Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar $$H_{2} -$$ H 2 - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed $$S_{d}^{*}$$ S d ∗ . It has been found that the correlation between $$S_{d}^{*}$$ S d ∗ and curvature remains negative and a significantly non-linear interrelation between $$S_{d}^{*}$$ S d ∗ and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of $$S_{d}^{*}$$ S d ∗ but allows for a non-linear stretch rate dependence of $$S_{d}^{*}$$ S d ∗ , has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express $$S_{d}^{*}$$ S d ∗ as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of $$S_{d}^{*}$$ S d ∗ more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of $$S_{d}^{*}$$ S d ∗ , has been shown to exhibit promising predictions of $$S_{d}^{*}$$ S d ∗ for all cases considered here.

The Effect Of Unsteady Stretch On Laminar Premixed Curved Flames

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.

The Effect Of Unsteady Stretch On Laminar Premixed Curved Flames

Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, strained laminar planar flames under steady conditions. The significance of transient strain has been discussed in the literature with most assertions being that their chemical time scales are sufficiently short compared to the turbulent time scales to treat them as quasi-steady. Less discussed is the unsteady motion of a curved flame front component of stretch rate. This thesis seeks further understanding of the effect of stretch rate on premixed flames by developing and validating a model for use with transient premixed laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). A FORTRAN code is developed and validated which models a laminar premixed flame exposed to an oscillating mass flowrate. This code solves transient equations of continuity, momentum, energy, and individual species in radial coordinates. In this model, flame response is studied when the flow and scalar fields remain aligned (i.e., no strain). The model is applied to conditions in which the flame expands (positive stretch) and contracts (negative stretch) radially by the addition of the externally-defined oscillating mass flow rate. The transient response of laminar premixed flames results in amplitude decrease and phase shift increase with increasing frequency. In order to implement the transient behaviour of flamelets in turbulent modelling more efficiently, a frequency response analysis is applied as a process characterization tool to simplify the complex non-linear behaviour using flame transfer functions. It is shown that with increasing frequency of the perturbation, when equivalence ratio is kept constant, or with decreasing equivalence ratio in the same frequency, non-linear behaviour of the flame becomes prominent. Therefore, linear models can only predict the flame behaviour with accuracy below the threshold of when the fluid and chemistry time scales are the same order of magnitude. Various nonlinear models are studied in order to find the most appropriate flame transfer function for higher frequencies to extend the predictive capabilities of these models.

A rate-dependent dynamic damage model in peridynamics for concrete under impact loading

To study the dynamic behavior and impact damage and failure of concrete materials and structures, a dynamic damage model was reformulated under the framework of the non-local peridynamic theory in this paper. The stretch rate of material bonds, equivalent to the strain rate in classical continuum mechanics, was introduced, and a rate-dependent peridynamic model describing the dynamic damage and failure of concrete materials was then proposed, taking both the dynamic failure of bonds and the rate-sensitivity of damage evolution under different stretch rate into account. The connection between the stretch rate and strength and tensile and compressive failure of concrete materials was established in the peridynamic model. To verify the proposed dynamic damage model for concrete failure, several typical examples simulating the mixed-mode fracture of concrete specimen were investigated. The failure mode, crack propagation paths and the crack propagation speed in the specimen in different cases were captured, which agree well with the experimental results and available numerical results. After model validation, the effect of the number and length of pre-existing cracks on the dynamic failure of concrete components was investigated further.

Calculation of jet characteristics from hydrocode analysis

The penetration performance of a shaped charge jet is affected strongly by factors such as straightness, stretch rate, and breakup time. Straightness is related to manufacturing tolerances, assembly techniques, and system integration features. Stretch rate and breakup time are controllable features of charge design. A higher stretch rate is desirable for short standoff performance. The stretch rate is easily altered by a change of explosive or modification of the angle with which the detonation wave sweeps the liner surface, however, an increased stretch rate generally results in a decreased breakup time. Many of the recent gains in shaped charge performance have been made possible by increasing the effective breakup time of the jet. Several models exist for calculating breakup time. They include analytic models, such as Chou & Carleone’s dimensionless strain rate model, and empirical or semi-empirical models such as Walsh’s theory and those proposed by Pearson, et al. These models can be applied to raw hydrocode calculation data and used to determine a Jet Characterization (JC) file. The JC file can then be used to perform further calculations, such as Penetration Versus Stand Off (PVSO) curves. This paper details adaptation of the Chou & Carleone model for predicting breakup time using hydrocode data. The hydrocode is used to determine the physical parameters of the jet which are then extrapolated back to a virtual origin for breakup time calculation. This results in a model that is design independent, relying on hydrocode determination of jet variables. The model implementation will be discussed, and comparisons of predicted jet characteristics will be made to test data for several charge geometries.