Investigation of high-pressure turbulent jets using direct numerical simulation

Direct numerical simulations of free round jets at a Reynolds number ($Re_{D}$) of $5000$, based on jet diameter ($D$) and jet-exit bulk velocity ($U_{e}$), are performed to study jet turbulence characteristics at supercritical pressures. The jet consists of $\mathrm{N_{2}}$ that is injected into $\mathrm{N_{2}}$ at same temperature. To understand turbulent mixing, a passive scalar is transported with the flow at unity Schmidt number. Two sets of inflow conditions that model jets issuing from either a smooth contraction nozzle (laminar inflow) or a long pipe nozzle (turbulent inflow) are considered. By changing one parameter at a time, the simulations examine the jet-flow sensitivity to the thermodynamic condition (characterized in terms of the compressibility factor ($Z$) and the normalized isothermal compressibility), inflow condition, and ambient pressure ($p_{\infty}$) spanning perfect- to real-gas conditions. The inflow affects flow statistics in the near-field (containing the potential core closure and the transition region) as well as further downstream (containing fully-developed flow with self-similar statistics) at both atmospheric and supercritical $p_{\infty}$. The sensitivity to inflow is larger in the transition region, where the laminar-inflow jets exhibit dominant coherent structures that produce higher mean strain rates and higher turbulent kinetic energy than in turbulent-inflow jets. Decreasing $Z$ at a fixed supercritical $p_{\infty}$ enhances pressure and density fluctuations (normalized by local mean pressure and density, respectively), but the effect on velocity fluctuations depends also on local flow dynamics. When $Z$ is reduced, large mean strain rates in the transition region of laminar-inflow jets significantly enhance velocity fluctuations (normalized by local mean velocity) and scalar mixing, whereas the effects are minimal in jets from turbulent inflow.Comment: In pres

Investigation of high-pressure turbulent jets using direct numerical simulation

Direct numerical simulations of free round jets at a Reynolds number (Re_D) of 5000, based on jet diameter (D) and jet-exit bulk velocity (U_e), are performed to study jet turbulence characteristics at supercritical pressures. The jet consists of Nitrogen (N₂) that is injected into N₂ at same temperature. To understand turbulent mixing, a passive scalar is transported with the flow at unity Schmidt number. Two sets of inflow conditions that model jets issuing from either a smooth contraction nozzle (laminar inflow) or a long pipe nozzle (turbulent inflow) are considered. By changing one parameter at a time, the simulations examine the jet-flow sensitivity to the thermodynamic compressibility factor (Z), inflow condition, and pressure (p) spanning perfect- to real-gas conditions. The inflow affects flow statistics in the near-field (containing the potential core closure and the transition region) as well as further downstream (containing fully-developed flow with self-similar statistics) at both atmospheric and supercritical p. The sensitivity to inflow is larger in the transition region, where the laminar-inflow jets exhibit dominant coherent structures that produce higher mean strain rates and higher turbulent kinetic energy than in turbulent-inflow jets. Decreasing Z at a fixed supercritical ambient pressure (p∞) enhances pressure and density fluctuations (non-dimensionalized by local mean pressure and density, respectively), but the effect on velocity fluctuations depends also on local flow dynamics. When Z is reduced, large mean strain rates in the transition region of laminar-inflow jets significantly enhance velocity fluctuations (non-dimensionalized by local mean velocity) and scalar mixing, whereas the effects of decreasing Z are minimal in jets from turbulent inflow

Time-stable high-order finite difference methods for overset grids

Overset grids provide an efficient and flexible framework for implementing high-order finite difference methods to simulate compressible viscous flows over complex geometries. Although overset methods have been widely used to solve time-dependent partial differential equations, very few proofs of stability exist for them. In practice, the interface treatments for overset grids are stabilized by adding numerical dissipation without any underlying theoretical analysis, impacting the accuracy and the conservation properties of the original method. In this work we discuss the construction of a provably time-stable and conservative method for solving hyperbolic problems on overset grids as well as their extension to solve the compressible Navier-Stokes equations. The proposed method uses interface treatments based on the simultaneous approximation term penalty method, and derivative approximations that satisfy the summation-by-parts property. Two cases of the method are analyzed. In the first case, no artificial dissipation is used and an eigenvalue analysis of the system matrix is performed to establish time-stability. The eigenvalue analysis approach for proving stability fails when the system matrix is not of a block triangular structure; therefore, we investigate the second case of the method where a localized numerical dissipation term is added to allow the use of energy method for stability proof. A framework for examining the conservation properties of the proposed method is discussed. Error analyses are performed to determine the order of interpolation that retains the accuracy of spatial finite difference operator. The performance of the proposed method is assessed against the commonly used approach of injecting the interpolated data onto each grid. Several one-, two- and three-dimensional, linear and non-linear numerical examples are presented to confirm the stability and the accuracy of the methods. The extension of the method to solve the three-dimensional compressible Navier-Stokes equations on curvilinear grids is examined by performing a large-eddy simulation of flow over a cosine-shaped hill

Mixing, scalar boundedness, and numerical dissipation in large-eddy simulations

Numerical schemes for scalar transport and mixing in turbulent flows must be high-order accurate, and observe conservation and boundedness constraints. Discretization accuracy can be evaluated from the truncation error, and assessed by its dispersion and dissipation properties. Dispersion errors can cause violation of physical scalar bounds, whereas numerical dissipation is key to mitigating those violations. Numerical dissipation primarily alters the energy at small scales that are critical to turbulent mixing. Influence of additional dissipation on scalar mixing in large-eddy simulations (LES) of incompressible temporally evolving shear flow is examined in terms of the resolved passive-scalar field, z. Scalar fields in flows with different mixing behavior, exhibiting both uniform and non-uniform mixed-fluid composition across a shear layer, are compared for different grid resolutions, subgrid-scale models, and scalar-convection schemes. Scalar mixing is assessed based on resolved passive scalar probability density function (PDF), variance, and spectra. The numerical-dissipation influence on mixing is found to depend on the nature of the flow. Mixing metrics sensitive to numerical dissipation are applied to examine the performance of limiting methods employed to mitigate unphysical scalar excursions. Two approaches, using a linear-scaling limiter for finite-volume schemes and a monotonicity-preserving limiter for finite-difference schemes, are studied. Their performance with respect to accuracy, conservation, and boundedness is discussed

Numerical aspects for physically accurate Direct Numerical Simulations of turbulent jets

Numerical simulations of turbulent isothermal round jets are performed at Reynolds number (based on jet diameter and jet orifice velocity) of 5000 and Mach number of 0.6 to assess influences of initial perturbation, numerical characterization, and boundary treatments on turbulence statistics. The aper documents preliminary results from an investigation eventually aimed at examining multicomponent species injection and mixing at high-pressure conditions relevant to combustion in diesel, gas-turbine and liquid-rocket engines. Lack of reliable experimental or computational results at high pressures of interest make code validation at those conditions infeasible. Therefore, single-species simulations at perfect-gas conditions are first performed to assess turbulence statistics sensitivity to numerical setup. Two cases with different inflow velocity perturbation amplitude are considered to examine influences on jet flow transition and self-similarity

Estimativas de parâmetros genéticos de características reprodutivas de ovinos Santa Inês utilizando inferência Bayesiana

The objective of this study was to estimate the values of the (co)variance components and genetic parameters for reproductive traits in Santa Inês sheep raised in different states and registered with the Associação Sergipana dos Criadores de Caprinos e Ovinos (Goat and Sheep Breeders Association of Sergipe). The database used was provided by the Association and comprised pedigree observations originating from 11,483 registered individuals, out of which 2,238 were born in the program and had calving records, being part of the relationship matrix. After restriction application, there remained 843 animals for analysis which had data related to the age at first calving (IPP1), 151 with data related to the median calving interval (IPM2), and 151 to the interval between first and second calvings (IPS3). To obtain the values of (co)variance components and genetic parameters, we used the Bayesian inference under an animal model with the Gibbs sampling algorithm aided by the MTGSAM program. The two-trait linear model used considered the contemporary group as the fixed effect for IPP1, IPM2, and IPS3, and the type of calving and the age of the animal at calving as the covariate effect. The estimated values of h2 for IPP1, IPM2, and IPS3 were equal to 0.19 ± 0.0459, 0.0169 ± 0:36, and 0:35 ± 0.016 respectively. The estimated heritability for IPP1is considered average and the values for IPM2 and IPS3 were considered high, which leads to the conclusion that these characteristics can be used as selection criteria in a breeding program of Santa Inês sheep. The estimated value for the correlation between IPP1 and IPM2, and IPP1 and IP2, were negative and equal to rg12 = -0.2569 ± 0.0546, rg13= -0.1134 ± 0.0553, which were physiological expected low values that represent a trend which suggests individual selection for those traits. However, the rg23 shows a positive and high trend of 0.9601 ± 0.0091 for IPM2 and IPS3 suggesting indirect selection as the best option for these traits.Objetivou-se estimar componentes de (co)variância e parâmetros genéticos para características reprodutivas de ovinos Santa Inês, criados em diferentes estados e registrados na Associação Sergipana dos Criadores de Caprinos e Ovinos. O banco de dados utilizado foi fornecido por esta associação, composto por observações de pedigree originadas de 11.483 indivíduos registrados dos quais 2.238 eram nascidos no programa e tinham registro de parto, permanecendo na matriz de parentesco. Após a aplicação das restrições, foram mantidas na análise 843 animais com dados referentes a característica idade ao primeiro parto (IPP1), 151 referentes a intervalo médio ao parto (IPM2) e 151 para intervalo entre primeiro e segundo parto (IPS3). Para obter os valores dos componentes de (co)variância e parâmetros genéticos utilizou-se analise bayesiana sob modelo animal mediante o algorismo Amostrador de Gibbs com o auxilio do programa MTGSAM. O modelo linear bicaracterística utilizado considerava como efeito fixo o grupo contemporâneo para as características IPP1, IPM2 e IPS3, considerou-se o efeito do tipo de parto e a idade do animal ao parto como efeito (co)variável. Os valores de h2 estimados para IPP1, IPM2 e IPS3 foram iguais a 0.19±0.0459, 0.36±0.0169 e 0.35±0.016 respectivamente. O valor estimado da herdabilidade para IPP1 é considerado médio e os valor para IPM2 e IPS3 alto, fato que leva a concluir que estas característica podem ser usadas como critério de seleção em um programa de melhoramento de ovinos da raça Santa Inês. O valor estimado para a correlação entre características IPP1 e IMP2; IPP1 e IPS2 foram negativos e iguais a rg12= -0.2569 ± 0.0546, rg13= -0.1134 ± 0.0553 valores fisiologicamente esperados de baixa magnitude que sugerem seleção individual para essas características, entretanto para IPM2 e IPS3 a rg23 mostra tendência positiva e muito elevada igual a rg23= 0.9601 ± 0.0091 valor que indica a seleção indireta o melhor caminho