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This study continues the exploration of temporal large-eddy simulation, particularly the extension of the temporal direct deconvolution method (TDDM) with a regularization term based on spatial dissipation. Furthermore, we aim to put insight stemming from previous work to test. Specifically, the hypothesis is that the temporal residual-stress leads to a reduction of the required artificial dissipation in under-resolved simulations. Moreover, this work seeks corroborate earlier discoveries with a posteriori results. We perform a numerical examination of two different spatial regularization terms in conjunction with TDDM: a spatial variant of selective frequency damping, functioning as a relaxation term that gradually drifts the velocity toward the filtered velocity, and the dynamic Smagorinsky model incorporating a prefactor. We test various cases, including the Taylor–Green vortex flow with a Reynolds number of Re = 3000, forced homogeneous isotropic turbulence with R e λ = 200 , turbulent channel flow at R e τ = 590 , and the flow over a periodic hill with Re = 10 935. Additionally, we also analyze the various dissipation contributions in TDDM as well as their interrelations. We also discuss grid artifacts and energy budget errors using these to compare the different models. Our results confirm the hypothesis that residual-stress dissipation reduces the necessary artificial dissipation. Because of the numerical ill-conditioning of deconvolution, whether temporal or spatial, there are practical limitations in the size of the filter width. Due to these limitations, the impact remains relatively minor. The a posteriori results of the new spatial regularization term show it to be effective in eliminating energy from the high wavenumber range. [ABSTRACT FROM AUTHOR]

Turbulent reactive flows laden with droplets appear in various energy systems but are difficult to understand and parametrize. Such flows involve interactions of turbulent fluctuations, phase changes, and chemical reactions that give rise to complex phenomena. To improve our knowledge, we performed direct numerical simulations of a canonical shear flow. It is composed of a hot, quiescent outer layer and a cold, turbulent inner layer that is laden with droplets. Due to the turbulent fluctuations, the droplets form clusters. Due to the high temperatures, the droplets evaporate quickly and flames emerge spontaneously at the interface of the two layers. We observed premixed flames that enclose droplet clusters and diffusion flames that enclose vapor pockets or single droplets. To examine these flame structures in more detail, we varied the droplet size, droplet loading, and shear rate. We found that the droplet size and droplet loading have significant effects, whereas the shear rate has only subtle effects. [ABSTRACT FROM AUTHOR]

The present paper investigates droplet laden turbulent gas flows with point droplet direct numerical simulations. A novel flow configuration is presented, which allows us to simulate statistically stationary homogeneous isotropic regions of turbulent sprays. This configuration enables a physical analysis with small statistical errors under controllable conditions. The length scales of clusters are analyzed with spectra of the droplet number density and vapor mass fraction fluctuations. The local conditions in clusters and voids are analyzed with probability density functions of the local droplet number density, local vapor mass fraction, and evaporation rate. Effects of the mass loading and Stokes number on the clustering of droplets and the mixing of vapor are characterized, and the compositions of clusters and voids are examined. As the mass loading increases from 2.5% to 12.5%, the fluctuations in the vapor mass fraction and droplet number density increase almost equally at all length scales. Clusters contain more droplets that together release more vapor, but their characteristic size remains unchanged. As the mean Stokes number increases from 1 to 4, the fluctuations in the vapor mass fraction and droplet number density decrease predominantly at small length scales. Clusters contain fewer droplets that together release less vapor, and their characteristic size increases. At a mass loading of 7.5% and a mean Stokes number of 2, clusters contain considerably more droplets and vapor than voids. Droplets located in clusters therefore evaporate more slowly than droplets located in voids. [ABSTRACT FROM AUTHOR]

Abstract: Different simulation methods are applicable to study turbulent mixing. When applying probability density function (PDF) methods, turbulent transport, and chemical reactions appear in closed form, which is not the case in second moment closure methods (RANS). Moreover, PDF methods provide the entire joint velocity-scalar PDF instead of a limited set of moments. In PDF methods, however, a mixing model is required to account for molecular diffusion. In joint velocity-scalar PDF methods, mixing models should also account for the joint velocity-scalar statistics, which is often under appreciated in applications. The interaction by exchange with the conditional mean (IECM) model accounts for these joint statistics, but requires velocity-conditional scalar means that are expensive to compute in spatially three dimensional settings. In this work, two alternative mixing models are presented that provide more accurate PDF predictions at reduced computational cost compared to the IECM model, since no conditional moments have to be computed. All models are tested for different mixing benchmark cases and their computational efficiencies are inspected thoroughly. The benchmark cases involve statistically homogeneous and inhomogeneous settings dealing with three streams that are characterized by two passive scalars. The inhomogeneous case clearly illustrates the importance of accounting for joint velocity-scalar statistics in the mixing model. Failure to do so leads to significant errors in the resulting scalar means, variances and other statistics. [Copyright &y& Elsevier]

Abstract: In this work, we propose a consistent turbulence-modeling framework for hybrid LES/RANS modeling. In this framework, the filtered and Reynolds averaged Navier–Stokes (RANS) equations are solved simultaneously in the whole domain on their respective meshes. Consistency between the two solutions is achieved in terms of velocity, pressure, and turbulent quantities through additional drift terms in the corresponding equations. This approach leads to clean conditions at the LES/RANS interfaces. Note that this general framework does not depend on the specific choice of LES and RANS models. A hybrid LES/RANS solver is developed within this framework and used to simulate the flow in a plane channel and that in a channel with periodic hills. The results demonstrate that the hybrid solver leads to significantly improved results with moderate computational overhead compared to traditional LES, making it a promising candidate for industrial flow simulations. [Copyright &y& Elsevier]

Abstract: In the present study, a framework for modeling two-phase evaporating flow is presented, which employs an Eulerian–Lagrangian–Lagrangian approach. For the continuous phase, a joint velocity-composition probability density function (PDF) method is used. Opposed to other approaches, such PDF methods require no modeling for turbulent convection and chemical source terms. For the dispersed phase, the PDF of velocity, diameter, temperature, seen gas velocity and seen gas composition is calculated. This provides a unified formulation, which allows to consistently address the different modeling issues associated with such a system. Because of the high dimensionality, particle methods are employed to solve the PDF transport equations. To further enhance computational efficiency, a local particle time-stepping algorithm is implemented and a particle time-averaging technique is employed to reduce statistical and bias errors. In comparison to previous studies, a significantly smaller number of droplet particles per grid cell can be employed for the computations, which rely on two-way coupling between the droplet and gas phases. The framework was validated using established experimental data and a good overall agreement can be observed. [Copyright &y& Elsevier]

Data assimilation (DA) plays a crucial role in extracting valuable information from flow measurements in fluid dynamics problems. Often only time-averaged data is available, which poses challenges for DA in the context of unsteady flow problems. Recent works have shown promising results in optimizing Reynolds-averaged Navier–Stokes (RANS) simulations of stationary flows using sparse data through variational data assimilation, enabling the reconstruction of mean flow profiles. In this study we perform three-dimensional variational data assimilation of sparse time-averaged data into an unsteady RANS (URANS) simulation by means of a stationary divergence-free forcing term in the URANS equations. Efficiency and speed of our method are enhanced by employing coarse URANS simulations and leveraging the stationary discrete adjoint method for the time-averaged URANS equations. The data assimilation codes were developed in-house using OpenFOAM for the URANS simulations as well as for the solution of the adjoint problem, and Python for the gradient-based optimization. Our results demonstrate that data assimilation of sparse time-averaged velocity measurements not only enables accurate mean flow reconstruction, but also improves the flow dynamics, specifically the vortex shedding frequency. To validate the efficacy of our approach, we applied it to turbulent flows around cylinders of various shapes at Reynolds numbers ranging from 3000 to 22000. Our findings indicate that data points near the cylinder play a crucial role in improving the vortex shedding frequency, while additional data points further downstream are necessary to also reconstruct the time-averaged velocity field in the wake region. [ABSTRACT FROM AUTHOR]

Turbulent flow simulations based on the Reynolds-averaged Navier–Stokes (RANS) equations continue to be the workhorse approach for industrial flow problems. However, due to the inherent averaging and the closure models required for the Reynolds stresses, their accuracy is limited. Experimental data, on the other hand, represents the true flow features but is potentially only available in limited locations or at low resolution. Data assimilation (DA) can be used to combine closure models with such experimental data to obtain accurate simulation results. In this scenario, the result of the DA process can be interpreted as a physics-based interpolation and serve as a basis for further studies of the flow. Moreover, such tuned models may be used in machine learning approaches aiming at a priori closure model enhancement. The main objective of this work is to recover a spatially varying eddy viscosity correction factor from sparsely distributed reference data. We use an efficient in-house data assimilation implementation based on the discrete adjoint method for RANS simulations in OpenFOAM to recover an optimal eddy viscosity field. A gradient optimization procedure is used to minimize a velocity-based cost function with a regularization term. All the partial derivatives in the gradient computation are evaluated with an efficient semi-analytical approach at the cost of approximately one forward solution step. The effectiveness of the proposed approach is demonstrated for a periodic hill test case at Re = 10595 with different spatial distributions of the reference data. The results show improvements in the agreement between simulation and reference for a range of reference data configurations and highlight the performance of linear eddy viscosity models. • We propose an efficient discrete adjoint gradient method for stationary problems. • We perform data assimilation of velocity reference data to correct the eddy viscosity in stationary RANS simulations. • We demonstrate the importance of regularization for sparsely distributed reference data. [ABSTRACT FROM AUTHOR]

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning. An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation. The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM , which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used. The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes. [ABSTRACT FROM AUTHOR]