Using direct numerical simulation to analyze and improve hot-wire probe sensor and array configurations for simultaneous measurement of the velocity vector and the velocity gradient tensor

Abstract

Multi-sensor, hot-wire probes of various configurations have been used for 25 years to simultaneously measure the velocity vector and the velocity gradient tensor in turbulent flows. This is the same period in which direct numerical simulations (DNS) were carried out to investigate these flows. Using the first DNS of a turbulent boundary layer, Moin and Spalart [“Contributions of numerical simulation data bases to the physics, modeling and measurement of turbulence,” NASA Technical Memorandum 100022 (1987)] examined, virtually, the performance of a two-sensor X-array probe with the sensors idealized as points in the numerical grid. Subsequently, several investigators have used DNS for similar studies. In this paper we use a highly resolved minimal channel flow DNS, following Jiménez and Moin [“The minimal flow unit in near-wall turbulence,” J. Fluid Mech. 225, 213 (1991)], to study the performance of an 11-sensor probe. Our previous studies of this type have indicated that, on balance, a probe of the design described here may provide the most accurate measurements of many of the statistics formed from the velocity vector and the velocity gradient tensor (rms and skewness values of the velocity and vorticity components as well as the Reynolds shear stress and the dissipation and production rates). The results of the present study show that, indeed, the sensor and array configurations of a probe of this design are considerably better than previous designs that have been used, and they are likely to give reasonably satisfactory results for such measurements with a real probe in a real bounded flow.