Reynolds Stress Anisotropy Research Articles

Large eddy simulation of highly underexpanded sonic jets from elliptical nozzles

The injection of high-pressure jets into quiescent air poses significant challenges in fluid dynamics, pertinent to various industrial engineering applications. This study used large eddy simulations on a massively parallel computational framework, employing a grid of over 600 million nodes, to investigate the behavior of highly underexpanded sonic jets from elliptical nozzles at a nozzle pressure ratio of 15. Three elliptical nozzles, with aspect ratios of 1.5, 2.2, and 3.0, each having a sectional area equivalent to that of a circular jet with a diameter of D=1 mm, were analyzed. The aim was to clarify the gasdynamic and mixing characteristics of these jets to guide the design of next-generation injectors. A detailed analysis of the flow provided insights into the mechanisms of turbulence generation and Reynolds stress anisotropy. This was achieved using the componentality contour approach and a modified barycentric color mapping scheme, offering valuable reference data for developing lower-order models. The results indicate a non-axisymmetric radial expansion of the jet boundary in all elliptical injectors, leading to an axis switch phenomenon. The use of elliptical orifices was found to reduce jet penetration, mitigating issues such as fuel impingement in small engine combustion chambers and promoting improved air–fuel mixing quality.

Sensitized Reynolds stress modeling of a bubbly jet emerging into a water cross-flow

The present work is concerned with the computational study of an air–water mixture stream emanating from a nozzle submerged in a water cross-flow inside a rectangular open channel to form a curved, intensively dispersed, bubbly jet. The work focuses on evaluating the predictive performance of an eddy-resolving turbulence model applied to the described case of a multiphase gas-liquid flow system characterized by a variety of closely coupled phenomena, including: turbulence anisotropy-induced secondary motion, free surface flow, bubbly jet propagation, and the varying interaction dynamics of the carrier water flow with the air bubble dispersion. Correspondingly, an appropriately extended differential near-wall Reynolds stress model, which describes the dynamics of unresolved subscale structures within the Sensitized Reynolds-Averaged Navier–Stokes (RANS) computational framework, is currently used in conjunction with a two-way coupled Euler–Lagrange approach to simulate this gas-water bubbly flow, with the operating and boundary conditions following the experimental reference of Zhang and Zhu (2013). Accordingly, the conditions at the free surface are adequately derived for all components of the residual turbulence stress tensor and the corresponding length scale determining variable. It is shown that the statistics of the bubble phase can be accurately captured, and the proper-orthogonal-decomposition analysis of the dynamic properties of the flow reveals at least two large-scale transient effects associated with the bubbly jet. Furthermore, in the preliminary part of this work it is shown that the currently applied turbulence model can be successfully used to correctly capture the effects of Reynolds stress anisotropy in the single-phase open-channel configuration, representing the incoming flow field of the main two-phase flow configuration.

Turbulent flow structures and Reynolds stress anisotropy in an asymmetric sinuous mobile channel

Turbulent flow structures and Reynolds stress anisotropy in an asymmetric sinuous mobile channel

Revisiting Tensor Basis Neural Network for Reynolds stress modeling: Application to plane channel and square duct flows

Recent advances in computing power devoted to Computational Fluid Dynamics (CFD) have opened up a new avenue for addressing the turbulence closure problem through Machine Learning (ML). Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence Reynolds-Averaged Navier–Stokes (RANS) modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However, persistent ambiguities remain regarding the physical adequacy of applying the General Eddy Viscosity Model (GEVM) within these frameworks. This work aims at investigating this aspect in an a priori stage for better predictions of the Reynolds stress anisotropy tensor, while preserving the Galilean and rotational invariances. In particular, we propose a general framework providing optimal tensor basis models for two types of canonical flows with increasing complexity: Plane Channel Flow (PCF) and Square Duct Flow (SDF). Subsequently, deep neural networks based on these optimal models are trained using state-of-the-art strategies to achieve a balanced and physically sound prediction of the full anisotropy tensor. A priori results obtained by the proposed framework are in very good agreement with the reference Direct Numerical Simulations (DNS) data. Notably, our shallow network with three layers excels in providing accurate predictions of the anisotropy tensor for PCF at unobserved friction Reynolds numbers, both in interpolation and extrapolation scenarios. The learning of the SDF case is more challenging because of its physical nature but also due to a lack of training data at various regimes. We propose a numerical strategy to alleviate this problem based on Transfer Learning (TL). In order to more efficiently generalize to an unseen intermediate Reτ regime, we take advantage of our prior knowledge acquired from a training with a larger and wider dataset. Our results indicate the potential of the developed network model, and demonstrate the feasibility and efficiency of the TL process in terms of training data size and training time. Based on these results, we believe there is a promising future by integrating these neural networks into an adapted in-house RANS solver.

Ensemble variational method with adaptive covariance inflation for learning neural network-based turbulence models

This work introduces an ensemble variational method with adaptive covariance inflation for learning nonlinear eddy viscosity turbulence models where the Reynolds stress anisotropy is represented with tensor-basis neural networks. The ensemble-based method has emerged as an important alternative to data-driven turbulence modeling due to its merit of non-derivativeness. However, the training accuracy of the ensemble method can be affected by the linearization assumption and sample collapse issue. Given these difficulties, we introduce the hybrid ensemble variational method, which inherits the merits of the ensemble method in non-derivativeness and the variational method in nonlinear analysis. Moreover, a covariance inflation scheme is proposed based on convergence states to alleviate the detrimental effects of sample collapse. The capability of the ensemble variational method in model learning is tested for flows in a square duct, flows over periodic hills, and flows around the S809 airfoil, with increasing complexity in the training data from direct observation to sparse indirect observation. Our results show that the ensemble variational method can learn relatively accurate neural network-based turbulence models in scenarios of small ensemble size and sample variances, compared to the ensemble Kalman method. It highlights the superiority of the ensemble variational method in practical applications, since small ensemble sizes can reduce computational costs, and small sample variance can ensure the training robustness by avoiding nonphysical samples of Reynolds stresses.

“Return to equilibrium” anisotropy model for non-equilibrium Reynolds stress closures

A long-standing question in the Reynolds-averaged modeling of turbulent flow is how to predict accurately flows with temporal or spatial unsteadiness. In this paper, we present a “return to equilibrium” approach to modeling the unsteady Reynolds stress anisotropy bij in terms of differential transport equations, the solutions to which are constrained by algebraic closures for bij in flows at equilibrium and by the corresponding rapid-distortion-theory solutions for flows far from equilibrium. When coupled with scale equations for the turbulent kinetic energy and the dissipation rate, these anisotropy evolution equations comprise a complete closure scheme for which no additional model coefficients are required. Evaluations of this closure scheme, in which two different existing equilibrium algebraic models for bij were employed, were carried out for homogeneous turbulence in flows with a step imposition of shear, with continuously oscillatory shear at different frequencies and with a prescribed time-dependent plane-strain rate. Good agreement was achieved between model predictions and experimental/simulation target data in all test cases, with either Girimaji's bij model or a structure-based bij model used as the equilibrium algebraic closure.

Data-driven approach for modeling Reynolds stress tensor with invariance preservation

The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) (Ling et al., 2016) are involved and applied. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier–Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user’s defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.

Flow analysis through a randomly packed pebble-bed geometry using computational fluid dynamics

This study presents a comprehensive analysis of the flow behavior in packed pebble-bed reactors using computational fluid dynamics (CFD) simulations. The pebble-bed geometry corresponds to an experimental facility located at the Texas A&M Thermal-Hydraulics Research Laboratory. The unsteady Reynolds-averaged Navier–Stokes (URANS) k−ω shear stress transport (SST) and the large eddy simulation (LES) approaches were selected to model the turbulence at different Reynolds numbers. The numerical models were first validated by comparing the pressure drop results obtained from the simulations against established correlations, finding the simulation predictions in accurate agreement. Secondly, the velocity first-order statistics from the URANS k−ω SST and LES calculations were also contrasted with the available experimental particle image velocimetry data to validate the numerical models. Results were found in reasonable agreement as the mean absolute error achieved values smaller than 10% of the inlet velocity for most of the analyzed velocity profiles. A comprehensive turbulence characterization was performed, including second-order statistics, Reynolds stress anisotropy, and turbulent kinetic energy production. The proper orthogonal decomposition of the fluctuating velocity was examined in the current flow domain. The turbulence characterization revealed the complex nature of turbulence in packed pebble-bed geometries, which is further complicated by the presence of an enclosing wall. Overall, the findings of this study provide a solid foundation for the development of more accurate CFD-based methodologies for predicting the behavior of flow through packed pebble-bed reactors.

Flow and thermal fields modeling in jet impingement configurations using a Reynolds stress turbulence closure within the RANS and Sensitized-RANS framework

The flow and thermal field characteristics underlying turbulent convective heat transfer in two reference configurations, representing a jet exiting a planar slot and a circular tube and impinging on a heated wall, are studied computationally. The performance of a conventional Reynolds Stress Model (RSM) and its scale-resolving variant, employed in the context of a time-accurate Reynolds-Averaged Navier–Stokes (RANS) simulation, is investigated in conjunction with different modeling approaches for the turbulent heat flux uj′θ′¯, whose gradient represents the turbulence-induced heat source in the temperature transport equation. In this so-called Sensitized-RANS modeling strategy, employing an improved eddy-resolving instability-sensitive Reynolds Stress Model (IISRSM, Jakirlić and Maduta (2015)), the unresolved ‘sub-scale’ turbulent correlations represent the solutions of a set of corresponding transport equations for the entire stress tensor ui′uj′¯. The turbulent scalar-flux models follow from the classical gradient-diffusion approach with the diffusion-like coefficients formulated as a function of both the scalar eddy-viscosity and the anisotropic Reynolds stress tensor. The latter model expressions also take into account various non-linear relationships in terms of turbulent stress components. The computational results of the fully-developed channel flow, featured only by the mean shear and constant wall heat flux, representing a preliminary investigated flow configuration, agree very well with the corresponding DNS (Direct Numerical Simulation) database for both RSM versions in conjunction with all the turbulent heat flux models adopted. However, the study of the two flow impingement cases with the different structure of the impinging jet and nozzle-to-wall distance variations, characterized by a much more complex flow straining, using the considered conventional Reynolds stress model shows significantly different results for the Reynolds stress and thermal fields compared to the available DNS data, especially in the immediate impact region manifested by a significant overprediction of the turbulence intensity. In contrast, the IISRSM-relevant results for the mean flow and temperature fields, the associated integral characteristics, and the corresponding turbulence quantities are in very good agreement with the reference DNS data, due to the much higher predictive capabilities of this eddy-resolving turbulence model compared to its baseline counterpart.

Reynolds stress anisotropy with higher-order turbulence in flow through rigid emergent vegetation: An experimental study

The flow turbulence and Reynolds stress anisotropy in flow over the smooth rigid bed with the emergent rigid vegetation in a straight channel have been experimentally investigated. Higher-order turbulence such as turbulent diffusivity, third-order moments of velocity fluctuation, quadrant analysis and flux of turbulence kinetic energy have been analysed. Reynolds stress anisotropy has been investigated by Anisotropic invariant maps (AIMs) with the use of eigenvalues for both vegetation and non-vegetation condition. In the vegetation zone, more diffusivity occurs and an apparent decrease in velocity causes larger eddies in the outer layer; whereas in the non-vegetation zone, larger eddies formation at near-bed has been found. Quadrant analysis has been done based on relative signs of velocity fluctuation which signifies that Reynolds shear stress is transported from the bed surface to the free surface when flow enters in the vegetation zone from the non-disturbed region. The longitudinal distribution of the anisotropy tensor near the bed surface for the vegetation zone provides the higher anisotropic flow than those of non-vegetation zone. Although, transverse and vertical distributions of the anisotropy tensor in the vicinity of the bed surface for the non-vegetation zone provide a lower anisotropic stream. Flow anisotropy can be understood by AIMs indicating axis-symmetric expansion in a non-vegetation zone whereas axis-symmetric contraction is in the vegetation zone. The outcomes of this study deliver a significant and detailed view of turbulent flow structures in vegetation and non-vegetation zone in an open channel flow.

Structural uncertainty quantification of Reynolds-Averaged Navier–Stokes closures for various shock-wave/boundary layer interaction flows

Accurate prediction of Shock-Wave/Boundary Layer Interaction (SWBLI) flows has been a persistent challenge for linear eddy viscosity models. A major limitation lies in the isotropic representation of the Reynolds stress, as assumed under the Boussinesq approximation. Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor. However, it remains uncertain whether this approach is effective for SWBLI flows, which involve compressibility and discontinuity. To address this issue, this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows. The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport (SST) model and reveal the impacts of anisotropy on the prediction of quantities of interest, such as separation and reattachment positions, wall static pressure, skin friction, and heat flux. The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model. Furthermore, a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty. The findings indicate that eigenspace perturbation primarily affects turbulent shear stress, while the prediction error of the SST model is more related to turbulent kinetic energy.

High-speed shock–boundary-layer interaction over deformed surfaces

This paper concerns the interaction of an oblique shock wave with a supersonic turbulent boundary layer over a thin panel surface, leading to shock–boundary layer interaction and panel buckling. We have performed high-order numerical simulations featuring various static two-dimensional surface deformations typically encountered in experiments. The deformation amplitudes we examined were at least half the height of the incoming turbulent boundary layer thickness. The results show that along the panel midspan, where the maximum deformation amplitude is located, the mean and root mean square pressure are affected by about 10%. Cases for which the pressure at the shock–boundary layer interaction was increased relative to the planar case showed to decrease downstream, and vice versa. Despite the weak response to the mean pressure amplitude, the mean pressure surface contour plots reveal that the streamwise, particularly the spanwise distribution, is affected more noticeably. For example, the surface deformation modes are shown to disrupt the spanwise constant mean pressure, forming higher (or lower) values at either the panel's midspan or edges, depending on the mode. Moreover, the surface curvature leads to a characteristic bending of the spanwise distribution, which can be concave or convex depending on the deformation mode. Analysis of the Reynolds stress anisotropy componentality at different heights from the buckled surface reveals a similar spanwise response of the turbulent velocity fluctuations. The results suggest that the deformation rate plays an important role alongside the deformation amplitude in the turbulent layer and shock–boundary layer interaction.

Feature importance in neural networks as a means of interpretation for data-driven turbulence models

This work aims at making the prediction process of neural network-based turbulence models more transparent. Due to its black-box ingredients, the model’s predictions cannot be anticipated. Therefore, this paper is concerned with the quantification of each feature’s importance for the prediction of trained and fixed NNs, which is one possible type of explanation for opaque models. Two conceptually different attribution methods, namely permutation feature importance and DeepSHAP, are chosen in order to assess global, regional and local feature importance. The neuralSST turbulence model, which serves as an example, will be investigated in greater detail. While the global importance scores provide a quick and reliable way to detect irrelevant features and may thus be used for feature selection, only the (semi-)local analysis provides meaningful and trustworthy interpretations of the model. In fact, the local importance scores suggest that hypotheses with a common high-level influence on the turbulence model, e.g. adjusting the net production of turbulent kinetic energy or the Reynolds stress anisotropy, are similarly affected by local mean flow structures such as attached boundary layers, free shear layers or recirculation zones.

Effect of cube spacings on the three-dimensional flow structure over an array of wall-mounted cube

The turbulent flow over an array of cubes mounted on one of the walls of a channel has been investigated using direct numerical simulation for cube spacing that ranges between 2.0 and 4.0. The Reynolds number based on the cube size and the average streamwise velocity is chosen to be 4000. The Navier–Stokes equations have been discretized using second-order spatial and temporal discretization schemes. The present investigation focuses on the flow structures and comprehensive characterization of the separated zones surrounding the cubes, as well as the associated wall-shear stress. A vortex shedding has been observed for the cube spacings of 3.0 and 4.0 without any evidence of vortex shedding for the lowest pitch of 2.0. For the two cases having pitches of 3.0 and 4.0, the presence of the unsteady separation bubbles at the cube's top and side surfaces results in a decrease in wall-shear stress. The quadrant analysis for the region close to the top surface of the cube is performed with the help of the joint probability density function, which reveals dual peaks within the recirculation bubble at the top surface of the cube for higher cube spacings. By conducting an invariant analysis of the Reynolds stress tensor for different cube spacings, we have explored the characteristic of Reynolds stress anisotropy due to the total fluctuations. The production of negative turbulent kinetic energy (TKE) is observed in different regions within the flow domain, among which the horseshoe vortex region for each cube spacing reveals its dominant presence. The physical mechanism responsible for the production of the negative TKE has also been attempted by decomposing the production term into two parts, namely, normal and shear components.

A divide-and-conquer machine learning approach for modeling turbulent flows

In this paper, a novel zonal machine learning (ML) approach for Reynolds-averaged Navier–Stokes (RANS) turbulence modeling based on the divide-and-conquer technique is introduced. This approach involves partitioning the flow domain into regions of flow physics called zones, training one ML model in each zone, then validating and testing them on their respective zones. The approach was demonstrated with the tensor basis neural network (TBNN) and another neural net called the turbulent kinetic energy neural network (TKENN). These were used to predict Reynolds stress anisotropy and turbulent kinetic energy, respectively, in test cases of flow over a solid block, which contain regions of different flow physics including separated flows. The results show that the combined predictions given by the zonal TBNNs and TKENNs were significantly more accurate than their corresponding standard non-zonal models. Most notably, shear anisotropy component in the test cases was predicted at least 20% and 55% more accurately on average by the zonal TBNNs compared to the non-zonal TBNN and RANS, respectively. The Reynolds stress constructed with the zonal predictions was also found to be at least 23% more accurate than those obtained with the non-zonal approach and 30% more accurate than the Reynolds stress predicted by RANS on average. These improvements were attributed to the shape of the zones enabling the zonal models to become highly locally optimized at predicting the output.

Wall-modelled large-eddy simulation of three-dimensional turbulent boundary layer in a bent square duct

We conduct wall-modelled large-eddy simulation (WMLES) of a pressure-driven three-dimensional turbulent boundary layer developing on the floor of a bent square duct to investigate the predictive capability of three widely used wall models, namely, a simple equilibrium stress model, an integral non-equilibrium model, and a partial differential equation (PDE) non-equilibrium model. The numerical results are compared with the experiment of Schwarz & Bradshaw (J. Fluid Mech., vol. 272, 1994, pp. 183–210). While the wall-stress magnitudes predicted by the three wall models are comparable, the PDE non-equilibrium wall model produces a substantially more accurate prediction of the wall-stress direction, followed by the integral non-equilibrium wall model. The wall-stress direction from the wall models is shown to have separable contributions from the equilibrium stress part and the integrated non-equilibrium effects, where how the latter is modelled differs among the wall models. The triangular plot of the wall-model solution reveals different capabilities of the wall models in representing variation of flow direction along the wall-normal direction. In contrast, the outer LES solution is unaffected by the type of wall model used, resulting in nearly identical predictions of the mean and turbulent statistics in the outer region for all the wall models. This is explained by the vorticity dynamics and the inviscid skewing mechanism of generating the mean three-dimensionality. Finally, the LES solution in the outer layer is used to study the anisotropy of turbulence. In contrast to the canonical two-dimensional wall turbulence, the Reynolds stress anisotropy exhibits strong non-monotonic behaviour with increasing wall distance.

Numerical simulation of bluff body turbulent flows using hybrid RANS/LES turbulence models

Many engineering applications involve turbulent flows around bluff bodies. Because of their intrinsically unsteady dynamics, bluff body characteristic flows feature unique turbulence-related phenomena, which makes their numerical modeling challenging. Accordingly, accounting for a circular bluff body flow configuration, three different turbulence modeling approaches are investigated in this work, (i) Reynolds-averaged Navier–Stokes (RANS), (ii) large eddy simulation (LES), and (iii) hybrid RANS/LES. Regarding the hybrid approaches, two variants of the detached eddy simulation (DES) one, delayed DES (DDES) and improved delayed DES (IDDES), are studied. As RANS model, the $$\mathrm{k}-\mathrm{\omega SST}$$ is utilized here. This RANS model is also used as the background one for both DDES and IDDES. Wall-adaptive local eddy viscosity (WALE) is used in turn as the sub-grid scale (SGS) model for LES. The velocity two-point correlation function is used to assess the mesh size requirements. When compared to experimental data, the obtained numerical results indicate that RANS overestimates the recirculating bubble length by over 18% and is not capable of describing the turbulent kinetic energy and the flow anisotropy in agreement with the experimental data. In contrast, LES, DDES, and IDDES are all within 1% of the recirculating bubble length while predicting both the Reynolds stress tensor components and the corresponding flow anisotropy in agreement with the measurements. Besides, normalized anisotropy tensor invariants maxima in the shear layer were reproduced by all scale resolving models studied here, but they failed to yield the local extrema measured within the wake recirculation region. A comparative analysis of the anisotropic Reynolds stress tensor invariances underscores the adequacy of the scale resolving models.

Development of explicit algebraic models of Reynolds stresses for flows in channels using gene expression programming

To build a data-driven approximation for the Reynolds-stress anisotropy (RSA), the symbolic regression method of gene expression programming (GEP) is applied. Two tensor-basis terms from the algebraic expansion for the RSA tensor are used in the GEP algorithm. A new RANS-GEP model is tested in several flows in channels without/with bumps at different physical and geometrical parameters, where DNS data of high fidelity involved as a target for RSA are available. The results of RANS-DNS runs are also obtained where the RSA values in the mean momentum equation are taken directly from DNS to show ability to improve the model performance versus the conventional linear eddy viscosity model (LEVM). Next, the training with carefully selected input features is performed to get an explicit non-linear algebraic model for RSA. The results of RANS-GEP study show potentials of the new tool to improve predictions.

A compressible turbulence model for the dissipation rate

In this work, the ability of a Reynolds stress model to compute turbulent homogeneous shear flow with significant compressibility effects is discussed. Several studies of compressible turbulent flows carried out in the past years have shown that the pressure strain correlation is mainly responsible for the strong changes in the magnitude of the Reynolds stress anisotropies. Two recent compressible models of this term are considered in conjunction with the standard model of the dissipation rate of the turbulent kinetic energy to predict compressible homogeneous flow highly sheared are tested. It is found that deficiencies appear in the calculations even if the pressure strain model is improved by compressibility corrections. Consistent with earlier studies, this deficiency is attributed to the use of the incompressible model for turbulent dissipation. However, a compressibility correction of this equation model uncovers the main focus of the present study. This correction makes the standard coefficients of this equation depend on the turbulent gradient Mach and Mach numbers. The proposed model is tested for low and strong compressibility cases from the DNS results of Sarkar. A comparison of the proposed model predictions with the DNS results shows good qualitative agreement. Therefore, compressibility correction for the incompressible model of the turbulent dissipation rate is found to be an important issue for the compressible homogeneous turbulent shear flow.

Turbulence-induced vibrations prediction through use of an anisotropic pressure fluctuation model

In nuclear fuel rod bundles, turbulence-induced pressure fluctuations caused by an axial flow can create small but significant vibrations in the fuel rods, which in turn can cause structural effects such as material fatigue and fretting wear. Fluid-structure interaction simulations can be used to model these vibrations, but for affordable simulations based on the URANS approach, a model for the pressure fluctuations must be utilised. Driven by the goal to improve the current state-of-the-art pressure fluctuation model, AniPFM (Anisotropic Pressure Fluctuation Model) was developed. AniPFM can model velocity fluctuations based on anisotropic Reynolds stress tensors, with temporal correlation through the convection and decorrelation of turbulence. From these velocity fluctuations and the mean flow properties, the pressure fluctuations are calculated. The model was applied to several test cases and shows promising results in terms of reproducing qualitatively similar flow structures, as well as predicting the root-mean-squared pressure fluctuations. While further validation is being performed, the AniPFM has already demonstrated its potential for affordable simulations of turbulence-induced vibrations in industrial nuclear applications.