On the effects of turbulence modelling in design optimisation for high-lift devices

Aerodynamic shape optimisation is being increasingly utilised as a design tool in the aerospace industry. In order to provide accurate results, design optimisation methods rely on the accuracy of the underlying CFD methods applied to obtain aerodynamic forces for a given configuration. Previous studies of the authors have highlighted that the variation of the order of accuracy of the CFD solver with a fixed turbulence model affects the resulting optimised airfoil shape for a single element airfoil. The accuracy of the underlying CFD model is even more relevant in the context of high-lift configurations where an accurate prediction of flow is challenging due to the complex flow physics involving transition and flow separation phenomena. This paper explores the effect of the fidelity of CFD results for a range of turbulence models within the context of the computational design of aircraft configurations. The NLR7301 multi-element airfoil (main wing and flap) is selected as the baseline configuration, because of the wealth of experimental an computational results available for this configuration. An initial validation study is conducted in order to establish optimal mesh parameters. A bi-objective shape optimisation problem is then formulated, by trying to reveal the trade-off between lift and drag coefficients at high angles of attack. Optimisation of the airfoil shape is performed with Spalart-Allmaras, k - ω SST and k - o realisable models. The results indicate that there is consistent and complementary impact to the optimum level achieved from all the three different turbulence models considered in the presented case study. Without identifying particular superiority of any of the turbu- lence models, we can say though that each of them expressed favourable influence towards different optimality routes. These observations lead to the exploration of new avenues for future research. © 2012 AIAA.

On the effects of turbulence modelling in design optimisation for high-lift devices

Aerodynamic shape optimisation is being increasingly utilised as a design tool in the aerospace industry. In order to provide accurate results, design optimisation methods rely on the accuracy of the underlying CFD methods applied to obtain aerodynamic forces for a given configuration. Previous studies of the authors have highlighted that the variation of the order of accuracy of the CFD solver with a fixed turbulence model affects the resulting optimised airfoil shape for a single element airfoil. The accuracy of the underlying CFD model is even more relevant in the context of high-lift configurations where an accurate prediction of flow is challenging due to the complex flow physics involving transition and flow separation phenomena. This paper explores the effect of the fidelity of CFD results for a range of turbulence models within the context of the computational design of aircraft configurations. The NLR7301 multi-element airfoil (main wing and flap) is selected as the baseline configuration, because of the wealth of experimental an computational results available for this configuration. An initial validation study is conducted in order to establish optimal mesh parameters. A bi-objective shape optimisation problem is then formulated, by trying to reveal the trade-off between lift and drag coefficients at high angles of attack. Optimisation of the airfoil shape is performed with Spalart-Allmaras, k - ω SST and k - ε realisable models. The results indicate that there is consistent and complementary impact to the optimum level achieved from all the three different turbulence models considered in the presented case study. Without identifying particular superiority of any of the turbu- lence models, we can say though that each of them expressed favourable influence towards different optimality routes. These observations lead to the exploration of new avenues for future research. © 2012 by the authors.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bayesian analysis of random regression models using B-splines to model test-day milk yield of Holstein cattle in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Genetic and environmental effects on age at first farrowing in sows in southeastern Brazil

We evaluated genetic and environmental factors affecting age at first farrowing of sows in the Brazilian southeast. For this purpose, 466 observations regarding the age at first farrowing were made for Dalland-C40 (c) animals belonging to two herds. The effects of the environmental factors on this trait were assessed by means of a model that included, as random effects, the influence of the sow's father and mother and, as fixed effects, the influence the year of birth, the herd and the birth season, along with the covariable litter size at birth. The variance components were estimated using the derivative-free restricted maximum likelihood method. The estimated mean was 354.8 +/- 25.87 days, with a coefficient of variation of 7.29%. Significant effects on the trait were observed for the herd, the year and the season of birth; but a linear effect of litter size at birth on the age at first farrowing was not observed. The boar did not significantly contribute to the variation occurring among the sows, whereas the sow's mother caused significant variation. The heritability estimate for the age at first farrowing was 0.44 +/- 0.15, which is considered high. We concluded that herd effect and year and season of birth should be taken into consideration for an accurate genetic comparison; consequently, the animals should be joined into contemporary groups.

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Genetic and environmental effects over milk production of buffalo cows in Brazil

The objective of this paper was to evaluate the relevance of environmental and genetics effects on milk production of buffalo cows in Brazil. The data were based on the Buffalo Genetic Improvement Program - PROMEBUL, using information of 1,911 cows (107 Jafarabadi, 101 Mediterranean, 1,056 Mu/Tab and 647 crossbred females) with parturition between 1982 and 2003. The mathematic model for evaluating milk production included the fixed effects of herd, parturition year (1982 to 2003) and month (January to December), calf's sex (male or female), genetic group (Jafarabadi, Mediterranean, Murrah, and crossbreed), number of milking (one or two), lactation order (1 to 12) and duration of lactation (as a linear effect). The mean milk production in herds was 1,590.36 +/- 609.25 kg. All sources of variation were significant (P<0.05) for the studied characteristics, except calf's sex. The mean milk production per genetic group was 1,651.4; 1,592.2; 1,578.3 and 1,135.5 kg, for Murrah, Mediterranean, Crossbred and Jafarabadi, respectively. The duration of lactation was the most important source of variation over milk production, followed by the year of parturition, herd, parturition order, genetic group and month of parturition.

Variances of direct genetic effects, maternal genetic effects, and cytoplasmic inheritance effects for milk yield, fat yield, and fat percentage

Milk yield, fat yield, and fat percentage during the first three lactations were studied using New York Holsteins that were milked twice daily over a 305-d, mature equivalent lactation. Those data were used to estimate variances from direct and maternal genetic effects, cytoplasmic effects, sire by herd interaction, and cow permanent environmental effects. Cytoplasmic line was traced to the last female ancestor using DHI records from 1950 through 1991. Records were 138,869 lactations of 68,063 cows calving from 1980 through 1991. Ten random samples were based on herd code. Samples averaged 4926 dams and 2026 cytoplasmic lines. Model also included herd-year-seasons as fixed effects and genetic covariance for direct-maternal effects. Mean estimates of the effects of maternal genetic variances and direct-maternal covariances, as fractions of phenotypic variances, were 0.008 and 0.007 for milk yield, 0.010 and 0.010 for fat yield, and 0.006 and 0.025 for fat percentage, respectively. Average fractions of variance from cytoplasmic line were 0.011, 0.008, and 0.009 for milk yield, fat yield, and fat percentage. Removal of maternal genetic effects and covariance for maternal direct effects from the model increased the fraction of direct genetic variance by 0.014, 0.021, and 0.046 for milk yield, fat yield, and fat percentage; little change in the fraction was due to cytoplasmic line. Exclusion of cytoplasmic effects from the model increased the ratio of additive direct genetic variance to phenotypic variance by less than 2%. Similarly, when sire by herd interaction was excluded, the ratio of direct genetic variance to phenotypic variance increased 1% or less.

Estimates of direct and maternal genetic effects for weights from birth to 600 days of age in Nelore cattle

Estimates of direct and maternal variance and heritability for weights at each week (up to 280 days of age) and month of age (up to 600 days of age) in Zebu cattle are presented. More than one million records on 200 000 animals, weighed every 90 days from birth to 2 years of age, were available. Data were split according to week (data sets 1) or month (data sets 2) of age at recording, creating 54 and 21 data sets, respectively. The model of analysis included contemporary groups as fixed effects, and age of dam (linear and quadratic) and age of calf (linear) effects as covariables. Random effects fitted were additive direct and maternal genetic effects, and maternal permanent environmental effect. Direct heritability estimates decreased from 0.28 at birth, to 0.12-0.13 at about 150 days of age, stayed more or less constant at 0.14-0.16 until 270 days of age and increased with age after that, up to 0.25-0.26. Maternal heritability estimates increased from birth (0.01) to a peak of 0.14 for data sets 1 and 0.07-0.08 for data sets 2 at about 180-210 days of age, before decreasing slowly to 0.07 and 0.05, respectively, at 300 days, and then rapidly diminished after 300 days of age. Permanent environmental effects were 1.5 to four times higher than genetic maternal effects and showed a similar trend.

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Test-day model for milk yield of dairy buffaloes in colombia

The test-day model is the preferred method for genetic evaluations in dairy cattle. For this study, 28372 test-day records of 1220 lactations from 1997 to 2009 were used. The (co)variance components for milk in test-day were estimated using a Uni and multiple-traits repeated animal model with the Restricted Maximum Likelihood method (REML). The Contemporary Group (herd, year, and season of parity) and the age of parity (linear and quadratic) fixed effects, and the additive genetic, permanent environmental, and residual random effects were included in the model. The heritabilities ranged between 0.06 and 0.45 during lactation. The genetic correlations were greater than 0.93. In conclusion, the test-day model is appropriate for the genetic evaluation of dairy buffaloes in Colombia.

Random regression models using different functions to model milk flow in dairy cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reaction norm model to describe environmental sensitivity across first lactation in dairy cattle under tropical conditions

Reaction norm models have been widely used to study genotype by environment interaction (G × E) in animal breeding. The objective of this study was to describe environmental sensitivity across first lactation in Brazilian Holstein cows using a reaction norm approach. A total of 50,168 individual monthly test day (TD) milk yields (10 test days) from 7476 complete first lactations of Holstein cattle were analyzed. The statistical models for all traits (10 TDs and for 305-day milk yield) included the fixed effects of contemporary group, age of cow (linear and quadratic effects), and days in milk (linear effect), except for 305-day milk yield. A hierarchical reaction norm model (HRNM) based on the unknown covariate was used. The present study showed the presence of G × E in milk yield across first lactation of Holstein cows. The variation in the heritability estimates implies differences in the response to selection depending on the environment where the animals of this population are evaluated. In the average environment, the heritabilities for all traits were rather similar, in range from 0.02 to 0.63. The scaling effect of G × E predominated throughout most of lactation. Particularly during the first 2 months of lactation, G × E caused reranking of breeding values. It is therefore important to include the environmental sensitivity of animals according to the phase of lactation in the genetic evaluations of Holstein cattle in tropical environments.