnets of alternating polarity and magnetization, respectively, generates a streamwise Lorentz force. Lielausis and Gailitis [3]. have proposed this arrangement already in 1961. The following figure shows a sketch of such a structure:
Stripwise arrangement alternating electric and magnetic poles to generate a streamwise Lorentz force |
The resulting Lorentz force has its maximum value directly at the wall and decays exponentially with the wall distance. One can use such a force to accelerated the boundary layer flow and to counteract an adverse pressure gradient.
Due to the accelerating action of the Lorentz force on the flow, separation on an inclined flat plate might be suppressed as shown in the next figures:
Flow around an inclined flat plate: Lorentz force OFF | Flow around an inclined flat plate: Lorentz force ON |
On a flat plate flow separation starts typically at an inclination angle of approximately 5° directly at the leading edge. The left figure shows the separated flow below the plate with the typical vortices marking the boundary between recirculating fluid and mean flow. The plate shown in the photographs is equipped with the stripwise arrangement of permanent magnets and electrodes described above. In the right figure, current is fed to the electrodes, therefore a Lorentz force acts in flow direction and keeps the boundary layer attached. Near the rear end of the plate the velocity of the near wall fluid is even higher than in the mean flow.
The flow around a circular cylinder can be controlled in a similar manner. An mpeg-movie (385kB) showing the naturally instationary flow (Kármán vortex street) and the stationary flow under the stabilizing influence of the Lorentz force can be found here . The Lorentz force F is fed into the boundary layer parallel to the cylinder surface, the orientation of the force and the direction of the mean flow U are denoted by arrows in the upper left corner. A detailed description of these experiments is given in [4].
Force measurements on two hydrofoils have been carried out in the arctic environmental test basin of the Hamburg Ship Model Basin (HSVA) . A sodium chlorine solution with a conductivity equal to that of typical seawater (3.5S/m) has been used for the experiments. The shape of the hydrofoils (PTL IV) is nearly this of a NACA 0017 airfoil. Both hydrofoils have the same overall dimensions (360mm span and 158mm chord length c), but differ in the width of the electrodes/magnets a and the electrode material used. A detailed description of the experimental arrangement has been given in [5] .
PTL IV Hydrofoil with a/c=0.03 | PTL IV Hydrofoil with a/c=0.06 |
To quantify the influence of the Lorentz force, one can use the so called interaction parameter N, which gives the ratio of the electromagnetic to the inertial forces. The following figure show the influence of a suction side Lorentz force on the measured lift at a chord Reynolds number Re=2.9 · 10^{4}.
Influence of a suction side Lorentz force on the lift of a PTL IV hydrofoil with a/c=0.06 |
For N=0, i.e. without the Lorentz force, separation takes place at an angle of attack of 13° leading to an abrupt lift decrease. If the Lorentz force is switched on, already at small inclination angles a lift increase compared to the N=0 case can be seen. This lift increase results from the additional circulation caused by the acceleration of the suction side flow. A much larger lift increase results from the delayed separation of the suction side flow at high angles of attack. The lift coefficient increases further monotonically with the angle of attack up to a point, where the Lorentz force is not any longer able to balance the pressure gradient. From the figure above, one can detect, that for the given hydrofoil at N=2.67 stall can be delayed up to an angle of attack of 21°. This results in an increase of the lift coefficient by 92% in comparison to the unforced flow. Direct numerical simulations at low Reynolds numbers confirm the physical tendencies of the experiments. A short review of the main results of the measurements can be found in [6].
To the Homepage of the MHD Department