{"title":"From Anomalous Dissipation Through Euler Singularities to Stabilized Finite Element Methods for Turbulent Flows","authors":"Niklas Fehn, Martin Kronbichler, Gert Lube","doi":"10.1007/s10494-025-00639-6","DOIUrl":"10.1007/s10494-025-00639-6","url":null,"abstract":"<div><p>It is well-known that kinetic energy produced artificially by an inadequate numerical discretization of nonlinear transport terms may lead to a blow-up of the numerical solution in simulations of fluid dynamical problems such as incompressible turbulent flows. However, the community seems to be divided whether this problem should be resolved by the use of discretely energy-preserving or dissipative discretization schemes. The rationale for discretely energy-preserving schemes is often based on the expectation of exact conservation of kinetic energy in the inviscid limit, which mathematically relies on the assumption of sufficient regularity of the solution. There is the (contradictory) phenomenological observation in turbulence that flows dissipate energy in the limit of vanishing molecular viscosity, an “anomalous” phenomenon termed dissipation anomaly or the zeroth law of turbulence. As already conjectured by Onsager, the Euler equations may dissipate kinetic energy through the formation of singularities of the velocity field. With the proof of Onsager’s conjecture in recent years, a consequence for designing numerical methods for turbulent flows is that the smoothness assumption behind conservation of energy in the inviscid limit becomes indeed critical for turbulent flows. The velocity field rather has to be expected to show singular behavior towards the inviscid limit, supporting the dissipation of kinetic energy. Our main argument is that designing numerical methods against the background of this physical behavior is a strong rationale for the construction of dissipative (or dissipation-aware) numerical schemes for convective terms. From that perspective, numerical dissipation does not appear artificial, but as an important ingredient to overcome problems introduced by energy-conserving numerical methods such as the inability to represent anomalous dissipation as well as the accumulation of energy in small scales, which is known as thermalization. This work discusses stabilized <span>(H^1)</span>, <span>(L^2)</span>, and <span>(H(mathrm{div}))</span>-conforming finite element methods for incompressible flows with a focus on the energy-stability of the numerical method and its dissipation mechanisms to predict inertial dissipation. Finally, we discuss the achievable convergence rate for the kinetic energy in under-resolved turbulent flow simulations.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"115 Simulation and Measurements","pages":"347 - 388"},"PeriodicalIF":2.0,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00639-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144100164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefan Hickel, Maria Vittoria Salvetti, Ivette Rodriguez, Oriol Lehmkuhl
{"title":"Progress in Engineering Turbulence Modelling and Measurement","authors":"Stefan Hickel, Maria Vittoria Salvetti, Ivette Rodriguez, Oriol Lehmkuhl","doi":"10.1007/s10494-025-00657-4","DOIUrl":"10.1007/s10494-025-00657-4","url":null,"abstract":"","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"115 Simulation and Measurements","pages":"1 - 2"},"PeriodicalIF":2.0,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144100165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrea Pati, Max Hasenzahl, Suad Jakirlic, Christian Hasse
{"title":"Large Eddy Simulation of the Piston Boundary Layer Evolution During the Compression Stroke in a Motored Internal Combustion Engine","authors":"Andrea Pati, Max Hasenzahl, Suad Jakirlic, Christian Hasse","doi":"10.1007/s10494-025-00649-4","DOIUrl":"10.1007/s10494-025-00649-4","url":null,"abstract":"<div><p>This work examines the momentum boundary layer evolution on the piston top of the Darmstadt optically accessible Internal Combustion Engine (ICE). For this purpose, a 3D-CFD wall-resolved Large Eddy Simulation (LES) under motored conditions was deployed. The piston wall is resolved down to 25 <span>(upmu)</span>m, corresponding to <span>({y^ + } < 1)</span>. For statistical purposes and to compare with experimental data, 33 consecutive engine cycles are simulated. A large-scale tumble motion characterizes the flow field. This flow impinges on the piston on the exhaust side, it moves along the flat piston wall and detaches on the intake side. The near-wall velocities of the simulations align well with the experiment. Analysis revealed regions of Favorable Pressure Gradient (FPG) on the exhaust side and Adverse Pressure Gradient (APG) on the intake side, separated by a sharp pressure inversion zone. The near-wall flow accelerates and then decelerates until detachment. Analysis of the non-dimensional <span>({u^ + } - {y^ + })</span> profiles reveals the absence of a logarithmic region in the boundary layer. This scaling procedure is sensitive to thermo-physical properties like density and viscosity that vary across the boundary layer, which complicates comparisons with canonical studies. The shape factor of the boundary layer suggests a fully turbulent state despite the low momentum thickness-based Reynolds number. The boundary layer height increases from the exhaust towards the intake side, especially in the presence of strong pressure gradients. Pressure gradients acting perpendicular to the boundary layer are observed. The comparison of ensemble-averaged and single-cycle instantaneous data shows high levels of cyclic fluctuations.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1269 - 1295"},"PeriodicalIF":2.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00649-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Claudio Alanis Ruiz, Twan van Hooff, Bert Blocken, GertJan van Heijst
{"title":"PIV Measurements and Validation of RANS Solutions for Plane Turbulent Impinging Co-Flowing and Angled Jets at Moderate Reynolds Numbers","authors":"Claudio Alanis Ruiz, Twan van Hooff, Bert Blocken, GertJan van Heijst","doi":"10.1007/s10494-025-00650-x","DOIUrl":"10.1007/s10494-025-00650-x","url":null,"abstract":"<div><p>Turbulent impinging jet (TIJ) flows are a canonical type of flow that is present in nature and in a wide range of industrial applications, making their study indispensable. Among them, multiple co-flowing and angled jets offer possibilities for various practical applications. However, fundamental information on these particular jet configurations is scarce, and there is also a lack of data for validating numerical simulations of these jet flows. Therefore, this paper presents an experimental analysis of isothermal plane turbulent impinging co-flowing and angled jets at moderate Reynolds numbers (<i>Re</i><sub><i>jet</i></sub> ≈ 8,700 and 10,000) and height-to-width ratio (<i>γ</i> = 40.5) utilizing 2D particle image velocimetry (PIV). It also validates the results of several RANS turbulence models that are commonly used for simulating single straight TIJs: standard <i>k-ε</i> (SKE) model, realizable <i>k-ε</i> model (RKE), renormalization group (RNG) <i>k-ε</i> model, baseline (BSL) <i>k-ω</i> model, shear-stress transport (SST) <i>k-ω</i> model, and a Reynolds-stress model (RSM). The analysis and validation focus on detailed velocity measurements while also providing insights into turbulence parameters. Results reveal strong similarities between the two analyzed TIJs and single straight TIJs at the developed free-jet (or combined jet region for the co-flowing jets configuration) and impingement regions. The validation study demonstrates that relatively inexpensive RANS simulations in combination with typical <i>k-ε</i> turbulence models are capable of resolving the mean velocity field of the two investigated TIJ configurations with good accuracy, which is especially the case for the RNG <i>k-ε</i> turbulence model that yields a very good match with the PIV data throughout.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1113 - 1147"},"PeriodicalIF":2.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00650-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alessandro Ercole, Daniel Lörstad, Christer Fureby
{"title":"Large Eddy Simulations of a Turbulent Premixed Swirling Flame with Finite-Rate Chemistry and Flame-Wrinkling Turbulent Combustion Models","authors":"Alessandro Ercole, Daniel Lörstad, Christer Fureby","doi":"10.1007/s10494-025-00652-9","DOIUrl":"10.1007/s10494-025-00652-9","url":null,"abstract":"<div><p>Lean, premixed, swirl-stabilized flames are widely used in modern Dry Low Emissions gas turbine combustors; however, the turbulent combustion process under those conditions is known to be extremely sensitive and prone to instabilities. Numerical simulations can be a valuable tool in predicting the effects of alternative fuels; however, the sensitivity of the results to different models ought to be outlined. In this work, we present the results of Large Eddy Simulations performed on the CECOST burner with both Finite Rate Chemistry and Flamelet Progress Variable combustion models, non-adiabatic boundary conditions, and radiation modeling. The results highlight a surprising sensitivity of the simulation results in terms of mean fields, flame macrostructure, and flame dynamics. We discuss the model effects on the coupling mechanisms between turbulence and combustion, e.g., thermal expansion, and we conclude that, in particularly sensitive cases, they are capable of locally altering the flowfield to the extent it influences key flow structures on which flame stabilization relies. Additionally, the interaction between the smallest resolved scales of turbulence and the flame front is also affected, resulting in distinct flame dynamics.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1377 - 1404"},"PeriodicalIF":2.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00652-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"LES Modeling of the DLR Generic Single-Cup Spray Combustor: Comparison of Exploratory Category C Jet Fuels","authors":"Arvid Åkerblom, Christer Fureby","doi":"10.1007/s10494-025-00653-8","DOIUrl":"10.1007/s10494-025-00653-8","url":null,"abstract":"<div><p>The combustion of conventional Jet A, alongside two alternative jet fuels, C1 and C5, is simulated with Large Eddy Simulations (LES) in a generic single-cup spray combustor during idle and cruise conditions. The spray is modeled using Lagrangian particle tracking and the combustion chemistry of each fuel is modeled by skeletal reaction mechanisms. The volatility and atomizability of each fuel directly affect the spray penetration depth, with Jet A having the longest spray and C5 the shortest. All fuels have qualitatively similar flames at idle conditions, but the Jet A flame is relatively lifted at cruise conditions. C1 and C5 have similar flames despite different spray lengths, likely due to the rapid breakup of C1. The fuels produce different emission profiles, which is connected to their respective H/C ratios, equivalence ratios, and aromatics contents. NO<sub>x</sub> emissions are particularly affected by the mixture fraction in the flame, resulting in high NO<sub>x</sub> emissions for the compact C1 and C5 flames. Thermoacoustic oscillations are observed in all simulations but are strongest for C1 and C5, which we hypothesize is a result of their high volatility.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1315 - 1339"},"PeriodicalIF":2.0,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00653-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rui Pei, Danping Jia, Lianggui Wang, Zhensheng Zang, Bo Liu, Yong Sun
{"title":"High Gas Void Fraction Two-Phase Flow Measurement Based on One-Dimensional Acoustic Wave in Pipeline","authors":"Rui Pei, Danping Jia, Lianggui Wang, Zhensheng Zang, Bo Liu, Yong Sun","doi":"10.1007/s10494-025-00646-7","DOIUrl":"10.1007/s10494-025-00646-7","url":null,"abstract":"<div><p>Parameter measurement of gas–liquid two-phase flow with a high gas void fraction has received great attention in the research field of multiphase flow. As a flowmeter on the sonar principle, the line array-mounted piezoelectric sensors can be applied for gas void fraction measurement of gas–liquid two-phase flow. Firstly, the formula for calculating the density and sound velocity of the medium is analyzed, including: the gas equation of air, the AGA8 and AGA10 standards of natural gas, and the IAPWS-IF97 model of water, combined with the Wood formula and the one-dimensional acoustic attenuation formula of the pipeline, it is deduced that in the gas void fraction > 50% high zone where the gas well is located, the mixed sound velocity increases with the increase of the gas void fraction, showing a monotony increasing correspondence. Secondly, the MVDR beamforming algorithm is applied to solve the “acoustic ridge” in the <span>(k - omega)</span> domain based on the one-dimensional acoustic model of the pipeline to realize the mixed sound velocity measurement of two-phase flow. Finally, the air and water standard device was used to replicate on-site gas well high gas void fraction experiments. The relative error was 2.62% and repeatability was 1.50% for vertically mounted large array spacing. The accuracy meets the requirements for gas well measurements, verifying the feasibility of using the acoustic method to measure gas void fraction. Therefore, it is of great engineering guiding significance to realize the measurement of gas void fraction in the on-site gas well.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1201 - 1232"},"PeriodicalIF":2.0,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guilherme Espíndola da Silva, Rafael Rezende Dias, Odenir de Almeida, Anderson Ramos Proença
{"title":"Experimental and Numerical Investigation of Scale Effects on the Flow Over a Sedan Vehicle","authors":"Guilherme Espíndola da Silva, Rafael Rezende Dias, Odenir de Almeida, Anderson Ramos Proença","doi":"10.1007/s10494-025-00651-w","DOIUrl":"10.1007/s10494-025-00651-w","url":null,"abstract":"<div><p>Experiments and numerical modeling on vehicle aerodynamics were conducted in a Reynolds (Re) number one order of magnitude lower than that of typical full-scale application. Drag coefficient, velocity profile measurements and flow visualization were the focus with the proposition of comparing scale effects of a 1:10 sedan passenger vehicle model with numerical data from full-scale (1:1) based on the Reynolds Averaged Navier–Stokes (RANS) approach. After the validation of the numerical approach at 1:10 scale, additional investigation of sharp and rounded fillets presented on the car’s geometry showed to be relevant to the calculation of the separating shear layers and drag prediction, although the general wake structures are qualitatively similar. Effects of the reduced scale are translated to low Reynolds number where viscous effects starts to play a role. Detailed flow features such as recirculating regions and reversing flow acts on the model’s surface while the near wake velocity field is well captured and evaluated both experimentally and numerically. The results permitted to characterize flow details based on Re number flow, to show the effects of sharp corners on the model and to scrutinize the influence of scale effects on vehicle’s aerodynamics.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1149 - 1177"},"PeriodicalIF":2.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Evolution of a Jet-in-Coflow","authors":"Rishikesh Sampat, Ferry Schrijer, Gangoli Rao Arvind","doi":"10.1007/s10494-025-00648-5","DOIUrl":"10.1007/s10494-025-00648-5","url":null,"abstract":"<div><p>The jet-in-coflow is a two-stream configuration having engineering applications in combustors and gas turbine engine exhausts. In practical systems, the coflow generates a boundary layer of the outer wall of the jet pipe and may also have a certain level of turbulence. In the current work, the evolution of this flow configuration is studied using an air-air turbulent jet in a low turbulence coflow (turbulence intensity < 6%), and the 2D velocity field is measured by planar particle image velocimetry. Cases of varying coflow ratio (ratio of coflow velocity to jet velocity) of 0 (turbulent free jet), 0.09, 0.15, and 0.33 are generated by keeping a constant velocity jet (Re = 14000) and varying the coflow velocity. The trends of jet centerline properties such as velocity decay, jet spread, and jet momentum of jet-in-coflow cases, scaled to represent an equivalent free jet, show deviations from that of the turbulent free jet. The radial profile of mean velocity shows a region of velocity deficit, compared to a turbulent free jet, on the coflow side in the jet-in-coflow cases. In contrast, the turbulence intensity and Reynolds shear stress profiles show an enhanced peak near the interface for the jet-in-coflow cases. Further, conditional statistics were extracted by detecting the interface between the jet and the surroundings, wherein the same trends are observed. The low turbulence levels of the coflow have little effect on the jet/coflow interface, as seen by the conditional enstrophy diffusion and tortuosity compared to a turbulent free jet. The differences at the jet/coflow interface of a jet-in-coflow with respect to a turbulent free jet are attributed to the boundary layer initially developed by the turbulent coflow over the pipe generating the jet, and these are seen throughout the near-to-intermediate field (0<span>(le)</span>x/D<span>(le)</span>40).</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"114 4","pages":"1087 - 1111"},"PeriodicalIF":2.0,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00648-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143856600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Axel Probst, Elrawy Soliman, Silvia Probst, Matthias Orlt, Tobias Knopp
{"title":"Towards Efficient Hybrid RANS–LES for Industrial Aeronautical Applications","authors":"Axel Probst, Elrawy Soliman, Silvia Probst, Matthias Orlt, Tobias Knopp","doi":"10.1007/s10494-025-00645-8","DOIUrl":"10.1007/s10494-025-00645-8","url":null,"abstract":"<div><p>Three complementary approaches for reducing the grid-resolution requirements in hybrid RANS–LES computations, namely (a) the use of wall functions, (b) the application of locally embedded WMLES instead of global WMLES, as well as (c) local grid adaptation in LES regions, are assessed for different test cases up to an industry-relevant aeronautical flow. In this context, targeted improvements and an extension to general 3D geometries of an embedded WMLES method in a second-order accurate, unstructured compressible finite-volume solver are presented. For the wall functions and the embedded WMLES, which are applied to the NASA hump flow and the CRM-HL aircraft configuration, significant computational efficiency gains relative to corresponding reference simulations are demonstrated, while the loss of predictive accuracy compared to experiments can be limited to acceptable levels. Using a refinement indicator based on the locally resolved turbulent kinetic energy, the grid adaptation applied to the NASA hump flow and the NACA0021 at stall conditions yields partly even improved results compared to computations on globally-refined fixed grids, but the computational overhead due to the iterative refinement and averaging process was not yet included in this study. With grid-point savings ranging between 1/3 and more than 2/3 of grid points compared to respective reference meshes, all considered methods offer potential towards more efficient hybrid RANS–LES simulations of complex flows, although their accumulated potential through combination still needs to be explored.</p></div>","PeriodicalId":559,"journal":{"name":"Flow, Turbulence and Combustion","volume":"115 Simulation and Measurements","pages":"141 - 167"},"PeriodicalIF":2.0,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10494-025-00645-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144100242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}