A dynamic variation principle for elastic-fluid contacts applied to elastohydrodynamic lubrication theory

This paper discusses the variational structure of the line contact problem between an elastic medium and a fluid. The equations for the deformation in the elastic material, and for the flow of the viscous fluid are assumed to be determined from an elastic energy E and a power functional P respectively. Then it is shown that a variational formulation of the combined system can be given: apart from the equations in the interior of both media also the equations expressing balance of forces on the separating boundary are obtained from the power functional\ud \ud Image\ud \ud . To that end time dependent deformations are to be considered for which the velocity in the elastic medium vanishes and for which the acceleration of particles on both sides of the common boundary is equal.\ud \ud This general result is employed in the rest of the paper to a typical problem from elastohydrodynamic lubrication theory. The flow of the lubricant allows a basic variational formulation by assuming it to be dominated by viscous dissipation. The complicated resulting expressions are simplified considerably by imposing the common restriction to small deformations and by exploiting the characteristic length scales of the problem. These approximations are performed directly into the governing power and energy functional. The formulation of the approximated system becomes a genuine variational principle and produces correctly the differential expressions. Moreover, it generates in a natural way efficient numerical methods to calculate the deformation of and the pressure at the free boundary if the time variable is discretized

Direct Numerical Simulations of turbulent flow in a driven cavity

Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large computing resources needed for DNS cost-effective and accurate numerical methods are to be selected. Here, various-order accurate spatial discretization methods for DNS have been evaluated by applying them to the 2D driven cavity at Re = 22,000. To analyze the results of the DNS of the 2D flow in a driven cavity at Re = 22,000 the proper orthogonal decomposition (POD) technique has been applied. POD is an unbiased method to determine coherent structures. The Galerkin projection of the Navier-Stokes equations on the space spanned by the POD-basis-functions yields a relatively low-dimensional set of ordinary differential equations that mimics the dynamics of the Navier-Stokes equations. 3D DNS with no-slip conditions at all walls of the cavity have been performed at both Re = 3,200 and Re = 10,000. The results reproduce the experimentally observed Taylor-Görtler-like vortices.

A method to detect baseline emission and plant damage induced volatile emission in a greenhouse

The objective of this research was to ascertain if 1) baseline emission and 2) damage induced emission of volatile plant substances could be detected under greenhouse conditions. A laboratory method was validated for analysing the air in a semi-closed greenhouse with 44 m2 floor area. This greenhouse, with a volume of 270 m3, was climate controlled and light was supplied with assimilation lamps. Sixty tomato plants (Lycopersicon esculentum Mill cv. Moneymaker) were grown in this greenhouse. These plants were artificially damaged on a weekly interval by stroking the stems. Continuous flow pumps were used to purge the air surrounding the plants through tubes containing an adsorbent. This sampling step was performed before and directly after damage of the plants. After sampling, the tubes were transferred to the lab for analysis. The analysis of volatile compounds was performed using a high-throughput gas chromatography-mass spectrometry system. The method enabled the detection of baseline level emission and the emission of volatiles released after artificially damaging the tomato plants during a 6 weeks growing period. Most dominant compounds for baseline emission were the monoterpenes ß-phellandrene, 2-carene, limonene, ¿-phellandrene and ¿-pinene. Directly after damage, these compounds showed an increase of up to 100 times compared to baseline level emission. With these results, we prove that it is possible to detect baseline- and plant damage induced volatile emission in a greenhouse. This area of research is promising but more research needs to be done to determine whether it is possible to detect plant damage due to pests and pathogens using volatile sensing

When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size ≥Δ, where Δ denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size <Δ are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than Δ; and (b) damp any disturbances having a scale of size smaller than Δ initially. From this we deduce that the eddy viscosity νe has to depend on the invariants q = ½tr(S^2) and r =−⅓tr(S^3) of the (filtered) strain rate tensor S. The simplest model is then given by νe = 3/2(Δ/π)^2|r|/q. This model is successfully tested for a turbulent channel flow (Reτ = 590).

Minimum-dissipation model for large-eddy simulation using symmetry-preserving discretization in OpenFOAM

The minimum-dissipation model is applied to channel flow up to $Re_\tau = 2000$, flow past a circular cylinder at $Re=3900$, and flow over periodic hills at $Re=10595$. Numerical simulations were performed in OpenFOAM which is based on the finite volume methods. We used both symmetry-preserving and standard second-order accurate discretization methods in OpenFOAM on structured meshes. The results are compared to DNS and experimental data. The results of channel flow demonstrate a static QR model performs equally well as the dynamic models while reducing the computational cost. The model constant of $C=0.024$ gives the most accurate prediction, and the contribution of the sub-grid model decreases with the increase of the mesh resolution and becomes very small (less than 0.2 molecular viscosity) if a fine mesh is used. Furthermore, the QR model is able to predict the mean and rms velocity accurately up to $Re_\tau = 2000$ without a wall damping function. The symmetry-preserving discretization outperforms the standard OpenFOAM discretization at $Re_\tau=1000$. The results for the flow over a cylinder show that the mean velocity, drag coefficient, and lift coefficient are in good agreement with the experimental data and the central difference schemes conjugated with the QR model predict better results. The various comparisons carried out for flows over periodic hills demonstrate the need to use central difference schemes in OpenFOAM in combination with the minimum dissipation model. The best model constant is again $C=0.024$. The single wind turbine simulation shows that the QR model is capable of predicting accurate results in complex rotating scenarios.Comment: 6 pages; 12 figures; ETMM14 conference paper. arXiv admin note: substantial text overlap with arXiv:2309.0441

Large-eddy simulations of stratified plane Couette flow using the anisotropic minimum-dissipation model

The anisotropic minimum-dissipation (AMD) model for large-eddy simulation (LES) has been recently developed, and here the model performance is examined in strat- ified plane Couette flow. To our knowledge this is the first use of the AMD model for resolved LES of stratified wall-bounded flow. A comparison with previously pub- lished direct numerical simulations (DNS) provides insight into model and grid re- quirements. Prandtl numbers of P r = 0.7 − 70 and a range of Richardson numbers show that the AMD LES performs well even with a strong stabilising buoyancy flux. We identify three new requirements for accurate LES of stratified wall-bounded flow. First, the LES must resolve the turbulent structures at the edge of the viscous sublayer in order to satisfy the Obukov length scale condition, L+s > 200. Other- wise the LES solution may laminarise where the DNS solution remains turbulent. Second, the LES must have enough vertical grid resolution within the viscous and diffusive sublayers to resolve the wall fluxes. Third, the grid must be reasonably isotropic (vertical-to-horizontal grid aspect ratio > 0.25) at the edge of the sublayer and through the turbulent interior for the AMD LES to correctly simulate the scalar flux. When these model requirements are fulfilled the AMD LES performs very well, producing vertical mean profiles, friction Reynolds number and Nusselt number con- sistent with DNS solutions at significantly higher grid resolution