Domain of dependence for wall-pressure measurements in high-speed boundary layers

Abstract

Measurements in high-speed flows are difficult to acquire. To maximise their utility, it is important to quantify the preceding events that can influence a sensor signal. Flow perturbations that are invisible to a sensor may prevent the detection of key physics. Conversely, perturbations that originate away from a sensor may impact its signal at the measurement time. The collection of the latter perturbations defines the domain of dependence (DOD) of the sensor, which can be evaluated efficiently using adjoint-variational methods. For Mach 4.5 transitional flat-plate boundary layers, we consider the DOD of an instantaneous and localised wall-pressure observation, akin to that by a piezoelectric probe. At progressively earlier times prior to the measurement, the DOD retreats upstream from the probe, and the sensitivity to flow perturbations expands spatially and is amplified. The expansion corresponds to a wider region where initial disturbances can influence the measurement, and the amplification is because these perturbations grow during their forward evolution before reaching the probe. The sensitivity has a wavepacket structure concentrated near the boundary-layer edge, and a portion that radiates into the free stream. The DOD is further interpreted as the optimal initial perturbation with unit energy that maximises the norm of the measurement, establishing a link to transient-growth analysis. We test this formulation for a laminar condition and contrast the sensor dependence on different components of the state vector. When the boundary layer is transitional, we adopt the general formulation to assess the impact of sensor placement within the transition and turbulent zones on the DOD, and we characterise the flow disturbances that most effectively influence the measurement in each regime.

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