Experimental Investigation Of Reynolds Stress Relaxing Complex Eddy Viscosity Tensor Model In Nonequilibrium Turbulence

In this paper, spatio-temporal relaxation effects in eddy viscosity model ofmodulated Reynolds stress for coherent structure in wall turbulence and Reynoldsstress for non-equilibrium turbulence have been experimentally investigated throughhot wire anemometry and particle image velocimetry. Temporal relaxation effects ofthe modulated Reynolds stress-strain in wall turbulence have been investigated by theuse of hot wire anemometry; Spatial relaxation effects of modulated Reynoldsstress-strain in wall turbulence have been experimentally explored throughtime-resolved two-dimensional PIV (TRPIV) and tomographic TRPIV;Spatio-temporal relaxation effects of the Reynolds stress-strain in the periodicalturbulence induced by axial fan have been researched through two-dimensionalTRPIV.The temporal relaxation effects of the modulated Reynolds stress-strain forcoherent structure in wall turbulence have been investigated through hot wireanemometry. Reynolds stress at different vertical locations in wall turbulence in awind tunnel, as well as rate of strain at corresponding locations have been finelymeasured by the use of hot wire anemometer with X wire probe and parallel wireprobe. The concept of temporal locally averaged velocity structure function isintroduced to perform the decompositions of streamwise velocity components. Thelocal module extremum for locally averaged velocity structure function is employedto educe the ejection and sweep processes. The coherent waveforms of modulatedReynolds stress and rate of strain are extracted by the phase-averaged technique. Thetime-phase relationship of modulated Reynolds stress-strain is obtained through thecorrelation function. Based on the theoretical analysis of eddy viscosity coefficient inrelaxation eddy viscosity model, temporal relaxation effects are studied.Spatial relaxation effects of modulated Reynolds stress-strain for coherentstructure in wall turbulence have been experimentally investigated through TRPIVand tomographic TRPIV. Time sequence signals of two dimensional velocity fields inwall turbulence in a water channel have been measured through TRPIV,3D velocityfields of the wall turbulence in water tunnel have been measured through tomographic TRPIV. The concept of spatial locally averaged velocity structure function isintroduced to perform the decompositions of velocity vector fields. The ejection andsweep events are deduced by the index of the local module extremum for spatiallocally averaged s structure function. The spatial phase-averaged topological modes ofvelocity, vorticity, modulated Reynolds stress and rates of strain are obtained byspatial phase-averaged technique. Spatial phase-averaged distribution modes ofmodulated Reynolds stress and rates of strain are compared.The spatio-temporal relaxation effects of the Reynolds stress-strain in thespatio-temporally periodical turbulence induced by axial fan have been researchedthrough TRPIV. TRPIV has been used to investigate the flow of60%span of blades,as well as the flow at the radial plane of fan outlet in a low-speed axial fan. Theperiodic phase-averaged method is used to process the velocity field of the axial fanfor yielding the time evolution of Reynolds stresses and velocity strain rates, and thecorrelation technology is used to investigate the spatial phase relationship between theboth. The phases between Reynolds stresses and velocity strain rates arespatio-temporally asynchronized.The classical linear eddy viscosity hypothesis can not exactly describe thephysical mechanism of nonequilibrium momentum transfer for eddy structures inturbulence. The relaxation eddy viscosity tensor model with should be employed.Because of the nonsynchronization between Reynolds stresses and rates of strain, thenumerical simulation of nonequilibrium turbulence is becoming a challengingproblem. The present proposed relaxation eddy viscosity tensor model should beemployed.