A methodology for the integration of stiff chemical kinetics on GPUs

Numerical schemes for reacting flows typically invoke the method of fractional steps in order to isolate the chemical kinetics model from diffusion/convection phenomena. Here, the reaction fractional step requires the solution of a collection of independent ODE systems which may be severely stiff. Recently, researchers have begun to explore the highly parallel structure of graphics processing units (GPUs) in order to accelerate integration schemes for these ODE systems. However, much of the existing work concentrates on explicit integration algorithms which may fall short in the presence of stiffness. In this light, we have carefully reimplemented in OpenCL C the Fortran 77 program of the 3-stage/5th order implicit Runge–Kutta method Radau5 by Hairer and Wanner (1991) and tested it extensively in the context of a transient equilibrium scheme for the flamelet model. Our implementation can easily be integrated with any existing reactive flow software in order to solve the reaction fractional step on an OpenCL-enabled GPU. Moreover, it is suited for any Chemkin-format reaction mechanism with ≲200≲200 species without incurring a loss in occupancy and it reaches its limit speedup (which is largely independent of the mechanism size) at a small problem size (≈500 ODE systems). In view of memory constraints, we include an optimized scheme for splitting the ODE systems across several kernel invocations and overlapping the kernel execution with data transfers. An in-depth evaluation is based upon runtime measurements of the CPU and the GPU implementation on a user level and a high-end CPU/GPU for an increasing number of ODE systems, reduced and detailed reaction mechanisms and a range of time step sizes

Population balance modelling and laser diagnostic validation of soot particle evolution in laminar ethylene diffusion flames

Laminar diffusion flames present an elementary configuration for investigating soot formation and validating kinetic models before these are transferred to turbulent combustors. In the present article, we present a joint experimental and modelling investigation of soot formation in a laminar co-flow burner. The diffusion flames are analysed with the aid of laser diagnostic techniques, including elastic light scattering (ELS), planar laser-induced fluorescence of OH (OH-PLIF) and line-of-sight attenuation (LOSA), to measure the spatial distribution of soot, gas phase species and the line-of-sight integrated soot volume fraction (ISVF), respectively. The experimental dataset is supplemented by location-specific TEM images of thermophoretically sampled soot particles. The simulation of the sooting flames is carried out with a recently developed discretisation method for the population balance equation (Liu and Rigopoulos, 2019, Combust. Flame 205, 506-521) that accomplishes an accurate prediction of the particle size distribution, coupled with an in-house CFD code. By minimising numerical errors, we ensure that the discrepancies on the modelling side are mainly due to kinetics and are able to carry out an investigation of alternative models. We include a complete set of soot kinetics for PAH-based nucleation and condensation, HACA-based surface growth and oxidation as well as size-dependent aggregation, and consider three different gas phase reaction mechanisms (ABF, BBP and KM2). Based on predictions of the gas phase composition and particle size distribution of soot, modelled counterparts of the laser diagnostic signals are computed and compared with the experimental measurements. The approach of directly predicting signals circumvents the difficulties of explicitly representing the OH concentration in terms of the measured OH-PLIF data and avoids using ‘hybrid’ modelled and measured values to approximate the OH concentration. Moreover, the LOSA signal is directly converted to the line-of-sight ISVF instead of a measure of local soot volume fraction to avoid tomographic inversion errors. Lastly, the predicted ELS signal is computed in terms of the particle size distribution resolved by the population balance model, thus circumventing the approximation of an integral soot property using a presumed size distribution. While we cannot obtain quantitative agreement between experiments and simulations, the accuracy of the numerical approach and the direct prediction of experimental signals allow us to conduct sensitivity analyses of key empirical parameters and investigate the importance of the PAH chemistry and its influence on the competition between nucleation, condensation and surface growth

The reaction Δ+N→N+N+ϕ\Delta+N\to N+N+\phi in ion-ion collisions

We study the threshold $\phi$-meson production in the process $\Delta+N\to N+N+\phi$, which appears as a possible important mechanism in high energy nuclei-nuclei collisions. The isotopic invariance of the strong interaction and the selection rules due to P-parity and total angular momentum result in a general and model independent parametrization of the spin structure of the matrix element in terms of three partial amplitudes. In the framework of one-pion exchange model these amplitudes can be derived in terms of the two threshold partial amplitudes for the process $\pi+N\to N+\phi$. We predict the ratio of cross sections for $\phi-$meson production in $pp$- and $\Delta N$-collisions and the polarization properties of the $\phi$-meson, in $\Delta+N\to N+N+\phi$, as a function of a single parameter, which characterizes the relative role of transversal and longitudinal $\phi$-meson polarizations in the process $\pi+N\to N+\phi$.Comment: 10 pages 3 figure

Cross section of the pp→K+Σ+npp\to K^+\Sigma^+n reaction close to threshold

We have measured inclusive data on $K^+$-meson production in $pp$ collisions at COSY J\"ulich close to the hyperon production threshold and determined the hyperon-nucleon invariant mass spectra. The spectra were decomposed into three parts: $\Lambda p$, $\Sigma^0p$ and $\Sigma^+n$. The cross section for the $\Sigma^+n$ channel was found to be much smaller than a previous measurement in that excess energy region. The data together with previous results at higher energies are compatible with a phase space dependence.Comment: accepted by Phys. lett. B some typos correcte

Strangeness production in proton-proton and proton-nucleus collisions

In these lectures we discuss the investigation of the strange meson production in proton-proton ($pp$) and in proton-nucleus ($pA$) reactions within an effective Lagrangian model. The kaon production proceeds mainly via the excitations of $N^*$(1650), $N^*$(1710), and $N^*$(1720) resonant intermediate nucleonic states, in the collision of two initial state nucleons. Therefore, the strangeness production is expected to provide information about the resonances lying at higher excitation energies. For beam energies very close to the kaon production threshold the hyperon-proton final state interaction effects are quite important. Thus, these studies provide a check on the models of hyperon-nucleon interactions. The in-medium production of kaons show strong sensitivity to the self energies of the intermediate mesons.Comment: 16 pages, 9 figures, Talk presented in the workshop on Hadron Physics, Puri, India, March 7-17,200

Strangeness Production in Hadron Reactions

The paper gives an overview of strangeness-production experiments at the Cooler Synchrotron COSY. Results on kaon-pair and $\phi$ meson production in $pp$, $pd$ and $dd$ collisions, hyperon-production experiments and $\Lambda p$ final-state interaction studies are presented as well as a search for a strangeness $S=-1$ resonance in the $\Lambda p$ system.Comment: Talk presented at Erice 201

Comparison of Lambda and Sigma(0) Threshold Production in Proton-Proton Collisions

Threshold measurements of the associated strangeness production reactions pp --> p K(+) Lambda and pp --> p K(+) Sigma(0) are presented. Although slight differences in the shapes of the excitation functions are observed, the most remarkable feature of the data is that at the same excess energy the total cross section for the Sigma(0) production appears to be about a factor of 28 smaller than the one for the Lambda particle. It is concluded that strong Sigma(0)-p final state interactions, and in particular the Sigma-N --> Lambda-p conversion reaction, are the likely cause of the depletion for the yield in the Sigma signal. This hypothesis is in line with other experimental evidence in the literature.Comment: 13 pages, 3 figures, 1 tabl

Influence of N*-resonances on hyperon production in the channel pp->K+ Lambda p at 2.95, 3.20 and 3.30 GeV/c beam momentum

Hyperon production in the threshold region was studied in the reaction pp -> K+Lp using the time-of-flight spectrometer COSY-TOF. Exclusive data, covering the full phase-space, were taken at the three different beam momenta of p_beam=2.95, 3.20 and 3.30 GeV/c, corresponding to excess energies of epsilon=204, 285 and 316 MeV, respectively. Total cross-sections were deduced for the three beam momenta to be 23.9+/-0.8 +/-2.0 ub, 28.4+/-1.3 +/-2.2 ub and 35.0+/-1.3 +/-3.0 ub. Differential observables including Dalitz plots were obtained. The analysis of the Dalitz plots reveals a strong influence of the N(1650)-resonance at p_beam=2.95 GeV/c, whereas for the higher momenta an increasing relative contribution of the N(1710)- and/or of the N(1720)-resonance was observed. In addition, the pL-final-state interaction turned out to have a significant influence on the Dalitz plot distribution.Comment: accepted for publication at Physics Letters B; some minor text changes were done; also the scale of the ordinates of figure 9 has been changed

An LES-PBE-PDF approach for predicting the soot particle size distribution in turbulent flames

In this article, we combine the large eddy simulation (LES) concept with the population balance equation (PBE) for predicting, in a Eulerian fashion, the evolution of the soot particle size distribution in a turbulent non-premixed hydrocarbon flame. In order to resolve the interaction between turbulence and chemical reactions/soot formation, the transport equations for the gas phase scalars and the PBE are combined into a joint evolution equation for the filtered pdf associated with a single realization of the gas phase composition and the soot number density distribution. With view towards an efficient numerical solution procedure, we formulate Eulerian stochastic field equations that are statistically equivalent to the joint scalar-number density pdf. By discretizing the stochastic field equation for the particle number density using an explicit adaptive grid technique, we are able to accurately resolve sharp features of evolving particle size distributions, while keeping the number of grid points in particle size space small. Compared to existing models, the main advantage of our approach is that the LES-filtered particle size distribution is predicted at each location in the flow domain and every instant in time and that arbitrary chemical reaction mechanisms and soot formation kinetics can be accommodated without approximation. The combined LES-PBE-PDF model is applied to investigate soot formation in the turbulent non-premixed Delft III flame. Here, the soot kinetics encompass acetylene-based rate expressions for nucleation and growth that were previously employed in the context of laminar diffusion flames. In addition, both species consumption by soot formation and radiation based on the assumption of optical thinness are accounted for. While the agreement of our model predictions with experimental measurements is not perfect, we indicate the benefits of the LES-PBE-PDF model and demonstrate its computational viability