The Ultraviolet Radiation Environment around M Dwarf Exoplanet Host Stars
Summary (3 min read)
1 Introduction
- Numerical tools for spray combustion help engineers to design more efficient and less pollutant aeronautical engines.
- These techniques seem also attractive for spray combustion and they have already been used to perform DNS (Direct Numerical Simulation) and LES of turbulent spray flames [1,8–10].
- Results are also compared to those of the 24-species chemistry to assess the accuracy of the tabulated method.
- The experimental configuration as well as the numerical setup are presented in Section 4.
- Then, the turbulent reactive two-phase flow is characterized in Section 5.
2 Chemical description
- In the following, the two different chemical descriptions considered, i.e. a multi-species kinetics and the FPI look-up table technique, are presented.
- 1 Multi-species chemistry A 24-species mechanism developed to perform DNS of n-dodecane spray flames [11,16] is considered here.
- The mixture fraction, defined as Yz = WF WCnCF Nspec∑ k=1 Yk nCkWC Wk (2) is often retained as a parameter of a look-up table method, where WC is the element weight of carbon atom, Yk, Wk and nCk are the mass fraction, the molar weight and the number of carbon atoms of the kth species, respectively.
- Any thermo-chemical quantity ϕ is then stored in a 2-D look-up table ϕ = ϕFPI[Yc, Yz], where ϕFPI is obtained from laminar premixed flames.
- 30], the global behavior of laminar spray flames is correctly reproduced by the FPI method.
3 LES system of equations
- LES of the MERCATO spray flame configuration is performed with the AVBP solver [31– 33] using an Euler-Euler approach under the assumption of monodisperse-monokinetic liquid phase.
- This assumption may affect the accuracy of the spray description but significantly reduces the simulation CPU cost.
- For the subgrid unclosed term τsgsij , a viscosity-type closure is used: τsgsij = 2µ tS̃ij − 1 3 τsgskk δij ; , (10) and the turbulent viscosity µt is evaluated using the WALE model of Nicoud et al. [36].
- The thickening factor F increases the molecular diffusion and decreases the reaction rate to thicken the flame front while preserving the laminar flame speed.
3.1.2 Thermodynamic and transport properties of the gaseous mixture
- In the multi-species description, all thermodynamic quantities are derived from enthalpy and entropy information for each species based on the JANAF tables [39].
- Concerning the transport properties, a simplified model based on constant and equal Schmidt (Sc) and Prandtl (Pr) numbers,4 i.e. unity Lewis number for all species, is considered here in order to guarantee consistency with the tabulated chemistry.
- It has to be noted that the flow temperature T obtained from Eq. (3) may differ from the tabulated value T FPI .
- While being negligible in incompressible flow, this subgrid pressure may become predominant in highly compressible flows, such as the Eulerian disperse phase.
- The retained formulation for the thermodynamic and transport properties at the droplet surface in the case of a multi-species chemistry is provided in the following section together with its extension to the tabulated approach.
3.2.1 Transport and thermodynamic properties in the droplet vicinity
- In analogy with the gaseous mixture treatment discussed in Section 3.1.1, Devap and λevap are calculated with both multi-species and tabulated approaches by using constant Schmidt and Prandtl numbers assumptions: ρDevap = µevapSc−1 and λevap = µevapcevapp Pr−1.
- Results on the finer 20 million-cell mesh using the tabulation approach are also added in red dotted lines to verify the grid convergence.
- In [47], the experimental droplet size distribution varies between 2 µm and 150 µm whereas the mean diameter is 44 µm.
5 Flame characterization
- The flame structure and the complex dynamics of the swirled spray flame MERCATO were not investigated experimentally.
- The presence of a secondary reaction zone is clearly identified by looking to the CO formation (positive in blue) and destruction (negative in red) zones in Fig. 6(c).
- Close to the injection, the IRZ is characterized by a moderate temperature (Fig.7(a)right) so that the evaporation is relatively slow and the mixture equivalence ratio slowly increases (Fig.7(a)-left).
- This complex flame structure is due to an intricate coupling between evaporation, mixing and combustion governing the stabilization location of the flame front.
- The liquid volume fraction presents an oscillating behaviour at the same frequency as the PVC, but with a phase shift due to its high Stokes number (StPV C ≈ 10).
6 Evaluation of the FPI tabulation method for swirled spray flames
- In Section 5, it has been discussed that the coupling between evaporation, mixing and combustion governs the flame dynamics, stabilisation and structure.
- Time-averaged results for the flame structure are presented in Fig. 10 for both the 24- species (left) and the FPI look-up table technique .
- The presence of an high CO concentration region is correctly reproduced by the FPI approach.
- This species can be an indication of the ability of the FPI model to describe the complex nature of the chemical processes leading to intermediates, minor species and radicals.
- It should be reminded that in the context of soot prediction a correct description of the acetylene and of the precur- sors, which are strongly sensitive to strain rate [51], is essential [52].
7 Conclusion
- LES of the MERCATO experimental benchmark has been performed using a detailed chemical description accounting for 24-species to study the behavior of an industrial swirled twophase injection system.
- Numerical results have been compared to the experimental flow in terms of mean and fluctuations of axial velocity of both gas and liquid phases as well as droplet diameter profiles.
- It has been shown that tabulated chemistry methods allow the numerical investigation of swirled industrial spray flames, at least for the prediction of global flame behavior, with a cost which is eight times smaller than the considered multi-species description.
- The first one is due to the spray monodisperse assumption, which cannot accurately predict equivalence ratio stratification.
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Frequently Asked Questions (13)
Q2. What is the way to constrain the variable UV radiation environment of planets around M dwarfs?
Continuous HST observing campaigns, spanning 6–10 orbits each, of a larger sample of exoplanet host stars will be essential to better constraining the frequency, duration, and amplitude of the variable UV radiation environment of planets around M dwarfs.
Q3. What is the spectral cutoff of a hypothetical star?
In the case of no UV flux, the short-wavelength spectral cutoff is determined by the photosphere of a theoretical star with Teff 3500 K, typically having negligible flux below 2500 Å and no chromospheric emission features.
Q4. What is the replenishment term from the escaping atmospheres of their short-period?
The replenishment term from the escaping atmospheres of their short-period planets is Φloss = Ṁlossm−1H2 F(H2/H i) V −1emit, where Ṁloss is the planetary atmosphere mass-loss rate, F(H2/H i) is the fraction of the total cloud in molecular form, and Vemit is the volume of the emitting area (Vemit = πr2H2zH2).
Q5. How do the authors reconstruct the intrinsic Ly radiation field strengths?
Using an iterative least-squares approach, the authors reconstruct the intrinsic Lyα radiation field strengths assuming a two-component Gaussian emission line.
Q6. What is the brightest line in the UV spectrum of low-mass stars?
Lyα is the brightest line in the UV spectrum of low-mass stars, although resonant scattering in the ISM makes direct line profiles inaccessible, even for the nearest stars (Wood et al. 2000, 2005).
Q7. How did the light curves in the MUSCLES data be extracted?
Light curves in several chromospheric and transition region lines were extracted from the calibrated three-dimensional data by exploiting the time-tag capability of the COS microchannel plate detector (France et al. 2010a).
Q8. What is the reliable method for determining the radiation field incident on planets orbiting M?
Until such time that stellar models of M-type stars can reliably predict the observed UV-through-IR spectrum, a direct UV observation will be the most reliable means for determining the radiation field incident on planets orbiting M dwarfs.
Q9. How can the H2 disk be sustained for mass-loss rates?
Keeping the crudeness of this approach in mind, the authors find that the H2 disk can be sustained for mass-loss rates Ṁloss 6 × 1010 g s−1, well within the range of mass-loss estimates of short-period planets around G-, K-, and M-type stars (Vidal-Madjar et al.
Q10. Why have M dwarfs been ignored by UV observers?
Outside of a few wellstudied flare stars (e.g., AU Mic, AD Leo, EV Lac, Proxima Cen), M dwarfs have largely been ignored by UV observers because most investigations were aimed at understanding the origin and nature of energetic events on low-mass stars.
Q11. What is the final possibility of the H2 emission from the GJ 436 system?
A final possibility is that the observed H2 fluorescence originates in a circumstellar gas envelope that is being replenished by atmospheric mass loss from escaping planetary atmospheres.
Q12. What is the way to measure the UV variability of M dwarfs?
A more complete understanding of UV variability on weakly active and inactive M dwarfs, in combination with better constrained flare frequencies for stars of a variety of activity strengths, would allow one to use the wealth of data from current and upcoming large optical surveys to inform planetary atmosphere models.
Q13. How much is the scaling relation for M dwarf exoplanets?
Factoring in uncertainties on the interstellar correction and the Lyα reconstruction, the authors estimate that this scaling relation is good to ∼30%, or the ISM-corrected intrinsic F(Lyα)/ F(Mg ii) ratio for weakly active M dwarf exoplanet host stars is 10 ± 3.