Nonlinear Subgrid-scale Model Research Articles

The multi-objective optimisation design of outlet guide vanes of diagonal flow fan based on sobol sensitivity analysis

Diagonal flow fans offer substantial energy-saving potential and find broad application across various sectors. Their performance relies heavily on factors like outlet guide vanes and spacing relative to moving blades. However, research into enhancing fan performance through optimized guide vanes and spacing remains limited. In this study, we focus on improving the accuracy of predicting the internal flow field of diagonal flow fans. This paper incorporate rotation and curvature effects using the Large Eddy Simulation (LES) model and introduce stress terms with helicity constraints to create a non-linear subgrid-scale model. This refined model enables more precise numerical simulations. By employing accurate simulations, we optimize the outlet guide vane configuration and conduct sensitivity analysis. We utilize a Radial Basis Function (RBF) model coupled with the Sobol method for this purpose. The optimized guide vane design exhibits enhanced resistance to airflow separation compared to the original, resulting in notable reductions in flow losses within the grille channel. Experimental tests are performed on the diagonal flow fan both before and after optimization. At the specified operating point, the second guide vane optimization leads to a 1.28 m3/min increase in fan flow, a 4.33% rise in total pressure efficiency, and a 2.2 dB noise reduction. These findings underscore the accuracy of the helicity correction model in predicting diagonal flow fan behavior. The multi-objective optimization approach, combining the RBF proxy model with the Sobol method, proves highly reliable. It offers valuable design insights for similar fans and establishes a credible design methodology.

Numerical investigation of condensation shock and re-entrant jet dynamics around a cavitating hydrofoil using a dynamic cubic nonlinear subgrid-scale model

Cavity shedding mechanisms, such as those due to re-entrant jets (RJ) and condensation shocks (CS), are important but challenging topics in cavitating flows. This study investigates unsteady cavity shedding around a NACA66 hydrofoil using a self-defined compressible cavitation solver based on OpenFOAM with a dynamic cubic nonlinear subgrid-scale model. The predictions give satisfactory agreement with experimental data for the quantitative pressure evolution and the cavity shedding behavior induced by the re-entrant jet and the pressure wave. Moreover, the numerical data provides deeper insight into the pressure wave characteristics (e.g. propagation speed, wave intensity, shock Mach number, etc.) during cavity contraction. Multi-perspective analyses demonstrate that the pressure wave is a condensation shock which is responsible for the attached cavity abruptly disappearing. Additionally, the different influences of the re-entrant jet and the condensation shock on the local flow patterns are compared in detail in terms of the duration, average motion velocity, cavity behavior, formation mechanism and pressure intensity. The results show the condensation shock is characterized by fast propagation speed, short duration and high pressure pulse, which differs from the re-entrant jet features. This research provides an improved understanding of the cavity shedding mechanism around a cavitating hydrofoil and demonstrates the effectiveness of the current compressible cavitation solver.

Numerical simulation of rotating channel flow based on a modified DES model

A new type of nonlinear sub-grid scale (SGS) model is adopted based on the helicity analysis and is verified by predicting the internal flow in a rotating channel. A stress term that contains helicity constraint is introduced into the original SGS model to construct a nonlinear sub-grid model. This additional term representing the helicity constraint effect in the momentum equations is shown to give predictions that are in better agreement with the experimental data. In this paper, the Detached-Eddy Simulation (DES) and the nonlinear SGS model are used to further study the turbulence statistics of the rotating channel flow. Combining with the Reynolds stress transport equations and the turbulent kinetic energy transport equation, the change of turbulence statistics near the wall of the rotating channel is analyzed. The newly added term changes the turbulent viscosity near the wall, which changes the velocity gradient near the wall and further affects other turbulence statistics near the wall.

Some notes on numerical simulation of the turbulent cavitating flow with a dynamic cubic nonlinear sub-grid scale model in OpenFOAM

The accuracy of large eddy simulation (LES) is highly dependent on the performance of sub-grid scale (SGS) model. In the present paper, a dynamic cubic nonlinear sub-grid scale model (DCNM) proposed by Huang et al. is implemented for the simulation of unsteady cavitating flow around a 3-D Clark-Y hydrofoil in OpenFOAM. Its performance in predicting the evolution of cloud cavitation is discussed in detail. The simulation with a linear model, the dynamic Smagorinsky model (DSM), is also conducted as a comparison. The results with DCNM show a better agreement with the available experimental observation. The comparison between DCNM and DSM further suggests that the DCNM is able to predict the backscatter more precisely, which is an important feature in LES. The characteristics of DCNM is analyzed to account for its advantages in the prediction of unsteady cloud cavitation as well. The results reveal that it is the nonlinear terms of DCNM that makes DCNM capture sub-grid scale vortices better and more suitable for studying the transient behaviors of cloud cavitation than DSM.

A dynamic simplified Lund model for large-eddy simulation and its application to a centrifugal pump

PurposeConstruct a new sub-grid scale (SGS) model which can improve the efficiency and maintain comparative accuracy comparing to the existing dynamic cubic non-linear SGS model (DCNM).Design/methodology/approachThe polynomial constitutive relation between the SGS stress tensor and both strain and rotation rate is selected as a basement. Simplification is achieved by eliminating the solid-body rotation term and adopting the assumption proposed by Kosovic. A dynamic procedure is applied to calculate three model coefficients in the new model. The new model (named dynamic simplified Lund model) and DCNM are applied to the rotating channel flow and the internal flow in a centrifugal pump impeller to examine the performance.FindingsThe new model is as accurate as DCNM but decreases 25 per cent computational resources. The ability of capturing rotation effect and reflecting backscatter is verified through cases. In addition, good numerical stability is shown during the calculation.Research limitations/implicationsMore benchmark and engineering cases should be used to get further confidence on the new model.Practical implicationsThe new model is promising in industrial application with the advantage of both accuracy and efficiency. For the flow with large-scale separation or more complicate phenomenon, the model is thought to give accurate flow structure.Originality/valueA new non-linear SGS model is proposed in this paper. The accuracy, numerical stability and efficiency are validated for this model. Therefore, it is promising in the prediction of the flow structure in centrifugal pumps.

Study of unsteady cavitation on NACA66 hydrofoil using dynamic cubic nonlinear subgrid-scale model

In this article, we describe the use of a new dynamic cubic nonlinear model, a new nonlinear subgrid-scale model, for simulating the cavitating flow around an NACA66 series hydrofoil. For comparison, the dynamic Smagorinsky model is also used. It is found that the dynamic cubic nonlinear model can capture the turbulence spectrum, while the dynamic Smagorinsky model fails. Both models reproduce the cavity growth/destabilization cycle, but the results of the dynamic cubic nonlinear model are much smoother. The re-entrant jet is clearly captured by the models, and it is shown that the re-entrant jet cuts the cavity into two parts. In general, the dynamic cubic nonlinear model provides improvement over the dynamic Smagorinsky model for the calculation of cavitating flow.

Large eddy simulation of rotating turbulent channel flow with a new dynamic global-coefficient nonlinear subgrid stress model

In this paper, a new dynamic global-coefficient nonlinear subgrid scale (SGS) model is proposed for large eddy simulation (LES) of rotating turbulent channel flow. The basic model is a nonlinear model with a tensorial polynomial relation between the SGS stress and the resolved strain rate tensor. A new dynamic procedure is proposed to determine the model coefficients of the nonlinear model. The new dynamic method is derived from the globally averaged transport equation of the Reynolds shear stress, on which the rotation has strong and direct effects. The new dynamic nonlinear SGS model is examined in rotating turbulent channel at Re=umh/ν=7000, Ro=2Ωh/um =0.3 and 0.6, where Reynolds number Re and Rotation number Ro are defined by bulk mean velocity um , half channel width h, kinematic viscosity ν and angular velocity of spanwise rotation Ω. The statistical results obtained from the new model agree well with those from direct numerical simulation (DNS). The new model also successfully predicts the major structures in rotating turbulent channel flow, such as Taylor–Görtler vortices and streaks.

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u i . The new model is inspired by the structure function formulation developed by Metais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ ij and the velocity increment tensor Q ij = δ u i δ u j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re τ = 520 and LES of round turbulent jet at Re D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.

A Large Eddy Simulation Study of a Quasi-Steady, Stably Stratified Atmospheric Boundary Layer

Using the large eddy simulation (LES) technique, the authors study a clear-air, stably stratified atmospheric boundary layer (ABL) as it approaches a quasi-steady state. The Beaufort Sea Arctic Stratus Experiment (BASE) dataset is used to impose initial and boundary conditions. The authors explore the parameter space of the boundary layer by varying latitude, surface cooling rate, geostrophic wind, inversion strength, and surface roughness. Recognizing the critical dependence of the results of LES on the subgrid-scale (SGS) model, they test and use a nonlinear SGS model, which is capable of reproducing the effects of backscatter of turbulent kinetic energy (TKE) and of the SGS anisotropies characteristic for shear-driven flows. In order to conduct a long-term LES so that an ABL can reach a quasi-steady state, a parallel computer code is developed and simulations with a spatial domain of up to 963 grid points are performed. The authors analyze the evolution of the mean wind, potential temperature, and turbulence profiles as well as the turbulence budgets. In their simulations, they observe the development of features that are characteristic of a stably stratified ABL: a two-layer ABL structure, an elevated inversion, and an associated inversion wind maxima. Good agreement is found between the LES results and the observations and with Nieuwstadt’s analytical model. The authors study the dependence of the boundary layer height on the flow parameters and determine model coefficients for a truncated Zilitinkevich–Mironov model.

Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers

It has been recognized that the subgrid-scale (SGS) parameterization represents a critical component of a successful large-eddy simulation (LES). Commonly used linear SGS models produce erroneous mean velocity profiles in LES of high-Reynolds-number boundary layer flows. Although recently proposed approaches to solving this problem have resulted in significant improvements, questions about the true nature of the SGS problem in shear-driven high-Reynolds-number flows remain open.We argue that the SGS models must capture inertial transfer effects including backscatter of energy as well as its redistribution among the normal SGS stress components. These effects are the consequence of nonlinear interactions and anisotropy. In our modelling procedure we adopt a phenomenological approach whereby the SGS stresses are related to the resolved velocity gradients. We show that since the SGS stress tensor is not frame indifferent a more general nonlinear model can be applied to the SGS parameterization. We develop a nonlinear SGS model capable of reproducing the effects of SGS anisotropy characteristic for shear-driven boundary layers. The results obtained using the nonlinear model for the LES of a neutral shear-driven atmospheric boundary layer show a significant improvement in prediction of the non-dimensional shear and low-order statistics compared to the linear Smagorinsky-type models. These results also demonstrate a profound effect of the SGS model on the flow structures.

A Nonlinear, Subgridscale Model for Incompressible viscous Flow Problems

We consider a nonlinear subgridscale model of the Navier–Stokes equations resulting in a Ladyzhenskaya-type system. The difference is that the power “p” and scaling coefficient $\mu (h) \doteq O(h^\sigma )$ do not arise from macroscopic fluid properties and can be picked to ensure both $L^\infty $-stability and yet be of the order of the basic discretization error in smooth regions. With a properly scaled p-Laplacian-type artificial viscosity one can construct a higher-order method which is just as stable as first-order upwind methods.

On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet

The properties of turbulence subgrid-scale stresses are studied using experimental data in the far field of a round jet, at a Reynolds number ofRλ≈ 310. Measurements are performed using two-dimensional particle displacement velocimetry. Three elements of the subgrid-scale stress tensor are calculated using planar filtering of the data. Usinga prioritesting, eddy-viscosity closures are shown to display very little correlation with the real stresses, in accord with earlier findings based on direct numerical simulations at lower Reynolds numbers. Detailed analysis of subgrid energy fluxes and of the velocity field decomposed into logarithmic bands leads to a new similarity subgrid-scale model. It is based on the ‘resolved stress’ tensorLij, which is obtained by filtering products of resolved velocities at a scale equal to twice the grid scale. The correlation coefficient of this model with the real stress is shown to be substantially higher than that of the eddy-viscosity closures. It is shown that mixed models display similar levels of correlation. During thea prioritest, care is taken to only employ resolved data in a fashion that is consistent with the information that would be available during large-eddy simulation. The influence of the filter shape on the correlation is documented in detail, and the model is compared to the original similarity model of Bardinaet al.(1980). A relationship betweenLijand a nonlinear subgrid-scale model is established. In order to control the amount of kinetic energy backscatter, which could potentially lead to numerical instability, anad hocweighting function that depends on the alignment betweenLijand the strain-rate tensor, is introduced. A ‘dynamic’ version of the model is shown, based on the data, to allow a self-consistent determination of the coefficient. In addition, all tensor elements of the model are shown to display the correct scaling with normal distance near a solid boundary.