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Register a new userInfluence of the spatial resolution on fine-scale features in DNS of turbulence generated by a single square grid
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We focus in this paper on the effect of the resolution of Direct Numerical Simulations (DNS) on the spatio-temporal development of the turbulence downstream of a single square grid. The aims of this study are to validate our numerical approach by comparing experimental and numerical one-point statistics downstream of a single square grid and then investigate how the resolution is impacting the dynamics of the flow. In particular, using the Q-R diagram, we focus on the interaction between the strain-rate and rotation tensors, the symmetric and skew-symmetric parts of the velocity gradient tensor respectively. We first show good agreement between our simulations and hot-wire experiment for one-point statistics on the centreline of the single square grid. Then, by analysing the shape of the Q-R diagram for various streamwise locations, we evaluate the ability of under-resolved DNS to capture the main features of the turbulence downstream of the single square grid.
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The previously reported non-equilibrium dissipation law is investigated in turbulent flows generated by various regular and fractal square grids. The flows are documented in terms of various turbulent profiles which reveal their differences. In spite of significant inhomogeneity and anisotropy differences, the new non-equilibrium dissipation law is observed in all these flows. Various transverse and longitudinal integral scales are measured and used to define the dissipation coefficient $C_{varepsilon}$. It is found that the new non-equilibrium dissipation law is not an artefact of a particular choice of the integral scale and that the usual equilibrium dissipation law can actually coexist with the non-equilibrium law in different regions of the same flow.
We investigate non-equilibrium turbulence where the non-dimensionalised dissipation coefficient $C_{varepsilon}$ scales as $C_{varepsilon} sim Re_{M}^{m}/Re_{ell}^{n}$ with $mapprox 1 approx n$ ($Re_M$ and $Re_{ell}$ are global/inlet and local Reynolds numbers respectively) by measuring the downstream evolution of the scale-by-scale energy transfer, dissipation, advection, production and transport in the lee of a square-mesh grid and compare with a region of equilibrium turbulence (i.e. where $C_{varepsilon}approx mathrm{constant}$). These are the main terms of the inhomogeneous, anisotropic version of the von K{a}rm{a}n-Howarth-Monin equation. It is shown in the grid-generated turbulence studied here that, even in the presence of non-negligible turbulence production and transport, production and transport are large-scale phenomena that do not contribute to the scale-by-scale balance for scales smaller than about a third of the integral-length scale, $ell$, and therefore do not affect the energy transfer to the small-scales. In both the non-equilibrium and the equilibrium decay regions, the peak of the scale-by-scale energy transfer scales as $(overline{u^2})^{3/2}/ell$ ($overline{u^2}$ is the variance of the longitudinal fluctuating velocity). In the non-equilibrium case this scaling implies an imbalance between the energy transfer to the small scales and the dissipation. This imbalance is reflected on the small-scale advection which becomes larger in proportion to the maximum energy transfer as the turbulence decays whereas it stays proportionally constant in the further downstream equilibrium region where $C_{varepsilon} approx mathrm{constant}$ even though $Re_{ell}$ is lower.
The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.
We experimentally study the influence of wall roughness on bubble drag reduction in turbulent Taylor-Couette flow, i.e. the flow between two concentric, independently rotating cylinders. We measure the drag in the system for the cases with and without air, and add roughness by installing transverse ribs on either one or both of the cylinders. For the smooth wall case (no ribs) and the case of ribs on the inner cylinder only, we observe strong drag reduction up to $DR=33%$ and $DR=23%$, respectively, for a void fraction of $alpha=6%$. However, with ribs mounted on both cylinders or on the outer cylinder only, the drag reduction is weak, less than $DR=11%$, and thus quite close to the trivial effect of reduced effective density. Flow visualizations show that stable turbulent Taylor vortices --- large scale vortical structures --- are induced in these two cases, i.e. the cases with ribs on the outer cylinder. These strong secondary flows move the bubbles away from the boundary layer, making the bubbles less effective than what had previously been observed for the smooth-wall case. Measurements with counter-rotating smooth cylinders, a regime in which pronounced Taylor rolls are also induced, confirm that it is really the Taylor vortices that weaken the bubble drag reduction mechanism. Our findings show that, although bubble drag reduction can indeed be effective for smooth walls, its effect can be spoiled by e.g. biofouling and omnipresent wall roughness, as the roughness can induce strong secondary flows.
Within the domain of Computational Fluid Dynamics, Direct Numerical Simulation (DNS) is used to obtain highly accurate numerical solutions for fluid flows. However, this approach for numerically solving the Navier-Stokes equations is extremely computationally expensive mostly due to the requirement of greatly refined grids. Large Eddy Simulation (LES) presents a more computationally efficient approach for solving fluid flows on lower-resolution (LR) grids but results in an overall reduction in solution fidelity. Through this paper, we introduce a novel deep learning framework SR-DNS Net, which aims to mitigate this inherent trade-off between solution fidelity and computational complexity by leveraging deep learning techniques used in image super-resolution. Using our model, we wish to learn the mapping from a coarser LR solution to a refined high-resolution (HR) DNS solution so as to eliminate the need for performing DNS on highly refined grids. Our model efficiently reconstructs the high-fidelity DNS data from the LES like low-resolution solutions while yielding good reconstruction metrics. Thus our implementation improves the solution accuracy of LR solutions while incurring only a marginal increase in computational cost required for deploying the trained deep learning model.
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