Analysis of errors in the measurement of energy dissipation with two-point LDA

Abstract

In the present study, an attempt has been made to identify and quantify, with a rigorous analytical approach, all possible sources of error involved in the estimation of the fluctuating velocity gradients % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaada % qadaqaaiabgkGi2kaadwhadaWgaaWcbaGaamyAaaqabaGccaGGVaGa % eyOaIyRaamiEamaaBaaaleaacaWGQbaabeaaaOGaayjkaiaawMcaam % aaCaaaleqabaGaaGOmaaaaaaaaaa!4030! $$\overline {\left( {\partial u_i /\partial x_j } \right)^2 } $$ when a two-point laser Doppler velocimetry (LDV) technique is employed. Measurements were carried out in a grid-generated turbulence flow where the local dissipation rate can be calculated from the decay of kinetic energy. An assessment of the cumulative error determined through the analysis has been made by comparing the values of the spatial gradients directly measured with the gradient estimated from the decay of kinetic energy. The main sources of error were found to be related to the length of the two control volumes and to the fitting range, as well as the function used to interpolate the correlation coefficient when the Taylor length scale % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca % qGVbGaaeOCaiaabccadaqdaaqaamaabmaabaGaeyOaIyRaamyDamaa % BaaaleaacaWGPbaabeaakiaac+cacqGHciITcaWG4bWaaSbaaSqaai % aadQgaaeqaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaaa % aOGaayjkaiaawMcaaaaa!444D! $$\left( {{\text{or }}\overline {\left( {\partial u_i /\partial x_j } \right)^2 } } \right)$$ are estimated.