Nonequilibrium Boundary Layer Research Articles

A dynamic linearized wall model for turbulent flow simulation: towards grid convergence in wall-modeled simulations

This paper addresses the common issue of (no-)grid convergence in wall-modeled numerical simulations and proposes a dynamic linearization technique applied to the Spalart-Allmaras wall model to achieve a proper behavior on fine grids and low-friction areas. A theoretical analysis of the numerical error committed on the shear stress balance close to the walls is performed. It shows that the error is due to the inappropriate imposition of too steep wall-normal velocity gradients that cannot be properly accounted for on the typical grids used for wall-modeled simulations. Based on this error quantification, a dedicated wall model linearization technique is proposed, following the approach developed by Tamaki, Harada and Imamura in 2017. In the proposed modified linearization method, the linearization distance is modified and adjusted dynamically. This is done according to the theoretical shear stress error estimate, in order to keep the numerical error below a user-defined threshold. The method is applied to well-referenced test cases of increasing complexity from the Turbulence Modeling Resource. Overall, the proposed wall model clearly exhibits appropriate grid convergence properties and is also able to predict accurately non-equilibrium boundary layers and flow separation using proper grid refinement.

Data-driven wall modeling for LES involving non-equilibrium boundary layer effects

PurposeWall-modeled large eddy simulation (LES) is a practical tool for solving wall-bounded flows with less computational cost by avoiding the explicit resolution of the near-wall region. However, its use is limited in flows that have high non-equilibrium effects like separation or transition. This study aims to present a novel methodology of using high-fidelity data and machine learning (ML) techniques to capture these non-equilibrium effects.Design/methodology/approachA precursor to this methodology has already been tested in Radhakrishnan et al. (2021) for equilibrium flows using LES of channel flow data. In the current methodology, the high-fidelity data chosen for training includes direct numerical simulation of a double diffuser that has strong non-equilibrium flow regions, and LES of a channel flow. The ultimate purpose of the model is to distinguish between equilibrium and non-equilibrium regions, and to provide the appropriate wall shear stress. The ML system used for this study is gradient-boosted regression trees.FindingsThe authors show that the model can be trained to make accurate predictions for both equilibrium and non-equilibrium boundary layers. In example, the authors find that the model is very effective for corner flows and flows that involve relaminarization, while performing rather ineffectively at recirculation regions.Originality/valueData from relaminarization regions help the model to better understand such phenomenon and to provide an appropriate boundary condition based on that. This motivates the authors to continue the research in this direction by adding more non-equilibrium phenomena to the training data to capture recirculation as well.

Receptivity of Mack modes to localized unsteady blowing and suction in a chemical non-equilibrium hypersonic boundary layer

Receptivity of Mack modes to localized unsteady blowing and suction in a chemical non-equilibrium hypersonic boundary layer

Strategies for Computational Fluid Dynamics Validation Experiments

Abstract The Benchmark Validation Experiment for Reynolds-averaged Navier–Stokes (RANS)/large eddy simulation (LES) Investigations (BeVERLI) aims to produce an experimental dataset of three-dimensional non-equilibrium turbulent boundary layers with various levels of separation that, for the first time, meets the most exacting requirements of computational fluid dynamics validation. The application of simulations and modeling in high-consequence engineering environments has become increasingly prominent in the past two decades, considerably raising the standards and demands of model validation and forcing a significant paradigm shift in the design of corresponding validation experiments. In this paper, based on the experiences of project BeVERLI, we present strategies for designing and executing validation experiments, hoping to ease the transition into this new era of fluid dynamics experimentation and help upcoming validation experiments succeed. We discuss the selection of a flow for validation, the synergistic use of simulations and experiments, cross-institutional collaborations, and tools, such as model scans, time-dependent measurements, and repeated and redundant measurements. The proposed strategies are shown to successfully mitigate risks and enable the methodical identification, measurement, uncertainty quantification, and characterization of critical flow features, boundary conditions, and corresponding sensitivities, promoting the highest levels of model validation experiment completeness per Oberkampf and Smith [1]. Furthermore, the applicability of these strategies to estimating critical and difficult-to-obtain bias error uncertainties of different measurement systems, e.g., the underprediction of high-order statistical moments from particle image velocimetry velocity field data due to spatial filtering effects, and to systematically assessing the quality of uncertainty estimates is shown.

History effects and wall-similarity of non-equilibrium turbulent boundary layers in varying pressure gradient over rough and smooth surfaces

Experimental investigations were conducted on non-equilibrium, turbulent boundary layers over rough and smooth surfaces. A NACA 0012 airfoil was systematically rotated to generate a family of bi-directional pressure fields on the research surface. The rough surface consisted of 2mm tall, staggered, circular cylindrical elements producing flow conditions that were in the fully rough regime. The velocity fields were measured using a custom Pitot-probe boundary layer rake and time-resolved particle image velocimetry (TR-PIV). The primary effect of the roughness was to increase the magnitude of the outer layer and skin friction parameters. Flows over both wall conditions exhibited “history effects” in the integrated boundary layer parameters, which indicates characteristic dependencies on the streamwise flow evolution. Indirect skin friction methods for non-equilibrium rough wall flows were sensitive to the regression fits of the empirical data, which were used in the absence of direct measurements. The effective sandgrain roughness parameter, ks, remained independent of pressure gradient flow history, within the uncertainty of empirical methods used for skin friction determination. Varying levels of wall-similarity were observed in the smooth and rough wall Reynolds stress profiles. Although past evaluations of wall-similarity have suggested that a sufficiently large boundary layer thickness to ks is sufficient for wall-similarity, the present results indicate a need for additional multivariable considerations including matching flow histories and considering local Reynolds numbers measurement resolution.

Comparison of smooth- and rough-wall non-equilibrium boundary layers with favourable and adverse pressure gradients

Measurements were made in rough-wall boundary layers subject to favourable, zero and adverse pressure gradients. Profiles of mean velocity and turbulence quantities were acquired and velocity fields were measured in multiple planes to document flow structure. Comparisons were made to equivalent smooth-wall cases with the same free stream velocity distributions. Outer layer similarity was observed between the rough- and smooth-wall cases in all quantities in the favourable and zero pressure gradient regions, but large differences were observed with adverse pressure gradients. In both the smooth- and rough-wall cases, the favourable pressure gradient reduced the turbulence in the boundary layer, and increased the size of turbulence structures relative to the boundary layer thickness in both the streamwise and spanwise directions, while lowering their inclination angle with respect to the wall. When the boundary layer was returned to a zero pressure gradient following the favourable pressure gradient region, the turbulence level and the size and inclination of the structures returned to their canonical zero pressure gradient condition. The response of the boundary layer was somewhat faster in the rough-wall case, causing it to reach equilibrium in a shorter streamwise distance after the changes in pressure gradient than in the smooth-wall case. The adverse pressure gradient increased turbulence levels relative to the wall friction velocity, reduced the size of turbulence structures relative to the boundary layer thickness and increased their inclination angle. The changes with the adverse pressure gradient were significantly larger with the rough wall than the smooth. The results suggest that similarity might be achieved with adverse pressure gradients if smooth- and rough-wall cases with the same Clauser pressure gradient parameter history are compared.

Modeling the Surface Pressure Spectrum Beneath Turbulent Boundary Layers in Pressure Gradients

A wide variety of models and methods for the prediction of the surface pressure spectrum beneath turbulent boundary layers is presented and assessed. A thorough review is made of the current state of the art in empirical and analytical pressure spectrum models; and predictions of zero, adverse, favorable, and nonequilibrium pressure gradient boundary layers are examined using a steady Reynolds-averaged Navier–Stokes (RANS) prediction of a subset of a pressure gradient boundary-layer benchmark flow case. The existing empirical models show either an inability to adapt to pressure gradient conditions or an oversensitivity to model inputs, producing nonphysical results under certain flow conditions. New empirical models are created using a gene expression programming machine-learning algorithm based on both experimental and RANS inputs. The various input options for analytical Toegepast Natuurwetenschappelijk Onderzoek (TNO) modeling are presented and assessed, and recommendations for best practices are made. The developed models show improvement in both accuracy and robustness over existing models.

Turbulence Model Comparative Study for Complex Phenomena in Supersonic Steam Ejectors with Double Choking Mode.

Scholars usually ignore the non-equilibrium condensing effects in turbulence-model comparative studies on supersonic steam ejectors. In this study, a non-equilibrium condensation model considering real physical properties was coupled respectively with seven turbulence models. They are the k-ε Standard, k-ε RNG, k-ε Realizable, k-ω Standard, k-ω SST, Transition SST, and Linear Reynolds Stress Model. Simulation results were compared with the experiment results globally and locally. The complex flow phenomena in the steam ejector captured by different models, including shock waves, choking, non-equilibrium condensation, boundary layer separation, and vortices were discussed. The reasons for the differences in simulation results were explained and compared. The relationship between ejector performance and local flow phenomena was illustrated. The novelty lies in the conclusions that consider the non-equilibrium condensing effects. Results show that the number and type of shock waves predicted by different turbulence models are different. Non-equilibrium condensation and boundary layer separation regions obtained by various turbulence models are different. Comparing the ejector performance and the complex flow phenomena with the experimental results, the k-ω SST model is proposed to simulate supersonic steam ejectors.

Modeling of Thermochemical Nonequilibrium Flows Using Open-Source Direct Simulation Monte Carlo Kernel SPARTA

Chemical reactions are usually coupled with transfer of internal energies in high-temperature gas and have been an ongoing challenge for the direct simulation Monte Carlo (DSMC) method. In this paper, three typical reaction models are compared quantitatively, and the impact of vibrational favoring effects as well as three-body recombination are analyzed. The recently developed open-source DSMC kernel SPARTA is employed and modified in the present study. The verification results indicate that the SPARTA code produces a satisfactory description of the nonequilibrium reacting flow. A further application is made to the hypersonic nonequilibrium boundary-layer flows past an obstacle. It is found that SPARTA is in excellent agreement with continuum-based method for the low-altitude condition (); however, considerable differences arise at high altitudes () due to locally rarefied gas effects.

Momentum boundary-layer characterisation from a pulsed impinging jet

The development of the unsteady boundary layer produced from an impinging jet with a temporal puslation forms part of the complex flow physics occurring within an internal combustion engine and its characterisation is crucial for improved modelling with lower-fidelity tools. The momentum boundary layer prediction of these flows currently relies on wall-modelling based on the logarithmic law of the wall for equilibrium zero pressure gradient boundary layers. However, it is not fully understood how these non-equilibrium boundary layers evolve and whether the reliance on the law of the wall is justified for modelling such flows. Thus, in this paper, we attempt to characterise the momentum boundary layer developing from a pulsed impinging jet through the use of highly-resolved large eddy simulations of a canonical setup. The simulations are conducted for three peak jet Reynolds numbers of 10,000, 20,000 and 50,000, achieved at the peak of the temporal pulse. The resulting boundary layer produced by the jet impingement is examined for the mean flow, the scaling of the outer-layer and the boundary layer parameters, such as the boundary layer thickness, the friction Reynolds number and the wall-scaled profiles. The effect of the jet Reynolds number on the different parameters is also evaluated statistically as well as temporally. The results show that the boundary layer’s development is highly unsteady, even statistically, with a large variation in the friction Reynolds number over the statistical sampling period. However, most of the values were found to be lower than the values seen for turbulent boundary layers. This leads to an at least 40% overprediction in the wall-scaled velocity when using the equilibrium law of the wall for modelling these boundary layers. The predictions of the wall-friction using the equilibrium law of the wall and select turbulence models was also tested and it was found that the latter could be useful as a recourse to the near-wall modelling of these flows.

Pulsed impinging jets: Momentum and heat-transfer

With increasing efficiencies of internal combustion engines, the accurate prediction of the heat transfer across walls, such as from temporally varying impinging jets, is of significant importance. To avoid the excessive cost of fully resolved simulations, this prediction often relies upon the modelling of the resulting non-equilibrium boundary layer using wall functions. Given the unsteady nature of the problem, it is important to understand the development of these boundary layers under non-equilibrium conditions and assess whether existing wall functions are suitable for modelling such flows. Thus, in this paper, the momentum and thermal boundary layers developing from a single pulsed impinging jet are investigated through the use of highly-resolved large eddy simulations of a representative canonical set-up. The simulations are conducted for three jet Reynolds numbers of 20,000, 50,000 and 100,000, based on the peak velocity of the temporal pulse. The jets are simulated at temperature ratios of 0.25 and 0.8, where the ratio is defined as the temperature of the wall to the centreline temperature of the jet. The resulting boundary layers produced by the jets’ impingement are examined in terms of the mean flow, the wall shear stress, wall heat-flux, and the wall-scaled profiles of velocity and temperature. Where possible, the results are used to test select wall functions, and it is observed that the momentum boundary layer is over-predicted with the classic log-law of the wall while the thermal boundary layer can be predicted to a certain degree with certain wall functions, particularly in cases where the Reynolds analogy is valid for the data used to compute the temperature profile.

Formula neiterativnog modela zida za neravnotežne tokove graničnog sloja

A novel non-iterative (explicit) formulation of generalized wall functions that applies to equilibrium and non-equilibrium boundary layer flows was proposed. The proposed formulation uses a set of variables that are more useful for computational fluid dynamics codes as they allow for calculating wall shear stress without an iterative procedure. In addition, an explicit form of the formulation was provided that applies to wall models with and without pressure gradients. The new variable transformation casts the generalizedwall function into a new form that simplifies the implementation and evaluation of wall-shear stress in computational codes.

Turbulence structure in non-equilibrium boundary layers with favorable and adverse pressure gradients

An experimental study was conducted to document the turbulence in boundary layers on smooth walls subject to a favorable pressure gradient followed by a zero pressure gradient recovery and an adverse pressure gradient. Two component velocity profiles were acquired along the spanwise centerline of the test section, and velocity fields were obtained at the same locations in streamwise wall-normal and streamwise–spanwise planes using PIV. The FPG was shown to reduce the turbulence in the outer part of the boundary layer, reducing the transport of this turbulence and the effect of sweeps toward the wall. This reduced the inclination angle of the large structures and increased their length scale, particularly in the streamwise and spanwise directions. Recovery from the FPG to a ZPG was rapid. The APG reduced the near wall shear, resulting in a reduced effect of ejections relative to sweeps. The APG had an opposite but smaller effect on the shape and size of structures compared to the FPG.

Direct numerical simulation of a non-equilibrium three-dimensional turbulent boundary layer over a flat plate

Abstract

A DNS/URANS approach for simulating rough-wall turbulent flows

A novel hybrid method combining direct numerical simulation (DNS) and the Reynolds-averaged Navier Stokes (RANS), denoted as a stress-blended method (SBM), has been developed. The SBM is targeted at simulating turbulent flows over arbitrary rough surfaces in which computational savings can be achieved by making the DNS domain as small as possible. Within the SBM framework, a RANS model is enforced above the roughness layer to prevent the momentum build-up which arises in simulations where the computational domain is too small to represent the largest eddies. The SBM is validated for turbulent channel flow, both for smooth wall turbulence and using a parametric forcing approach to mimic roughness effects, with a computational cost that scales linearly with Reτ. The method is then applied to selected subsets of a scanned grit-blasted surface. For the same subset, the roughness function is found to be within 1% of available DNS. Comparisons of small and large subsets showed differences of over a factor of two in equivalent sand grain roughness, indicating the importance of choosing representative surface samples. Simulations in the fully rough regime are carried out using one to two orders of magnitude fewer points than in a typical DNS. Since no assumptions on the roughness properties or the flow structure (such as outer layer similarity) are made, we expect the SBM to be applicable to non-equilibrium turbulent boundary layer flows.

Effect of a bidirectional coupling of an LTE arc column to a refractory cathode in atmospheric pressure argon

An appropriate coupling of an arc plasma column in the state of local thermodynamic equilibrium to a refractory cathode necessarily involves the non-equilibrium boundary layer between them. A model has been developed that combines a model of an equilibrium direct current arc plasma in atmospheric pressure argon with the assembly of a cathode made of tungsten and the boundary layer. A bidirectional coupling has been realized that allows us to consider a variable voltage drop across the boundary layer for different positions on the cathode. The results are obtained for arc currents between 10 and 150 A in the cases of both a unidirectional and a bidirectional coupling. The results show differences in the distributions of the temperature and the normal current density on the cathode surface and the radial and axial distributions of the plasma temperature. Comparison with the results of a fully non-equilibrium model of the arc plasma and experimental findings from optical emission spectroscopy shows a fair agreement for currents, where the deviations from equilibrium in the arc column can be ignored. For arc currents beyond 100 A, the arc attachment on the cathode appears in two forms, which differ from each other in the distributions of the temperature and the normal current density on the cathode surface, whereas the values of the total arc voltage are close to each other.

Competition mechanism during oxidation of pyrolysis gases in nonequilibrium boundary layer on thermal protection performance of charring composites

AbstractThe influence of gas‐phase reactions in chemical nonequilibrium boundary layer on the thermal protection performance of charring materials has been analyzed in this work. These reactions are exothermic and compose of oxidation between the multicomponent pyrolysis gases and the oxidative gas components in the chemical nonequilibrium hypersonic boundary layer. During the reactions, the consumption amount of oxidizing components competes with the amount of exothermicity of gas‐phase oxidation reactions. We built the physical and mathematical models for the coupling of thermal and ablative responses of material, hypersonic flow response, and chemical response in chemical nonequilibrium boundary layer. Moreover, a new surface energy balance equation is built for bridging the multifield coupling mathematical models. In addition, the exothermic heat produced from the oxidation reactions of multicomponent pyrolysis gases is taken into consideration. The numerical example for the fluid‐chemical‐thermal‐ablative coupled behavior for a charring ablator and its environment for an Apollo‐like reentry vehicle in chemical nonequilibrium is simulated by using our two‐way coupling computer codes. Numerical results indicate that the oxidation of multicomponent pyrolysis gases in chemical nonequilibrium boundary layer weakens the mass ablation of surface char. Although the pyrolysis gas in the nonequilibrium boundary layer oxidizes and releases heat, the weakening effect of oxygen consumption on the surface is much more significant, especially when the cold heat flux is smaller.

Effects of upstream perturbations on the solution of the laminar and fully turbulent boundary layer equations with pressure gradients

The aim of this work is to contribute to the understanding of sensitivity of boundary layers to the upstream boundary condition and history effects for both laminar and fully turbulent states in equilibrium conditions as well as some nonequilibrium turbulent boundary layers. Solutions of the two-dimensional boundary layer equations are obtained numerically for this study together with the Reynolds-averaged Navier-Stokes approach for turbulence modeling. The external pressure gradient is imposed through an evolution of the external velocity of the form Ue∝(x−x0)m, and boundary layers are initialized from a profile giving a perturbed shape factor. It is found that laminar boundary layers require very long distances for convergence toward the nondisturbed profiles in terms of the initial boundary layer thickness (∼104δin) and that this distance is dependent on m. In turbulent boundary layers, much shorter distances, although still large (∼102δin), are observed and they are also dependent on m. The maximum adverse pressure gradient for which convergence to a reference solution is possible is also studied finding that there is no limit for attached laminar boundary layers, whereas turbulent boundary layers do not converge once they are out of equilibrium. The convergence distances in turbulent boundary layers are also studied in terms of the turnover length (δUe+) because it has been shown to be more appropriate to refer the convergence distance to this length rather than the boundary layer thickness. The values for convergence using this criterion are extended to pressure gradient boundary layers. Moreover, an equivalent criterion is proposed and studied for laminar boundary layers based on the viscous characteristic time.

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1,000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressure-strain correlation which ultimately inhibits the generation of Reynolds stress. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium, three-dimensional flows.

The Design and Validation of a Thermal Boundary Layer Wall Plate

A feedback controlled thermal wall plate designed to investigate thermal boundary layer flows is described and validated. The unique capabilities of the design are the ability to modify the thermal boundary conditions in a variety of ways or to hold the wall-temperature fixed even when the flow above the wall is unsteady and strongly three-dimensional. These capabilities allow for the generation and study of thermal transport in nonequilibrium boundary layer flows driven by different perturbations and of varying complexity. The thermal wall plate and the experimental facility in which the thermal wall plate is installed are first described. The wall-plate is then validated in a zero-pressure-gradient (ZPG) boundary layer flow for conditions of a uniform wall temperature and a temperature step. It is then shown that the wall temperature can be held constant even when a hemisphere body is placed on the wall that produces large localized variations in the convective heat transfer coefficient. Last, since the thermal wall plate is intended to support the study of thermal transport in a variety of nonequilibrium boundary layer flow, several possible experimental configurations are presented and described.