Production Terms Research Articles

Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers.

Large-eddy simulation of a temporally evolving Kelvin-Helmholtz (KH) mixing layer is performed with the tenth-order compact difference code miranda to examine the steady-state behavior of a passive scalar in a shear-driven mixing layer. It is shown that the integral behavior of scalar variance in a KH mixing layer behaves similarly to the integral behavior of scalar variance in a Rayleigh-Taylor (RT) mixing layer, and mixedness of the simulated KH shear layer tends towards a value of about 0.8. It is further shown that if the k-L-a-V Reynolds-averaged Navier-Stokes (RANS) model [B. E. Morgan et al., Phys. Rev. E 98, 033111 (2018)2470-004510.1103/PhysRevE.98.033111], calibrated to reproduce steady-state mixing in an RT layer, is applied to simulate a KH mixing layer, the RANS model will significantly overpredict the magnitude of scalar variance in the KH layer. A straightforward addition to the k-L-a-V model is then suggested, and self-similarity analysis is applied to determine constraints on model coefficients. It is shown that with the addition of a buoyancy production term in the model equation for scalar variance, it becomes possible to eliminate the model deficiency and match steady-state mixedness in simulations of both RT and KH mixing layers with a single model calibration.

Thermodynamics of scale-dependent Friedmann equations

In this work, the role of a time-varying Newton constant under the scale-dependent approach is investigated in the thermodynamics of the Friedman equations. In particular, we show that the extended Friedman equations can be derived either from equilibrium thermodynamics when the non-matter energy momentum tensor is interpreted as a fluid or from non-equilibrium thermodynamics when an entropy production term, which depends on the time-varying Newton constant, is included. Finally, a comparison between black hole and cosmological thermodynamics in the framework of scale-dependent gravity is briefly discussed.

A Lagrangian probability-density-function model for turbulent particle-laden channel flow in the dense regime

Modeling particle-laden turbulent flows at high volume fractions requires accounting for the coupling between phases. The latter is often a sensitive point, and proper closure of the exchange and production terms due to the presence of particles is not straightforward. In the present work, a Lagrangian probability-density-function model developed for homogeneous cluster-induced turbulence is extended to a channel flow. The key features are consistent two-way coupling and the decomposition of the particle velocity into spatially correlated and uncorrelated components, which is crucial for dense flows and which allows dealing with collisions from a statistical point of view. A numerical scheme for the coupled solution of the stochastic differential equations for the particles and a Reynolds-stress model for the fluid is developed. Tests with tracer particles without two-way coupling are done to assess the validity and the consistency of the numerical scheme. Finally, two sets of numerical simulations with particles with different diameters in a turbulent channel flow at a shear Reynolds of Reτ=300 are reported. The effect of two-way coupling by varying the mass loading of the dispersed phase in the mass-loading range φ= 0–2 is analyzed, and the results are compared to previous Eulerian–Lagrangian and Eulerian–Eulerian direct-numerical simulation (DNS) studies. Mean velocities and turbulent kinetic energy show good agreement with DNS, especially regarding the trend with respect to mass loading. Consistent with prior work, increased mass loading causes a drastic reduction of turbulent kinetic energy in the range φ= 0–2.

Uncertainty Quantification of Spalart–Allmaras Turbulence Model Coefficients for Compressor Stall

Abstract The turbulence model in Reynolds-averaged Navier–Stokes simulations is crucial in the prediction of the compressor stall margin. In this paper, parametric uncertainty of the Spalart–Allmaras turbulence model in predicting two-dimensional airfoil stall and three-dimensional compressor stall has been investigated using a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within physically acceptable ranges. The quantities of interest include characteristic curves, stall limit, blockage size, and turbulence magnitude. Results show that the characteristics can be well predicted in the stable flow range, but the inaccuracy and the uncertainty increase when approaching stall. The stall point of the airfoil can be enveloped by the parametric uncertainty range, but that of the rotor cannot. Sensitivity analyses identified the crucial model coefficients to be source related, where an increase in the predicted turbulence level will delay the onset of stall. Such results imply that implementing new turbulence production terms with respect to the rotor-specific flow features is likely to improve the model accuracy. The findings in this paper not only provide engineering rules of thumb for the model users but also guide the future implementation of a data-driven turbulence model for the model developers.

Formatting Elliptic Model From SST k-ω Closure

A single-equation turbulence model is devised from the shear-stress transport (SST) k-ω closure without an assumption of equal-diffusion coefficients; evolving diffusion/destruction terms are habitually avoided owing to their numerical stiffness and complexity. Rearranging retained terms yields a production term naturally with an elliptic identity in the R-equation and hence, the production term confronts an elliptic blending. A near-wall damping function is introduced with the elliptic-relaxation model in order to moderate the numerical burden on viscous length-scale coefficient. The overall approach represents a combination of wall-blocking (non-local) and wall-viscous (low-Reynolds number) effects encountered in anisotropic turbulence. A few well-documented test cases are utilised to validate the model competency; a good correlation is obtained with experimental and DNS (direct numerical simulation) data. Comparisons dictate that the present elliptic model remains competitive with widely used SST k-ω and Spalart-Allmaras models.

Time-resolved wake dynamics of finite wall-mounted circular cylinders submerged in a turbulent boundary layer

Abstract

Study on the characteristics of the pressure fluctuations and their contribution to turbulence kinetic energy

In this study, the integral and microscopic turbulent statistical characteristics of pressure fluctuations, applicability of the pressure gradient and pressure flux divergence to the Monin-Obukhov similarity theory (MOST), and contribution of the pressure transport term to turbulence kinetic energy (TKE) were analyzed using the turbulence observational data obtained from a field observational station over the Horqin Sandy Land in Inner Mongolia, China. The normalized standard deviations of the pressure fluctuations have no obvious relationship with the dimensionless stability parameter (z/L). The turbulent variance spectra of pressure fluctuations Sp(n) follow the n−2 scaling law with a peak frequency of approximately one to two orders of magnitude lower than that of the wind speed and temperature. The spectral gap also shifts to lower frequencies, and the transition from turbulent scale to the larger scale is sharper. The normalized vertical pressure gradient (κzp∗∂p¯∂z) has no significant relationship with z/L. The non-dimensional pressure transport term (φp=κzρ¯u∗3∂w'p'¯∂z) represents the pressure flux divergence and is well related to the z/L with expressions of φp = ± (1 − 14.5z/L) for unstable stratifications and φp = ± (1 + 15.0z/L) for stable stratifications. The relative importance of pressure transport term in the TKE budget equation with respect to the shear production and buoyancy terms is larger at larger scales. The pressure transport term is averagely one order of magnitude larger than the sum of these two terms at scales above 5 min. The contribution of the pressure transport term to the TKE is non-negligible.

Analytical solution of two-dimensional conservative solute transport in a heterogeneous porous medium for varying input point source

In the present study, an analytical solution is obtained for two-dimensional advection–dispersion equation with variable coefficients in a semi-infinite heterogeneous porous medium. Dispersion coefficient and groundwater velocity are assumed to vary temporally as well as spatially while the retardation factor varies spatially only. The first-order decay and zero-order production terms are also considered into account. The variations in parameters along both longitudinal and transverse directions are of exponentially decreasing nature. Initially the geological formation is considered not solute free. The nature of pollutant is considered of conservative and is assumed to be originating from time-dependent varying point source. New time and space variables are introduced to convert the variable coefficients of the advection–dispersion equation into constant coefficients. Analytical solution of the proposed model is obtained by employing Laplace integral transformation technique (LITT). The proposed analytical solution is illustrated graphically to study the effects of various parameters on the solute transport for temporally exponentially decreasing and sinusoidal nature velocities.

Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer

Abstract

Tropospheric ozone in CMIP6 simulations

Abstract. The evolution of tropospheric ozone from 1850 to 2100 has been studied using data from Phase 6 of the Coupled Model Intercomparison Project (CMIP6). We evaluate long-term changes using coupled atmosphere–ocean chemistry–climate models, focusing on the CMIP Historical and ScenarioMIP ssp370 experiments, for which detailed tropospheric-ozone diagnostics were archived. The model ensemble has been evaluated against a suite of surface, sonde and satellite observations of the past several decades and found to reproduce well the salient spatial, seasonal and decadal variability and trends. The multi-model mean tropospheric-ozone burden increases from 247 ± 36 Tg in 1850 to a mean value of 356 ± 31 Tg for the period 2005–2014, an increase of 44 %. Modelled present-day values agree well with previous determinations (ACCENT: 336 ± 27 Tg; Atmospheric Chemistry and Climate Model Intercomparison Project, ACCMIP: 337 ± 23 Tg; Tropospheric Ozone Assessment Report, TOAR: 340 ± 34 Tg). In the ssp370 experiments, the ozone burden increases to 416 ± 35 Tg by 2100. The ozone budget has been examined over the same period using lumped ozone production (PO3) and loss (LO3) diagnostics. Both ozone production and chemical loss terms increase steadily over the period 1850 to 2100, with net chemical production (PO3-LO3) reaching a maximum around the year 2000. The residual term, which contains contributions from stratosphere–troposphere transport reaches a minimum around the same time before recovering in the 21st century, while dry deposition increases steadily over the period 1850–2100. Differences between the model residual terms are explained in terms of variation in tropopause height and stratospheric ozone burden.

A nonlinear partially-averaged Navier–Stokes model with near-wall correction for separated turbulent flow

A nonlinear Partially-Averaged Navier–Stokes model with near-wall correction is developed for separated turbulent flow simulations. The periodic hills flow is simulated to validate the new model and the results are compared with the standard [Formula: see text] model, MPANS model, MSST PNAS model, standard [Formula: see text] PANS model, and experimental/LES results. It is found that the new model shows better performance in the prediction of both mean velocity and turbulent statistics compared to the other models. From the prediction of the near-wall friction coefficient of periodic hills flow, the new model shows good resolution in the near-wall region by considering the near-wall damping function to turbulent viscosity, gradient production term, and turbulence scale correction term for the near-wall region. From the analysis of anisotropy-invariant and sub-filtered stress (SFS), it can be found that the nonlinear term is necessary for prediction accuracy improvement in turbulent flow simulation with strong separation.

Energy budget analysis and neutral curve characteristics for the linear instability of Couette–Poiseuille flow

Here, we present some interesting new results on the linear modal stability of the Couette–Poiseuille flow (CPF), by numerically solving the Orr–Sommerfeld equation within the temporal framework. We provide a mechanistic explanation to the well-known result that the upper plate movement causes progressive stabilization of the CPF. The temporal energy budget reveals appearance of a region of negative energy production with plate movement, which is located near the plate that has a higher relative velocity in the direction of the bulk flow. This has a negative contribution to the integral production term, which, along with the expectation that energy dissipation is nominally constant (to leading order) at a given Reynolds number (Re), reduces the growth rate of kinetic energy, thereby causing flow stabilization with an increase in plate speed. Next, we compare the linear stability portrait of the CPF for positive and negative plate speeds and find that the upper and lower neutral branches in the frequency-Re plane cross over each other (to form a “loop”) for a certain range of negative plate speeds. Interestingly, this behavior is not seen for positive plate speeds. At high Re and small plate speeds (positive/negative), we observe that the CPF supports an additional unstable mode manifested in the neutral curves as a bifurcation of the unstable region into primary and secondary regions. The secondary unstable mode is found to be sufficiently distinct in character from the primary mode. These results contribute to the contemporary efforts to better understand the stability of the CPF.

Thermodynamic uncertainty relation for energy transport in a transient regime: A model study.

We investigate a transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy production. We explore this relation in the context of energy transport in a bipartite setting for three exactly solvable toy model systems (two coupled harmonic oscillators, two coupled qubits, and a hybrid coupled oscillator-qubit system) and analyze the role played by the underlying statistics of the transport carriers in the TUR. Interestingly, for all these models, depending on the statistics, the TUR ratio can be expressed as a sum or a difference of a universal term which is always greater than or equal to 2 and a corresponding entropy production term. We find that the generalized version of the TUR, originating from the universal fluctuation symmetry, is always satisfied. However, interestingly, the specialized TUR, a tighter bound, is always satisfied for the coupled harmonic oscillator system obeying Bose-Einstein statistics. Whereas, for both the coupled qubit, obeying Fermi-like statistics, and the hybrid qubit-oscillator system with mixed Fermi-Bose statistics, violation of the tighter bound is observed in certain parameter regimes. We have provided conditions for such violations. We also provide a rigorous proof following the nonequilibrium Green's function approach that the tighter bound is always satisfied in the weak-coupling regime for generic bipartite systems.

Effect of spatial dimension on a model of fluid turbulence

A numerical study of the $d$ -dimensional eddy damped quasi-normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and energy and transfer spectra are derived for the $d$ -dimensional case. Additionally, an equation for the $d$ -dimensional enstrophy analogue is derived and related to the velocity derivative skewness. Comparisons are made to recent four-dimensional direct numerical simulation results. Measured energy spectra show a magnified bottleneck effect which grows with dimension whilst transfer spectra show a varying peak in the nonlinear energy transfer as the dimension is increased. These results are consistent with an increased forward energy transfer at higher dimensions, further evidenced by measurements of a larger asymptotic dissipation rate with growing dimension. The enstrophy production term, related to the velocity derivative skewness, is seen to reach a maximum at around five dimensions and may reach zero in the limit of infinite dimensions, raising interesting questions about the nature of turbulence in this limit.

Micropolar medium in a funnel-shaped crusher

In this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia tensor containing a production term. The constitutive equations of the medium describe a linear viscous material with a viscosity coefficient depending on the characteristic particle moment of inertia, the so-called microinertia. A coupled system of equations is presented and solved numerically in order to determine the distribution of the fields for velocity, pressure, viscosity coefficient, and microinertia in all points of the continuum. The numerical solution to this problem is found by using the implicit finite difference method and the upwind scheme.

A mechanism for the amplification of interface distortions on liquid jets

Abstract

Improved compressible hybrid lattice Boltzmann method on standard lattice for subsonic and supersonic flows

A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation of both compressible subsonic and supersonic flows. This HLBM is an extension of the model of Feng et al. [1], which has been found, via different test cases, to be unstable for supersonic regimes. To circumvent this limitation, we propose:: (1) a new discretization of the lattice closure correction term that makes possible the simulation of supersonic flows, (2) a corrected viscous stress tensor that takes into account polyatomic gases, and (3) a novel discretization of the viscous heat production term fitting with the regularized formalism. The result is a hybrid method that resolves the mass and momentum equations with an LBM algorithm, and resolves the entropy-based energy equation with a finite volume method. This approach fully recovers the physics of the Navier–Stokes–Fourier equations with the ideal gas equation of state, and is valid from subsonic to supersonic regimes. It is then successfully assessed with both smooth flows and flows involving shocks. The proposed model is shown to be an efficient, accurate, and robust alternative to classic Navier–Stokes methods for the simulation of compressible flows.

Modeling of orientational polarization within the framework of extended micropolar theory

In this paper the process of polarization of transversally polarizable matter is investigated based on concepts from micropolar theory. The process is modeled as a structural change of a dielectric material. On the microscale it is assumed that it consists of rigid dipoles subjected to an external electric field, which leads to a certain degree of ordering. The ordering is limited, because it is counteracted by thermal motion, which favors stochastic orientation of the dipoles. An extended balance equation for the microinertia tensor is used to model these effects. This balance contains a production term. The constitutive equations for this term are split into two parts, one , which accounts for the orienting effect of the applied external electric field, and another one, which is used to represent chaotic thermal motion. Two relaxation times are used to characterize the impact of each term on the temporal development. In addition homogenization techniques are applied in order to determine the final state of polarization. The traditional homogenization is based on calculating the average effective length of polarized dipoles. In a non-traditional approach the inertia tensor of the rigid rods is homogenized. Both methods lead to similar results. The final states of polarization are then compared with the transient simulation. By doing so it becomes possible to link the relaxation times to the finally observed state of order, which in terms of the finally obtained polarization is a measurable quantity.

Large-Eddy Simulation of Unsteady Pitching Aerofoil using a Oneequation Subgrid Scale (SGS) Model based on Dynamic Procedure

Large-Eddy Simulations (LES) for an oscillating NACA0012 aerofoil at Reynolds number 1.35 × 105 have been performed to investigate the capability of a new approach of a One-equation SGS model. The phenomena of the oscillating aerofoil at higher amplitude angle (𝛼𝑎𝑚𝑝) is believed to produce deep dynamic stall in which strong non-equilibrium turbulence could also visible. Hence, a new approach of a one-equation SGS model is proposed where the coefficient of production term in the kSGS transport equation is defined dynamically. From the simulations, the leading-edge vortex (LEV), dynamic stall vortex (DSV), shedding mechanism and trailing edge vortex (TEV) are captured in this study.

Polytropic gas modelling at kinetic and macroscopic levels

<p style='text-indent:20px;'>In this paper, we consider the kinetic model of continuous type describing a polyatomic gas in two different settings corresponding to a different choice of the functional space used to define macroscopic quantities. Such a model introduces a single continuous variable supposed to capture all the phenomena related to the more complex structure of a polyatomic molecule. In particular, we provide a direct comparison of these two settings, and show their equivalence after the distribution function is rescaled and the cross section is reformulated. We then focus on the kinetic model for which the rigorous existence and uniqueness result in the space homogeneous case is recently proven. Using the cross section proposed in that analysis together with the maximum entropy principle, we establish macroscopic models of six and fourteen fields. In the case of six moments, we calculate the exact, nonlinear, production term and prove its total agreement with extended thermodynamics. Moreover, for the fourteen moments model, we provide new expressions for relaxation times and transport coefficients in a linearized setting, that yield both matching with the experimental data for dependence of the shear viscosity upon temperature and a satisfactory agreement with the theoretical value of the Prandtl number.