Welcome to IC2's second post in a series titled, "A Guide to Wall Shear Stress Measurement." In Part 1 - Overview, we discussed the high level outline of the various measurement techniques as well as the applications and challenges of measuring wall shear stress. In this section, we will focus on indirect measurement techniques.
Wall shear stress measurement methods are broadly classified into direct and indirect techniques. Indirect techniques depend on the ability to infer shear stress from another flow quantity. Prior knowledge of the sensing environment is required to estimate shear stress from the other measurement, limiting the potential applications where these methods can be used effectively.
Indirect techniques depend on the ability to infer shear stress from another flow quantity, necessitating prior knowledge of the flow environment.
As described above, indirect methods rely on inference. Another quantity, such as pressure drop, heat transfer, or velocity profile is measured and wall shear stress is inferred via empirical correlations. These methods require some form of prior knowledge of the sensing environment (via additional measurements) and are often limited to very specific flow environments where those relations are well-defined. Three main types of indirect measurement approaches are typically employed: surface/flow obstacles, heat/mass transfer, and velocity profiles. The following sections cover each of these techniques in more detail.
(Preston tubes, Stanton tubes, razor blades, microfences, micropillars)
Methods based on flow obstacles are indirect techniques that strategically obstruct the flow and estimate wall shear stress by measuring the pressure drop from the obstruction. Preston tubes , Stanton tubes , and razor blades are examples of such obstacles and are common due to their ease of implementation; however, the measurements made using these techniques are limited to flow environments with thick boundary layers and can only be used to infer mean wall shear stress. Microfences (and surface fences, their larger counterpart) are placed in the boundary layer to create a pressure drop across the fence that is related to wall shear stress using a calibration curve. Whereas conventional surface fences employ pressure ports to measure the pressure drop, microfences typically use integrated piezoresistors to measure pressure induced deflection of the protruding structure (e.g. Pirskawetz et al. , and Ma et al.). Micropillars, in contrast, take a different approach by using remote optical access to enable a two-dimensional mapping of the velocity field (e.g. Brücker et al. , and Große et al. ). The height of the pillar is limited to the viscous sublayer region. Furthermore, limited image resolution, significant image post-processing, and optical/structural vibrations limit real-time measurements and result in wall shear stress estimation errors. Microfences and micropillars provide both mean and fluctuating data, although the bandwidth is typically fairly limited.
Figure 1: Concept drawings of A) Stanton Tube B) Razor Blade C) Preston Tube D) Micropillar and E) Microfence approaches to infer shear-stress.
(Hot wires, hot films, MEMS thermal shear stress sensors)
Heat transfer techniques, such as hot-wires – and hot-films –, rely on convective heat transfer as a basis for wall shear stress estimation. Similarly, MEMS-based thermal shear stress sensors  use the same technique but employ micromachined structures in an attempt to improve performance and address some of the drawbacks of heat-transfer methods. All of these operate by converting heat-transfer rate into voltage via a temperature-resistive transducer.
Heat-transfer techniques, although indirect, offer the potential for both mean and fluctuating wall shear stress information; however, the accuracy of the shear stress estimation is limited because an empirical correlation is required between the measured heating rate and the wall shear stress. As a result, rigorous in situ calibrations are required prior to use. The sensors must be calibrated in the operating environment under actual operating conditions for the correlation to hold. Furthermore, during calibration, there is difficulty in obtaining a unique relationship between the heat-transfer rate and the wall shear stress. Additionally, mean temperature drift leads to changes in resistance and the heat-transfer rate, resulting in measurement errors.
Another drawback is the intrusive nature of these techniques. Hot-films may be physically non-intrusive (as a thin-film along a flow surface) but still impart a flow perturbation due to heat transfer from the sensor into the surrounding fluid. Hot-wires create a similar disturbance issue but also physically protrude into the flow. These techniques also do not give directional information (positive/negative shear stress), providing only the magnitude of the heat-transfer rate/wall shear stress. Finally, due to frequency-dependent heat conduction to the supporting structure, a low-frequency roll-off in the sensitivity occurs, complicating both the gain and phase information in the frequency response. Naughton and Sheplak  and Sheplak et al.  provide more detailed reviews of these limitations. In summary, heat-transfer based methods have the following drawbacks:
- Limited accuracy due to empirical correlations between heat transfer and wall shear stress
- Difficulty in obtaining a unique relationship between the heat-transfer rate and wall shear stress
- In-situ calibrations (under actual operating conditions) required for correlations to hold
- Measurement errors caused by mean temperature drift
- Flow disturbances arising from physical protrusion and heat transfer to the flow
- Lack of wall shear stress directional information
- Frequency-dependent gain and phase response due to heat conduction to supports
Figure 2: Concept drawing of a thermal shear stress sensor
Velocity Profile and Gradient Measurements
(LDV, PIV, Pitot/Hot Wire survey)
Laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) are two indirect techniques that use velocity profile measurements as a means to estimate wall shear stress. In LDV, the flow is seeded with particles to enable light scattering and a coherent beam from a laser is split into two halves which are then crossed in a small region known as a probe volume. The crossing generates interference fringes which are reflected off the particles in the flow. The reflected fringes are frequency-shifted (Doppler effect) by the velocity of the particles and thus contain that velocity information when picked up by a photodetector. By sweeping the location of the probe volume, the velocity profile is measured and used to estimate wall shear stress.
Similarly, in PIV the flow is seeded with particles; however, in this case, a pulsed light sheet is used to illuminate the target area and a camera is used to capture images of that area from each pulse. Once an image sequence is captured, the individual images are divided up into smaller regions known as interrogation areas and then cross-correlated from one image frame to the next. The correlations identify common particle displacements between images, from which velocity is extracted.
Both LDV and PIV enable non-intrusive measurements as the optical generation and readout equipment is located external to the flow field; however, neither provides a direct measurement of wall shear stress, which instead must be estimated from the velocity profile. Additionally, these techniques are limited to thicker boundary layers because it is difficult to seed close to a wall in flow and even with whatever seeding you can get close to the wall, the density of seeding there is limited.
Hot wires, originally discussed above as a heat transfer technique, can also be used for velocity profile measurements if the hot wire probes are mounted on a traverse and swept through the boundary layer to extract a velocity profile, from which wall shear stress is then estimated. Pitot probes can also be used in a similar manner, sweeping through the boundary layer to extract a velocity profile. In this case, the pitot probe measures stagnation pressure at each location, and these stagnation pressures are then converted to a velocity profile.
Near-wall velocity gradients (rather than velocity profile) can be measured via a laser Doppler technique and used to estimate the shear stress. The operating principle (Figure 3) is based on measurement of the Doppler shift of a set of diverging optical fringe patterns , . In addition to the usual limitations of indirect measurements (controlled test environments, large uncertainty, etc), this method is further restricted by low data rates and limited in resolution by probe measurement volume.
Figure 3: Concept drawings for measurement of velocity gradient via laser Doppler methods. [DOE - Diffractive Optical Element]
LDV and pitot/hot-wire techniques provide only mean measurement techniques, whereas PIV allows for acquiring fluctuating data as well. The PIV method, however, is prohibitively expensive to get a full system that provide measurement bandwidths on the order of 1kHz, therefore this method is typically only used for mean measurements.
The next section of "A Guide to Wall Shear Stress Measurements" will cover direct measurement techniques, including film-based techniques and floating element sensors.
Table of Contents
- Part 1 - Overview
- Part 2 - Comparing Techniques - Indirect Measurements
- Part 3 - Comparing Techniques - Direct Measurements***
- Part 4 - Transduction Method - Piezoresistive
- Part 5 - Transduction Method - Piezoelectric
- Part 6 - Transduction Method - Capacitive
- Part 7 - Transduction Method - Optical
- Part 8 - Transduction Method - Summary and Guidelines
- Part 9 - Sensor Construction - Conventional
- Part 10 - Sensor Construction - MEMS
- Part 11 - Summary and References
(*** indicates latest post in A Guide to Wall Shear Stress Measurement Blog Series)
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