Quantification of uncertainties in Reynolds–Averaged Navier–Stokes (RANS) simulations has gained a considerable interest in turbulence modeling. We present two different approaches for the ...quantification and propagation of model-form and operational uncertainties in context of wind turbine RANS simulations. The first approach is based on a stochastic RANS solver in OpenFOAM using intrusive polynomial chaos method (Parekh and Verstappen, 2023). Here the uncertainties are propagated through a single (large) simulation for the coupled coefficients of the polynomial expansion. The second approach is a surrogate based uncertainty quantification (SBUQ) method. The surrogate model comprises of a 3D U-Net neural network (trained over a single wind turbine) combined with a wake superposition model in order to the prediction of flow field in an array of wind turbines. The above-mentioned approaches are applied for uncertainty quantification analysis in RANS simulations of two turbulent engineering flow problems — (i) a wake past a single wind turbine, and (ii) wake interactions and power losses in an array of wind turbines. The results show that the uncertain RANS solutions from the two approaches are able to reasonably capture the reference high-fidelity solution. We also discuss comparisons between the two approaches including computational cost, applicability, generality etc. The two methods can be further explored and applied to engineering applications where it is critical to compute the turbulent RANS solution in presence of various sources of uncertainties.
•Wind turbine RANS simulations are susceptible to multiple sources of uncertainties.•Stochastic RANS is resource efficient and applicable to diverse CFD applications.•3D U-Net surrogate is capable of accurate wind turbine/farm flow field predictions.•Surrogate based UQ analysis is reasonably accurate and computationally inexpensive.
A fully-conservative discretization is presented in this paper. The same principles followed by Verstappen and Veldman (2003) 3 are generalized for unstructured meshes. Here, a collocated-mesh scheme ...is preferred over a staggered one due to its simpler form for such meshes. The basic idea behind this approach remains the same: mimicking the crucial symmetry properties of the underlying differential operators, i.e., the convective operator is approximated by a skew-symmetric matrix and the diffusive operator by a symmetric, positive-definite matrix. A novel approach to eliminate the checkerboard spurious modes without introducing any non-physical dissipation is proposed. To do so, a fully-conservative regularization of the convective term is used. The supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed. Finally, the new discretization method is successfully tested for a buoyancy-driven turbulent flow in a differentially heated cavity.
The fate of human adipose tissue stem cells (ASCs) is largely determined by biochemical and mechanical cues from the extracellular matrix (ECM), which are sensed and transmitted by integrins. It is ...well known that specific ECM constituents influence ASC proliferation and differentiation. Nevertheless, knowledge on how individual integrins regulate distinct processes is still limited. We performed gene profiling of 18 alpha integrins in sorted ASCs and adipocytes, identifying downregulations of RGD-motif binding integrins integrin-alpha-V (ITGAV) and integrin-alpha-5 (ITGA5), upregulation of laminin binding and leukocyte-specific integrins and individual regulations of collagen and LDV-receptors in differentiated adipocytes in-vivo. Gene function analyses in in-vitro cultured ASCs unraveled differential functions of ITGA5 and ITGAV. Knockdown of ITGAV, but not ITGA5 reduced proliferation, caused p21(Cip1) induction, repression of survivin and specific regulation of Hippo pathway mediator TAZ. Gene knockdown of both integrins promoted adipogenic differentiation, while transgenic expression impaired adipogenesis. Inhibition of ITGAV using cilengitide resulted in a similar phenotype, mimicking loss of pan-ITGAV expression using RNAi. Herein we show ASC specific integrin expression patterns and demonstrate distinct regulating roles of both integrins in human ASCs and adipocyte physiology suggesting a negative impact of RDG-motif signaling on adipogenic differentiation of ASCs via ITGA5 and ITGAV.
•A symmetry-preserving second-order time-accurate PISO-based method.•Comparison with conservative symmetry-preserving projection method of Trias et al. (2014).•Error sources causing the numerical ...dissipation.•Both methods are effectively fully-conservative when an incremental-pressure approach is used.
A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. 35. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method.
Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods.
Harlow and Welch Phys. Fluids 8 (1965) 2182–2189 introduced a discretization method for the incompressible Navier–Stokes equations conserving the secondary quantities kinetic energy and vorticity, ...besides the primary quantities mass and momentum. This method was extended to fourth order accuracy by several researchers 25,14,21. In this paper we propose a new consistent boundary treatment for this method, which is such that continuous integration-by-parts identities (including boundary contributions) are mimicked in a discrete sense. In this way kinetic energy is exactly conserved even in case of non-zero tangential boundary conditions. We show that requiring energy conservation at the boundary conflicts with order of accuracy conditions, and that the global accuracy of the fourth order method is limited to second order in the presence of boundaries. We indicate how non-uniform grids can be employed to obtain full fourth order accuracy.
The multifaceted appearance of soft robots in the form of swimmers, catheters, surgical devices, and drug-carrier vehicles in biomedical and microfluidic applications is ubiquitous today. ...Jellyfish-inspired soft robotic swimmers (jellyfishbots) have been fabricated and experimentally characterized by several researchers that reported their swimming kinematics and multimodal locomotion. However, the underlying physical mechanisms that govern magnetic-field-induced propulsion are not yet fully understood. Here, we use a robust and efficient computational framework to study the jellyfishbot swimming kinematics and the induced flow field dynamics through numerical simulation. We consider a two-dimensional model jellyfishbot that has flexible lappets, which are symmetric about the jellyfishbot center. These lappets exhibit flexural deformation when subjected to external magnetic fields to displace the surrounding fluid, thereby generating the thrust required for propulsion. We perform a parametric sweep to explore the jellyfishbot kinematic performance for different system parameters-structural, fluidic, and magnetic. In jellyfishbots, the soft magnetic composite elastomeric lappets exhibit temporal and spatial asymmetries when subjected to unsteady external magnetic fields. The average speed is observed to be dependent on both these asymmetries, quantified by the glide magnitude and the net area swept by the lappet tips per swimming cycle, respectively. We observe that a judicious choice of the applied magnetic field and remnant magnetization profile in the jellyfishbot lappets enhances both these asymmetries. Furthermore, the dependence of the jellyfishbot swimming speed upon the net area swept (spatial asymmetry) is twice as high as the dependence of speed on the glide ratio (temporal asymmetry). Finally, functional relationships between the swimming speed and different kinematic parameters and nondimensional numbers are developed. Our results provide guidelines for the design of improved jellyfish-inspired magnetic soft robotic swimmers.
Predicting the behavior of turbulent flows using large-eddy simulation requires a modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the ...dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical basis to mix (functional) eddy-viscosity models with the (structural) Bardina model. By taking an anisotropic minimum-dissipation (AMD) model for the eddy viscosity, we obtain the (single-layer) AMD–Bardina model. In order to also obtain a physics-conforming model for wall-bounded flows, we further develop this mixed model into a two-layer approach: the near-wall region is parameterized with the AMD–Bardina model, whereas the outer region is computed with the Bardina model. The single-layer and two-layer AMD–Bardina models are tested in turbulent channel flows at various Reynolds numbers, and improved predictions are obtained when the mixed models are applied in comparison to the computations with the AMD and Bardina models alone. The results obtained with the two-layer AMD–Bardina model are particularly remarkable: both first- and second-order statistics are extremely well predicted and even the inflection of the mean velocity in the channel center is captured. Hence, a very promising model is obtained for large-eddy simulations of wall-bounded turbulent flows at moderate and high Reynolds numbers.
Since direct numerical simulations cannot be computed at high Reynolds numbers, a dynamically less complex formulation is sought. In the quest for such a formulation, we consider regularizations of ...the convective term that preserve the symmetry and conservation properties exactly. This requirement yielded a novel class of regularizations Verstappen R. On restraining the production of small scales of motion in a turbulent channel flow. Comput Fluids 2008;37:887–97. that restrains the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations must preserve the symmetry and conservation properties too. To do so, one of the most critical issues is the discrete filtering. The method requires a list of properties that, in general, is not preserved by classical filters for LES unless they are imposed
a posteriori. In the present paper, we propose a novel class of discrete filters that preserves such properties
per se. They are based on polynomial functions of the discrete diffusive operator,
D
∼
, with the general form
F
=
I
+
∑
m
=
1
M
d
m
D
∼
m
. Then, the coefficients,
d
m
, follow from the requirement that, at the smallest grid scale
k
c
, the amount by which the interactions between the wavevector-triples (
k
c
,
k
c
−
q,
q) are damped must become virtually independent of the
qth Fourier-mode. This allows an optimal control of the subtle balance between convection and diffusion at the smallest grid scale to stop the vortex-stretching. Finally, the resulting filters are successfully tested for the Burgers’ equation.
Since direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a ...formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations Comput Fluids 2008;37:887 that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore, the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (
Pr
=
0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4
×
10
8
⩽
Ra
⩽
10
11 shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with
Ra up to 10
17. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of
Ra.
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