Drag and Lift Acting on a Circular Cylinder in Laminar Boundary Layer: Part 1 — Verification of Force Transducer for Measuring Small Force

Experimental investigations on a circular cylinder in a flow have been carried out extensively over the years because of the simplicity of its shape. The wake past the cylinder has been investigated in detail, it has been reported that the vortices shedding from the surface of the cylinder in a uniform flow form a symmetric vortex or a Karman vortex sheet, depending on Reynolds number, and there are several modes of the vortex sheet observed in the wake of the cylinder in a laminar or a turbulent boundary layer. On the other hand, flow forces acting on the cylinder have been measured in detail and drag and lift coefficients acting on it in a uniform flow can be found easily in any data-books. The coefficients in the case of the turbulent boundary layer have also been measured. The forces acting in the case of the laminar boundary layer, however, have yet to be reported. This is mainly because it is very difficult to measure a small flow force of some mN with commercial force transducers. The principle of Hatamura-type force transducers that are made use of frequently in measuring forces is that force acting on the block supported by two parallel spring plates is calculated from the strains detected by four strain gauges that are attached on each of the surfaces of the plates and constitute a Wheatstone’s bridge. It can be applied to measure the small force, that is, it can be calculated from the displacement of the block that is measured by a non-contact type of commercial gap sensor when the stiffness of the supporting springs is made moderately small. In the present report, which is a part of the study that aims at measuring the small flow force acting on a circular cylinder in a laminar boundary layer, a force transducer is developed that the force of some mN can be precisely measured with, based on the concept of the Hatamura-type force transducer. The accuracy of the transducer is verified by measuring the forces acting on the cylinder in a uniform flow and comparing it with the given values in the data book.