58618 - Numerical calibration and investigation of the influence of Reynolds number on measurements with five hole probes in compressible flows 

The detailed understanding of flow phenomena in turbomachinery is still an ongoing challenge. Probes with a high spatial resolution are required to accurately resolve the flow within modern high-speed compressors or turbines. Pneumatic multihole probes are widely used for the measurement of pressures, angles and – after combining with temperatures – velocity components in turbomachinery. These probes are usually calibrated in wind tunnels for different Mach numbers, but all under uniform, steady flow conditions at low turbulence levels and ambient pressure conditions. In high-speed turbomachinery applications, however, the probes are subjected to highly unsteady flows with strong shear gradients, high turbulence levels and quite often also to significantly different Reynolds numbers due to pressure levels larger than ambient. All of these can have non-negligible influences on the calibration characteristics of the probes, and thus on the measured flow properties.

Some correction methods are available in the literature. For example, with the help of the streamline projection method (Willinger/Haselbacher, 2003), the displacement effect (Ranga Raju, 1997) and the apparent incidence (Appukuttan/Miller/Hodson 2004; Dixon, 1977), some tools are available for correcting the effect of shear flows on angle measurements. Estimates for the maximum error caused by flow unsteadiness on time-averaged and time-resolved measurements can be obtained from the simplified analysis by Lou/Aalburg/Hourmouziadis (1998). However, corrections for effects such as Reynolds number and turbulence intensity on five-hole probe characteristics are not readily available. Ideally, these should also be considered in combination with shear flow effects.

In this study, a numerical model is developed for a five-hole probe from a commercial vendor in order to carry out systematic investigations under controlled conditions of the effects of turbulence, Reynolds number and shear flow variations on the calibration characteristic of the probe. The probe considered in this study is a drilled elbow probe with a head diameter of 1.59 mm. The numerical model is set up with Ansys Meshing and computed with Ansys Fluent. In order to reproduce the probe’s behavior in the best possible manner, a full 3D model of the probe was developed based on the nominal shape and dimensions of the probe. This includes the stem and the head with five holes, at the bottom of which the pressures are numerically measured. Due to the complex geometry, the Mosaic Meshing Technology with the Poly-Hexcore feature provides a suitable solution to match different types of meshes. A layered polyprism mesh in the boundary layer is connected with general polyhedral elements to the octree hexes in the bulk region. This facilitated simulating different yaw and pitch angles by rotating the probe in an otherwise fixed domain with constant boundary conditions, but requiring a unique mesh for every angle setting. The generalized k-omega (GEKO) two-equation turbulence model was used to investigate different turbulence boundary conditions.

After an initial mesh resolution study, the numerical model was used to reproduce conditions equivalent to those of a calibration tunnel with a uniform flow at low turbulence and ambient conditions, but over different Mach numbers and at varying yaw and pitch angles to obtain a numerical calibration map of the probe. The pressures inside the probe holes served as the convergence criteria. The results provide a generally good agreement with the calibration data from the wind tunnel. Some differences are likely caused by deviations between actual and nominal probe geometries, which could be observed by microscope. To investigate the influence of the high turbulence intensity that can be expected in real high-speed compressor environments, simulations were performed with turbulence intensity levels of approximately 1%, 10% and 20% near the probe head. In order to obtain the Reynolds number effect on the probe characteristics, the probe Reynolds number was increased by a factor of two and eight relative to the ambient conditions by increasing the pressure level at a given Mach number. Finally, a combination of different turbulence levels and Reynolds numbers is simulated to analyze the combination of effects.