The PANS equations model is used to predict the transitional Taylor-Green vortex (TGV) flow at Re=3000. A new form of the closure is proposed, in which the PANS procedure is applied to a variant of the BHR turbulence model. The TGV is a benchmark case for transitional flows in which the onset of turbulence is driven by vortex-stretching and reconnection mechanisms. Since these physical phenomena are observed in numerous flows of variable-density, this study constitutes the first step toward extending the PANS method to such a class of problems. We start by deriving the governing equations of the model and analyze the selection of the parameters controlling its physical resolution, fe and fk, through a-priori testing. Afterward, we conduct PANS computations at different constant physical resolutions to evaluate the model's accuracy and cost predicting the TGV flow. This is performed through simple verification and validation exercises, and the physical and modeling interpretation of the numerical predictions. The results confirm that PANS can efficiently (accuracy vs. cost) predict the present flow problem. Yet, this is closely dependent on the physical resolution of the model. Whereas high-physical resolution (fk<0.50) computations are in good agreement with the reference DNS studies, low-physical resolution (fk>=0.50) simulations lead to large discrepancies with the reference data. The physical and modeling interpretation of the results demonstrates that the origin of these distinct behaviors lies in the model's ability to resolve the phenomena driving the onset of turbulence not amenable to modeling by the closure. The comparison of the computations' cost indicates that high-physical resolution PANS achieves the accuracy of DNS (fk=0.00) at a fraction of the cost. We observe a cost reduction of one order of magnitude at the current Re, which is expected to grow with Re.
The partially-averaged Navier-Stokes (PANS) equations are used to predict the variable-density Rayleigh-Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number $500$. This is a prototypical problem of material mixing featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS BHR-LEVM closure. The…
This work extends the framework of the partially-averaged Navier-Stokes (PANS) equations to variable-density flow, \text{i.e.}, multi-material and/or compressible mixing problems with density variations and production of turbulence kinetic energy by both shear and buoyancy mechanisms. The proposed methodology is utilized to derive the PANS BHR-LEVM closure. This includes \textit{a-priori} testing to analyze and develop guidelines toward the efficient selection of the parameters controlling the physical resolution and, consequently, the range of resolved scales of PANS. Two archetypal test-case…
Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor--Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, 3-D roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (\textit{Phys. Fluids}, vol. 18, 0…
We investigate the existence of multiple turbulent states in highly turbulent Taylor-Couette flow in the range of $\mathrm{Ta}=10^{11}$ to $9\cdot10^{12}$, by measuring the global torques and the local velocities while probing the phase space spanned by the rotation rates of the inner and outer cylinder. The multiple states are found to be very robust and are expected to persist beyond $\mathrm{Ta}=10^{13}$. The rotation ratio is the parameter that most strongly controls the transitions between the flow states; the transitional values only weakly depend on the Taylor number. However, complex p…
Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of {Re_i=10^5} for a radius ratio of {η=r_i/r_o=0.714} between the inner and outer cylinder. With increasing {Re_i}, the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large--scale rolls completely drive the meridional flow while in the second one the coherent structures recover only on average. The presence of…
We investigate the quasi two-dimensional Taylor-Couette system in the regime where the radius ratio is close to unity - a transitional regime between three and two dimensions. By systematically increasing the Reynolds number we observe a number of standard transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF), as well as the transition to fully developed turbulence. Prior to the onset of turbulence we observe intermittent burst patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs)…
We investigate the local self-sustained process underlying spiral turbulence in counter-rotating Taylor-Couette flow using a periodic annular domain, shaped as a parallelogram, two of whose sides are aligned with the cylindrical helix described by the spiral pattern. The primary focus of the study is placed on the emergence of drifting-rotating waves ({\sc drw}) that capture, in a relatively small domain, the main features of coherent structures typically observed in developed turbulence. The transitional dynamics of the subcritical region, far below the first instability of the laminar circul…
In this study we report numerical results of turbulent transport of heat $Nu$ and angular momentum $ν_{t}/ν$ in Taylor-Couette (TC) flows subjected to a radial temperature gradient. Direct numerical simulations are performed in a TC cell with a radius ratio $η=0.5$ and an aspect ratio $Γ=8$ for two Rayleigh numbers ($Ra=10^5$, $10^6$) and two Prandtl numbers ($Pr=0.7$, $4.38$), while the Reynolds number $Re$ varies in the range of $0 \le Re \le 15000$. With increasing $Re$, the flows undergo two distinct transitions: the first transition being from the convection-dominated regime to the transi…
Effect of gap width on turbulent transition in Taylor-Couette flow
Faculty of Mechanical Engineering, Zhejiang Sci-Tech University（浙江理工大学机械工程学院）；School of Mechanical Engineering, Zhejiang University of Water Resources and Electric Power（浙江水利水电学院机械工程学院）；School of Mechanical Engineering, Hangzhou Dianzi University（杭州电子科技大学机械工程学院）
Several competing artificial compressibility methods for the incompressible flow equations are examined using the high-order flux reconstruction method. The established artificial compressibility method (ACM) of \citet{Chorin1967} is compared to the alternative entropically damped (EDAC) method of \citet{Clausen2013}, as well as an ACM formulation with hyperbolised diffusion. While the former requires the solution to be converged to a divergence free state at each physical time step through pseudo iterations, the latter can be applied explicitly. We examine the sensitivity of both methods to t…
A new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier-Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech, 6…
