Molecular Gas Radiation Research Articles

A detailed modeling study of radiative heat transfer in a heavy-duty diesel engine

In recent years, the importance of radiative heat transfer in combustion has been increasingly recognized. Detailed models have become available that accurately represent the complex spectral radiative properties of reacting gas mixtures and soot particles, and new methods have been developed to solve the radiative transfer equation (RTE). At the same time, the trends toward higher operating pressures and higher levels of exhaust-gas recirculation in compression-ignition engines, together with the demand for higher quantitative accuracy from in-cylinder CFD models, has led to renewed interest in radiative transfer in engines. Here an in-depth investigation of radiative heat transfer is performed for a heavy-duty diesel truck engine over a range of operating conditions. Results from 10 different combinations of turbulent combustion models, spectral radiation property models, and RTE solvers are compared to provide insight into the global influences of radiation on energy redistribution in the combustion chamber, heat losses, and engine-out pollutant emissions (NO and soot). Also, the relative importance of the individual contributions of molecular gas versus soot radiation, the spectral model, the RTE solver, and unresolved turbulent fluctuations in composition and temperature (turbulence–radiation interactions – TRI) are investigated. Local instantaneous temperatures change by as much as 100 K with consideration of radiation, but the global influences of radiation on heat losses and engine-out emissions are relatively small (in the 5–10% range). Molecular gas radiation dominates over soot radiation, consideration of spectral properties is essential for accurate predictions of reabsorption, a simple RTE solver (a first-order spherical harmonics – P1 – method) is sufficient for the conditions investigated, and TRI effects are small (less than 10%). While the global influences of radiation are relatively small, it is nevertheless desirable to explicitly account for radiation in in-cylinder CFD. To that end, a simplified CFD radiation model has been proposed, based on the findings reported here.

A simplified CFD model for spectral radiative heat transfer in high-pressure hydrocarbon–air combustion systems

Detailed radiation modeling in piston engines has received relatively little attention to date. Recently, it is being revisited in light of current trends towards higher operating pressures and higher levels of exhaust-gas recirculation (EGR), both of which enhance molecular gas radiation. Advanced high-efficiency engines also are expected to function closer to the limits of stable operation, where even small perturbations to the energy balance can have a large influence on system behavior. Detailed radiation modeling using sophisticated tools like photon Monte Carlo/line-by-line (PMC/LBL) is computationally expensive. Here, guided by results from PMC/LBL, a simplified stepwise-gray spectral model in combination with a first-order spherical harmonics (P1 method) radiative transfer equation (RTE) solver is proposed and tested for engine-relevant conditions. Radiative emission, reabsorption and radiation reaching the walls are computed for a heavy-duty compression-ignition engine at part-load and full-load operating conditions with different levels of EGR and soot. The results are compared with those from PMC/LBL, P1/FSK (P1 with a full-spectrum k-distribution spectral model) and P1/Gray radiation models to assess the proposed model’s accuracy and computational cost. The results show that the proposed P1/StepwiseGray model can calculate reabsorption locally and globally with less than 10% error (with respect to PMC/LBL) at a small fraction of the computational cost of PMC/LBL (a factor of 30) and P1/FSK (a factor of 15). In contrast, error in computed reabsorption by the P1/Gray model is as high as 60%. It is expected that the simplified model should be broadly applicable to high-pressure hydrocarbon–air combustion systems, with or without soot.

Natural convection in a differentially heated cubical cavity under the effects of wall and molecular gas radiation at Rayleigh numbers up to 3 × 109

Numerical simulations are carried out to analyze the effects of wall and molecular gas radiation on weakly turbulent natural convection in a differentially heated cubical cavity in the Rayleigh number range 3 × 107 – 3 × 109. Two opposite vertical walls are maintained at different temperatures and the four other walls are adiabatic. A direct numerical simulation (pseudo-spectral Chebyshev collocation) method for flow and temperature fields has been combined with direct ray-tracing method for radiation field, and, at the highest Rayleigh number, a spectral subgrid scale radiation model has been implemented to account for the smallest, though non-optically thin, turbulent scales. The effects of radiation on mean temperature and flow fields are to substantially decrease the thermal stratification in the core of the cavity (through different mechanisms in wall and gas radiation cases), to promote the organization of the flow near the top and bottom walls in the form of relatively thin horizontal boundary layers, and to lead to significant intensification of the mean circulation in the cavity. Both wall and gas radiation are shown to increase mechanical and thermal turbulence levels and to strongly modify the spatial distribution of the most turbulent regions. In the case of wall radiation, significant turbulence production is found upstream the vertical boundary layers due to Rayleigh-Bénard instabilities in unstably stratified regions along the horizontal walls. Gas radiation is shown to act as an additional dissipation mechanism for both the mean temperature variance and the variance of temperature fluctuations. However, radiative damping of temperature fluctuations decreases as the Rayleigh number increases.

Transitional regimes of natural convection in a differentially heated cubical cavity under the effects of wall and molecular gas radiation

The transition to unsteadiness and the dynamics of weakly turbulent natural convection, coupled to wall or gas radiation in a differentially heated cubical cavity with adiabatic lateral walls, are studied numerically. The working fluid is air with small contents of water vapor and carbon dioxide whose infrared spectral radiative properties are modelled by the absorption distribution function model. A pseudo spectral Chebyshev collocation method is used to solve the flow field equations and is coupled to a direct ray tracing method for radiation transport. Flow structures are identified by means of either the proper orthogonal decomposition or the dynamic mode decomposition methods. We first retrieve the classical mechanism of transition to unsteadiness without radiation, characterized by counter-rotating streamwise-oriented vortices generated at the exit of the vertical boundary layers. Wall radiation through a transparent medium leads to a homogenization of lateral wall temperatures and the resulting transition mechanism is similar to that obtained with perfectly conducting lateral walls. The transition is due to an unstable stratification upstream the vertical boundary layers and is characterized by periodically oscillating transverse rolls of axis perpendicular to the main flow. When molecular gas radiation is accounted for, no periodic solution is found and the transition to unsteadiness displays complex structures with chimneys-like rolls whose axes are again parallel to the main flow. The origin of this instability is probably due to centrifugal forces, as suggested previously for the case without radiation. Above the transition to unsteadiness, at Ra = 3 × 108, it is shown that both wall and gas radiation significantly intensify turbulent fluctuations, decrease the thermal stratification in the core of the cavity, and increase the global circulation.

A transported probability density function/photon Monte Carlo method for high-temperature oxy–natural gas combustion with spectral gas and wall radiation

A computational fluid dynamics model for high-temperature oxy–natural gas combustion is developed and exercised. The model features detailed gas-phase chemistry and radiation treatments (a photon Monte Carlo method with line-by-line spectral resolution for gas and wall radiation – PMC/LBL) and a transported probability density function (PDF) method to account for turbulent fluctuations in composition and temperature. The model is first validated for a 0.8 MW oxy–natural gas furnace, and the level of agreement between model and experiment is found to be at least as good as any that has been published earlier. Next, simulations are performed with systematic model variations to provide insight into the roles of individual physical processes and their interplay in high-temperature oxy–fuel combustion. This includes variations in the chemical mechanism and the radiation model, and comparisons of results obtained with versus without the PDF method to isolate and quantify the effects of turbulence–chemistry interactions and turbulence–radiation interactions. In this combustion environment, it is found to be important to account for the interconversion of CO and CO2, and radiation plays a dominant role. The PMC/LBL model allows the effects of molecular gas radiation and wall radiation to be clearly separated and quantified. Radiation and chemistry are tightly coupled through the temperature, and correct temperature prediction is required for correct prediction of the CO/CO2 ratio. Turbulence–chemistry interactions influence the computed flame structure and mean CO levels. Strong local effects of turbulence–radiation interactions are found in the flame, but the net influence of TRI on computed mean temperature and species profiles is small. The ultimate goal of this research is to simulate high-temperature oxy–coal combustion, where accurate treatments of chemistry, radiation and turbulence–chemistry–particle–radiation interactions will be even more important.

Turbulence-radiation interactions in large-eddy simulations of luminous and nonluminous nonpremixed flames

Turbulence-radiation interactions (TRI) are explored in large-eddy simulations (LES) of luminous and nonluminous nonpremixed jet flames. The simulations feature a transported filtered density function (FDF) method for subfilter-scale fluctuations in composition and temperature, and a fully coupled photon Monte Carlo (PMC) method for radiative transfer with line-by-line (LBL) spectral resolution. The model is exercised to isolate and quantify individual contributions to TRI for conditions that range from small optically thin flames to relatively large optically thick flames, including spectral molecular gas radiation and broadband soot radiation. The results provide new physical insight into TRI and guidance for modeling. In all cases, emission TRI are responsible for a significant fraction of the radiative emission, and that fraction increases with increasing optical thickness. For simulations where 84% of the turbulence kinetic energy is resolved, contributions of subfilter-scale fluctuations to emission TRI exceed those of resolved-scale fluctuations. The largest contributions to emission TRI are the absorption coefficient–temperature correlation and the temperature self-correlation. Absorption TRI are evident only for relatively high optical thicknesses. In all cases, the contributions of subfilter-scale fluctuations to absorption TRI are negligible.

Efficient generation of short terahertz pulses via stimulated Raman adiabatic passage

We have analyzed the efficiency of coherent scattering of infrared radiation in molecular gases for the production of intense, short terahertz (THz) pulses by using stimulated Raman adiabatic passage for the preparation of coherence. We show that coherently driven molecular media potentially yield strong, controllable, short pulses of THz radiation. The pulses have energies ranging from several nanojoules to microjoules and time durations from several femtoseconds to nanoseconds at room temperature.

Generation of VUV/XUV coherent radiation in molecular gases

Tunable coherent radiation of wavelength between 92 nm and 122 nm has been produced in molecular gases of N2, CO, H2 and CH4 by resonant and nonresonant third harmonic generation. Factors with respect to the frequency conversion efficiency, including the line strength of the nonlinear susceptibility, the density of the media and the phase-matching, are discussed. By analyzing the characteristics of the four-wave mixing spectra in molecular gases, some physical parameters and the population of the energy levels are obtained. This indicates that nonlinear optical frequency conversion process provides a useful method to study the structure and spectra of molecules.

Analysis of Molecular Gas Radiation: Real Gas Property Effects

Molecular gas radiation calculations have been performed for CO 2 and H 2 O with a line-by-line high-resolution transmission molecular absorption database, with and without particle scattering. Both line-by-line (Monte Carlo) and K-distribution calculations were conducted. The results confirmed that, if the absorption-coefficient distribution function is sufficiently resolved, essentially line-by-line accuracy can be achieved. In addition, comparison was made between line-by-line results and an exponential wideband model combined with Elsasser narrowband model predictions to assess real gas property effects on radiative heat transfer

Similarity of heat radiation from turbulent buoyant jets

The thermal radiation similarity of buoyant turbulent jets is studied. The principal condition for the radiation similarity is the similarity of the temperature and the concentration fields in the near-nozzle region because the main part of radiation is generated by this most heated section of the jet. The k- ε- T′ 2 turbulent viscosity model is used to study numerically the gas dynamic similarity in the near-nozzle zone. It is shown that the excess temperature and concentration fields of different jets can be described by a universal function of the dimensionless coordinates that are longitudinal and transverse coordinates normalized with respect to the special longitudinal and transverse scales. It is found, as a result of the gas dynamic similarity, that the dimensionless spectral intensity (normalized with respect to the production of spectral radiance at the edge of the nozzle and the nozzle area) is described by a universal function which is the same for a wide class of jets and which depends on the exit parameters, radiation frequency and on the steepness of the temperature dependence of the absorption coefficient. The results obtained are generalized for the case of molecular gas radiation in finite spectral intervals containing many spectral lines. A simple and effective method for jet radiation prediction, which does not require a detailed information about the jet gas dynamic structure, is developed.

Nongray Gas Analyses for Reflecting Walls Utilizing a Flux Technique

A flux formulation for a planar slab of molecular gas radiation bounded by diffuse reflecting walls is developed. While this formulation is limited to the planar geometry, it is useful for studying approximations necessary in modeling nongray radiative heat transfer. The governing equations are derived by considering the history of multiple reflections between the walls. Accurate solutions are obtained by explicitly accounting for a finite number of reflections and approximating the spectral effects of the remaining reflections. Four approximate methods are presented and compared using a single absorption band of H2O. All four methods reduce to an identical zeroth-order formulation, which accounts for all reflections approximately but does handle nonreflected radiation correctly. A single absorption band of CO2 is also considered using the best-behaved approximation for higher orders. A zeroth-order formulation is sufficient to predict the radiative transfer accurately for many cases considered. For highly reflecting walls, higher order solutions are necessary for better accuracy. Including all the important bands of H2O, the radiative source distributions are also obtained for two different temperature and concentration profiles.

Self-focusing of laser radiation in molecular gases

Self-focusing and self-defocusing of CO2 laser pulses of 1.6 to 80 nsec duration was observed in SF6 gas for several lines in the 10P branch. It was observed that self-focusing depends on the vibrational excitation of the molecules and on their distribution function. This new self-focusing mechanism may be useful for propagation of high-power laser radiation in the atmosphere.

Scaling Rules for Total Absorptivity and Emissivity of Gases

Hottel’s Rule and Penner’s Rule for estimating the total absorptivity of a homogeneous gas from a total emissivity chart or expression are generalized. The generalized rule is developed from an examination of the functional relationships between total and spectral molecular gas radiation properties. It gives a rational prescription for finding the absorptivity or emissivity at arbitrary pressure from the one-atmosphere total emissivity. Calculations of total properties from band absorption data correlations are used to find the needed map of pressure scaling exponent versus path-length-pressure product and gas temperature. Also addressed is the question of allowing for reflecting walls in the calculation of radiation heat transfer between a homogeneous gas and its enclosing walls. Both exact and high-accuracy-approximate calculations are shown to be possible using only total properties.

Saturation and secondary Stokes effects in coherent anti-Stokes Raman spectroscopy

Coupled differential equations are formulated to model the generation of coherent anti-Stokes Raman radiation in molecular gases. They include the basic coherent interaction of incident pump and idler (Stokes) waves to generate the anti-Stokes radiation plus other radiation and absorption processes which influence saturation due to population depletion of the lowest energy level. Other factors considered are simultaneous excitation of more than one vibration frequency, a quasi-monochromatic idler beam slightly off the true Stokes frequency, and the temporal laser pulse shape. Some effects of these various physical factors on saturation are presented graphically.

Molecular Gas Radiation in the Thermal Entrance Region of a Duct

The effect of molecular gas radiation upon the thermal development downstream from a step change in wall temperature is examined for both laminar and turbulent flow in a black-walled flat-plate duct. The exponential-tailed band model is used to represent spectral variations in gas absorption and emission. Values of total and radiative Nusselt numbers, cold-wall-layer transmission factors, and dimensionless bulk temperatures are reported for several dimensionless axial locations and for various sets of the dimension-less controlling parameters. Even in the entrance region, self absorption by wall layer gas blocks significantly the radiation exchange between the gas core and wall. An approximate correlation is proposed for both plane-duct and pipe turbulent entrance flows.

Methods of calculating molecular-gas radiation on the basis of spectral-composition modeling

A method is proposed for the calculations of the radiation of inhomogeneous molecular gases at low pressures; the method is based on the summation of the equivalent widths of spectral lines and a quasiexponential model of the absorption band.

Molecular gas radiation and laminar or turbulent heat diffusion in a cylinder with internal heat generation

Simultaneous nongray radiation and thermal diffusion in a thermally and hydrodynamically established laminar or turbulent pipe flow with uniform internal heat generation is treated. The governing integro-differential thermal energy equation is solved using the Galerkin technique for the laminar case and finite difference and numerical iteration techniques for turbulent flow. Solutions are presented for radiative and convective Nusselt number as a function of the radiation to molecular conductance ratio N rm , the optical depth τ R along the radius at a photon wavenumber spectrally located at the head of an exponential-tailed absorption band, and a turbulent Reynolds number R t . The radiative Nusselt number is found to increase almost linearly with N rm and linearly with τ R at small τ R but approximately logarithmically at large τ R . The radiative transfer also increases with increasing turbulence R t , as the turbulence improves the effective wall layer gas transmissivity.

Effect of diffusion on absorption and saturation of infrared radiation in molecular gases

Effect of diffusion on absorption of infrared radiation and saturation of absorption in molecular gases is considered. Incorporating the diffusion term, a theory is developed from multi-level rate equations, both for homogeneous and inhomogeneous broadening cases. It is shown that the effect of diffusion is characterized by a diffusion functionK'(k2a), which varies inversely with the radius of the laser beam at low pressures and small beam sizes. Experimental results with seven molecular gases pumped by the CO2 laser beam around 10.6 μm are reported.

Slab band absorptance for molecular gas radiation

Nongray molecular gas radiation can be formulated in terms of slab band absorptance, which can be calculated from correlations of laboratory-measured values of band absorption. Slab-band absorptance is not only useful for obtaining the emissivity or mean beam length but also for the formulation of the radiant flux in a nonisothermal gas. Effects of nongray self-absorption by cold boundary layers can then be readily estimated. Illustrative results are presented for gas in a channel with simple straight-line boundary layer profiles at the walls and constant temperature in the center.