The Wilcox $ k-\omega $ k-omega turbulence model predicts turbulent boundary layers well, both fully-developed channel flows and flat-plate boundary layers. However, it predicts too low a turbulent kinetic energy. This is a feature it shares with most other two-equation turbulence models. When comparing the terms in the k equations with DNS data it is found that the production and dissipation terms are well predicted but the turbulent diffusion is not. In the present work the poor modelling of the turbulent diffusion is improved using Physics Informed Neural Network (PINN) and Neural Network (NN). The k equation is turned into an ordinary differential equation for the turbulent viscosity in the k equation, $ u _{t,PINN} $ nu t,PINN, which is solved using PINN. A new turbulent Prandtl number is then computed as $ \sigma _{k,PINN} = u _{t}/ u _{t,PINN} $ sigma k,PINN=nu t/nu t,PINN where $ u _t = k/\omega $ nu t=k/omega. Hence, the turbulent Prandtl number, $ \sigma _{k,PINN} $ sigma k,PINN, is determined using PINN, followed by the use of DNS data for estimating $ C_{k,PINN} $ Ck,PINN and $ C_{\omega 2,PINN} $ C omega 2,PINN which appear in the destruction terms in the k and omega equation, respectively. Neural networks are then used to generalise these results and thus construct a turbulence model. All Python PINN, NN and pySR scripts as well as the Python CFD code can be downloaded [Davidson. Using physical informed neural network (PINN) and neural network (NN) to improve a $ k-\omega $ k-omega turbulence model: python CFD code and PINN script. In: Division of fluid dynamics. Gothenburg: Dept. of Mechanics and Maritime Sciences, Chalmers University of Technology; 2025].

Machine Learning (ML) is used for developing wall functions for Improved Delayed Detached Eddy Simulations (IDDES). The ML model is based on KDTree which essentially is a fast look-up table. It searches the nearest target datapoint(s) for which y(+) and U+ are closest to the CFD y(+) and U+ cells. The target y(+) value gives the friction velocity. Two target databases - diffuser flow with opening angle alpha=15(degrees) and hump flow - are created from time-averaged data of wall-resolved IDDES (WR-IDDES, i.e. wall-adjacent cells at y(+)<1). The new ML wall function is used to predict five test cases: diffuser flow with opening angles alpha=15(degrees) and alpha=10(degrees), the hump flow, channel flow at Re-tau=16,000 and flat-plate boundary layer. A novel grid strategy is used. The wall-adjacent cells are large. But further away from the wall, the wall-normal cell distribution is identical to that of a WR-IDDES grid. This new grid is found to improve the predictions compared to a standard wall-function grid. It is found that the number of cells for a wall-resolved IDDES grid (grid stretching 15%) is a factor of 0.2ln(Re-tau) larger than that of a standard wall-functions mesh (constant wall-normal grid cells). The new ML wall function is found to perform well compared to the WR-IDDES and better than the Reichardt's wall function.

This study explores the potential of oppositely charged dielectric barrier discharge (DBD) plasma actuators to reduce skin friction in turbulent channel flow by generating wall-normal plasma jets. Leveraging the lightweight structure of electrodes, this technique presents a promising approach to minimizing aerodynamic drag on moving surfaces. A plasma force is applied to the bottom wall of the channel, targeting the suppression of organized flow structures inherent to turbulence. The investigation is conducted at a frictional Reynolds number Reτ=180 using Direct Numerical Simulation (DNS), providing a detailed assessment of flow dynamics. The results demonstrate that wall-normal plasma jets, induced by spanwise-aligned actuators, achieve a modest reduction in skin friction drag, approximately 4%. This reduction highlights the viability of the method while underscoring the need for parameter optimization to enhance its effectiveness. The study provides insights into the mechanisms of drag reduction, emphasizing the influence of the plasma jet on turbulent structures. Future research is encouraged to refine actuator configurations and operating parameters to realize greater aerodynamic efficiency.

Data-driven approaches offer novel opportunities for improving the performance of turbulent flow simulations, which are critical to wide-ranging applications from wind farms and aerodynamic designs to weather and climate forecasting. While conventional continuum Navier-Stokes solvers have been the subject of a significant amount of work in this domain, there has hitherto been very limited effort in the same direction for the more scalable and highly performant lattice Boltzmann method (LBM), even though it has been successfully applied to a variety of turbulent flow simulations using large-eddy simulation (LES) techniques. In this work, we establish a data-driven framework for the LES-based lattice Boltzmann simulation of near-wall turbulent flow fields. We do this by training neural networks using improved delayed detached eddy simulation data. Crucially, this is done in combination with physics-based information that substantially constrains the data-driven predictions. Using data from turbulent channel flow at a friction Reynolds number at $5200$, our simulations accurately predict the behaviour of the wall model at arbitrary friction Reynolds numbers up to $1.0 \times 10^6$. In contradistinction with other models that use direct numerical simulation datasets, our physics-informed model requires data from very limited regions within the wall-bounded plane, reducing by three orders of magnitude the quantity of data needed for training. We also demonstrate that our model can handle data configurations when the near-wall grid is sparse. Our physics-informed neural network approach opens up the possibility of employing LBM in combination with highly specific and therefore much more limited quantities of macroscopic data, substantially facilitating the investigation of a wide-range of turbulent flow applications at very large scale.

High-lift device is a potent airframe noise contributor. The conventional slat, commonly used in a high-lift device, is known as one of the dominant noise sources. Here, we combine an experimental and a numerical approach to investigate the noise generation of a conventional slat and two Krueger flaps as leading-edge devices in a high-lift configuration. To reduce the computational cost, a short span of the entire high-lift device is selected as the focusing region for scale-resolving and acoustic computations using Improved Delayed Detached Eddy Simulation (IDDES) coupled with the Ffowcs-Williams and Hawkings (FWH) analogy. Simulation results show that turbulent cross flows induce slightly lower-level noise spectra at frequencies less than 300 Hz when the two spanwise sides of the FWH permeable integral surface are closed. Wind-tunnel test results show that the reference and optimal Krueger configurations effectively attenuate the dominant tone of the conventional slat by 4 and 6 dB, respectively. Besides, the optimal configuration is very effective in noise reduction in a wide frequency range. However, the reference Krueger configuration increases the noise level by 0 − 4 dB at frequencies exceeding 5, 500 Hz. Overall, the optimal Krueger configuration is a good choice for high-lift device noise mitigation.

A solid fairing and a wire-mesh fairing consisting of very fine wires and pores are numerically and experimentally investigated for the mitigation of landing gear noise. A slightly modified LAGOON landing gear and two configurations, one equipped with a solid fairing and the other with a wire-mesh fairing, are numerically simulated using the Improved Delayed Detached-Eddy Simulation (IDDES) in combination with the Ffowcs Williams and Hawkings (FW-H) analogy. Instead of resolving the detailed flow features through the wire mesh, a recently proposed numerical model is used to represent the effect of the wire-mesh fairing. The simulated flow fields and the far-field noise spectra are validated against the experiments conducted in an anechoic wind tunnel. The superiority of the recently proposed wire-mesh model over a classical wire-mesh model in modelling both the aerodynamic and aeroacoustic effects of the wire mesh is demonstrated. Results also show that the dense wire-mesh fairing functions very similarly to the solid fairing and that significant noise can be reduced through the installation of a solid fairing or a wire-mesh fairing upstream of the landing gears. For the baseline landing gear, the torque link and the brakes are identified noise sources. With the aerodynamic penalty of a 50% increase in drag, both fairings mitigate the pressure fluctuation on the torque link and brakes, resulting in the reduction of surface noise sources. The noise directivity shows that a solid fairing or a dense wire-mesh fairing contributes to a noise reduction of 4-6 dB in all radial directions. The findings in this study pave the way for the low-noise design of aircraft landing gears.

In this paper, we proposed a novel fluid flow model for pressure loss through plates with circular perforations in both laminar and turbulent flows. The design of this model is based on the recent measurements conducted at ONERA in the framework of the ongoing European Union H2020 INVENTOR project, as well as an existing model for laminar flows. The new model is then validated against existing numerical simulations in the laminar regime and experiments in the turbulent regime. Overall, the predictions given by the new model agree well with the numerical simulations and experiments, and are superior to other models in the literature. This is significant, considering that the present model is much simpler than these previous models. To demonstrate the applicability of the new model in numerical simulations, two-dimensional channel flows are simulated using Reynolds-averaged Navier–Stokes (RANS) equations with the new model as a pressure-drop source term added to the momentum equations. Results show that the RANS predictions agree very well with the present model predictions.

Two passive add-on porous fairings, comprised of diamond grids varying in size, are numerically and experimentally investigated for their effectiveness in mitigating landing gear noise. The baseline landing gear, a modified version of the LAGOON landing gear with its inner rim cavities closed, along with two configurations equipped with diamond-lattice fairings, are numerically simulated using the Improved Delayed Detached-Eddy Simulation (IDDES) in combination with the Ffowcs Williams and Hawkings (FW-H) analogy. Instead of resolving the detailed flow features through the diamond-lattice fairings, a numerical model is employed to represent the effect of fairing. Prior to integrating the numerical model into the simulations of landing gears, rigorous validation of the model against experimental data in a channel flow is performed. Subsequently, the predicted flow fields and far-field noise spectra of the baseline and controlled landing gears are validated against the experiments conducted in the anechoic A-Tunnel at Delft University of Technology. The results indicate that implementing a diamond-lattice fairing upstream of the landing gear can effectively diminish far-field noise in the frequency range exceeding 200 Hz. For the baseline landing gear, the torque link and brakes are potent noise sources. For the controlled landing gears, both diamond-lattice fairings mitigate the pressure fluctuations on the torque link and brakes, leading to a reduction of surface noise sources. The noise directivity shows that the DL 4.5mm fairing produces a noise reduction of 2-6 dB whereas the DL 2.5mm fairing generates a noise reduction of 3-7 dB across all radial directions. These findings pave the way for the low-noise design of aircraft landing gears.

Neural Network (NN) is used to improve an Explicit Algebraic Reynolds Stress Model (EARSM). The turbulent kinetic energy and its dissipation are predicted using the standard k-ω model. The NN model is trained in channel flow of Re_τ = 10,000 . The NN model is stored to disk and subsequently loaded into the CFD code. The NN model is called every iteration to compute the β coefficients in the EARSM, i.e. the CFD solver and the NN model are fully coupled. The Reynolds stresses are used in the momentum equations and the production term in the k and ω equations. It is found that when training the NN model, the target data cannot only be taken from DNS. The reason is that the stress-strain relation and the turbulent kinetic energy of the DNS data are different from those of the k-ω model. Hence, the target data are taken both from DNS and a k-ω simulation. The new EARSM-NN model is used for predicting channel flow at Re_τ = 2000, 5200 and 10, 000 and flat-plate boundary layer at 2500 ≤ Re_θ≤ 8000 . The EARSM-NN model gives much better results than the standard EARSM.

Carbon dioxide methanation is a way of storing excess electrical energy as grid compatible gas. Spatially resolved channel plate reactor experiments were used to validate competing reactor (1D, 2Dx-z) models. Parallel exothermic carbon dioxide methanation and endothermic reverse water gas shift reactions were considered. The kinetic model, where the rate determining step is between an oxygenated complex (HCOO*) and an active site (*), was used in 2Dx-z CFD simulations for six laminar inflow conditions and variations in pressure, temperature, H2/CO2 ratio, methane, and steam co-feeds. The performance is improved by decreasing flowrate, and increasing H2/CO2 ratio, pressure, and temperature. Co-feeding methane has a negligible effect on reactor performance. However, co-feeding steam significantly reduces performance. At relatively high conversions, differential rates are obtained. This is due to the negligible dependence of the rate of carbon dioxide conversion with the equilibrium term of the reverse water gas shift reaction. With these studies, a link between the reaction mechanism and reactor performance is established at conditions relevant to power-to-gas applications.

A novel wire mesh consisting of very fine wires and pores is numerically investigated for the purpose of noise reduction. To develop a numerical model for this wire mesh, a set of experimental flow-field data has been deployed for the model validation. The experimental data were measured with only 22% of the wind-tunnel cross section covered by the wire mesh, taking into account the vortex shedding from both sides of the wire-mesh fairing. It is found that existing wire-mesh models using a damping-type source term proportional to the square of flow velocity do not perform well in modeling this novel wire mesh. To tackle this issue, an improvement is proposed by additionally introducing a linear term to account for the permeability of the wire mesh, based on another set of experiments with the wind-tunnel cross section fully covered by the wire mesh. The proposed model is then validated against the experimental data, demonstrating its capability in modeling the wire mesh. Subsequently, the model is applied to a tandem cylinder configuration. Results show that a wide but short-span wire mesh significantly reduces the dominant tone of tandem cylinders, noise at higher frequencies, as well as the overall sound pressure levels.

Abstract. The interest in trading intraday markets has been increasing due to the growth of renewable intermittent energy production. With the growing renewable energy capacity, which mostly comes from wind energy, the intraday market volume has been continuously increasing every year. In Europe, countries work with different lead times ranging from 5 to 90 minutes and trading blocks of 15 minutes. Several countries, including Sweden, use 15-minute trading blocks with 60 minutes lead time. Market participants use the intraday market to optimize their position after the day-ahead market closes. Since new methods become available, such as better forecasts on short-term renewable energy power output and demand, the intraday market has become more important for energy traders in order to maximize their profit. The primary objective of this study is to enhance the intraday forecasting of wind power by improving the forecasting methods using machine learning. A hybrid approach that combines a mode decomposition method, Empirical Mode Decomposition (EMD), with Support Vector Regression (SVR), is used. In addition, the forecasting with the SVR method is improved by applying a cross-validation method that tunes the parameters used. The study utilized three months (92 days) of wind turbine power data from 21 June 2017 to 20 September 2017. 80 % of the data was used for training, and the remaining data were used for predictions. The results showed that combining SVR with a hybrid method that incorporates EMD predictions can lead to higher prediction accuracy. Furthermore, our results stress that parameter-tuning algorithms can improve machine-learning methods. We believe that the methods proposed in this study will be beneficial for the planning of dispatchable energy generation and pricing for the intraday electricity market.

The amount of energy that has to be delivered for the following day is currently predicted by power system operators using day-ahead load forecasts. With the use of this forecast, generation resources can be committed a day in advance, some of them may require several hours’ notice to be ready to produce power the following day. In order to determine how much wind power will be available for each hour of the following day, power systems with large penetrations of wind generation rely on day-ahead predictions. The main objective of this study is to improve the day-ahead forecasting of wind power by improving the forecasting method using machine learning. A hybrid approach, which combines a mode decomposition method, Empirical Mode Decomposition (EMD), with Support Vector Regression (SVR), is used. The results suggest that using Support Vector Regression together with the hybrid method, which includes the Empirical Mode Decomposition to predictions can improve the accuracy of predictions. Higher accuracy forecasting of wind power is expected to improve the planning of dispatchable energy generation and pricing for the day-ahead power market.

The synthetic turbulence generator (STG) lies at the interface of the Reynolds averaged Navier–Stokes (RANS) simulation and large-eddy simulation (LES). This paper presents an STG for the multiple-relaxation-time lattice Boltzmann method (LBM) framework at high friction Reynolds numbers, with consideration of near-wall modeling. The Reichardt wall law, in combination with a force-based method, is used to model the near-wall field. The STG wall-modeled LES results are compared with turbulent channel flow simulations at Reτ=1000,2000,5200 at different resolutions. The results demonstrate good agreement with direct numerical simulation, with the adaptation length of 6–8 boundary layer thickness. This method has a wide range of potentials for hybrid RANS/LES-LBM related applications at high friction Reynolds numbers.

A fluid flow through a perforated plate is a common problem in a wide variety of practical applications in thermal, mechanical, chemical, civil, nuclear, ocean and aerospace engineering. In this paper, we proposed a novel fluid flow model for the pressure loss through plates with circular perforations in both laminar and turbulent flows. The design of this model is based on the recent measurements conducted at ONERA in the framework of the on-going European Union H2020 INVENTOR project, as well as an existing model for laminar flows. The new model is then validated against existing numerical simulations in the laminar regime and experiments in the turbulent regime. Overall, the predictions given by the new model agree well with the numerical simulations and experiments, and are superior to other models in the literature. This is significant, considering that the present model is much simpler than these previous models. To demonstrate the application of the new model in numerical simulations, two-dimensional channel flows are simulated using Reynolds-averaged Navier-Stokes (RANS) equations with the new model as a pressure-drop source term added to the momentum equations. Results show that the RANS predictions agree very well with the present model predictions.

The synthetic turbulence generator (STG) lies at the interface of the Reynolds averaged Navier-Stokes (RANS) simulation and large eddy simulation (LES). This paper presents a STG for the multiple-relaxation-time(MRT) lattice Boltzmann method(LBM) framework at high friction Reynolds numbers, with consideration of near wall modeling. The Reichardt wall law, in combination with a force-based method, is used to model the near wall field. The STG wall-modeled(STG-WM) LES results are compared with turbulent channel flow simulations at $Re_{\tau}=1000,2000,5200$ at different resolutions. The results demonstrate good agreement with DNS, with the adaptation length of 6 to 8 boundary layer thickness. This method has a wide range of potentials for hybrid RANS/LES-LBM related applications at high friction Reynolds numbers.

A comprehensive study is conducted on a second-order low-dissipation low-dispersion (LD2) scheme in scale-resolving simulations of both incompressible and compressible flows, using a node-based unstructured CFD solver. The scheme deploys a higher order central reconstruction of the face values (up to fourth-order on structured meshes) and a matrix dissipation formulation to reduce the dispersive and dissipative numerical errors. The LD2 scheme is examined for compressible flow cases involving shock discontinuities, LD2-Compressible (LD2C), and is verified in a classical shock-tube problem. The scheme is then further verified in Large-Eddy Simulations (LES) of decaying isotropic turbulence (DIT) in comparison with available experimental data. It is shown that in scale-resolving simulations, the LD2C scheme is able to significantly improve the prediction as compared to a conventional second-order central scheme. The scheme is then further assessed and verified in hybrid Reynolds-Averaged Navier–Stokes (RANS)-LES computations for the subsonic and supersonic turbulent channel flow, where excellent agreement with reference DNS and correlations are observed. Moreover, a supersonic base flow is simulated using hybrid RANS-LES, where improved predictions are observed. The LD2C scheme exploits a shock sensor incorporating vorticity and is shown to improve the prediction of the resolved shear stress in the shear layer of compression.

Computational analysis of nucleate boiling occurring in liquid cooled applications, such as internal combustion engines is often implemented within a single phase Computational Fluid Dynamics (CFD) framework, owing to low vapor fractions involved. With increase in specific power and the resulting higher thermal loads, accounting for the presence of the vapor phase using a multiphase framework is required in certain conditions, despite the higher computational costs. While detailed resolution of the liquid and vapor phases in nucleate boiling using a two fluid model is excessively computationally expensive, the homogeneous mixture multiphase framework is a good compromise between resolution and computational cost. In this article a numerical wall boiling model is implemented within both, a single phase and the mixture multiphase frameworks. Results from the two approaches are compared with measurements in a channel flow. The results from both approaches are in good agreement with experiments. The single phase approximation is valid when the vapor generation is low. The sensitivity of the results to the computational grid is also discussed in detail. Further, the two frameworks are used to simulate the heat transfer in the coolant jacket of a four-cylinder petrol engine. The results from the numerical simulations are compared with measurements. Both computational frameworks compare reasonably well with the measurements in terms of local metal temperature. However, the advantage of accounting for the vapor phase using the mixture multiphase framework is evident when the parameter related to vapor bubble interactions is analyzed in detail.

A grey area mitigation method is proposed for hybrid RANS-LES modeling. The proposed methodology is evaluated using a hybrid RANS-LES method based on a Low-Reynolds-Number k - omega model applied to channel flow, boundary layer flow and a spatially developing mixing layer flow. Emphasis is put on the use of commutation terms at the RANS-LES interfaces in the transport equations for the turbulent kinetic energy, the specific dissipation rate and the momentum equation in order to rapidly reduce the turbulent viscosity across a RANS-to-LES interface and to stimulate the development of resolved turbulent fluctuations. The proposed methodologies are applied at both wall-normal (and inlet) and wall-parallel RANS-LES interfaces. The proposed methodology gives a rapid reduction of the turbulent viscosity at the wall-normal BANS-LES interface from its RANS level to its LES level. Moreover, the proposed methodology contributes to a substantially more rapid establishment of the turbulence-resolving LES flow downstream of the wall-normal RANS-LES interface than if no grey-area mitigation method is applied. However, the proposed methodology has a weaker effect at wall-parallel RANS-LES interfaces, due to a stronger entrainment of LES contents into the near-wall BANS region, than at the wall-normal RANS-LES interfaces. Good agreement with experimental data is obtained with the proposed interface method for the evaluated flow cases. The most obvious grey area mitigation effect is given in the simulated mixing layer flow. Turbulent velocity fluctuations are efficiently established with the commutation term in the momentum equation at the RANS-LES interface in this flow as well as a rapid reduction of the turbulent viscosity due to the commutation terms in the k and omega equations, which gives an almost negligible delay in the development of the resolved turbulence.