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REVIEW 3 major objections 5 minor 46 references

Non-Equilibrium Phase Changes in Aircraft Exhaust: A Computational Study on Early Contrail Formation

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Non-equilibrium phase-change kinetics, resolved through a moment-based multiphase CFD model, shift and shrink predicted early contrails compared with equilibrium criteria.

desk verdict Useful framework paper with an honest scope, but the heterogeneous condensation source term as written makes soot concentration irrelevant to condensation—a load-bearing bug that has to be fixed before the hydrogen comparison can be trusted. read the letter →

arxiv 2504.20742 v1 pith:Q5XNV6L2 submitted 2025-04-29 physics.flu-dyn physics.ao-phphysics.comp-ph

Katharina Tegethoff , Andrew P. S. Wheeler This is my paper · ORCID
classification physics.flu-dynphysics.ao-phphysics.comp-ph
keywords contrailformationnon-equilibriumcondensationhomogeneousnucleationheterogeneousicemethodofmomentsaircraftexhaustplumeRANSmultiphaseflow
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper builds a numerical model of the first seconds of contrail formation that does not assume water instantly condenses and freezes once saturation is reached. Instead it resolves the finite rates at which vapor clusters nucleate into droplets, droplets freeze into ice, and both grow, using kinetic models adapted from steam-turbine and cloud-microphysics work. Run on a high-bypass turbofan nozzle at cruise conditions, the model predicts that equilibrium-style assumptions overstate how soon, how much, and how widely condensed and frozen water appears. The authors argue that capturing these kinetic delays changes the predicted shape of the young contrail and matters for assessing fuels and nozzle designs.

What carries the argument

The carrying object is a coupled, moment-based population balance for each dispersed phase, embedded in a steady compressible RANS flow solver. For liquid droplets, ice crystals, and soot, the radius distribution is tracked through its first moments, with nucleation sources from classical nucleation theory (homogeneous and soot-assisted) and freezing from water-activity and active-site parameterizations, and with growth rates taken from a droplet-growth law including Knudsen and Prandtl corrections. A surface-area-weighted radius closes the growth term, and the moments feed back into the flow through interphase mass, momentum, and energy source terms. That coupling is what lets kinetics alter the flow and the flow alter kinetics, and it is what the equilibrium treatment omits.

What would settle it

Compare the predicted non-equilibrium condensation onset—its axial and radial position and peak droplet number—against test-rig or in-flight measurements in a well-characterized high-bypass plume: if droplets appear as early and as broadly as the equilibrium model predicts, the kinetic delay is an artifact; if they appear when and where the non-equilibrium model predicts, the equilibrium-based overprediction is confirmed.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central discovery is that non-equilibrium phase-change kinetics are first-order for early contrail structure, not a small correction. In the unmixed nozzle case, the equilibrium treatment condenses immediately at saturation and produces a broad, continuous ice shell; the non-equilibrium treatment delays condensation, narrows and displaces the liquid region, and concentrates ice along the plume edges, with peak condensed mass substantially lower. The model attributes these differences to the nucleation energy barrier, finite growth rates, and separate momentum transport of vapor, liquid, and ice phases. It also reports a bimodal droplet spectrum—many tiny homogeneously nucleated droplets plus fewer larger soot-activated droplets—and shows that a hydrogen-like case with no soot can still produce ice through homogeneous nucleation. A mixed-flow nozzle delays and weakens condensation by homogenizing the exhaust.

Load-bearing premise

The load-bearing premise is that the steady RANS turbulence model with a constant turbulent Schmidt number faithfully reproduces the entrainment and mixing that set local supersaturation, so that the computed nucleation timing and location are not artifacts of the mixing closure.

Editorial extensions

If this is right

  • Equilibrium contrail criteria should be read as upper bounds on condensed mass and contrail extent, not as precise onset predictors.
  • Near-field contrail morphology is sensitive to nozzle mixing: unmixed exhaust produces earlier and stronger condensation than mixed exhaust.
  • Fuel-type effects enter through water vapor content and soot availability; a hydrogen-like high-water, soot-free case can still nucleate ice homogeneously.
  • Droplet size distributions at the contrail start are bimodal, so liquid-phase microphysics should be part of downstream contrail-evolution models.
  • The numerical framework is modular enough to swap fuels, nozzle geometries, and microphysical parameterizations without changing core assumptions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the same kinetic core could be used as a screening tool: before full engine data exist, the model's homogeneous-nucleation result suggests soot-free contrails may still form and freeze early, shifting the question from whether they form to how many ice crystals they seed.
  • Beyond the paper, the bimodal droplet spectrum implies a freezing cascade in which larger heterogeneous droplets freeze first while small homogeneous droplets remain supercooled, so contrail ice crystal number may depend sensitively on the relative rates of the two nucleation pathways.
  • Beyond the paper, the model's sensitivity to the mixing closure suggests a direct computational test: replacing the steady turbulence closure with a turbulence-resolving simulation would show whether the computed nucleation timing and location survive a more faithful representation of entrainment.
  • Beyond the paper, the mixed-nozzle result reframes nozzle design as a possible contrail mitigation lever, since internal mixing can delay and weaken the early condensed phase before any atmospheric processes take over.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper develops a numerical framework for near-field contrail formation that couples compressible, multi-component RANS flow with non-equilibrium phase-change modeling: homogeneous and heterogeneous condensation, homogeneous and immersion freezing, and polydispersed droplet/ice/soot populations via a method-of-moments approach. The framework is applied to two simplified axisymmetric high-bypass turbofan nozzle configurations under cruise conditions. The central claim is that resolving finite-rate nucleation and growth materially changes the onset, location, and morphology of condensed phases relative to an equilibrium Schmidt–Appleman-style treatment, which is said to overpredict condensed mass and spatial extent. A parametric hydrogen-like case and a mixed-nozzle geometry are also examined.

Significance. If the central claim holds, the paper would provide a useful physics-based complement to equilibrium contrail criteria and a modular platform for studying fuel and nozzle effects on early plume microphysics. It has clear strengths: the thermophysical properties are taken from established sources (IAPWS-95, REFPROP), the microphysics models are adapted from published frameworks, a grid-convergence check is reported, and the solver is described in enough detail to be reproduced by a specialist group. However, the heterogeneous condensation model as written does not depend on soot loading, which directly affects the soot-mediated pathway, the bimodal droplet spectra, and the kerosene/hydrogen comparison. The quantitative predictive claims are therefore conditional on a correction to Equation (10) and on sensitivity of the results to the mixing and microphysical parameters.

major comments (3)
  1. [II.B, Eq. (10)] The heterogeneous condensation rate J_het in Eq. (10) is written with the same kinetic prefactor as the homogeneous rate and depends on soot only through the reduced barrier exp(-f(theta) Delta G* / kT). It contains no factor proportional to the soot number concentration N_p or to the soot surface-area concentration. The text immediately below Eq. (11) confirms this: "Their influence on nucleation is determined solely by the assumed contact angle." Consequently, the soot loading specified in Table 2 (10^8 cm^-3, log-normal distribution with mean radius 50 nm) has no effect on the heterogeneous condensation rate as written, and the kerosene versus no-soot hydrogen comparison in Section IV.C reduces to toggling the mechanism on or off rather than testing soot-mediated condensation. This also undermines the attribution of the bimodal droplet spectrum in Fig. 5 to a soot-activated heterogeneous mode. Standard heterogeneous nucleation theory (Fletcher, Ref. [29]) requires a prefactor proportional to the aerosol surface-area concentration (e.g., N_p 4 pi r_p^2 times a suitable kinetic coefficient). This is an internal inconsistency with Eq. (14), where the heterogeneous freezing rate explicitly contains n_{p,i} 4 pi r_{p,i}^2. The authors should correct Eq. (10) and re-evaluate the affected results, or justify in detail why a volume-based rate without soot surface area is appropriate.
  2. [III.A, III.B, IV.B] The quantitative claims about onset, location, and morphology depend on the steady RANS representation of turbulent mixing, specifically the Spalart–Allmaras closure with a constant turbulent Schmidt number Sct = 0.7. Since nucleation rates are exponentially sensitive to the local supersaturation, errors in entrainment and scalar mixing can shift the supersaturated region and thus the nucleation timing and location that are central to the equilibrium versus non-equilibrium comparison. The manuscript acknowledges in Section V that turbulence effects are not treated in detail and will be addressed with turbulence-resolving simulations, but the central claim would be substantially strengthened by at least a sensitivity study over Sct (for example, 0.5 to 1.0) or by a comparison with a turbulence-resolving simulation for one configuration. Without such a check, the reader cannot distinguish model-specific mixing errors from the physical non-equilibrium effects that the paper emphasizes.
  3. [II.B, Table 2, IV.B, IV.C] The microphysical parameters that control the phase-change kinetics are fixed without uncertainty quantification: the contact angle theta = 90 degrees, the ice-active surface site density n_s = 10^8 m^-2, and the soot concentration and size distribution. Given the exponential sensitivity of nucleation rates to the barrier and the direct proportionality of heterogeneous rates to n_s and to soot surface area, the reported quantitative differences (for example, the liquid mass-fraction peaks in Section IV.B) should be accompanied by a sensitivity range, at least for theta and n_s. This is especially important for the hydrogen-like case in Section IV.C, where the claim that homogeneous nucleation alone can initiate contrail formation depends on the absence of soot and on the kinetic competition between pathways.
minor comments (5)
  1. [II.B, Growth Kinetics, Eq. (16)] The coefficients alpha and beta in Eq. (16) are not defined in the text or nomenclature beyond being called "parameters according to Young"; the reader is told that alpha = 11 and beta = 0 but not their physical meaning or units.
  2. [Fig. 5] In the right panel of Fig. 5, the ordinate is described as "normalized" but the normalization reference is not stated, and the axis labels are missing; please specify the normalization used for both nucleation-rate profiles.
  3. [IV.B] The statement that "the simulated ice crystal concentrations and sizes remained below typical optical visibility thresholds for contrails" is given without a quantitative threshold or citation; please state the visibility criterion used and its source.
  4. [IV.C] In the mixed-nozzle case, the statement that freezing is "delayed" and that "no ice is detected within the region shown" should be tied explicitly to the downstream extent of the plotted domain, since ice may form farther downstream.
  5. [General] There are several typographical inconsistencies, including occasional use of "homogenous" where "homogeneous" is intended (e.g., Fig. 5 caption and Section II.B); a careful proofreading pass would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the physical models come from external benchmarks, the equilibrium comparator is a limit rather than a fit, and the only self-citations are solver tooling.

full rationale

The paper's central claim is that finite-rate nucleation and growth change predicted contrail onset, extent, and morphology relative to an equilibrium assumption. The derivation chain is externally anchored: thermodynamic properties use REFPROP and IAPWS-95, homogeneous condensation uses classical nucleation theory with Kantrowitz correction, freezing uses Koop et al., growth uses Young's formulation, and heterogeneous ice nucleation uses Vali's active-site approach with literature-selected surface site density. The equilibrium case is not a fitted surrogate but the instantaneous-saturation limit of the same thermodynamic setup, so the comparison is not constructed from the result it claims to show. The only self-citations are to the authors' prior thesis and a numerical flux scheme, which are implementation tools rather than load-bearing evidence for the physical conclusion. The paper explicitly states it 'does not claim to introduce fundamentally new physical models,' further confirming that the components are imported rather than redefined around the output. A reviewer concern that Eq. (10) omits soot number concentration or surface area in the heterogeneous condensation prefactor is a modeling-correctness issue, not a circularity: it does not make the predicted non-equilibrium fields equal to any fitted input or to the equilibrium comparator. Accordingly, no step in the paper reduces by definition, by fitted parameter, or by self-citation to its own inputs.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central simulation results depend on a chain of established but unverified-for-this-regime assumptions: classical nucleation theory holds in the metastable plume; the Young growth law and moment closure represent polydispersed droplet and ice evolution; soot is dilute, spherical, non-depleting with fixed contact angle; and the RANS mixing model captures entrainment. Validation against measurements is planned but not yet available.

free parameters (4)
  • Contact angle theta for heterogeneous condensation = 90 degrees
    Fixed at a representative mid-range value in Section II.B (Eqs. 8-9). This parameter controls the energy barrier reduction for soot-activated droplet formation and directly affects the heterogeneous nucleation pathway.
  • Ice-active surface site density n_s for immersion freezing = 1e8 m^-2
    Fixed constant in Section II.B (Eq. 14), stated as consistent with experimental data. It controls the heterogeneous freezing rate and thus the timing and location of ice onset.
  • Turbulent Schmidt number Sct = 0.7
    Assumed constant in Section III.A for turbulent diffusion of vapor and moments. It modulates the mixing rate and therefore the supersaturation field that drives nucleation.
  • Core soot population parameters = 1e8 cm^-3, mean radius 50 nm, sigma 30%
    Prescribed in Section IV.A as log-normal distribution at the core inflow. These inputs set the surface area available for heterogeneous nucleation and are based on engine assumptions rather than measurement in this study.
assumptions (5)
  • domain assumption IAPWS-95 and REFPROP v10 accurately describe water and mixture properties over the plume range, including metastable states built by bilinear extrapolation.
    Invoked in Section II.A; all thermodynamic property evaluation rests on these external databases and the smooth extension into metastable regions.
  • domain assumption Classical nucleation theory with the Kantrowitz non-isothermal correction quantitatively describes homogeneous condensation in the plume.
    Equations (2)-(6) in Section II.B; the model assumes CNT is valid in the strong supersaturation and high-gradient regime of the near-field exhaust.
  • domain assumption Young's growth law and the r20 moment closure adequately represent polydispersed droplet and ice growth.
    Equations (16) and (21) in Section II.B; the moment closure replaces the full size distribution with a surface-averaged radius, which is an approximation to the true growth dynamics.
  • domain assumption Dispersed phases are dilute, spherical, and non-interacting; soot is non-depleting, non-reactive, and does not coagulate.
    Stated in Sections II.A, II.B, and III.A; the model neglects coagulation, collisions, and soot aging, which could alter the available surface area and droplet interactions.
  • domain assumption Steady RANS with Spalart-Allmaras closure and a constant turbulent Schmidt number captures near-field entrainment and mixing.
    Sections III.A and III.B; the flow solution that drives supersaturation depends on this turbulence model, and the authors themselves acknowledge turbulence effects are not treated in detail.

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Pith. "Pith review of Non-Equilibrium Phase Changes in Aircraft Exhaust: A Computational Study on Early Contrail Formation." pith.science (2026). https://pith.science/paper/Q5XNV6L2

@misc{pith2026250420742,
  author       = {Pith},
  title        = {Pith review of: Non-Equilibrium Phase Changes in Aircraft Exhaust: A Computational Study on Early Contrail Formation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q5XNV6L2}},
  note         = {Machine review of arXiv:2504.20742}
}
read the original abstract

A numerical framework is developed to model contrail formation in the near-field exhaust of aircraft engines, resolving non-equilibrium phase transitions in compressible, multi-component, non-ideal fluid flows. The approach combines well-established methods from steam turbine modeling for liquid-phase transitions with cloud microphysics models for ice formation. It resolves homogeneous and heterogeneous nucleation, interphase momentum exchange, and polydispersed size distributions of droplets, ice crystals, and soot particles. These models are implemented in a parallelized finite-volume solver and applied to a high-bypass turbofan exhaust configuration with simplified geometry. Results indicate that non-equilibrium effects strongly influence condensation and freezing dynamics, while nozzle geometry and water vapor content modulate local supersaturation and phase transition pathways. The findings underscore the limitations of equilibrium-based models and highlight the value of physics-based, scalable tools for analyzing contrail formation across fuels and propulsion systems.

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Reference graph

Works this paper leans on

46 extracted references · 36 canonical work pages

  1. [29]

    SizeEffectinHeterogeneousNucleation,

    Fletcher,N.H.,“SizeEffectinHeterogeneousNucleation,” TheJournalofChemicalPhysics ,Vol.29,No.3,1958,pp.572–576. https://doi.org/10.1063/1.1744540

    work page doi:10.1063/1.1744540 1958

  2. [1]

    Global radiative forcing from contrail cirrus,

    Burkhardt, U., and Kärcher, B., “Global radiative forcing from contrail cirrus,”Nature Climate Change, Vol. 1, 2011, pp. 54–58. https://doi.org/10.1038/nclimate1068

    work page doi:10.1038/nclimate1068 2011

  3. [2]

    A contrail cirrus prediction model,

    Schumann, U., “A contrail cirrus prediction model,”Geoscientific Model Development, Vol. 5, 2012, pp. 543–580. https://doi.org/10.5194/gmd-5-543-2012

    doi:10.5194/gmd-5-543-2012 2012

  4. [3]

    Formation and radiative forcing of contrail cirrus,

    Kärcher, B., “Formation and radiative forcing of contrail cirrus,”Nature Communications, Vol. 9, No. 1, 2018, p. 1824. https://doi.org/10.1038/s41467-018-04068-0

    work page doi:10.1038/s41467-018-04068-0 2018

  5. [4]

    The contribution of global aviation to anthropogenic climate forcingfor2000to2018,

    Lee, D. S., Fahey, D. W., Skowron, A., Allen, M. R., Burkhardt, U., Chen, Q., Doherty, S. J., Freeman, S., Forster, P. M., Fuglestvedt, J., Gettelman, A., De León, R. R., and Lim, L. L., “The contribution of global aviation to anthropogenic climate forcingfor2000to2018,” AtmosphericEnvironment,Vol.244,2021,p.117834.https://doi.org/10.1016/j.atmosenv.2020.117834

    work page arXiv 2021

  6. [5]

    Die Entstehung von Eisnebel aus den Auspuffgasen von Flugmotoren,

    Schmidt, E., “Die Entstehung von Eisnebel aus den Auspuffgasen von Flugmotoren,”Schriften der Deutschen Akademie der Luftfahrtforschung, Vol. 44, 1941, pp. 1–15

    work page 1941

  7. [6]

    The formation of exhaust condensation trails by jet aircraft,

    Appleman, H., “The formation of exhaust condensation trails by jet aircraft,”Bulletin of the American Meteorological Society, Vol. 34, No. 1, 1953, pp. 14–20. https://doi.org/10.1175/1520-0477-34.1.14

    doi:10.1175/1520-0477-34.1.14 1953

  8. [7]

    On Conditions for Contrail Formation from Aircraft Exhausts,

    Schumann, U., “On Conditions for Contrail Formation from Aircraft Exhausts,”Meteorologische Zeitschrift, Vol. 5, No. 1, 1996, pp. 4–23. https://doi.org/10.1127/metz/5/1996/4

    work page doi:10.1127/metz/5/1996/4 1996

Show all 46 references
  1. [8]

    Theroleofplume-scaleprocessesinlong-termimpactsofaircraft emissions,

    Fritz,T.M.,Eastham,S.D.,Speth,R.L.,andBarrett,S.R.H.,“Theroleofplume-scaleprocessesinlong-termimpactsofaircraft emissions,”Atmospheric Chemistry and Physics, Vol. 20, 2020, pp. 5697–5717. https://doi.org/10.5194/acp-20-5697-2020

    2020 doi

  2. [9]

    The microphysical pathway to contrail formation,

    Kärcher, B., Burkhardt, U., Bier, A., Bock, L., and Ford, I. J., “The microphysical pathway to contrail formation,”Journal of Geophysical Research: Atmospheres, Vol. 120, 2015, pp. 7897–7927. https://doi.org/10.1002/2015JD023491

    2015 doi

  3. [10]

    Contrail formation on ambient aerosol particles for aircraft with hydrogen combustion: a box model trajectory study,

    Bier, A., Unterstrasser, S., Zink, J., Hillenbrand, D., Jurkat-Witschas, T., and Lottermoser, A., “Contrail formation on ambient aerosol particles for aircraft with hydrogen combustion: a box model trajectory study,”Atmospheric Chemistry and Physics, Vol. 24, No. 4, 2024, pp. ...

    2024 doi

  4. [11]

    Regional and seasonal impact of hydrogen propulsion systems on potential contrail cirrus cover,

    Kaufmann, S., Dischl, R., and Voigt, C., “Regional and seasonal impact of hydrogen propulsion systems on potential contrail cirrus cover,”Atmospheric Environment: X, Vol. 100298, 2024. https://doi.org/10.1016/j.aeaoa.2024.100298

    2024

  5. [12]

    MeasurementsofparticleemissionsofanA350-941burning100%sustainableaviationfuels in cruise,

    Dischl, R., Sauer, D., Voigt, C., Harlaß, T., Sakellariou, F., Märkl, R., Schumann, U., Scheibe, M., Kaufmann, S., Roiger, A., Dörnbrack,A.,Renard,C.,Gauthier,M.,Swann,P.,Madden,P.,Luff,D.,Johnson,M.,Ahrens,D.,Sallinen,R.,Schripp,T.,Eckel, G.,Bauder,U.,andLeClercq,P.,“Measurem...

    2024 doi

  6. [13]

    Large-eddysimulationstudyofcontrailmicrophysicsandgeometryduringthevortexphaseandconsequences on contrail-to-cirrus transition,

    Unterstrasser,S.,“Large-eddysimulationstudyofcontrailmicrophysicsandgeometryduringthevortexphaseandconsequences on contrail-to-cirrus transition,”Journal of Geophysical Research: Atmospheres, Vol. 119, 2014, pp. 7537–7555. https: //doi.org/10.1002/2013JD021418

    2014 doi

  7. [14]

    A Large-Eddy Simulation Study of Contrail Ice Number Formation,

    Lewellen, D. C., “A Large-Eddy Simulation Study of Contrail Ice Number Formation,”Journal of the Atmospheric Sciences, Vol. 77, No. 7, 2020, pp. 2585 – 2604. https://doi.org/10.1175/JAS-D-19-0322.1

    2020 doi

  8. [15]

    Contrail microphysics in the near wake of a realistic wing through RANS simulations,

    Guignery, F., Montreuil, E., Thual, O., and Vancassel, X., “Contrail microphysics in the near wake of a realistic wing through RANS simulations,”Aerospace Science and Technology, Vol. 23, No. 1, 2012, pp. 399–408. https://doi.org/10.1016/j.ast.2011. 09.011

    2012 doi

  9. [16]

    Numerical simulation of aerosols in an aircraft wake using a 3D LES solver and a detailed microphysical model,

    Vancassel, X., Garnier, F., and Mirabel, P., “Numerical simulation of aerosols in an aircraft wake using a 3D LES solver and a detailed microphysical model,”International Journal of Sustainable Aviation, Vol. 1, 2014, pp. 139–159. https://doi.org/10.1504/IJSA.2014.065480

    2014

  10. [17]

    Eulerian–Lagrangian CFD-microphysics modeling of a near- field contrail from a realistic turbofan,

    Cantin, S., Chouak, M., Morency, F., and Garnier, F., “Eulerian–Lagrangian CFD-microphysics modeling of a near- field contrail from a realistic turbofan,”International Journal of Engine Research, Vol. 23, No. 4, 2021, pp. 661–677. https://doi.org/10.1177/1468087421993961

    2021 doi

  11. [18]

    SpontaneousCondensationofSteaminSupersonicNozzles,

    Young,J.B.,“SpontaneousCondensationofSteaminSupersonicNozzles,”TechnicalReportA-Turbo,UniversityofCambridge, Department of Engineering, Cambridge, UK, 1980

    1980

  12. [19]

    Classical Nucleation Theory and Its Application to Condensing Steam Flow Calculations,

    Bakhtar, F., Young, J., White, A., and Simpson, D., “Classical Nucleation Theory and Its Application to Condensing Steam Flow Calculations,”Proceedings of The Institution of Mechanical Engineers Part C-journal of Mechanical Engineering Science - PROC INST MECH ENG C-J MECH E, ...

    2005 doi

  13. [20]

    Aparameterizationofcirruscloudformation: Heterogeneousfreezing,

    Kärcher,B.,andLohmann,U.,“Aparameterizationofcirruscloudformation: Heterogeneousfreezing,” JournalofGeophysical Research: Atmospheres, Vol. 108, No. D14, 2003, p. 4402. https://doi.org/10.1029/2002JD003220

    2003 doi

  14. [21]

    Persistent Contrails and Contrail Cirrus. Part I: Large-Eddy Simulations from InceptiontoDemise,

    Lewellen, D. C., Meza, O., and Huebsch, W. W., “Persistent Contrails and Contrail Cirrus. Part I: Large-Eddy Simulations from InceptiontoDemise,” JournaloftheAtmosphericSciences ,Vol.71,No.12,2014,pp.4399–4419. https://doi.org/10.1175/JAS- D-13-0316.1

    2014 doi

  15. [22]

    NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0, National Institute of Standards and Technology,

    Lemmon, E. W., Bell, I. H., Huber, M. L., and McLinden, M. O., “NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 10.0, National Institute of Standards and Technology,” , 2018. https://doi.org/https://doi.org/10.18434/...

    doi

  16. [23]

    The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,

    Wagner, W., and Pruß, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,”Journal of Physical and Chemical Reference Data, Vol. 31, No. 2, 2002, pp. 387–535. https://doi.org/10.1063/1.1461829. 27

    1995 doi

  17. [24]

    Advancements in the field of hygrometry,

    Sonntag, D., “Advancements in the field of hygrometry,”Meteorologische Zeitschrift, Vol. 3, 1994, pp. 51–66. https: //doi.org/10.1127/metz/3/1994/51

    1994 doi

  18. [25]

    Effect of sulfuric acid coating on heterogeneous ice nucleation by soot aerosol particles,

    Möhler, O., Büttner, S., Linke, C., Schnaiter, M., Saathoff, H., Stetzer, O., Wagner, R., Krämer, M., Mangold, A., Ebert, V., and Schurath, U., “Effect of sulfuric acid coating on heterogeneous ice nucleation by soot aerosol particles,”Journal of Geophysical Research: Atmosphe...

    2005 doi

  19. [26]

    Nucleus Formation in Supersaturated Systems,

    Volmer, M., and Weber, A., “Nucleus Formation in Supersaturated Systems,”Zeitschrift für Physikalische Chemie, Vol. 119, No. 1, 1926, pp. 277–301. https://doi.org/10.1515/zpch-1926-11927

    1926 doi

  20. [27]

    Kinetische Behandlung der Keimbildung in übersättigten Dämpfen,

    Becker, R., and Döring, W., “Kinetische Behandlung der Keimbildung in übersättigten Dämpfen,”Annalen der Physik, Vol. 416, No. 8, 1935, pp. 719–752. https://doi.org/10.1002/andp.19354160806

    1935 doi

  21. [28]

    Nucleation in Very Rapid Vapor Expansions,

    Kantrowitz, A., “Nucleation in Very Rapid Vapor Expansions,”The Journal of Chemical Physics, Vol. 19, No. 9, 2004, pp. 1097–1100. https://doi.org/10.1063/1.1748482

    2004 doi

  22. [30]

    Experimental characterization of aircraft combustor soot: Microstructure, surface area, porosity and water adsorption,

    Popovitcheva, O., Persiantseva, N., Trukhin, M., Rulev, G., Shonija, N., Buriko, Y., Starik, A., Demirdjian, B., Ferry, D., and Suzanne, J., “Experimental characterization of aircraft combustor soot: Microstructure, surface area, porosity and water adsorption,”Physical Chemistr...

    doi

  23. [31]

    Wetting and hydration of insoluble soot particles in the upper troposphere,

    Persiantseva, N., Popovicheva, O., and Shonija, N., “Wetting and hydration of insoluble soot particles in the upper troposphere,” Journal of environmental monitoring : JEM, Vol. 6, 2005, pp. 939–45. https://doi.org/10.1039/b407770a

    2005 doi

  24. [32]

    Water interaction with hydrophobic and hydrophilic soot particles,

    Popovicheva, O., Persiantseva, N., Shonija, N., DeMott, P., Koehler, K., Petters, M., Tishkova, V., Demirdjian, B., and Suzanne, J., “Water interaction with hydrophobic and hydrophilic soot particles,”Physical chemistry chemical physics : PCCP, Vol. 10, 2008, pp. 2332–44. https...

    2008 doi

  25. [33]

    R., and Klett, J

    Pruppacher, H. R., and Klett, J. D.,Microphysics of Clouds and Precipitation, Springer, 1997. https://doi.org/10.1007/978-0- 306-48100-0

    1997 doi

  26. [34]

    Water Activity as the determinant for homogeneous ice nucleation in aqueous solutions,

    Koop, T., Luo, B., Tsias, A., and Peter, T., “Water Activity as the determinant for homogeneous ice nucleation in aqueous solutions,”Nature, Vol. 406, 2000, pp. 611–4. https://doi.org/10.1038/35020537

    doi

  27. [35]

    Modelling of cirrus clouds - Part 1a: Model description and validation,

    Spichtinger, P., and Gierens, K. M., “Modelling of cirrus clouds - Part 1a: Model description and validation,”Atmospheric Chemistry and Physics Discussions, Vol. 8, No. 1, 2008, pp. 601–686. https://doi.org/10.5194/acp-9-685-2009

    2008 doi

  28. [36]

    Quantitative evaluation of experimental results on the heterogeneous freezing nucleation of supercooled liquids,

    Vali, G., “Quantitative evaluation of experimental results on the heterogeneous freezing nucleation of supercooled liquids,” Journal of the Atmospheric Sciences, Vol. 28, No. 3, 1971, pp. 402–409. https://doi.org/10.1175/1520-0469(1971)028<0402: QEOERO>2.0.CO;2. 28

    1971 doi

  29. [37]

    A New Ice Nucleation Active Site Parameterization for Desert Dust and Soot,

    Ullrich, R., Hoose, C., Möhler, O., Niemand, M., Wagner, R., Höhler, K., Hiranuma, N., Saathoff, H., and Leisner, T., “A New Ice Nucleation Active Site Parameterization for Desert Dust and Soot,”Journal of the Atmospheric Sciences, Vol. 74, No. 3, 2017, pp. 699–717. https://do...

    2017 doi

  30. [38]

    Some problems in particle technology: A statistical mechanical formulation,

    Hulburt, H. M., and Katz, S., “Some problems in particle technology: A statistical mechanical formulation,”Chemical Engineering Science, Vol. 19, 1964, pp. 555–574. https://doi.org/10.1016/0009-2509(64)85047-8

    1964 doi

  31. [39]

    Condensation of water vapour during supersonic expansion in nozzles,

    Hill, P. G., “Condensation of water vapour during supersonic expansion in nozzles,”Journal of Fluid Mechanics, Vol. 25, No. 3, 1966, p. 593–620. https://doi.org/10.1017/S0022112066000284

    1966 doi

  32. [40]

    A comparison of modelling methods for polydispersed wet-steam flow,

    White, A. J., “A comparison of modelling methods for polydispersed wet-steam flow,”International Journal for Numerical Methods in Engineering, Vol. 57, No. 6, 2003, pp. 819–834. https://doi.org/https://doi.org/10.1002/nme.705

    2003 doi

  33. [41]

    Numerical simulations of homogeneously nucleated natural cirrus and contrail-cirrus. Part 1: How different are they?

    Unterstrasser, S., Gierens, K., Sölch, I., and Lainer, M., “Numerical simulations of homogeneously nucleated natural cirrus and contrail-cirrus. Part 1: How different are they?”Meteorologische Zeitschrift, Vol. 26, No. 6, 2017, pp. 621–642. https://doi.org/10.1127/metz/2016/0777

    2017 doi

  34. [42]

    Contribution to the development of numerical methods for the investigation of phase change processes of compressiblenon-idealfluids,

    Tegethoff, K., “Contribution to the development of numerical methods for the investigation of phase change processes of compressiblenon-idealfluids,”Ph.D.thesis,UniversityofDuisburgEssen,Oct2024.https://doi.org/10.17185/duepublico/82536

    doi

  35. [43]

    A robust numerical scheme for flux calculation in non-ideal flows with phase change,

    Tegethoff, K., and Brillert, D., “A robust numerical scheme for flux calculation in non-ideal flows with phase change,”Journal of Computational Physics, 2025. (under review)

    2025

  36. [44]

    Trent 1000: Boeing 787 Engine,

    Rolls-Royce plc, “Trent 1000: Boeing 787 Engine,” https://www.rolls-royce.com/products-and-services/civil-aerospace/ widebody/trent-1000.aspx, 2025. Accessed April 19, 2025

    2025

  37. [45]

    Quantification of Uncertainity in Computational Fluid Dynamics,

    Roache, P. J., “Quantification of Uncertainity in Computational Fluid Dynamics,”Annual Review of Fluid Mechanics, Vol. 29, No. 1, 1997, pp. 123–160. https://doi.org/10.1146/annurev.fluid.29.1.123

    1997 doi

  38. [46]

    Aerodynamic Contrails: Microphysics and Optical Properties,

    Kärcher, B., Mayer, B., Gierens, K., Burkhardt, U., Mannstein, H., and Chatterjee, R., “Aerodynamic Contrails: Microphysics and Optical Properties,”Journal of the Atmospheric Sciences, Vol. 66, No. 2, 2009, pp. 227 – 243. https://doi.org/10.1175/ 2008JAS2768.1. 29

    2009

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.