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Cited by 2Spacecraft and Cryogenic TechnologiesSuperconducting Materials and ApplicationsGas Dynamics and Kinetic Theory

Model Based Exploration of Physical Parameters for Liquid Hydrogen System Insulation Performance

Open access
Maynard, N, Louriou, C, Estebe, B·2024·IOP Conference Series: Materials Science and Engineering
DOI 10.1088/1757-899x/1301/1/012067
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Abstract

Cryogenic Systems require a highly efficient insulation so as to limit the heat ingress and boil-off, which is generally achieved through the use of vacuum combined with an insulated media. The performance of Multi layer Insulation (MLI) will be investigated with detailed thermal models developed to account for all the heat transfer contributions, solid conduction, gaseous conduction and radiation. Results are presented for an usual cold vacuum pressure (CVP) corresponding to high vacuum (<10−6 torr) and compared with available experimental measurements for state of the art technologies. The nominal thermal performances are then evaluated for a cold temperature of 20K (representative of liquid hydrogen storage temperature), for a degraded CVP with hydrogen and nitrogen as residual gasses and for increased hot boundary temperatures. Other parameters are also discussed such as, the number of layers, material, layers density, venting options, assembly process and material optical properties. Finally, a sensitivity of the thermal performance is also presented with a pressure gradient through the insulation thickness, that could be induced by cryopumping, materials outgassing, pumping times or small leakages.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper develops and compares bulk and layer-by-layer thermal models for MLI cryogenic insulation, extending gas-conduction treatment across 10^-6 to 10^3 torr and evaluating parameters for liquid-hydrogen-relevant 20 K cold boundary conditions. It finds the high-vacuum-to-no-vacuum transition is not well captured by uniform-pressure models, and couples MOLFLOW+ TPMC with layer-by-layer modeling to show non-uniform residual pressure and cryopumping on cold layers can affect heat-flux predictions.

Key findings

  • The modified gas-conduction formulation extends the models from high vacuum (<10^-6 torr) to 10^3 torr and predicts HV and NV heat flux reasonably for the N2 baseline, but the original linear pressure dependence fails in the soft-vacuum transition around 10^-3 torr.
  • Parameter study: the thermal accommodation coefficient shifts the transition to lower pressure when increased (base TAC around 0.8 for N2 and 0.2 for H2); changing gas shifts heat flux according to atmospheric conductivity, with H2 having greater conductivity; increasing temperature differential increases heat flux across the pressure range; varying thickness decorrelates number of layers and density and shows their uniform impact; low emissivity is justified.
  • The layer-by-layer model with an in-house thermal solver and temperature-varying TAC/emissivity (0.015 at 80 K, 0.03 at 273 K) gives no significant changes from bulk models, which questions the uniform residual pressure assumption.
  • TPMC MOLFLOW+ simulations of 40-layer MLI (25 layers/cm, no spacers) show non-uniform pressure distributions; the perforated geometry (3.4 mm square holes, 0.075% void) has a lower transition slope than the nonperforated side-evacuated case; cryopumping at 20 K causes a sudden behavior change before a new “stable” state.

Methods

  • Bulk semi-empirical Lockheed/McIntosh models separate solid, gas, and radiation contributions; gas conduction is modified via Eq. 2 linking Kennard’s HV formulation to atmospheric gas conductivity, and TAC is extended via Eq. 3 from Song and Yovanovich. Results are compared against the Fesmire Kaganer k-line baseline: 26 experimental tests, 6 unperforated MLI assemblies, N2 residual gas, 10^-6 to 10^3 torr, 77–293 K, 29 layers, and 16.1 layer/cm.
  • A layer-by-layer model is solved with an in-house thermal solver between nodes linked by thermal resistances; radiation is modeled as two planar gray bodies, solid conduction uses the spacer conductivity, and TAC and emissivity vary with temperature.
  • TPMC MOLFLOW+ simulations model residual pressure in two 40-layer MLI geometries (perforated vs. nonperforated side evacuation), with N2 only; outgassing is set at 1E-8 mbar L/s/cm, a sticking factor of 0.1 is used for evacuation, and cryopumping is modeled with a sticking factor of 1E-3 below 77 K starting at the 9th layer and increasing inward by 1E-3. Arbitrary distributions tested include a Gaussian mean 20 with standard deviation 6, linear decreasing from 1000% to 10%, and linear increasing from 10% to 1000%.

Limitations

  • Stated: no H2 data is available for the Lockheed models; TAC data are scarce for cryogenic ranges and the extension is based on correlations covering temperatures over 300 K; MOLFLOW+ is validated only in HV and cannot handle multispecies, so only N2 is considered; the steady-state approach may be compromised by transient and complex interactions at higher pressure; cryotrapping cannot be modeled; the two geometries are hardly comparable because side evacuation can drop the whole distribution by several decades; and it is too early to establish formal recommendations.
  • Stated/evident: bulk models use the average temperature in the MLI, so a finer understanding of cold-boundary-temperature effects is not possible; no parameter affects the slope of the transitional state except adding a nonphysical pressure power coefficient, which is ruled out.
  • Evident from the text: cryopumping heat-flux behavior may be hard to witness and potentially nonphysical due to exothermic N2 deposition and transient cold-boundary changes; results depend on empirical constants and modeling assumptions.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1088/1757-899x/1301/1/012067

Cites

9 of 9 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

1 of 5 cited sources checked · 0 supported · 0 flagged · accuracy not yet measured

  • Findingreasoning

    The transitional state between high vacuum and no vacuum displays a curve that is not well captured.

    “It has been noticed that the transitional state between HV and NV displays a curve that is not well captured”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.
  • Findingown data

    The layer-by-layer model results do not provide significant changes from the bulk models.

    “The results do not provide significant changes from the bulk models”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.
  • Findingown data

    The model predicts rather well the heat flux values in high vacuum and no vacuum state for the specific set with N2 residual gas and a cold boundary temperature of 77K.

    “At first, it can be seen that the model predicts rather well the heat flux values in HV and NV state, which gives us a hint on the proper modelisation of the solid and radiative contributions”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.
    • The authors state this as an assumption: The upper limit of heat flux is the gas conductivity at atmospheric pressure for the specific set with N2 residual gas and a cold boundary temperature equal to 77K.
  • Findingnone given

    None of the studied parameters has an effect on the slope of the transitional state.

    “Furthermore, none of them has an effect on the slope of the transitional state”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.
  • Findingnone given

    The thermal accommodation coefficient shifts the transitional state towards lower pressure when increasing.

    “The TAC shifts the transitional state towards the lower pressure when increasing (the base TAC considered is around 0.8 for N2 and 0.2 for H2).”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.
  • May combine two claims. 17
  • Classified as probably not a substantial claim. 8

  • May combine two claims.

    Premisecitation

    Hastings comparison with experimental data on a range from 10^-6 torr to 10^3 torr emphasized that while Lockheed non-modified equations provide good results in high vacuum, the linear dependence in pressure of the gas contribution does not capture properly the degraded vacuum transitional state nor the no vacuum state.

    “while providing good results in high vacuum (HV) in the case of the Lockheed non modified equations, the linear dependance in pressure of the gas contribution, which takes over at around 10 -3 torr, does not capture properly the degraded vacuum transitional state (soft vacuum (SV)) nor the no vacuum (NV) state”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [1] Fesmire, 2018, Cylindrical Cryogenic Calorimeter Testing of Six Types of Multilayer Insulation Systems, Cryogenics source

      Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingnone given

    The linear increasing distribution has a consistent lower slope all along the transitional range, with lower values of pressure in the distribution.

    “Finally, the Linear increasing has a consistent lower slope all along the transitional range, with lower values of pressure in the distribution”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Findingnone given

    Solid conduction usually takes over radiation in high vacuum.

    “while solid conduction usually takes over radiation in HV”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Findingreasoning

    While the slope is unchanged for the non perforated case, it is lower in the perforated case.

    “While the slope is unchanged for the non perforated case, as the pressure is not fluctuating a lot, it is lower in the perforated case”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Findingreasoning

    The evacuation of the side plays an important role, and can make the whole distribution drop from several decades, therefore the comparison of the two geometries is hardly comparable.

    “Moreover, the evacuation of the side plays an important role, and can make the whole distribution drop from several decades, therefore the comparison of the two geometries is hardly comparable.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    Changing the gas nature shifts the heat flux with regard to the conductivity value of the gas at atmospheric pressure, with H2 having a greater conductivity.

    “Changing the gas nature will shift the heat flux with regard to the conductivity value of the gas at atmospheric pressure, H2 having a greater conductivity.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Findingown data

    Varying thickness permits decorrelation of the number of layers and density, and shows their quite uniform impact overall.

    “the result displayed, with varying thickness, permits to decorrelate the two, and show their quite uniform impact overall.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Findingreasoning

    The option set is impacting greatly the pressure as molecules outgassed or reaching the innermost layers, though the probability is low, will hit so many times the surfaces that they will eventually be captured.

    “The option set is impacting greatly the pressure as the molecules outgassed or reaching the innermost layers, though the probability is low, will hit so many times the surfaces that they will eventually be captured.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    When cryopumping is considered at non-uniform pressure 20K, while it does not seem to affect the lower pressures, a change of behavior happens rather suddenly before reaching a new stable state.

    “When cryopumping is considered (non-uniform pressure 20K), while it does not seem to affect the lower pressures, a change of behavior happens rather suddenly before reaching a new”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Findingnone given

    The linear decreasing distribution starts at a lower slope, but quickly matches the uniform, only showing a worsening of the predicted values.

    “The linear decreasing seems to also start at a lower slope, but quickly matches the uniform, only showing a worsening of the predicted values.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Findingnone given

    The gaussian pressure distribution shows a lower slope around 10^-3 Pa, and then matches the slope of the uniform distribution.

    “The gaussian shows a lower slope around 10 -3 Pa, and then matches the slope of the uniform.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Data on thermal accommodation coefficient for cryogenic ranges of temperature are rather hard to find; some fixed values depending only on the molar mass of gas and surface material are found in [5].

    “Data on TAC for cryogenic ranges of temperature are rather hard to find, some fixed values depending only on the molar mass of gas and surface material are found in [5].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [5] Kaganer, 1969, Thermal Insulation in Cryogenic Engineering, Israel Program for Scientific Translations Jerusalem

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The thermal accommodation coefficient tends to the value 1 when the gas reaches its boiling point, and decreases with temperature.

    “It is reported in various studies as in [6] that the TAC tends to the value 1 when the gas reaches its boiling point, and decreases with temperature.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [6] McIntosh Glen, 1994, Layer by Layer MLI Calculation Using a Separated Mode Equation source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    One could expect an interesting improvement of the prediction from the linear increasing distribution considering Figure 2.

    “one could expect to see an interesting improvement of the prediction considering the Figure 2.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    If the active vacuum pumping is stopped too soon, this could have an impact with the remaining outgassing.

    “This remark is important, as if the active vacuum pumping is stopped too soon, this could have an impact with the remaining outgassing.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationown data

    The gaussian distribution situation shows a possible improvement of the prediction seen in Figure 2.

    “This situation as it is, shows a possible improvement of the prediction seen in Figure 2.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning

    MOLFLOW+ cannot handle multispecies, so the present development only considers N2 as residual gas.

    “MOLFLOW+ can not handle multispecies, the present development only considers N2 as residual gas, as it is the principal component of air.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationnone given

    The results presented support the evaluation of the theoretical heat ingress into a liquid hydrogen tank and the process manufacturing of MLI blankets.

    “The results presented in this work support the evaluation of the theoretical heat ingress into a liquid hydrogen tank and the process manufacturing of MLI blankets.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • May combine two claims.

    Premisecitation

    Song and Yovanovich [10] reported an extensive study over various materials and gas, but only covering temperatures over 300K.

    “An extensive study was reported by Song and Yovanovich [10] over various materials and gas, but only covering the temperatures over 300K.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [10] Song, 1987, Correlation of Thermal Accommodation Coefficient for Engineering Surfaces, ASME HTD

  • May combine two claims.

    Interpretationown data

    The model based exploration has established a review of two ways of modeling MLI cryogenic insulation, bulk with average temperature and layer-by-layer models, while extending their application domain to a wider range of pressure through a modification of the gaseous contribution.

    “This model based exploration has established a review of two ways of modeling MLI cryogenic insulation: bulk with average temperature and layer-by-layer models, while extending their application domain to a wider range of pressure (10 -6 to 10 3 torr) through a modification of the gaseous contribution.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductnone given

    MOLFLOW's validated use is only in high vacuum, and the transient and complex interactions at higher pressure might compromise the steady-state approach.

    “Those results have to be considered carefully, as MOLFLOW's validated use is only in HV, and the transient and complex interactions at higher pressure might compromise the steady-state approach.”
    Quote in the paperSubstantial claim
21 of 21

  • The authors state this as an assumption.

    The heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity.

    “It is assumed in those models and later on in this paper that the heat transfer contributions through solid contacts, gas, and radiation can be separated and added to recover the total effective conductivity, which is expressed in Equation ( 1).”

  • The authors state this as an assumption.

    The upper limit of heat flux is the gas conductivity at atmospheric pressure for the specific set with N2 residual gas and a cold boundary temperature equal to 77K.

    “as well as a good assumption that the upper limit is the gas conductivity at atmospheric pressure, for the specific set previously detailed with N2 residual gas and a CBT equal to 77K.”

  • The authors state this as an assumption.

    The residual pressure distribution in MLI is uniform.

    “This insight questions the hypothesis of residual uniform pressure distribution, which is tackled in the following development.”

  • The paper relies on this without support.

    No data is available for H2 in the Lockheed models.

    “No data is available for H2, which is a first limitation of those models that are limited in this case.”
4 of 4

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • McIntosh is cited as reference [7], which lists Lafferty

    Minor

    The reference list identifies [7] as Lafferty's work; the McIntosh paper is [6].

  • Hastings is cited as reference [1], which lists Fesmire and Johnson

    Minor

    The reference list identifies [1] as a paper by Fesmire and Johnson. Hastings is listed under [3].

  • Heat-flux results point to Figure 4 rather than Figure 5

    Minor

    The passage says the layer-by-layer heat-flux results are displayed in Figure 4, whose caption describes pressure distributions. Figure 5 is captioned as the resulting heat flux.

3 of 3

Cites

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Related

Authors
Maynard, N., Louriou, C., & Estebe, B.
Affiliations
Airbus (France) (FR)
Corresponding author
Louriou, C
Venue
IOP Conference Series: Materials Science and Engineering
Publisher
IOP Publishing
Published
2024-05-01
Volume
1301
Issue
1
Pages
012067
ISSN
  • 1757-8981 (ISSN-L)
  • 1757-899X
DOI
10.1088/1757-899x/1301/1/012067
OpenAlex
W4400360717
Semantic Scholar
14c3ab08d22199b1bdd7a930aa92ce44cc9aaa78
Cited by
2
References
8
Citations by year
2025: 1 · 2024: 1
FWCI
1.64
Type
conference paper
Language
en
Open access
Licence
Locations
IOP Conference Series Materials Science and Engineering (publishedVersion, cc-by)
Topics
  • Physical Sciences › Engineering › Aerospace Engineering › Spacecraft and Cryogenic Technologies
  • Physical Sciences › Engineering › Biomedical Engineering › Superconducting Materials and Applications
  • Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
Keywords
liquid hydrogen storage, multilayer insulation, cryogenic insulation, thermal modeling, heat transfer, radiation heat transfer, boil-off, residual gas, insulation density, venting, optical properties, sensitivity analysis, cryopumping, outgassing

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