Momentum And Heat Transport And Energy Dissipation In A Turbulent Wake

Flow around bluff body widely exists in aviation,navigation,ocean exploration,transport,building environment and other fields in industry and daily life.Therefore,it is of great importance to have a good understand of the property of the flow around bluff bodies.Flow around cylinder is one classical case of flow around bluff bodies.When the shear layer sheds from the cylinder,it forms the well-known Kármán vortex street.The large-scale Kármán vortex has significant effect on the momentum and passive scalar transport as well as the behavior of the small scales.During the developing of the flow from near to far wake,the strength of the coherent structures like the Kármán vortex and the longitudinal rib-like structures all decrease;their influence on the above mentioned property of the flow also varies.The present study sets up from the study of the examination of the effect of the coherent motions in the near wake on the momentum and heat(passive scalar)transport and the statistics of the small scales in the flow.The present study starts with the examination of the three dimensional structures of the vortex,momentum and heat transport in the turbulent near wake.Because the turbulent flow is essentially three dimensional,the momentum and heat transport are all three dimensional as well.However,because of the difficulty in measuring the three components of the vorticity vector,very rare available references have measured the vorticity vector,except for some numerical simulation work.In the present study,a multiwire probe composed of 4 X-wires and 4 cold wires is used to measure the velocity vector,vorticity vector,temperature fluctuation and the temperature gradient vector at nominally the same place in the wake.Measurement is made in the downstream of the cylinder at x/d= 10,20 and 40,where d is the cylinder diameter.The Reynolds number based on the free stream velocity and the diameter of the cylinder is 2.5 × 103.In the analysis,a developed phase-average technique is used to separate the coherent structures associated with the Kármán vortex from the remaining smaller random scales.It is found that the coherent vortex has an essential different influence on the momentum and heat transport at x/d = 10 and the rest two x/d places.At x/d = 10,both the spanwise Kármán vortex and streamwise rib-like vortex has effect on the heat transport,while at x/d = 20 or 40,the heat transport is mainly associated with the Kármán vortex,while the rib-like vortex plays an important role in the diffusion of heat towards the outside of the Kármán vortex.The study also confirms that the production of the turbulent kinetic energy and the temperature variance can be underestimated by 22% and 13%,respectively.This error is expected to be even larger in downstream.Based on the vorticity,momentum and heat structures,the study proposes a three dimensional topological model of the momentum and heat transport in the near wake.Compared with the two dimensional model in the literature,the present model highlights the effect of the rib-like structures on the effect of the heat transport.Also,the present model emphasizes the upstream half the vortex in heat diffusion outside of the Kármán vortex,rather than only the quarter of the vortex near the wake centerline.Based on the understanding of the flow structures,the study turns to the spatial distribution of the turbulent kinetic energy dissipation rate and the temperature variance dissipation rate.In the present measurement,10 out of the 12 terms of the mean turbulent energy dissipation rate and all the three terms of the temperature dissipation rate are measured simultaneously.Based on the assumption of local homogeneity in the lateral plane of the flow,a reference value of the turbulent energy dissipation rate can be obtained.The spectra of the velocity derivatives indicate that the local axisymmetry is first satisfied in the small scales,while the departure in the large scales is caused by the Kármán vortex.It is also found that the chart method proposed by Djenidi and Antonia for estimating the mean turbulent kinetic energy dissipation rate,which is based on the universality of the dissipation range of the streamwise velocity spectrum when it scales on the Kolmogorov scales,is also valid in the present flow field,despite the affect of the coherent motions.The applicability of the chart method in the present flow is consistent with the report in the report that the two major assumptions of Kolmogorov's first similarity hypothesis,i.e.vary large Reynolds numbers and local isotropy can be greatly relaxed.The study also confirms that the spectra of the vorticity are more sensitive in testing the Kolmogorv's first similarity hypothesis than the velocity fluctuation spectra.The results indicate that both the energy dissipation rate and the temperature variance dissipation rate mainly happens within the Kármán vortex.The study at last compares the velocity and temperature fields in terms of their spectraand physical structures.It is found that in the small scales,the analogy between the spectra of enstrophy and the temperature dissipation rate is well satisfied when x/d ? 20,particularly where the Kármán vortex is very weak.For large scales,the spectrum of streamwise velocity and that of the temperature have a better analogy than those of the turbulent kinetic energy and temperature,which is mainly because the lateral velocity fluctuation is highly organized in the flow and makes great contribution to the organization of the turbulent kinetic energy.The findings suggest that the velocity and temperature fields have closer relationship in small scales rather than large scales in the present flow.