Eddy Viscosity Research Articles

Toward discretization-consistent closure schemes for large eddy simulation using reinforcement learning

This study proposes a novel method for developing discretization-consistent closure schemes for implicitly filtered large eddy simulation (LES). Here, the induced filter kernel and, thus, the closure terms are determined by the properties of the grid and the discretization operator, leading to additional computational subgrid terms that are generally unknown in a priori analysis. In this work, the task of adapting the coefficients of LES closure models is thus framed as a Markov decision process and solved in an a posteriori manner with reinforcement learning (RL). This optimization framework is applied to both explicit and implicit closure models. The explicit model is based on an element-local eddy viscosity model. The optimized model is found to adapt its induced viscosity within discontinuous Galerkin (DG) methods to homogenize the dissipation within an element by adding more viscosity near its center. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid DG and finite volume (FV) scheme. The resulting optimized discretization yields more accurate results in LES than either the pure DG or FV method and renders itself as a viable modeling ansatz that could initiate a novel class of high-order schemes for compressible turbulence by combining turbulence modeling with shock capturing in a single framework. All newly derived models achieve accurate results that either match or outperform traditional models for different discretizations and resolutions. Overall, the results demonstrate that the proposed RL optimization can provide discretization-consistent closures that could reduce the uncertainty in implicitly filtered LES.

Assessment of the DDES-γ Model for the Simulation of a Highly Loaded Turbine Cascade

Abstract The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using delayed detached eddy simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales, and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark large eddy simulations (LES). The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution, and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale, is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier–Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved LES. Additionally, the results of the transitional DDES model are compared to DDES without a transition model, an RANS eddy viscosity model, and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, the transition process, and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

A Mixed Zero-Equation and One-Equation Turbulence Model in Fluid-Film Thrust Bearings

Abstract A thrust bearing is a rotary bearing that facilitates rotational movement between components and is specifically engineered to provide support for a load that is parallel to the axis of rotation. The generation of the inter-surface film pressure is attributed to the relative motion (rotation) of the surfaces, which results in the lubricant being drawn into the converging wedge formed between them. The interface between the unmovable and moving parts is demarcated by a slender layer of lubricating fluid, including but not limited to oil, water, air, or other process fluid. The conventional zero-equation model can be enhanced to achieve higher precision in forecasting and reduce dependence on empirical data, owing to its inherent limitations. A novel turbulence model that combines zero-equation and one-equation approaches has been developed and implemented in the recently introduced modeling tool package for thrust bearings. In the Prandtl one-equation turbulence model, the length scale is a necessary but undetermined term. A novel mixed model has been implemented utilizing the Prandtl one-equation along with a novel-length scale. The tool package is a Thermo-Hydrodynamic (THD) code that involves iterative computations between the Reynolds’ equation, turbulence equation, energy equation within the film, and conduction equation in pad and runner. The new model yields an eddy viscosity that exhibits a substantial level of proximity to both eddy viscosity transport (EVT) and direct numerical simulation (DNS), and exhibits significant enhancements in comparison to the traditional Ng–Pan zero-equation turbulence model.

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier–Stokes (RANS) equations are solved using turbulence modelling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been performed for similar performance with two-equation models of the k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically refined mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the model itself. Additionally, in this paper analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layer with Spatially Varying Pressure Gradients

Wall-modeled large-eddy simulations of turbulent boundary layers subjected to spatially varying streamwise pressure gradients are conducted to assess the predictive performance of three wall models: ordinary differential equation equilibrium, integral nonequilibrium, and partial differential equation (PDE) nonequilibrium models. The test case is based on experiments conducted by Volino (Journal of Fluid Mechanics, Vol. 897, Aug. 2020, p. A2), where the flow is subjected successively to zero pressure gradient (ZPG), favorable pressure gradient (FPG), recovery ZPG, and adverse pressure gradient (APG) regions. Skin friction is overpredicted in FPG by all the wall models. For equilibrium and integral models, this overprediction is attributed to the strong deviation of mean velocity profiles within FPG from the log law, used explicitly in the equilibrium and implicitly in the integral model. The overprediction is more pronounced for the PDE model, which is attributed to dynamic correction of wall-model eddy viscosity for resolved stresses and a lack of correction for pressure gradient. Potential remedies to mitigate this problem are proposed. Grid refinement improves wall-stress predictions in both FPG and APG but only affects the outer profiles in APG, revealing that accurate wall-flux modeling is more critical for APG. Anisotropic grid analysis shows streamwise grid refinement to be more crucial than spanwise for the convergence of skin-friction, outer velocity, and Reynolds stress profiles.

Insights into CFD Modelling of Water Hammer

A problem with 1-D water hammer modelling is in the application of accurate unsteady friction. Moreover, investigating the time response of fluid dynamics and unsteady turbulence structures during the water hammer is not possible with a 1-D model. This review article provides a summary of 1-D modelling using the recent finite volume approach and the discussion extends to a quasi-2-D model and historical developments as well as recent advancements in 3-D CFD simulations of water hammer. The eddy viscosity model is excellent in capturing pressure profiles but it is computationally intensive and requires more computational time. This article reviews 3-D CFD simulations with sliding mesh, an immersed solid approach, and dynamic mesh approaches for modelling valve closures. Despite prediction accuracy, a huge computational time and high computer resources are required to execute 3-D flow simulations with advanced valve modelling techniques. Experimental validation shows that a 3-D CFD simulation with a flow rate reduction curve as a boundary condition predicted accurate pressure variation results. Finally, a brief overview of the transient flow turbulence structures for a rapidly accelerated and decelerated pipe flow using DNS (Direct numerical simulation) data sets is presented. Overall, this paper summarises past developments and future scope in the field of water hammer modelling using CFD.

Two self-similar Reynolds-stress transport models with anisotropic eddy viscosity.

Two Reynolds-averaged Navier-Stokes models with full Reynolds-stress transport (RST) and tensor eddy viscosity are presented. These new models represent RST extensions of the k-2L-a-C and k-ϕ-L-a-C models by Morgan [Phys. Rev. E 103, 053108 (2021)10.1103/PhysRevE.103.053108; Phys. Rev. E 105, 045104 (2022)10.1103/PhysRevE.105.045104]. Self-similarity analysis is used to derive constraints on model coefficients required to reproduce expected growth parameters for a variety of canonical flows, including Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH) mixing layers. Both models are then applied in one-dimensional simulation of RT and KH mixing layers, and the expected self-similar growth rates and anisotropy are obtained. Next, models are applied in two-dimensional simulation of the so-called "tilted rocket rig" inclined RT experiment [J. Fluids Eng. 136, 091212 (2014)10.1115/1.4027587] and in simulation of a shock-accelerated localized patch of turbulence. It is found that RST is required to capture the qualitative growth of the shock-accelerated patch, and an anisotropic eddy viscosity provides substantial improvement over a Boussinesq treatment for the tilted rocket rig problem.

Euler-Euler LES of bubble column bubbly flows by considering sub-grid scale turbulent dispersion effect on modulating bubble transport

It has now been recognised and generally accepted that turbulent dispersion may be modelled using the time average of the fluctuating part of the interphase momentum, employing the drag the Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. As the turbulent eddies in the surrounding of bubbles interact strongly with the bubbles in bubbly flow, the bubble trajectories and bubble oscillation take place accordingly as the consequence of continuous deformation of the bubble surfaces. When using large eddy simulation for modelling bubbly flow, the sub-grid scale (SGS) filtered velocity fluctuations of liquid phase can be interpreted as many small eddies that may act on the surface of bubbles, consequently giving rise to bubble shape variations and the dispersion of bubbles. This study employs Euler/Euler large-eddy simulation (LES) modelling to demonstrate that the turbulent dispersion force model can be used to effectively indicate the influence of turbulent eddies on bubble dynamics, in particular the bubble cluster oscillations, which leads to remarkable improvements in the prediction of bubble lateral dispersion behaviour. The use of spatial filtering to model the SGS bubble dispersion is proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble induced turbulence. The results of the time-averaged LES modelled bubble velocities and bubble volume fraction profiles are in good agreement with the experimental data while the turbulent kinetic energy spectrum obtained at different locations on the centreline of the bubble column still exhibits the conventional −5/3 scaling for shear induced turbulence and a −3 scaling for bubble induced turbulence.

Two-dimensional turbulent thermal classical far wake

The two-dimensional turbulent thermal classical far wake is investigated. The turbulence is described by the Boussinesq hypothesis for the Reynolds stresses with Prandtl’s mixing length model for the eddy viscosity and eddy thermal conductivity. Two conservation laws are derived for the thermal boundary layer equations for the far wake using the multiplier method and two conserved quantities are obtained from the conserved vectors and boundary conditions. The Lie point symmetry associated with the momentum and thermal conserved vectors is derived. It is found that the momentum and thermal mixing lengths are proportional. In obtaining the invariant solution the cases ν≠0, κ≠0 and ν=0, κ=0 needed to be treated separately, where ν is the kinematic viscosity and κ is the thermal conductivity of the fluid. When ν≠0, κ≠0 the associated Lie point symmetry is determined in full but an analytical solution of the reduced ordinary differential equations could not be derived. The invariant solution is obtained numerically using a shooting method with the two conserved quantities as targets. The width of the wake is infinite. When ν=0, κ=0 the width of the wake is finite. In order to obtain the associated Lie point symmetry in full, Prandtl’s hypothesis that the mixing length is proportional to the width of the wake was imposed. The invariant solution is obtained analytically. The lines of constant mean temperature difference and the streamlines for the mean velocity deficit are plotted. The numerical and analytical solutions agree in the limit ν→0, κ→0.

A local eddy viscosity parameterization for wind-driven estuarine exchange flow, Part II: Entrainment

Structure and intensity of estuarine exchange flow depend significantly on the eddy viscosity Av profile which is dynamically linked to various forces (e.g., gravitational, tidal, wind-driven). The impact of winds on the exchange flow is complex due to its direct (local and remote changes in shear and density stratification) and indirect (modifications to Av profiles) contributions. This study aims (i) to include wind entrainment effects in the tidally averaged Av parameterization; (ii) to develop an analytical one-dimensional model for the wind driven exchange flow by using this novel parameterization and assess the tidally averaged dynamics over a relevant physical parameter-space, subdomains of which have not yet been explored numerically. This one-dimensional model is based on a balance between frictional forces and pressure gradient, calibrated with a tidally-resolving one-dimensional water-column model with second-moment closure. Structure and intensity of the resulting exchange flow profiles are analyzed with respect to three dimensionless parameters (the unsteadiness of boundary layer mixing Un, scaled-directional wind stress W, and horizontal stratification Si). While down-estuarine winds enhance the gravitational circulation, up-estuarine winds result in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow (favored by relatively strong Si, weak W, and moderate Un) that is up-estuarine at the surface with classical two-layer circulation underneath. Relative thickness of surface and bottom boundary layers affect both the intensity and the inflection depth of the exchange flow layers. Up-estuarine winds with W≳0.5 yield unstable stratification and reduce the exchange flow intensity with increasing W.

Complex turbulent exchange coefficient in Akerblom–Ekman model

Abstract The turbulent exchange in boundary layer models is usually characterized by a scalar eddy viscosity coefficient assumed to be a positive function of the vertical variable. We introduce a more general form for the turbulence exchange description, which includes two functions that describe the turbulence without any assumption about their positivity. We construct a model of the Akerblom–Ekman type, but with a complex coefficient of turbulent exchange. The basic quality criterion for these models and algorithms is the maximal agreement with meteorological observations. We optimize the agreement between the global meteorological archive of high-resolution wind observations that are provided by World Meteorological Organization (WMO) in Binary Universal Form for the Representation (BUFR). The main result of our work is that agreement between model solutions and observations will be much better if the turbulent exchange coefficient is optimized in the space of all complex-valued functions, and not limited to the cone of real positive functions.

Large-Eddy Simulations of the Tropical Cyclone Boundary Layer at Landfall in an Idealized Urban Environment

Abstract Populated urban areas along many coastal regions are vulnerable to landfalling tropical cyclones (TCs). To the detriment of surface parameterizations in mesoscale models, the complexities of turbulence at high TC wind speeds in urban canopies are presently poorly understood. Thus, this study explores the impacts of urban morphology on TC-strength winds and boundary layer turbulence in landfalling TCs. To better quantify how urban structures interact with TC winds, large-eddy simulations (LESs) are conducted with the Cloud Model 1 (CM1). This implementation of CM1 includes immersed boundary conditions (IBCs) to represent buildings and eddy recycling to maintain realistic turbulent flow perturbations. Within the IBCs, an idealized coastal city with varying scales is introduced. TC winds impinge perpendicularly to the urbanized coastline. Numerical experiments show that buildings generate distinct, intricate flow patterns that vary significantly as the city structure is varied. Urban IBCs produce much stronger turbulent kinetic energy than is produced by conventional surface parameterizations. Strong effective eddy viscosity due to resolved eddy mixing is displayed in the wake of buildings within the urban canopy, while deep and enhanced effective eddy viscosity is present downstream. Such effects are not seen in a comparison LES using a simple surface parameterization with high roughness values. Wind tunneling effects in streamwise canyons enhance pedestrian-level winds well beyond what is possible without buildings. In the arena of regional mesoscale modeling, this type of LES framework with IBCs can be used to improve parameters in surface and boundary layer schemes to more accurately represent the drag coefficient and the eddy viscosity in landfalling TC boundary layers. Significance Statement This is among the first large-eddy simulation model studies to examine the impacts of tropical cyclone–like winds around explicitly resolved buildings. This work is a step forward in bridging the gap between engineering studies that use computational fluid dynamics models or laboratory experiments for flow through cities and mesoscale model simulations of landfalling tropical cyclones that use surface parameterizations specialized for urban land use.

Flow enhancement from wall pressure observations: A compressible continuous adjoint data assimilation model

This study establishes a compressible continuous adjoint data assimilation (C2ADA) approach for reproducing a complete mean flow from sparse wall pressure observations. The model-form error induced by the Boussinesq approximation is corrected by the addition of a spatially varying additive forcing term. The linear part of the eddy viscosity, computed using the conventional Reynolds-averaged Navier–Stokes model, is incorporated for ensuring the well-posedness of the optimization. The model is derived theoretically to minimize discrepancies between the wall pressure measurements and the numerical predictions of the primary-adjoint system, thereby enabling determination of the optimal contribution of the Reynolds force vector. The effects of divergence schemes and turbulence models are investigated by examining flow over a 30P30N airfoil. The C2ADA model, employing two distinct schemes, demonstrates significant improvements in velocity estimation, but the first-order scheme introduces excessive dissipation, resulting in an under-prediction of spanwise vorticity. The C2ADA model combined with different eddy-viscosity models uniquely recovers the Reynolds force vectors and obtains mean fields that outperform those achieved solely through conventional eddy viscosity models. The practicability of the C2ADA model for capturing complex flow phenomena is confirmed by applying it to study three-dimensional flow over a 65° delta wing. Despite limited wall pressure observations, the C2ADA model has shown a notable improvement in accurately estimating the intensity and location of both the primary and secondary vortices. Recovery errors in the apex region are significantly diminished by incorporating a paucity of observations account for the effect of inboard vortex. The study broadens the applicability of continuous adjoint-based approaches for modeling compressible flow, as our C2ADA approach is easily implemented in existing computational fluid dynamics solvers and has significantly higher computational efficiency than other approaches.

Experimental study on turbulent characteristics of dispersed bubbly flow in a narrow rectangular channel by two-phase PIV

Narrow rectangular channels are widely used in high heat flux applications, due to the high heat transfer efficiency and compact structure. However, a rare understanding was known about the two-phase turbulent characteristics. In this study, an experimental investigation of bubble and turbulent characteristics of dispersed bubbly flow in the narrow rectangular channel was carried out by using the high-speed camera and two-phase particle image velocimetry. The bubble size effect was studied independently using the continuous spectrum bubble generator. According to the results, the bubble size distribution conforms to a Weibull distribution, and the wall-peak void fraction distributions were found. Both turbulent enhancement and suppression were observed in current conditions. Large bubbles enhance turbulence intensity, while small bubbles suppress it. The eddy viscosity ratio ϕ characterizes the modification of turbulence intensity by bubbles, with a critical value of ϕ=1.

Effect of Blade Trimming Length on the Performance of Marine Centrifugal Pump

To study the hydrodynamic characteristics of blade trimming length in centrifugal pumps, Delayed Detached Eddy Simulation (DDES) with nonlinear eddy viscosity was utilized to conduct unsteady calculations on the centrifugal pump. A comprehensive examination of the fluid dynamic properties of the centrifugal pump, including external features, flow conditions, and pressure fluctuations, was carried out. By applying the theory of entropy production, the areas of high energy loss within the centrifugal pump were identified, and the correlations between local entropy production, energy loss, and unsteady flow in different areas with varying blade trimming lengths were analyzed. The results indicate that with the increase in blade trimming length, under rated flow conditions, the head decreases by 1.8%, 3.2%, and 5.7% for different blade trimming lengths, respectively, compared to normal impellers. Similarly, the efficiency decreases by 0.5%, 0.8%, and 1.0% for different blade trimming lengths, respectively. Similar trends were observed under other working conditions as well. As the degree of blade trimming increases, the irreversible losses after the failure of the centrifugal pump also increase significantly, indicating that the flow inside the centrifugal pump becomes disorder. Blade trimming leads to a disorderly fluid flow inside the centrifugal pump, causing an increase in the radial force during operation, which in turn leads to an increase in vibration amplitude and affects its operational stability. Blade trimming failure has a significant impact on the frequency and amplitude of pressure pulsation, resulting in abnormal pressure pulsation and abnormal vibration of the centrifugal pump. Therefore, early warning and diagnosis of blade trimming can be achieved through pressure pulsation monitoring.

Large Eddy Simulation of a Low-Pressure Turbine Cascade with Turbulent End Wall Boundary Layers

We present results of implicit large eddy simulation (LES) and different Reynolds-averaged Navier–Stokes (RANS) models of the MTU 161 low pressure turbine at an exit Reynolds number of 90000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90\\,000$$\\end{document} and exit Mach number of 0.6. The LES results are based on a high-order discontinuous Galerkin method and the RANS is computed using a classical finite-volume approach. The paper discusses the steps taken to create realistic inflow boundary conditions in terms of end wall boundary layer thickness and freestream turbulence intensity. This is achieved by tailoring the input distribution of total pressure and temperature, Reynolds stresses and turbulence length scale to a Fourier series based synthetic turbulence generator. With this procedure, excellent agreement with the experiment can be achieved in terms of blade loading at midspan and wake total pressure losses at midspan and over the channel height. Based on the validated setup, we focus on the discussion of secondary flow structures emerging due to the interaction of the incoming boundary layer and the turbine blade and compare the LES to two commonly used RANS models. Since we are able to create consistent setups for both LES and RANS, all discrepancies can be directly attributed to physical modelling problems. We show that both a linear eddy viscosity model and a differential Reynolds stress model coupled with a state-of-the-art correlation-based transition model fail, in this case, to predict the separation induced transition process around midspan. Moreover, their prediction of secondary flow losses leaves room for improvement as shown by a detailed discussion of turbulence kinetic energy and anisotropy fields.

Implications of Reynolds Averaging for Reactive Tracers in Turbulent Flows

RANS simulations have been broadly used to investigate turbulence in the oceans and atmosphere. Within these environments there are a multitude of tracers undergoing reactions (e.g., phytoplankton growth, chemical reactions). The distribution of these reactive tracers is strongly influenced by turbulent mixing. With a 50 member ensemble of two-dimensional Rayleigh–Taylor-induced turbulent mixing, we show that the dynamics of a reactive tracer growing according to Fisher’s equation are poorly captured by the ensemble mean. A fluctuation-dependent sink introduced by Reynolds averaging Fisher’s equation transfers tracer concentration from the mean to the fluctuations. We compare the dynamics of the reactive tracer with those of a passive tracer. The reaction increases the reactive tracer’s concentration thereby increasing Fickian diffusion and allowing the reactive tracer to diffuse into turbulent structures that the passive tracer cannot reach. A positive feedback between turbulent mixing and fluctuation growth is identified. We show that eddy viscosity and diffusivity parameterizations fail to capture the bulk trends of the system and identify a need for negative eddy diffusivities. One must, therefore, be cautious when interpreting RANS results for reactive tracers.

Research on the Performance Characteristics and Unsteady Flow Mechanism of a Centrifugal Pump under Pitch Motion

Pitch motion is the key factor affecting the performance characteristics of centrifugal pumps on board ships and exacerbates hydraulic excitation to induce the unsteady vibration of pump units. A hydraulic test platform with swing motion is established to explore the effects of pitch motion on a pump’s performance characteristics. An obvious hump zone exists in the head characteristic curve in the low-flow-rate condition due to the pitch motion. The pump head in the shut-off condition has a significant decrease due to the pitch motion, compared to the static state. The head decrease gradually increases as the maximum pitch angle increases or the pitch period shortens. Specifically, the head in the rated flow condition decreases by 6.3 % to reach a minimum at the maximum pitch angle of 20 degrees in a period of 5 s. Based on a multiple-reference coordinate system, a large eddy simulation with a shear-modified eddy viscosity model is employed to simulate inner flow characteristics under the influence of pitch motion. A distinct vortex flow appears near the blade suction surface and becomes increasingly turbulent as the pitch period shortens. The pitch motion intensifies the unsteady stretching and deformation of vortices. The periodic variations in fluid-induced pressure over time present parabolic features, and the amplitude in the frequency domain reaches its maximum value within a pitch period of 5 s.

Study of the linear models in estimating coherent velocity and temperature structures for compressible turbulent channel flows

Linear models, based on stochastically forced linearized equations, are deployed for spectral linear stochastic estimation (SLSE) of the velocity and temperature fluctuations in compressible turbulent channel flows with a bulk Mach number of 1.5. Through comparison with the direct numerical simulation (DNS) data, an eddy-viscosity-enhanced model (eLNS) outperforms the one not enhanced (LNS) in computing the coherence and amplitude ratio of streamwise velocity at different wall-normal heights, but they both largely deviate from DNS regarding the temperature prediction. For further investigation, the eigenspectra and pseudospectra of the linear operators are scrutinized. The eddy viscosity is shown to stabilize the eigenmodes and decrease the non-normality of the vortical modes. Consequently, the relative importance of acoustic and entropy modes increases, and they can contribute 20 % to 55 % of the response growth, which is not supported by DNS. Hence, it is an intrinsic defect of the eLNS model introduced by turbulence modelling. After a procedure of cospectrum decomposition, the contributions of acoustic and entropy components are filtered out. The resulting SLSE quantities for velocity, temperature and their coupling are basically agreeable with DNS, demonstrating that the coherent temperature fluctuation is dominated by advection and other vortical motions, instead of the compressibility effects. Moreover, a parameter study of Reynolds and Mach numbers (from 0.3 to 4) is conducted. The semi-local units are shown to well collapse the velocity SLSE quantities to the incompressible case for streamwise-elongated structures of high coherence.

Development of an Interpolated RANS-LES solver for wall-bounded turbulent fluid flows

Scale-resolving hybrid RANS-LES models are being increasingly used to numerically simulate wall-bounded turbulent flows since they are computationally efficient compared to LES (Large Eddy Simulation) while also being more accurate compared to RANS (Reynolds-Averaged Navier–Stokes) models. Existing hybrid RANS-LES models typically either suffer from modeled stress depletion or they can introduce a sharp jump in the mean Reynolds stress across the RANS-LES zone. We present a novel interpolated RANS-LES (IRL) solver implemented in OpenFOAM, in which the RANS equations (for eddy-viscosity) and LES equations (for filtered velocity) are evolved simultaneously on the same computational grid. Based on the distance from the no-slip wall, the flow domain is demarcated into a near-wall, free-stream, and a “hybrid” region, sandwiched between the near-wall and free-stream regions. Spalart Allmaras (S-A) model has been used to evolve the RANS eddy viscosity, while the Wall Adapting Local Eddy Viscosity (WALE) model is used for evolving the filtered LES velocity. Using a novel scheme based on solving a partial differential equation, the turbulent eddy-viscosity is interpolated between the RANS eddy viscosity in the near wall region and the effective eddy viscosity from the resolved LES fluctuations in the free-stream region. The mean subgrid stress in the LES momentum equation is then corrected in the near-wall and hybrid regions using the interpolated turbulent eddy-viscosity. IRL’s grid resolution requirements are the same as DES’s (Detached Eddy Simulation). Grid convergence and sensitivity studies have been carried out for two canonical flow geometries. For turbulent channel flow simulations, the IRL solver does not display the typical mean stress depletion observed in DES while also predicting resolved Reynolds stresses accurately in the free-stream region. For simulations of flow over backward facing step, the IRL solver can predict the friction factor and coefficient of pressure better than that DES, especially after the reattachment point.