Secondary Flow Structures Research Articles

Benchmark Simulation of Laminar Reactive Micromixing Using Lattice Boltzmann Methods

Micromixers are chemical processing devices with complex flow patterns applied for both mixing and reaction of chemical species. In current research, laminar reacting multicomponent flows are considered. Despite the laminar streaming regime (e.g., Re = 186), there exist secondary flow microstructures. For this setup, accurate predictions of those structures are possible with a large-eddy simulation on a fine mesh resolving till the Batchelor microscales. Utilizing the open-source lattice Boltzmann method (LBM) framework, OpenLB, a benchmark simulation of the reacting micromixer, is re-established with new, more precise computation results. In this context, a Schmidt-number-based stabilization method for LBM-discretized reactive advection–diffusion equations by laminar secondary flow structures is used. A convergence study is performed, which is also a novelty. All computations have been performed on the high-performance computing cluster HoreKa using up to 160 NVIDIA A100 graphics processing units.

Unsteady Secondary Flow Structure at a Large River Confluence

AbstractRiver confluences, which are characterized by complex hydrodynamics, are key nodes for flood control and environmental protection. Two field surveys were carried out at the confluence of the Yangtze River and Poyang Lake to investigate the transient character of flow structures, which are often assumed steady. Repeat‐transect acoustic Doppler current profile measurements were processed and analyzed, adopting a new method to separate mean flow from turbulence and measurement error based on physics‐informed generalized Tikhonov regularization. The two field surveys were characterized by two distinct mixing interface modes: A so‐called Kelvin–Helmholtz (KH) mode, and a wake mode. In KH mode, large‐scale flow fluctuations were observed. These flow fluctuations exert a substantial influence on the alternation of secondary flows by changing the water surface pressure gradient, affecting the intensity of secondary flows rather than their spatial structure. We infer that temperature‐induced stratification is the main cause of this. In the wake mode, multiple vortices in the wake region at the confluence apex also produced flow fluctuations, directly related to the primary velocity gradient. We argue that even for constant incoming flows, secondary flow at river confluences can exhibit channel‐scale unsteadiness related to migration of the turbulent mixing interface. Our findings highlight the crucial role of density effects in regulating secondary flow unsteadiness, which is essential for understanding contaminant and sediment dispersal in river systems.

Effect of Local Concave Non-axisymmetric Endwall Profiling on Endwall Secondary Flows of a Highly-Loaded Turbine Cascade

Non-axisymmetric endwall profiling (NAEP) has been widely utilized in reducing secondary flow loss of turbines. However, most of NAEP are designed for the endwall of the entire blade passage, which presents challenges to the design of cooling structures of turbine endwall. This study aims to explore the local concave non-axisymmetric endwall profiling (LCNP) method with the same effect as whole passage NAEP, and reveal the influence mechanism of LCNP on endwall secondary flow structures of a highly-loaded turbine cascade. Under the condition that the maximum depth of LCNP is unchanged, the axial length effect and pitchwise location effect of LCNP are studied, the influence mechanism of LCNP on the secondary flow loss is analyzed, and the genetic algorithm is utilized to optimize LCNP at the optimal position. Results show that as the axial length of the LCNP increases and the pitchwise location gets closer to the suction surface, the intensity and range of the passage vortex are decreased, and the total pressure loss coefficient (loss coefficient) of the turbine cascade is decreased. When LCNP is 100% axial chord in length and at the position of 2/9 pitch, the loss coefficient is reduced by 5.49%. LCNP was optimized at the optimal position, and the optimal LCNP reduced the loss coefficient of the turbine cascade by 6.73%. After the local concave endwall profiling, the loading in the middle of the endwall of the turbine cascade is reduced, and the intensity of the passage vortex is effectively inhibited, which is the mechanism that the loss coefficient of the turbine cascade is reduced. However, after the local concave endwall profiling, the loading in the trailing of the endwall of the turbine cascade is increased, the transverse migration of the new boundary layer in the endwall is accelerated, and the loss coefficient of the near endwall is increased.

Hydrodynamic Structure of Secondary Polymer Melt Flows in Channels with Changing Geometry

Hydrodynamic Structure of Secondary Polymer Melt Flows in Channels with Changing Geometry

Flow and heat transfer characteristics of low water content jet fuel in U-bend tubes: A numerical study using LES and DPM approaches

This study provides an in-depth analysis of the flow and heat transfer behavior of low-water-content jet fuel (α ≤ 2 %) in U-bend tubes, utilizing Large Eddy Simulations (LES) and Discrete Phase Models (DPM). The research focus on the influence of radii of curvature ratio (r/D), flow rates (Qtp) and α on flow dynamics and heat transfer mechanisms. Flow fields for r/D = 1 and r/D ≥ 2.5, where distinct secondary flow structures, play a critical role in shaping internal flow behavior. These vortices significantly enhance flow mixing and heat transfer, especially on the inner wall, through complex multi-level vortex interactions. The local wall Nusselt number shows a close correlation with vorticity trends, initially increasing and then decreasing, with notable deviations near the inlet and outlet regions. This non-uniform heat transfer is primarily driven by the interaction of secondary flow structures and adverse pressure gradients near the inner wall, while higher Qtp and smaller r/D can improve heat transfer uniformity under certain flow conditions. The presence of droplets increases the total wall Nusselt number by 4 % to 60 % compared to single-phase jet fuel flow, due to two-phase interaction and boundary layer disruption. Finally, the study proposes modified correlations for pressure drop gradients and total wall Nusselt numbers, accounting for effects of r/D and multiphase heat transfer processes. These correlations, validated with RRMSEs of 3.54 % and 6.80 % respectively, provide valuable insights for improving heat transfer efficiency in fuel systems and form a theoretical foundation for real-time monitoring technologies in aircraft fuel lines.

Application of microreactor constructed with micro-mixing channel featuring 3D lateral secondary flow structure for ultra-small particle size preparation of magnetic chitosan nanodrug carriers

Magnetic chitosan nanoparticles serve as reliable carriers for drug delivery, but conventional macroscopic synthesis methods are associated with a number of disadvantages. Efficient micromixing is a crucial aspect of the controlled synthesis of nanoparticles. However, enhancing the mixing efficiency of micromixers at low Reynolds numbers (Re) remains a significant challenge. Fortunately, the addition of lateral structures to the microchannel sidewalls has been demonstrated to be an effective method for enhancing mixing performance at low Re. In this work, the secondary flow effect of 3D lateral structure was numerically studied, and the reason why the multi-dimensional secondary flow effect can effectively promote mixing was analyzed. A high-efficiency microreactor (3D(S)-SWM) was constructed by combining the spherical (S) 3D lateral structure with the square wave (SW) channel. In comparison to other microreactors, 3D(S)-SWM exhibits a shorter full mixing cycle and a smaller pressure drop. Magnetic chitosan nanoparticles were prepared in one step by using the 3D(S)-SWM. The introduction of the 3D lateral structure enables the rapid preparation of magnetic chitosan nanoparticles at low Re. The production of a product with a particle size as low as 18–26 nm, while maintaining superparamagnetic. The nanoparticles prepared can effectively load drugs and achieve sustained drug release. This has significant implications for the targeted transport of drug carriers and their metabolism in vivo. It is anticipated that 3D(S)-SWM will expand the scope of drug delivery applications and facilitate the treatment of diseases.

Integrated positron emission particle tracking (PEPT) and X-ray computed tomography (CT) imaging of flow phenomena in twisted tape swirl flow

A combined positron emission particle tracking (PEPT) and X-ray computed tomography (CT) technique is presented, and its utility is demonstrated through investigation of flow in a pipe with twisted tape swirl insert with varying flow conditions (diameter-based Reynolds numbers 16,300–63,300). A description of this technique is given, as well as data handling practices used to relate geometric information captured by CT to fluid flow data gathered via PEPT. It is found that the CT component is readily capable of capturing the stainless steel insert geometry in this present system, but the use of combined plastic and metal materials leads to artifacts in imaging of the plastic surface. Nonetheless, CT data are related to PEPT flow measurements, and average velocity fields are calculated via a pseudo-framing and interpolation scheme and used to visualize and interrogate key flow phenomena within the system. Radial velocity profiles of the mean flow characteristics are seen to collapse to a nearly common form across all flow conditions considered. Helical vortices are seen propagating through the flow field, generated by bypass flow around the gap between the insert and pipe wall, with additional coherent secondary flow structures seen in the higher Reynolds number cases. These findings enhance the understanding of the mixing mechanisms in these swirl flows and encourage the continued development of PEPT-CT methodologies for 3D flow measurements in optically inaccessible systems.

Influence of Herringbone Grooves Inspired by Bird Feathers on Aerodynamics of Compressor Cascade under Different Reynolds Number Conditions

Nowadays, high aerodynamic load has made blade separation an issue for compact axial compressors under high-altitude low-Reynolds-number conditions. In this study, herringbone grooves inspired by bird feathers were applied to suppress the suction side separation and reduce loss. To study the effect of bio-inspired herringbone grooves on the aerodynamic performance of compressor cascades, a high subsonic compressor cascade was taken as the research object. Under the conditions of different Reynolds numbers, the effects of herringbone grooves of different depths on the flow separation were numerically studied. The research results show that at a high-Reynolds-number condition (Re = 5.6 × 105), the sawtooth-shaped wake induced by herringbone grooves increases the turbulent mixing loss near the suction surface, and the blade performance deteriorates. At a low-Reynolds-number condition (Re = 1.3 × 105), the span-wise secondary flow and micro-vortex structure induced by the herringbone grooves effectively suppress the laminar separation on the suction surface of the blade, and there is an optimal depth for the herringbone grooves that reduces the profile loss by 8.33% and increases the static pressure ratio by 0.55%. The selection principle of the optimal groove depth with the Re is discussed based on the research results under six low-Reynolds-number conditions.

Secondary flow characteristics in confluent streams with vegetation

Vegetation commonly exists in river confluences and alters flow structures, affecting the strength and direction of secondary flows. This study investigated the impact of vegetation on the secondary flow structures of a confluence by measuring three-dimensional instantaneous velocities under different vegetative conditions. By utilizing downstream and horizontal flow velocity characteristics, a secondary flow coefficient concept was introduced to describe secondary flow vorticity directions and strengths. The influence of vegetation was assessed in the context of Reynolds stress, the relative strength of secondary flows, and the direction of secondary flow vorticities to clarify the mechanisms by which vegetation affects secondary flows. The findings reveal opposing vertical forces in the confluent section due to incoming tributary flows, resulting in secondary flow generation. Vegetation redistributes cross-sectional water energy, increasing energy convergence within vegetated areas. This amplifies secondary flow strengths and alters vorticity directions. The impact of vegetation on secondary flows is evident in the increase in rotational intensity. Considering various factors, such as the confluence ratio, flow velocity, and distance from the confluence, is crucial, as the influence of vegetation on flows is multifaceted.

Towards Time-Resolved Multi-Property Measurements By Single-Frequency FRS

The filtered Rayleigh scattering technique (FRS), extended by the method of frequency scanning, has historically been limited to time-averaged multi-property flow measurements. In our recently published work, we present a concept that potentially enables the combined measurement of time-resolved pressure, temperature and three-component (3C) velocity fields. It is based on the observation of the region of interest from six perspectives and a single excitation frequency. This work summarizes and expands on a follow-up publication that experimentally verifies this concept on an aspirated circular duct flow. For this purpose, the results obtained from single-frequency data processing are compared with reference pressures, temperatures and corresponding LDA velocity measurements. Overall, a very good agreement is found for all operating points with accuracies of 3.4% in pressure, 1.3% in temperature and ±2 m/s in axial velocity. Concerning precision, a newly developed multistage evaluation procedure enables values for pressure, temperature and velocity as low as 3 hPa, 2.2 K and 1.7 m/s. In a second flow configuration, an axial swirler is introduced into the duct. The resulting secondary flow structure and deformation of the axial velocity field caused by swirler geometry and support are very well captured with the single-frequency analysis. A closing discussion on the implementation challenges of a single-frequency multi-property FRS instrument with pulsed laser radiation reveals significant obstacles to overcome. Due the considerable optimization potential identified, chances are high that true time-resolved multi-property measurements by FRS will become a reality.

Variations of the shock and secondary flow structure in a transonic compressor cascade with outlet back pressure

The effects of back pressure on the transonic cascade operating state are crucial and can determine the structure of internal shock waves and secondary flows. In this paper, numerical methods validated by experiments were employed to investigate the evolution mechanisms of the inlet flow field, shock structure, secondary flow structure, and cascade performance under different back pressures. Analysis revealed that transonic cascade exhibited unique incidence characteristics in the inlet flow field under both subsonic and supersonic regimes, although these two regimes involved different physical mechanisms. The results revealed that the operating state of the transonic compressor cascade under the unique incidence condition was influenced by the outlet back pressure, and there existed a critical static pressure ratio. The critical static pressure ratio shifted from 1.61 for two-dimensional flow to 1.37 for three-dimensional (3D) flow at M1 = 1.1, due to the corner separation and the characteristics of 3D shocks. The 3D shock structure exhibited a non-uniform distribution along the spanwise direction due to the influence of back pressure and the separated boundary layer. The vortex structures analysis revealed that the secondary flow structure on the sidewalls of the transonic compressor cascade was primarily dominated by corner vortices, whose formation mechanism was related to the interaction between the shock wave and the sidewall boundary layer. Additionally, this interaction also led to the formation of detached shock and lip shock vortex structures. Finally, loss analysis indicated that the wake region of the transonic cascade primarily includes six types of loss, and the total loss of the cascade decreased with the rise in back pressure.

On the Secondary Flow System of an Aggressive Inter Compressor Duct

Abstract In contrast to the highly optimized rotating components, the inter compressor duct (ICD) is offering a high potential for further improvements. Due to a more aggressive design, the length of the whole engine can be reduced. Shorter and thus lighter engines are leading to further fuel savings for the next engine generation. The design of current ICDs is very conservative because of high uncertainties in design space. An extensive test campaign on two highly aggressive ICDs has been conducted at an annular cascade at German Aerospace Center (DLR) Cologne to explore these limitations. The test section consists of low-pressure compressor (LPC)-OGVs, struts, and high-pressure compressor (HPC)-inlet guide vanes (IGVs). To simulate the influence of the last rotor of the LPC and to vary the incidence of the OGV, a moveable swirler is placed in front of the OGV. This simplification results in differences compared to a real rotor outlet flow. Due to geometric constraints, the ability to move the swirler can only be achieved by adding partial gaps in the rear part of the swirler at hub and shroud. These gaps have a huge impact on the secondary flow structure of the swirler outflow and therefore on the inflow of the ICD. In this article, the secondary flow system of an aggressive ICD is analyzed in detail by the means of experimentally validated computational fluid dynamics (CFD) simulations. Special attention is given to the influence of the nonrotating swirler on the secondary flow system. Furthermore, a recommendation for future experimental setups with respect to the described effects is concluded.

Experimental Investigation of Tip Design Effects on the Unsteady Aerodynamics and Heat Transfer of a High-Speed Turbine

Abstract While modern engine manufacturers devote significant efforts to the development of reliable and efficient machines, the introduction of novel, optimized components in the hot gas path represents a risky opportunity. Accurate experimental and numerical data are critical to assess the impact of new technologies on the harsh engine environment. The present study addresses the impact of a selection of high-performance rotor blade tips on the aerodynamic and heat flux field of a high-pressure turbine (HPT) stage. A combined numerical and experimental approach is employed to characterize the interaction of the tip leakage flow with the rotor secondary flows and the casing heat transfer mechanisms for each individual tip geometry. The turbine stage is tested at engine-scaled conditions in the rotating turbine facility of the von Karman Institute. In the present study, the turbine rotor is operated in rainbow configuration to allow the simultaneous testing of multiple blade tip geometries. Reynolds-averaged Navier–Stokes (RANS) simulations are employed to predict the aerodynamic and thermal fields of the individual profiles using test-calibrated boundary conditions. Isothermal steady computations are performed at different wall temperatures to compute the adiabatic wall temperature and the heat transfer convective coefficient. Low-order models are used to represent the over-tip thermal field and the driving heat transfer mechanisms. The time-resolved outlet flow is characterized using a vortex tracking technique and high-frequency aerodynamic measurements to identify the rotor secondary flow structures.

Purge–Mainstream Interactions in a Turbine Stage With Rotor Endwall Contouring

Abstract Purge flows are prevalent in modern gas turbine design, allowing for increased turbine entry temperatures. The purge flow passes through a rim seal and interacts with the mainstream flow, modifying the blade secondary flow structures and reducing stage efficiency. These structures may be controlled using end wall contouring (EWC), though experimental demonstration of their benefit is seldom reported in the literature. The optically accessible turbine at the University of Bath was designed to directly measure and visualize the flow field within the blade passage for a rotor with EWC. The single-stage turbine enables phase-locked flow field measurements with volumetric particle image velocimetry (PIV). Purge flow was supplied to investigate a range of operating conditions in which the secondary flow structures were modified. The modular turbine rotor allowed for expedient change of a bladed ring, or bling, featuring non-axisymmetric EWC. The identified secondary flow structures were the pressure-side leg of the horse shoe vortex (PS-HSV) and an egress vortex (EV) of concurrent rotational direction. An increase in purge flowrate monotonically shifted the EV toward the suction-side (SS) of the adjacent blade. The migration of the PS-HSV toward the SS caused the two aforementioned vortices to merge. The EWC rotor design included a leading-edge (LE) feature to alter the PS-HSV and a trough to guide the EV low spanwise in the passage and maintain displacement from the adjacent suction-side. The EWC rotor was found to be effective at altering the formation and positioning of the secondary flow structures at a range of purge flow conditions.

Prediction of the Influence of the Inlet End-Wall Boundary Layer on the Secondary Flow of a Low Pressure Turbine Airfoil Using RANS and Large-Eddy Simulations

Abstract This paper analyzes the effect of the inlet end-wall boundary layer on the secondary flow of a low pressure turbine airfoil cascade at Reynolds number 2 × 105 using RANS and implicit large-eddy simulations (LES). The results are compared against experimental data obtained at two low-speed linear cascade facilities, one located at the Whittle Laboratory of the University of Cambridge and the other at the Polytechnic University of Madrid. The RANS turbulence model is the k−ω−γ−Reθt and no sub-grid scale model has been used in the LES. An unstructured mesh of hexahedra and prisms is used, with high order elements used in the boundary layer region to better describe the airfoil shape in the LES. Two inlet end-wall boundary layers that produce different secondary flow patterns are analyzed: a laminar thin velocity profile and a turbulent thick velocity profile with several inlet turbulent intensities. The agreement between LES numerical predictions and experimental measurements of the position and intensity of the secondary vortices is very good for both cases. RANS simulations are much cheaper in terms of computational cost and reasonably predict most of the flow features, except when the inlet turbulence is low and turbulent transition prediction becomes critical. The effect of the inlet velocity profiles and inlet turbulence on the secondary flow structure is quite pronounced. The velocity profile thickness determines the spanwise penetration of the passage vortex, and different inlet turbulence intensities modify its mixing. Higher inlet turbulence intensities lead to a decrease of the secondary losses due to the passage vortex and an increase of end-wall losses.

Linear and nonlinear Granger causality analysis of turbulent duct flows

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

Impact of High-Pressure-Turbine Purge Flow on the Evolution of Turbulence in a Turbine Vane Frame

Abstract This paper describes the measurement and postprocessing of turbulence data. The experiments were carried out in a two-stage, two-spool transonic turbine test rig at the Institute for Thermal Turbomachinery and Machine Dynamics at the Graz University of Technology, which includes relevant purge and turbine rotor tip leakage flows. The test setup consists of a high-pressure turbine (HPT) stage, a turbine vane frame (TVF) with turning struts and splitters, and a counter-rotating low-pressure turbine (LPT) to allow engine realistic measurements. Time-resolved area traverse measurements have been performed for three different operating conditions in three measurement planes downstream of the HPT rotor, which enable the measurement of the turbulence quantities at the TVF inlet and outlet as well as the LPT outlet. The turbulence quantities are evaluated using triaxial- and single hot-film probes by means of Constant-Temperature-Anemometry, and their results were validated with five-hole probe (FHP) measurements. Ensemble- and time-averaging, as well as Fourier transforms, were applied for data reduction. It is shown how the turbulence intensity and integral length scale vary over different purge flowrates (PFR). The acquired measurement data illustrate that the interaction of the ejected purge flow with mean flow enhances the turbulent mixing in the secondary flow structures at the TVF inlet and TVF outlet, respectively. Furthermore, the flow downstream of the LPT rotor is affected by TVF and LPT rotor secondary flow structures, which are identified as high turbulence regions. These regions strongly depend on the purge flowrate. These results acquired under engine realistic rig flow conditions enable a deeper understanding of the relationship between loss and turbulence quantities and will help improve the application of computational fluid dynamics turbulence models to turbomachinery modeling.

Experimental investigation of secondary flow losses in a variable geometry linear turbine cascade with winglet tip

Variable geometry turbines (VGT) hold a crucial role in gas turbines and variable cycle engines (VCE) by allowing adjustments to different operational conditions. In order to realize the adjustable function of the VGT stator blade, there will be partial gap structure at both ends of the stator blade, which will lead to partial leakage flow and serious secondary flow loss at the blade end that cannot be ignored, especially in a large angle adjustment range. At present, there are few researches on turbine cascades considering the real partial gap structure and winglet tip, and the numerical simulation calculation is mainly used, while the in-depth study using wind tunnel test is rarely seen. Therefore, this study attempts to analyze the internal flow characteristics of variable geometry turbine cascade by using five-hole pneumatic probe scanning and surface oil flow visualization, and discusses the mechanism of controlling partial clearance leakage flow and reducing secondary flow loss in the cascade by using winglet tip flow control technology. The winglet offset distance and the change of the relationship between the pivot and the clearance position on the flow field and flow loss is studied experimentally for the first time. The results show that the influence mechanism of winglet tip applied in VGT partial gap is quite different from that of typical blade tip clearance application, and more consideration should be given to the influence of pivot structure. Reasonable parameter selection can achieve a maximum loss reduction of 13.4 % and 20.2 % with and without pivot, respectively, while the unreasonable flow control scheme may lead to the loss or even increase with pivot. The interaction between the new secondary flow structure induced by pivot in the gap and other gap leakage flows is analyzed to explore the new mechanism of using winglet tip to reduce the loss of gap leakage flow.

Numerical study of mixing vane spacer grid effect on subchannel mixing in a 5 × 5 rod bundle

Turbulent flow in rod bundle with spacer grid without mixing vanes and with mixing vanes of inclination angles from 10° to 30° was investigated by Reynolds Stress Transportation (RST) model under Reynolds numbers (Re) from 3.96 × 103 to 3.96 × 105. The predicted results were validated by experimental data of lateral velocity field in 5 × 5 rod bundle. The cross-flow velocity was relatively well predicted against experimental data, while lateral Reynolds normal stress was underpredicted near spacer grid and overpredicted far from spacer grid. The mixing vanes in one sub-channel generate high pressure region at the upstream side of mixing vane and low-pressure region at the downstream side of mixing vane, forming secondary flow structures. The lateral velocity increases with inclination angle and Re increasing. The lateral Reynolds stress increases with inclination angle increasing and decreases with Re increasing. The anisotropic turbulent states were studied by Lumley triangle method. The mixing vanes are the main factor dominating the turbulent states in rod bundle. The space grid resistance follows decreasing power function of Re and increases with inclination angle increasing. The secondary flow intensity follows an exponentially decaying function of distance from spacer grid and increases with inclination angle and Re increasing. The turbulent mixing coefficient model is an exponentially decreasing function of the distance from spacer grid, and it increases with inclination angle increasing and decreases with Re increasing. This paper studied the inclination angle and Re effect on the sub-channel mixing in a relatively large range of inclination angle and Re, improving the understandings of the sub-channel mixing phenomena.

Data-driven turbulence modeling for fluid flow and heat transfer in peripheral subchannels of a rod bundle

This study presents a comparison of the performance of machine learning (ML) techniques, specifically multi-dimensional gene expression programming (MGEP), tensor basis neural network (TBNN), and also proposes a novel universally interpretable machine learning architecture to model the turbulent scalar flux (UIML-s) to enhance turbulence models for fluid flows at different Prandtl numbers in channels with complex shapes of walls in the channel cross section. In particular, peripheral subchannels of rod bundles are of primary interest. However, the accuracy of mean velocity and scalar distributions predicted by commonly used turbulence models still poses a challenge compared to data extracted from high-fidelity eddy-resolving numerical simulations, particularly for engineering applications involving complex geometry flows. In the present study, by utilizing an explicit algebraic expression for the nonlinear Reynolds-stress term obtained through both the evolutionary MGEP optimization and TBNN, the secondary flow structure has been adequately predicted in the cross-wise mean velocity distributions in the square duct and the rectangular channel with three longitudinal rods. This structure is also observed in the data from the concurrent runs performed by direct numerical simulation (DNS) but is completely absent in the results produced by a baseline Reynolds-averaged Navier–Stokes (RANS) closure, which employs the linear eddy viscosity model for the Reynolds stress tensor. Comparison of MGEP and TBNN has shown their nearly equal performance in a square duct flow; however, MGEP works better for the more complex geometry channel with three rods. Furthermore, based on the velocity field produced by the RANS-MGEP model, the ML modification of the gradient diffusion hypothesis, integrated into the aforementioned novel RANS-ML model called as UIML-s, significantly improves the mean scalar distributions in a flow with three bumps serving as a prototype for the peripheral subchannel of rod bundle. The normalized root mean squared error decreases from 13.5% to 7.6%, bringing the predicted distributions closer to the DNS data, particularly in the near-wall region. Another approach, MGEP-s, also yields the acceptable results, which are nearly identical to those from UIML-s. These findings highlight the potential of using data-driven calibration of turbulence models with nonlinear closures to enhance the predictability for RANS simulations of fluid flows, heat, and mass transfer in channels with complex geometry.