Investigation Of Spanwise Rotating Channel Flow Based On Thermal Analogy

Fluid flows in rotating reference frames are common in astrophysics,geophysics,and turbomachinery.Spanwise rotating channel flow is one of the classical simplified models of rotating shear flows and is important for both theoretical and applied research of fluid mechanics.In the present work,theoretical analysis mainly based on thermal analogy and direct numerical simulations are performed on spanwise rotating channel flow.Stability of the laminar solution,flow structures in turbulent flow,and the influence of flow structures on turbulence statistics are investigated.Based on the results and analysis,a blowing/suction control strategy to enhance turbulence transport is introduced and examined.The methods are also applicable for other rotating wall turbulence.First,the Taylor-G(?)rtler stability of the one-dimensional laminar solution of spanwise rotating channel flow is investigated and its parameter reduction is given special attention.Thermal analogy and variable substitution show that the original stability problem is fully equivalent to the two-dimensional stability problem of a specific type of stratified fluid.The equivalent density field shows unstable stratification near the pressure side and stable stratification near the suction side.With the characteristic scales of the unstably stratified region,a Rayleigh number is defined.A conjecture is proposed that the original problem controlled by the Reynolds number and rotation number is dominated by the properties of the unstably stratified region and could be simplified consequently to a one-parameter problem controlled by the Rayleigh number.The analysis of the eigenvalue problem verifies this conjecture by showing that the critical curves and eigenfunctions of the original problem well collapse after rescaling.Second,based on the equivalence between two-dimensional spanwise rotating channel flow and two-dimensional penetrative convection,another conjecture is proposed that threedimensional spanwise rotating turbulent channel flow has similar flow structures as penetrative convection.Direct numerical simulation data are analyzed and visualized to verify this conjecture.Flow visualizations show that small-scale plumes exist near the pressure side.The probability density functions of streamwise and wall-normal velocity fluctuation near the pressure side also show similar features as thermal plumes and could be fitted with a semi-empirical model.Linearized equations and flow visualizations show that large-scale inertial waves which are similar to internal gravity waves exist near the suction side.In three-dimensional flows at low and medium rotation numbers,plumes near the pressure side may gather to form largescale plume currents whose number and spanwise locations continuously vary with time.A modified clustering algorithm eliminating the phase difference is introduced,with which the identification and analysis of the patterns of plume clusters can be performed.The identified patterns of plume clusters also explain the behaviours of large-scale Taylor-G(?)rtler vortices.Third,based on the new interpretations of flow structures in spanwise rotating turbulent channel flow,theoretical analysis are performed on turbulence statistics which are not fully understood.The local linear law of the non-dimensionalized velocity profile at medium rotation numbers with a slope close to the rotation number can be derived in two-dimensional cases with thermal analogy and the locally constant temperature profile of penetrative convection,and can be explained in general cases with the Lagrangian form of the streamwise velocity equation.In the laminarized region at high rotation numbers,the relatively large fluctuation of streamwise velocity and the nearly negligible Reynolds shear stress can be explained with the amplitude and phase relations between the streamwise and wall-normal components of inertial waves.At small and medium rotation numbers,conditional average based on clustering analysis shows that the distribution of plume currents has significant influence on the turbulent transport of passive scalar,and a pattern with sparser plume currents is usually more efficient in scalar transport.This result provides an important inspiration for the design and analysis of flow control strategy.At last,based on the influence of the distribution of plume currents on scalar transport,a blowing/suction control strategy for three-dimensional spanwise rotating channel flow is introduced.This strategy applies weak blowing/suction through the pressure side to control the distribution of plume currents and scalar convective flux.Direct numerical simulations show that proper distributions of blowing/suction slots at low and medium rotation numbers can make plume currents form above blowing slots and consequently fix their number and locations,which could significantly increase the amplitude of the corresponding distribution patterns of plume currents.The blowing/suction control can also enhance the scalar convective flux in both rotating and non-rotating turbulent channel flow.In rotating cases,if a blowing/suction control makes the distribution pattern of plume currents slightly smaller than the dominating pattern of plume currents in the corresponding uncontrolled case,it can achieve significant enhancement of scalar convective flux.In comparison,blowing/suction through the stable side has very little influence on the large-scale flow modes and scalar transport.This is because plumes near the pressure side are not sensitive to perturbations on the suction side.