@misc{LignellLansingerMedinaMendezetal., author = {Lignell, David O. and Lansinger, Victoria B. and Medina M{\´e}ndez, Juan Ali and Klein, Marten and Kerstein, Alan R. and Schmidt, Heiko and Fistler, Marco and Oevermann, Michael}, title = {One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application}, series = {Theoretical and Computational Fluid Dynamics}, volume = {32}, journal = {Theoretical and Computational Fluid Dynamics}, number = {4}, issn = {0935-4964}, doi = {10.1007/s00162-018-0465-1}, pages = {495 -- 520}, abstract = {The one-dimensional turbulence (ODT) model resolves a full range of time and length scales and is computationally efficient. ODT has been applied to a wide range of complex multi-scale flows, such as turbulent combustion. Previous ODT comparisons to experimental data have focused mainly on planar flows. Applications to cylindrical flows, such as round jets, have been based on rough analogies, e.g., by exploiting the fortuitous consistency of the similarity scalings of temporally developing planar jets and spatially developing round jets. To obtain a more systematic treatment, a new formulation of the ODT model in cylindrical and spherical coordinates is presented here. The model is written in terms of a geometric factor so that planar, cylindrical, and spherical configurations are represented in the same way. Temporal and spatial versions of the model are presented. A Lagrangian finite-volume implementation is used with a dynamically adaptive mesh. The adaptive mesh facilitates the implementation of cylindrical and spherical versions of the triplet map, which is used to model turbulent advection (eddy events) in the one-dimensional flow coordinate. In cylindrical and spherical coordinates, geometric stretching of the three triplet map images occurs due to the radial dependence of volume, with the stretching being strongest near the centerline. Two triplet map variants, TMA and TMB, are presented. In TMA, the three map images have the same volume, but different radial segment lengths. In TMB, the three map images have the same radial segment lengths, but different segment volumes. Cylindrical results are presented for temporal pipe flow, a spatial nonreacting jet, and a spatial nonreacting jet flame. These results compare very well to direct numerical simulation for the pipe flow, and to experimental data for the jets. The nonreacting jet treatment overpredicts velocity fluctuations near the centerline, due to the geometric stretching of the triplet maps and its effect on the eddy event rate distribution. TMB performs better than TMA. A hybrid planar-TMB (PTMB) approach is also presented, which further improves the results. TMA, TMB, and PTMB are nearly identical in the pipe flow where the key dynamics occur near the wall away from the centerline. The jet flame illustrates effects of variable density and viscosity, including dilatational effects.}, language = {en} } @misc{ArshadKongKersteinetal., author = {Arshad, Salman and Kong, Bo and Kerstein, Alan R. and Oevermann, Michael}, title = {A strategy for large-scale scalar advection in large eddy simulations that use the linear eddy sub-grid mixing model}, series = {International Journal of Numerical Methods for Heat and Fluid Flow}, volume = {28}, journal = {International Journal of Numerical Methods for Heat and Fluid Flow}, number = {10}, issn = {0961-5539}, doi = {10.1108/HFF-09-2017-0387}, pages = {2463 -- 2479}, abstract = {Purpose: The purpose of this numerical work is to present and test a new approach for large-scale scalar advection (splicing) in large eddy simulations (LES) that use the linear eddy sub-grid mixing model (LEM) called the LES-LEM. Design/methodology/approach: The new splicing strategy is based on an ordered flux of spliced LEM segments. The principle is that low-flux segments have less momentum than high-flux segments and, therefore, are displaced less than high-flux segments. This strategy affects the order of both inflowing and outflowing LEM segments of an LES cell. The new splicing approach is implemented in a pressure-based fluid solver and tested by simulation of passive scalar transport in a co-flowing turbulent rectangular jet, instead of combustion simulation, to perform an isolated investigation of splicing. Comparison of the new splicing with a previous splicing approach is also done. Findings: The simulation results show that the velocity statistics and passive scalar mixing are correctly predicted using the new splicing approach for the LES-LEM. It is argued that modeling of large-scale advection in the LES-LEM via splicing is reasonable, and the new splicing approach potentially captures the physics better than the old approach. The standard LES sub-grid mixing models do not represent turbulent mixing in a proper way because they do not adequately represent molecular diffusion processes and counter gradient effects. Scalar mixing in turbulent flow consists of two different processes, i.e. turbulent mixing that increases the interface between unmixed species and molecular diffusion. It is crucial to model these two processes individually at their respective time scales. The LEM explicitly includes both of these processes and has been used successfully as a sub-grid scalar mixing model (McMurtry et al., 1992; Sone and Menon, 2003). Here, the turbulent mixing capabilities of the LES-LEM with a modified splicing treatment are examined. Originality/value: The splicing strategy proposed for the LES-LEM is original and has not been investigated before. Also, it is the first LES-LEM implementation using unstructured grids.}, language = {en} } @misc{LackmannKersteinOevermann, author = {Lackmann, Tim and Kerstein, Alan R. and Oevermann, Michael}, title = {A representative linear eddy model for simulating spray combustion in engines (RILEM)}, series = {Combustion and Flame}, volume = {193}, journal = {Combustion and Flame}, issn = {0010-2180}, doi = {10.1016/j.combustflame.2018.02.008}, pages = {1 -- 15}, abstract = {The design of new combustion concepts for low emission, high efficiency internal combustion engines often leads to combustion under low temperature conditions. Under those conditions, the assumption of fast chemistry, which has been the cornerstone of many turbulent combustion models, is not strictly valid anymore and the validity and applicability of classical combustion models such as flamelet models might be limited. In this paper we present an updated version of a recently developed regime independent modeling approach for turbulent non-premixed combustion with an emphasis on applications to internal combustion engines. The model utilizes the mode- and regime-independent linear eddy model (LEM) as a combustion and micro-mixing model in a representative way. This is achieved by time advancing only one LEM realization representing the combustion process in the whole engine domain and coupling it to a RANS simulation with a presumed β-function PDF approach for the mixture fraction. The use of LEM rather than flamelet combustion closure has several benefits, an important one being regime independence. Additionally, LEM incorporates a physically based representation of the stochastic variability of turbulent eddy motions, implying an intrinsic representation of scalar dissipation rate fluctuations. In order to capture key features of engine spray-combustion environments, the LEM methodology is extended by introducing a conical LEM domain to approximate spray spatial development, fuel vapor input based on CFD-prescribed spray evaporation, and a representation of large scale turbulent motions distinct from the inertial-range turbulence that develops at smaller scales. The representative character of LEM states is evaluated by comparing mixture fraction statistics and scalar dissipation rates generated by LEM and the CFD. The performance and predictive capability of the model for typical engine applications is evaluated by simulating a standard test case - Spray B of the Engine Combustion Network (ECN) - and comparing the results with experimental data. The results demonstrate the capability of the model to represent the spray combustion process with reasonable accuracy but also reveal some limitations. The limitations and shortcomings of the model are discussed and an outlook for further development of the approach into a regime- and mode-independent combustion model for internal engine applications is given.}, language = {en} } @misc{MovagharLinneHerrmannetal., author = {Movaghar, Amirreza and Linne, Mark and Herrmann, Marcus A. and Kerstein, Alan R. and Oevermann, Michael}, title = {Modeling and numerical study of primary breakup under diesel conditions}, series = {International Journal of Multiphase Flow}, volume = {98}, journal = {International Journal of Multiphase Flow}, issn = {0301-9322}, doi = {10.1016/j.ijmultiphaseflow.2017.09.002}, pages = {110 -- 119}, abstract = {A recently introduced stochastic model for reduced numerical simulation of primary jet breakup is evaluated by comparing model predictions to DNS results for primary jet breakup under diesel conditions. The model uses one-dimensional turbulence (ODT) to simulate liquid and gas time advancement along a lateral line of sight. This one-dimensional domain is interpreted as a Lagrangian object that is advected downstream at the jet bulk velocity, thus producing a flow state expressed as a function of streamwise and lateral location. Multiple realizations are run to gather ensemble statistics that are compared to DNS results. The model incorporates several empirical extensions of the original ODT model that represent the phenomenology governing the Weber number dependence of global jet structure. The model as previously formulated, including the assigned values of tunable parameters, is used here without modification in order to test its capability to predict various statistics of droplets generated by primary breakup. This test is enabled by the availability of DNS results that are suitable for model validation. Properties that are examined are the rate of bulk liquid mass conversion into droplets, the droplet size distribution, and the dependence of droplet velocities on droplet diameter. Quantities of greatest importance for engine modeling are found to be predicted with useful accuracy, thereby demonstrating a more detailed predictive capability by a highly reduced numerical model of primary jet breakup than has previously been achieved.}, language = {en} } @misc{LackmannHewsonKnausetal., author = {Lackmann, Tim and Hewson, John and Knaus, Robert and Kerstein, Alan R. and Oevermann, Michael}, title = {Stochastic modeling of unsteady extinction in turbulent non-premixed combustion}, series = {Proceedings of the Combustion Institute}, volume = {36}, journal = {Proceedings of the Combustion Institute}, number = {2}, issn = {0082-0784}, doi = {10.1016/j.proci.2016.07.014}, pages = {1677 -- 1684}, abstract = {Turbulent fluctuations of the scalar dissipation rate have a major impact on extinction in non-premixed combustion. Recently, an unsteady extinction criterion has been developed (Hewson, 2013) that predicts extinction dependent on the duration and the magnitude of dissipation rate fluctuations exceeding a critical quenching value; this quantity is referred to as the dissipation impulse. The magnitude of the dissipation impulse corresponding to unsteady extinction is related to the difficulty with which a flamelet is exintguished, based on the steady-state S-curve. In this paper we evaluate this new extinction criterion for more realistic dissipation rates by evolving a stochastic Ornstein-Uhlenbeck process for the dissipation rate. A comparison between unsteady flamelet evolution using this dissipation rate and the extinction criterion exhibit good agreement. The rate of predicted extinction is examined over a range of Damk{\"o}hler and Reynolds numbers and over a range of the extinction difficulty. The results suggest that the rate of extinction is proportional to the average dissipation rate and the area under the dissipation rate probability density function exceeding the steady-state quenching value. It is also inversely related to the actual probability that this steady-state quenching dissipation rate is observed and the difficulty of extinction associated with the distance between the upper and middle branches of the S-curve.}, language = {en} } @misc{KleinKersteinSchmidt, author = {Klein, Marten and Kerstein, Alan R. and Schmidt, Heiko}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection}, series = {25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, journal = {25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {2}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for thermal convection with internal sources}, address = {IPAM Workshop: Transport and Mixing in Complex and Turbulent Flows (CTF2021), University of California, Los Angeles, CA, USA}, pages = {1}, language = {en} } @misc{FistlerKersteinWunschetal., author = {Fistler, Marco and Kerstein, Alan R. and Wunsch, Scott and Oevermann, Michael}, title = {Turbulence modulation in particle-laden stationary homogeneous shear turbulence using one-dimensional turbulence}, series = {Physical Review Fluids}, volume = {5}, journal = {Physical Review Fluids}, number = {12}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.5.124303}, pages = {28}, abstract = {Turbulence modulation in particle-laden stationary homogeneous shear turbulence (HST) is investigated using one-dimensional turbulence (ODT), a low-dimensional stochastic flow simulation model. For this purpose, an ODT formulation previously used to study turbulence modulation in forced homogeneous isotropic turbulence (HIT) is extended, so that the model emulates the anisotropic character of HST and, potentially, anisotropic turbulence in general. This is done by limiting the kinetic-energy redistribution during an eddy event to an exchange involving two velocity components, where the three possible choices of the omitted component define three eddy types whose relative likelihoods control the anisotropy. Comparisons of ODT and direct-numerical-simulation results with reference to signatures of turbulence modulation are the basis of a broader ODT parameter study that is reported. Owing to the reduced dimensionality of ODT, it is found that the fidelity of the model for single-phase HST does not extend to particle effects on flow anisotropy, but for quantities averaged over components, parametric trends are captured. The consistent approach to case comparisons that was introduced in the HIT study to evaluate sensitivities to particle-phase parameters in a given flow configuration is extended here to a cross-comparison of HST and HIT model results, and its efficacy is again confirmed. The results provide an overall characterization of the potential for ODT to support the incorporation of particle-induced turbulence modulation into subgrid-scale closures of large-eddy simulations.}, language = {en} } @misc{FistlerKersteinOevermann, author = {Fistler, Marco and Kerstein, Alan R. and Oevermann, Michael}, title = {A new LES subgrid-scale approach for turbulence modulation by droplets}, series = {ICLASS 14th Triennial International Conference on Liquid Atomization and Spray Systems Chicago, USA, 2018-07-21 - 2018-07-26}, journal = {ICLASS 14th Triennial International Conference on Liquid Atomization and Spray Systems Chicago, USA, 2018-07-21 - 2018-07-26}, pages = {8}, abstract = {We present a new modelling approach for turbulence modulation by droplets on the subgrid-scale (SGS) level of Large-Eddy-Simulations (LES). Many SGS models exist for the effect of gas phase SGS on the droplet phase, but very few for the mechanisms vice versa on the turbulent intensity of the gas phase. The reasons are a lack of physical understanding and limited computational resources for extensive DNS studies. To address both problems a dimension-reduced and consequently less costly model, namely One-Dimensional- Turbulence (ODT), is used to gather information about this specific flow phenomena. ODT is a stochastic tool simulating turbulent flows along a notional 1D line of sights. For modeling the turbulent advection instantaneous maps are applied to the line which represent the effect of individual eddies on property fields and the dispersed phase. After validating the general test case of a droplet-laden shear flow against DNS data, a concept is presented on how to gather turbulence modulation for several parameter ranges in a data base and how to make them accessible on the flight for LES. The three most significant parameters, the unladen flow Reynolds number, the droplet loading and the particle momentum number, are chosen to construct an efficient data base.}, language = {en} } @incollection{MovagharChiodiDesjardinsetal., author = {Movaghar, Amirreza and Chiodi, Robert and Desjardins, Olivier and Oevermann, Michael and Kerstein, Alan R.}, title = {A Subgrid-Scale Model for Large-Eddy Simulation of Liquid/Gas Interfaces Based on One-Dimensional Turbulence}, series = {Turbulent Cascades II}, booktitle = {Turbulent Cascades II}, publisher = {Springer Nature Switzerland AG}, address = {Schweiz}, isbn = {978-3-030-12547-9}, doi = {10.1007/978-3-030-12547-9_10}, pages = {83 -- 91}, abstract = {The interface/turbulence interaction between two fluids in a turbulent environment has an important role in many technical processes, e.g. primary liquid atomization in combustion devices. Primary atomization has a significant role in spray formation and its characteristics. The resulting dynamics typically span 4-6 orders of magnitude in length scales, making detailed numerical simulations exceedingly expensive. This motivates the need for modeling approaches based on spatial filtering such as large-eddy simulation (LES). In this paper, a new approach based on One-Dimensional turbulence (ODT) is presented to describe the subgrid interface dynamics. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends. ODT has previously been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here a new approach called VODT is presented which produces a size-conditioned as well as a total time rate of generation of droplets for given flow conditions at an interface. At the LES level, the total droplet generation from VODT is interpreted as a rate of mass conversion of LES-resolved liquid into unresolved droplets. Preliminary results of applying VODT to a cell with a planar-shear-layer are discussed at the end of the paper.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for radiatively driven turbulent convection}, series = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, journal = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochasticmodel for thermal convection with internal sources}, pages = {1}, abstract = {It is well established that heat transfer in turbulent Rayleigh-Bénard convection and angular momentum transfer in turbulent Taylor-Couette flow are similar in nature. This similarity manifests itself by isomorphic scaling laws for corresponding flow regimes. However, it is not clear at present if this similarity extends to flows with internal sources and different types of boundary conditions. Internal sources may occur, for example, due to radiative heating in dry or condensation in moist convection, or due to internal wave breaking and mean flow excitation in rotating Taylor-Couette-like flows. In this study, heat transfer in radiatively-driven turbulent Rayleigh-Bénard convection is investigated using the stochastic one-dimensional-turbulence model (ODT). A Boussinesq fluid of Prandtl number 1 is confined between two horizontal adiabatic no-slip walls that are located at z = 0 and H, respectively. The fluid is exposed to constant background gravity that points in vertical (-z) direction. A flow is driven by radiative heating from below yielding the local heating rate Q(z) = (P/l) exp(-z/l), where P is the prescribed mean total heat flux and l the absorption length that controls the thermal boundary layer thickness. ODT resolves all relevant scales of the flow, including molecular-diffusive scales, along a vertical one-dimensional domain, whereas stochastically sampled eddy events represent the effects of turbulent advection. ODT results reproduce and extrapolate available reference experiments of Lepot et al. (Proc. Natl. Acad. Sci. USA, 115, 2018, pp. 8937-8941) and Bouillaut et al. (J. Fluid Mech., 861, 2019, R5) in particular capturing the turbulent transition from the classical to the 'ultimate' regime. For these regimes, the exponent values in N u ∼ Ra^p scaling are found to be p ≈ 0.33 and p ≈ 0.55, respectively, in agreement with measured values. Joint probabilities of turbulent eddy size and location suggest that the regime transition is associated with a suppression of small-scale near-wall turbulent motions. The latter observation is found consistent with recent direct numerical simulations of heat transfer between permeable walls (Kawano et al., J. Fluid Mech., 914, 2021, A13).}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection, 25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {1}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinFreireLignelletal., author = {Klein, Marten and Freire, Livia S. and Lignell, David O. and Kerstein, Alan R. and Schmidt, Heiko}, title = {Ein stochastischer Ansatz zur Modellierung fluktuierender Oberfl{\"a}chenfl{\"u}sse in turbulenten Grenzschichten}, series = {Kurzfassungen der Meteorologentagung DACH}, volume = {2022}, journal = {Kurzfassungen der Meteorologentagung DACH}, publisher = {Copernicus}, doi = {10.5194/dach2022-22}, pages = {1 -- 1}, abstract = {Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskr{\"a}fte ber{\"u}cksichtigt werden k{\"o}nnen. Das Modell wird beispielhaft als unabh{\"a}ngiges, numerisches Werkzeug angewendet, um fluktuierende Oberfl{\"a}chenfl{\"u}sse in turbulenten Kanalstr{\"o}mungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (por{\"o}se) Oberfl{\"a}chen betrachtet. Anhand neuer Ergebnisse wird demonstriert, dass der Modellansatz in der Lage ist, Referenzdaten zufriedenstellend zu reproduzieren und extrapolieren. Daneben werden aktuelle Arbeiten zur Kopplung des stochastischen Modellansatzes mit Large-Eddy-Simulationen vorgestellt. Es wird gezeigt, dass die stochastische Modellierung oberfl{\"a}chennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitteraufl{\"o}sung zu verringern.}, language = {de} } @misc{KersteinLignellSchmidtetal., author = {Kerstein, Alan R. and Lignell, David O. and Schmidt, Heiko and Starick, Tommy and Wheeler, Isaac and Behrang, Masoomeh}, title = {Using Hips As a New Mixing Model to Study Differential Diffusion of Scalar Mixing in Turbulent Flows}, series = {2021 AIChE Annual Meeting}, journal = {2021 AIChE Annual Meeting}, abstract = {Mixing two or more streams is ubiquitous in chemical processes and industries involving turbulent liquid or gaseous flows. Modeling turbulent mixing flows is complicated due to a wide range of time and length scales, and non-linear processes, especially when reaction is involved. On the other hand, in turbulent reacting flows, sub-grid scales need to be resolved accurately because they involve reactive and diffusive transport processes. Transported PDF methods use mixing models to capture the interaction in the sub-grid scales. Several models have been used with varying success. In this study, we present a novel model for simulation of turbulent mixing called Hierarchical Parcel Swapping (HiPS). The HiPS model is a stochastic mixing model that resolves a full range of time and length scales with the reduction in the complexity of modeling turbulent reacting flows. This model can be used as a sub-grid mixing model in PDF transport methods, as well as a standalone model. HiPS can be applied to transported scalars with variable Schmidt numbers to capture the effect of differential diffusion which is important for modeling scalars with low diffusivity like soot. We present an overview of the HiPS model, its formulation for variable Schmidt number flows, and then present results for evaluating the turbulence properties including the scalar energy spectra, the scalar dissipation rate, and Richardson dispersion. These model developments are an important step in applying HiPS to more complex flow configurations.}, language = {en} } @misc{StarickBehrangLignelletal., author = {Starick, Tommy and Behrang, Masoomeh and Lignell, David O. and Schmidt, Heiko and Kerstein, Alan R.}, title = {Turbulent mixing simulation using the Hierarchical Parcel Swapping (HiPS) model}, series = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, publisher = {Department of Fluid Mechanics, University of Technology and Economics}, address = {Budapest, Hungary}, isbn = {978-963-421-881-4}, pages = {1 -- 7}, language = {en} } @misc{MenonKersteinOevermann, author = {Menon, Abhilash and Kerstein, Alan and Oevermann, Michael}, title = {Assessing the multi-regime capability of the Super-Grid Linear Eddy Model (SG-LEM) using the Darmstadt multi-regime burner}, series = {Flow, Turbulence and Combustion}, volume = {2024}, journal = {Flow, Turbulence and Combustion}, publisher = {Springer Science and Business Media LLC}, issn = {1386-6184}, doi = {10.1007/s10494-024-00602-x}, pages = {26}, abstract = {AbstractRecent advances in combustion modelling for Large Eddy Simulation (LES) have increasingly utilised lower-dimensional manifolds, such as Flamelet Generated Manifolds and Flamelet/Progress Variable methods, due to their computational efficiency. These methods typically rely on one-dimensional representations of flame structures, often assuming premixed or non-premixed configurations. However, practical combustion devices frequently operate under partially-premixed conditions and present challenges due to mixture inhomogeneities and complex flow features. The Linear Eddy Model (LEM) offers an alternative by directly simulating turbulence-chemistry interactions without presuming specific flame structures. However, traditional LES-LEM approaches are computationally quite expensive due to the need for resolved LEM domains to be embedded in every LES cell.The authors developed the Super-Grid LEM (SG-LEM) method (Comb. Theor. Model.  28, 2024) to address these computational challenges by coarse-graining the LES mesh and embedding individual LEM domains within clusters of LES cells. This study evaluates SG-LEM in the context of the Multi-Regime Burner (MRB) introduced by Butz et al. (Combust. Flame, 210, 2019), which features both premixed and non-premixed flame characteristics. SG-LEM simulations of the MRB case demonstrate the method's sensitivity to clustering parameters, with flow-aligned clusters significantly improving flame stability. LEM domains on the super-grid were able to represent the MRB flame topology while LES radial profiles including velocity, mixture fraction, temperature, and \$\${\textrm{CO}}\$\$ CO mass fraction, were validated against experimental data and also reference simulations using standard combustion closures. The work also investigates discrepancies in CO profiles using conditional statistics and stand-alone LEM simulations. Finally, the work identifies areas of improvement for the SG-LEM framework, in particular relating to cluster generation, and (advective and diffusive) mass exchange between neighbouring LEM domains, as well as possible solutions for future SG-LEM implementations which could improve the model's predictive capability.}, language = {en} } @misc{MovagharChiodiOevermannetal., author = {Movaghar, Amirreza and Chiodi, Robert and Oevermann, Michael and Desjardins, Olivier and Kerstein, Alan}, title = {Assessment of a multiphase formulation of one-dimensional turbulence using direct numerical simulation of a decaying turbulent interfacial flow}, series = {Physical Review Fluids}, volume = {9}, journal = {Physical Review Fluids}, number = {10}, publisher = {American Physical Society (APS)}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.9.104003}, abstract = {The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024}, language = {en} } @misc{MenonOevermannKerstein, author = {Menon, Abhilash M. and Oevermann, Michael and Kerstein, Alan R.}, title = {A super-grid approach for LES combustion closure using the linear eddy model}, series = {Combustion Theory and Modelling}, volume = {28}, journal = {Combustion Theory and Modelling}, number = {1}, publisher = {Informa UK Limited}, issn = {1364-7830}, doi = {10.1080/13647830.2023.2260351}, pages = {99 -- 126}, abstract = {LES-LEM is a simulation approach for turbulent combustion in which the stochastic Linear Eddy Model (LEM) is used for sub-grid mixing and combustion closure in Large-Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly local turbulent flame statistics, captures finite rate chemistry effects and directly incorporates turbulence-chemistry interaction. However, the approach is computationally expensive as it requires advancing an LEM-line in each LES cell. This paper introduces a novel turbulent combustion closure model for LES using LEM to address this issue. It involves coarse-graining the LES mesh to generate a coarse- level 'super-grid' comprised of cell-clusters. Each cell-cluster, instead of each LES cell, then contains a single LEM domain. This domain advances the combined advection-reaction-diffusion solution and also provides suitably conditioned statistics for thermochemical scalars such as species mass fractions. Local LES-filtered thermochemical states are then obtained by probability-density-function (PDF) weighted integration of binned conditionally averaged scalars, akin to standard presumed PDF approaches for reactive LES but with physics-based determination of the full thermochemical state for particular values of the conditioning variables. The proposed method is termed 'super-grid LEM' or 'SG-LEM'. The paper describes LEM reaction-diffusion advancement, the LEM representation of turbulent advection, a novel splicing algorithm (a key feature of LES-LEM) formulated for the super-grid approach, a wall treatment, and a thermochemical LES closure procedure. To validate the proposed model, a pressure-based solver was developed using the OpenFOAM library and tested on a premixed ethylene flame stabilised over a backward facing step, a setup for which some DNS data is available. SG-LEM provides high resolution flame structures, temperature and mass fractions suitable for LES thermochemical closure. Additionally, it provides reaction-rate data at the coarse level, a unique feature compared to other mapping-type closure methods. Quantitative comparisons are made between the proposed model and time-averaged DNS data, focussing on velocity, temperature and species mass fraction. Results show good agreement downstream of the step. Furthermore, comparison with an equivalent Partially-Stirred Reactor (PaSR) simulation demonstrates the superior predictive capability of SG-LEM. Additionally, the paper briefly examines the sensitivity of the model to coarse-graining parameters and finally, explores computational efficiency highlighting the substantial speedup achieved when compared to the standard LES-LEM approach with potentially significant speedup relative to PaSR closure for the intensely turbulent regimes of principal interest.}, language = {en} } @article{DoubianiKersteinOevermann, author = {Doubiani, Nidal and Kerstein, Alan R. and Oevermann, Michael}, title = {A pressure-coupled Representative Interactive Linear Eddy Model (RILEM) for engine simulations}, series = {Fuel}, volume = {355 (2024)}, journal = {Fuel}, publisher = {Elsevier BV}, issn = {0016-2361}, doi = {10.1016/j.fuel.2023.129423}, pages = {1 -- 15}, abstract = {The Representative Linear Eddy Model (RILEM) was introduced by Lackmann et al. (2018) as an alternative modeling approach to simulate turbulent non-premixed combustion in engines. The model utilizes a RANS approach for turbulence and the Linear Eddy Model (LEM) with a presumed probability density function (PDF) approach for combustion closure. A distinct feature of RILEM is its potential to handle arbitrary combustion regimes and the consideration of complex physical phenomena such as differential diffusion effects. The original version of RILEM implemented a volume-based coupling between LEM and the flow solver. This work presents a new variant of RILEM, i.e., Multiple Representative Interactive Linear Eddy Model (MRILEM) based on a pressure-based coupling, to overcome some deficiencies of the original RILEM, namely statistical fidelity. Due to the introduced pressure coupling, the effects of heat losses (wall heat fluxes, latent heat of evaporation) on combustion are intrinsically included via the pressure trace. Furthermore, we introduce a new step function PDF for the progress variable defined by its mean value only. Issues with an incomplete solution space for mixture fraction and progress variable due to the stochastic nature of LEM are remedied with a PDF scaling technique, aided by a novel parameterization of the progress-variable PDF The new variant of RILEM is evaluated using part- and full-load cases of a heavy-duty metal engine. The impact of utilizing multiple LEM lines on the completeness of the solution space and its influence on the distribution of scalar values in the CFD domain was demonstrated. Results for pressure trace, flame structure, and CO emissions are analyzed and compared with simulations using the Multi-Zone Well-Mixed Model (MZWM) model and experiments. While pressure traces agree well among the different models and experiments, noteworthy differences are observed between the models regarding CO emissions and temperature. Effects of turbulence chemistry interaction were noticed when comparing MRILEM to the results of the MZWM simulation, namely flame brush and species mass fraction distribution.}, language = {en} } @misc{MenonKersteinOevermann, author = {Menon, Abhilash M. and Kerstein, Alan and Oevermann, Michael}, title = {Investigation of coarse-graining parameters for super-grid LEM closure applied to LES of practical bluff-body flames}, series = {Combustion Theory and Modelling}, volume = {2024}, journal = {Combustion Theory and Modelling}, publisher = {Taylor\&Francis}, issn = {1364-7830}, doi = {10.1080/13647830.2024.2428156}, pages = {1 -- 22}, abstract = {Large Eddy Simulation (LES) coupled with the Linear Eddy Model (LEM) provides a robust method for studying turbulent combustion, but it is computationally expensive due to the need for highly resolved sub-grid LEM domains. These domains simulate sub-grid stirring through stochastic rearrangements of scalar fields, while large-scale transport is modelled using a Lagrangian 'splicing' scheme. To address the computational cost of LES-LEM, a super-grid (SG) framework for LEM closure was developed by the authors (Comb. Theor. Model. 28, 2024), which uses coarse-graining, on-the-fly chemistry tabulation and a presumed PDF approach to reconstruct thermochemical fields at LES resolution. This study applies SG-LEM to a challenging setup, Case 1 of the Volvo Validation Rig, which involves a bluff-body-stabilised turbulent premixed propane-air flame, as a stress test to identify limitations that were not revealed by the previous application, in particular that of the coarse-graining parameters used to generate the super-grid. The intent is to yield a more realistically constrained assessment of the current capabilities of the method, and insight into possible ways for improving it. Four simulations were conducted using three SG cluster sizes. The finest resolution was tested with a global 2-step mechanism, showing good agreement with experimental data for temperature and velocity, particularly near the bluff body. The two larger cluster sizes used a 66-step skeletal mechanism for more detailed chemical closure but led to unphysical quenching due to splicing inaccuracies. To mitigate these issues, two novel additions were introduced: an intra-cluster-stirring routine and a method to control SG cluster shapes to reduce numerical dissipation. These methods improved flame stability with coarser SG clusters and more detailed mechanisms. Comparison with experiments showed good agreement for temperature and velocity, though elevated CO levels were observed in the recirculation region. Potential methods for further improving SG-LEM's capabilities are discussed.}, language = {en} } @misc{LignellBehrangKersteinetal., author = {Lignell, David O. and Behrang, Masoomeh and Kerstein, Alan R. and Wheeler, Isaac and Starick, Tommy and Schmidt, Heiko}, title = {Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model}, series = {77th Annual Meeting of the Division of Fluid Dynamics, November 24-26, 2024; Salt Lake City, Utah}, journal = {77th Annual Meeting of the Division of Fluid Dynamics, November 24-26, 2024; Salt Lake City, Utah}, publisher = {American Physical Society}, abstract = {Hierarchical Parcel Swapping (HiPS) is a stochastic model of turbulent mixing. HiPS is based on a binary tree structure consisting of nodes emanating from the top of the tree and terminating in parcels at the base of the tree containing fluid properties. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent mixing is modeled by swapping subtrees at different tree levels. Swaps involving single parcels result in micromixing that changes scalar states. Swaps are implemented as a Poisson process at rates corresponding to level time scales. HiPS is extended to simulation of multiple scalars with arbitrary diffusivities, considering transport in the inertial, viscous-advective, and inertial-diffusive ranges. Fundamental analysis of particle dispersion is presented with comparisons to theoretical results and DNS data in the inertial and viscous ranges. Scalar energy spectra are analysed in the three ranges and reproduce known scaling exponents. Scalar dissipation statistics are analysed and reproduce the experimental and theoretical lognormal distribution with negative skewness represented by a stretched-exponential function. DNS data are used to evaluate empirical coefficients, facilitating quantitative applications. The physical fidelity demonstrated with HiPS suggests its use as a low-cost subgrid model for coarse-grained flow simulation, for which parcel-pair mixing is a common treatment.}, language = {en} } @misc{StarickBehrangLignelletal., author = {Starick, Tommy and Behrang, Masoomeh and Lignell, David O. and Schmidt, Heiko and Kerstein, Alan R.}, title = {Turbulent mixing simulation using the Hierarchical Parcel-Swapping (HiPS) model}, series = {Technische Mechanik}, volume = {43}, journal = {Technische Mechanik}, number = {1}, issn = {0232-3869}, doi = {10.24352/UB.OVGU-2023-044}, pages = {49 -- 58}, abstract = {Turbulent mixing is an omnipresent phenomenon that permanently affects our everyday life. Mixing processes also plays an important role in many industrial applications. The full resolution of all relevant flow scales often poses a major challenge to the numerical simulation and requires a modeling of the small-scale effects. In transported Probability Density Function (PDF) methods, the simplified modeling of the molecular mixing is a known weak point. At this place, the Hierarchical Parcel-Swapping (HiPS) model developed by A.R. Kerstein [J. Stat. Phys. 153, 142-161 (2013)] represents a computationally efficient and novel turbulent mixing model. HiPS simulates the effects of turbulence on time-evolving, diffusive scalar fields. The interpretation of the diffusive scalar fields or a state space as a binary tree structure is an alternative approach compared to existing mixing models. The characteristic feature of HiPS is that every level of the tree corresponds to a specific length and time scale, which is based on turbulence inertial range scaling. The state variables only reside at the base of the tree and are understood as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub-trees at rates determined by turbulent time scales associated with the sub-trees. The mixing of adjacent fluid parcels is done at rates consistent with the prevailing diffusion time scales. In this work, a standalone HiPS model formulation for the simulation of passive scalar mixing is detailed first. The generated scalar power spectra with forced turbulence shows the known scaling law of Kolmogorov turbulence. Furthermore, results for the PDF of the passive scalar, mean square displacement and scalar dissipation rate are shown and reveal a reasonable agreement with experimental findings. The described possibility to account for variable Schmidt number effects is an important next development step for the HiPS formulation. This enables the incorporation of differential diffusion, which represents an immense advantage compared to the established mixing models. Using a binary structure allows HiPS to satisfy a large number of criteria for a good mixing model. Considering the reduced order and associated computational efficiency, HiPS is an attractive mixing model, which can contribute to an improved representation of the molecular mixing in transported PDF methods.}, language = {en} } @misc{BehrangStarickWheeleretal., author = {Behrang, Masoomeh and Starick, Tommy and Wheeler, Isaac and Schmidt, Heiko and Kerstein, Alan and Lignell, David}, title = {Hierarchical parcel-swapping representation of turbulent mixing : part 4 : extension to the viscous range and to mixing of scalars with non-unity Schmidt numbers}, series = {Journal of fluid mechanics}, volume = {1020}, journal = {Journal of fluid mechanics}, publisher = {Cambridge University Press}, address = {Cambridge}, issn = {0022-1120}, doi = {doi:10.1017/jfm.2025.10512}, pages = {1 -- 39}, abstract = {Hierarchical parcel swapping (HiPS) is a multiscale stochastic model of turbulent mixing based on a binary tree. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent eddies are represented by swapping subtrees. Lowest-level swaps change fluid parcel pairings, with new pairings instantly mixed. This formulation suitable for unity Schmidt number Sc is extended to non-unity Sc. For high Sc, the tree is extended to the Batchelor level, assigning the same time scale (governing the rate of swap occurrences) to the added levels as the time scale at the base of the Sc=3 tree. For low Sc, a swap at the Obukhov-Corrsin level mixes all parcels within corresponding subtrees. Well-defined model analogues of turbulent diffusivity, and mean scalar-variance production and dissipation rates are identified. Simulations idealising stationary homogeneous turbulence with an imposed scalar gradient reproduce various statistical properties of viscous-range and inertial-range pair dispersion, and of the scalar power spectrum in the inertial-advective, inertial-diffusive and viscous-advective regimes. The viscous-range probability density functions of pair separation and scalar dissipation agree with applicable theory, including the stretched-exponential tail shape associated with viscous-range scalar intermittency. Previous observation of that tail shape for Sc=1, heretofore not modelled or explained, is reproduced. Comparisons to direct numerical simulation allow evaluation of empirical coefficients, facilitating quantitative applications. Parcel-pair mixing is a common mixing treatment, e.g. in subgrid closures for coarse-grained flow simulation, so HiPS can improve model physics simply by smarter (yet nearly cost-free) selection of pairs to be mixed.}, language = {en} }