A Detailed Validation Study of Multi-Environment Eulerian Probability Density Function Transport Method for Modeling Turbulent Nonpremixed Combustion

The current work involves the validation of presumed shape multi-environment Eulerian probability density function (PDF) transport method (MEPDF) using direct quadrature method of moments (DQMOM)-interaction by exchange with mean (IEM) approach for modeling turbulence chemistry interactions in nonpremixed combustion problems. The joint composition PDF is represented as a collection of finite number of Delta functions. The PDF shape is resolved by solving the governing transport equations for probability of occurrence of each environment and probability-weighted mass fraction of species and enthalpy in Eulerian frame for each environment. A generic implementation of the MEPDF approach is carried out for an arbitrary number of environments. In the current work, the MEPDF approach is used for a series of problems to validate each component of MEPDF approach in an isolated manner as well as their combined effect. First of all, a nonreactive turbulent mixing problem with two different Reynolds numbers (Re = 7000 and 11,900) is used for validation of the mixing and correction terms appear in the MEPDF approach. The second problem studied is a diffusion flame with infinitely fast chemistry having an analytical solution. The reaction component is validated by considering a 1D premixed laminar flame. In order to validate the combined effect of mixing and turbulence chemistry interactions, two different turbulent nonpremixed problems using global one-step chemistry are used. The first reactive problem used is H2 combustion (DLR Flame H3), while the second reactive validation case is a pilot-stabilized CH4 flame. The current predictions for all validation problems are compared with experimental data or published results. The study is further extended by modeling a turbulent nonpremixed H2 combustion using finite-rate chemistry effects and radiative heat transfer. The current model predictions for different flame lengths as well as minor species are compared with experimental data. The current model gave excellent predictions of minor species like OH. The differences in the current predictions with experimental data are discussed.

Download Full-text

A Detailed Validation Study of Multi-Environment Eulerian PDF Transport Method for Modeling Turbulent Non-Premixed Combustion

ASME 2012 Gas Turbine India Conference ◽

10.1115/gtindia2012-9640 ◽

2012 ◽

Cited By ~ 1

Author(s):

Rakesh Yadav ◽

Abhijit Kushari ◽

Vinayak Eswaran ◽

Atul K. Verma

Keyword(s):

Experimental Data ◽

Laminar Flame ◽

Current Model ◽

Premixed Combustion ◽

Combined Effect ◽

Current Work ◽

Finite Rate ◽

Efficient Manner ◽

Mixing Problem ◽

Transport Method

PDF transport modeling has been known to be the most accurate for modeling turbulence chemistry interactions with finite rate chemistry effects. But, this is computationally very expensive. The Direct quadrature method of moments with Interaction by exchange with mean closure (DQMOM-IEM) can be a potential alternative to solve the PDF transport equation in an efficient manner. The current work involves the validation of presumed shape multi-environment Eulerian PDF Transport method (MEPDF) using DQMOM-IEM approach for modeling turbulence chemistry interactions in non-premixed combustion problems. The joint composition PDF is represented as a collection of finite number of Delta functions. The PDF shape is resolved by solving the governing transport equations for probability of occurrence of each environment and probability weighted mass fraction of species and enthalpy in Eulerian frame for each environment. A generic implementation of the MEPDF approach is carried out for an arbitrary number of environments. In the current work, the MEPDF approach is used for a series of problems to validate each component of MEPDF approach in an isolated manner as well as their combined effect. First of all, a non reactive turbulent mixing problem with two different Reynolds number (Re = 7000, 11900) is used for validation of the mixing and correction terms appear in the MEPDF approach. The second problem studied is a diffusion flame with infinitely fast chemistry having an analytical solution. The reaction component is validated by considering a 1D premixed laminar flame. In order to validate the combined effect of mixing and turbulence chemistry interactions, two different turbulent non premixed problems using global one step chemistry are used. The first reactive problem used is H2 combustion (DLR Flame H3) while the second reactive validation case is a pilot stabilized CH4 flame. The current predictions for all validation problems are compared with experimental data or published results. The study is further extended by modeling a turbulent non premixed H2 combustion using finite rate chemistry effects and radiative heat transfer. The current model predictions for different flame lengths as well as minor species are compared with experimental data. The current model gave excellent predictions of minor species like OH. The differences in the current predictions with experimental data are discussed.

Download Full-text

Microstructural Constitutive Equation for Sprain Analysis

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2008-67709 ◽

2008 ◽

Author(s):

Zheying Guo ◽

Raffaella De Vita

Keyword(s):

Experimental Data ◽

Probability Density Function ◽

Constitutive Equation ◽

Weibull Distribution ◽

Probability Density ◽

Density Function ◽

Damage Evolution ◽

Linear Elastic ◽

Proposed Model ◽

Collagenous Tissues

A new constitutive equation is presented to describe the damage evolution process in parallel fibered collagenous tissues such as ligaments and tendons. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straighten out at different stretches that are defined by a Weibull probability density function. After becoming straight each fiber is assumed to be linear elastic. Its waviness is defined by a Weibull distribution. Tissue’s damage is assumed to occur at the fiber level and is defined as a reduction in the fiber’s stiffness. The proposed model is validated by using experimental data published in the biomechanics literature by Provenzano et al. [1].

Download Full-text