Direct Force Methods

Direct force methods involve removing part of the wall and inserting a flush-mounted element that can move freely. A transducer is attached to the floating element to directly measure the drag force (Brown & Joubert 1969), and the output is calibrated against a known force. A schematic of such a floating element is given in Figure 6.1, and a photograph of the floating element installed in the UTAS Water Tunnel is given in Figure 6.2. The output signal may be provided by a linear variable differential transformer or a bridge arrangement of strain gauges, as in the present study.

The shear force on the floating element is the product of the wall shear stress, τw, and the surface

area of the floating element exposed to the flow. However, there are several secondary forces and effects which also need to be considered. Winter (1977) and Brown and Joubert (1969) provide comprehensive reviews of floating element force balances, and list the following problems which must be considered when designing or using one:

• A transducer that is capable of measuring small forces is required;

• A compromise is required between the need to measure the local properties and the necessity of having an element of sufficient size that the forces on it can be measured accurately;

Figure 6.1 Floating element schematic (with parallel linkages)

Figure 6.2 Floating element in UTAS Water Tunnel

transducer

Floating element U

y

cavity parallel linkage

τ

Parallel linkages

U

• Effects of the necessary gaps around the floating element:

o _{The gap around the floating element acts as a source of roughness, particularly if} there is any misalignment between the floating element and the roof of the channel;

o _{The floating element is free to move in the gap, which may cause changes in the} flow pattern through the gap;

• Forces arising from pressure gradients;

• Sensitivity of result to misalignment of the element with the surrounding surface; • Effects of temperature changes; and

• Effects of leaks:

o _{The pressure gradient (if one exists) will cause a pressure difference between the} fluid in the boundary layer and the fluid in the cavity above the floating element. The resultant flow through the gap, presumably into the cavity on the high pressure side and out of the cavity on the low pressure side, will result in a momentum exchange between the fluid in the cavity and the fluid in the boundary layer. At least part of the force needed to maintain this momentum exchange will be transferred to the floating element.

Perhaps the greatest cause of inaccuracy is the alignment of the face of the element with the surface in which it is mounted. Figure 6.3 demonstrates the forces caused by misaligning the floating element. For an element that protrudes into the flow, the pressure rise caused by the forward-facing step and the pressure drop caused by the rearward-facing step which act on the edges of the element will result in an increased force reading. For a parallel-linkage balance, such as the one used in the present study, the effects of a recessed element are limited to the forces acting on the ends, unlike a pivoted balance where the effects of separation which cause forces acting normal to the plate will contribute to the moment measured (Winter 1977).

The balance used in the current study is of the parallel-linkage type (Figure 6.2) and thus the errors incurred by misalignment of the element are limited to the axial forces. For a protruding element, it is necessary to consider both the forces on the edge of the element that protrudes, and the forces on the edges within the gaps. Winter (1977) states that it is usually assumed that the pressure forces act over half of the thickness of the edges of the element. For a recessed element, the only axial forces occur within the gaps.

The gap size is a critical factor in floating element force balance design. Increasing the gap size around the floating element reduces the effect of misalignment. However, having a large gap may be expected to disturb the flow over the surface (Winter 1977). For flows in pressure gradients, the minimum possible gap and edge thickness are desirable to reduce the flow through the gaps and its effects on the pressure at the edges (Winter 1977).

Brown and Joubert (1969) investigated the secondary forces acting on a floating element due to both the direct effects of a pressure gradient, and the distortion of the boundary layer flow caused by the gap around the floating element. They found that the greatest secondary force for their system was 15% of the wall shear stress force.

Schultz (1998) and Candries (2001) point out that accurate measurements of the skin friction on rough walls using a floating element force balance are difficult. The surface of the floating element should accurately mimic the surrounding surface, which was obviously not the case for the rough and biofouled plate measurements made in the present study.

Figure 6.3 Effect of misalignment of floating plate on end forces (adapted from Winter (1977))

Normal force Edge force

Normal force Edge force

The floating element force balance used in the current study is described in detail in Chapter 4. The data analysis procedures for the total drag measurements are presented in Section 6.3, along with results from repeatability tests on both smooth and rough plates.