====== NASA Rotor 67 ======

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  * [[#tab-en|English]]

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This page contains various informations associated to one of the rotor 67 blade model used in LAVA publications.
 
<btn type="warning" size="md" modal="modal_en">Downloadable files</btn>
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**[[https://gitlab.lava.polymtl.ca/depots_publics/modeles/nasa/rotor67|Git project]]**
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===== Original model =====
  * Original technical report [(cite:urasek1979design>Reid. «Performance of two-stage fan having low-aspect-ratio first-stage rotor blading » 1979.  {{ https://ntrs.nasa.gov/citations/19780025165|pdf}})]: <code>@TechReport{urasek1979design,
author      = {Urasek, D. C. and Gorrell, W. T. and Cunnan, W. S.},
title       = {Performance of two-stage fan having low-aspect-ratio first-stage rotor blading},
institution = {NASA Lewis Research Center Cleveland, OH, United States},
note        = {NASA-TP-1493, url~: \url{https://ntrs.nasa.gov/citations/19790018972}, 1979 (accessed 2021-09-09)}}  
</code>
  * Pictures : <grid>
<col md="6"> 
{{ ..:rotor_67:r67_1.png?nolink&750 |}}
<caption>Fig 1. https://catalog.archives.gov/id/17500553 </caption>
</col>
<col md="6"> 
{{ ..:rotor_67:r67_2.jpeg?nolink&300 |}}
<caption>Fig 2. https://catalog.archives.gov/id/17500556 </caption>
</col>
</grid><code>@Misc{huebler1977records,
author   = {Laity, D.},
title    = {Stage 67 rotor and stage 67 casing half stators mounted. {R}ecords of the {N}ational {A}eronautics and {S}pace {A}dministration, 1903 - 2006. {P}hotographs relating to agency activities, facilities and personnel, 1973 - 2013},
note     = {\href{https://catalog.archives.gov/id/17500553}{https://catalog.archives.gov/id/17500553}, 1980 (accessed 2021-09-09)}, % Fig 1
note     = {\href{https://catalog.archives.gov/id/17500556}{https://catalog.archives.gov/id/17500556}, 1980 (accessed 2021-09-09)}, % Fig 2
}
</code>
  
===== Finite element mesh =====


<grid>
<col md="6"> 
  * Number of nodes: 20393
  * Total number of elements: 6232
  * Number of degrees of freedom: 59964
  * Element type: quadratic pentahedron

{{ ..:rotor_67:r67_mesh_pz.png?nolink&250 }}
<caption> finite element mesh overview (coarse mesh) - {{ :public:modeles:rotor_67:r67_coarse.zip |LaTeX source files}}</caption>
</col>
<col md="6"> 
  * Number of nodes: 83393
  * Total number of elements: 28560
  * Number of degrees of freedom: 246960
  * Element type: quadratic pentahedron

{{ ..:rotor_67:r67_mesh_pz_fine.png?nolink&285 }}
<caption> finite element mesh overview (refined mesh) - {{ :public:modeles:rotor_67:r67_fine.zip |LaTeX source files}}</caption>
</col>
</grid>

===== Material properties =====
  * The original material of the rotor 67 is not defined in the NASA report 
  * Considered properties: Ti-6Al-4V, generic titanium: 
     - Young's modulus E = 108 GPa 
     - density$\rho$ = 4400 kg/m3 
     - Poisson's ratio $\nu$ = 0.34
     - yield stress $\sigma_Y$ = 0.824 GPa
  * First three predicted natural frequencies (with clamped root) for the coarse mesh:
     - 1B: 2040.7 rad/s  / 324.8 Hz
     - 2B: 6345.9 rad/s / 1010.0 Hz
     - 1T: 10734.6 rad/s / 1708.5 Hz
  * First three predicted natural frequencies (with clamped root) for the refined mesh:
     - 1B: 2039.7 rad/s  / 324.6 Hz
     - 2B: 6340.6 rad/s / 1009.1 Hz
     - 1T: 10735.0 rad/s / 1708.5 Hz
===== Featured references from the LAVA =====
  * //Stratégie numérique pour l’analyse qualitative des interactions aube/carter// [(cite:colaitis2021thesis>Colaïtis. « Stratégie numérique pour l’analyse qualitative des interactions aube/carter » 2021.  {{ https://tel.archives-ouvertes.fr/tel-03318777|oai}})] <btn type="primary" modal="art01" size="xs"> BibTex</btn><modal id="art01">
    @Article{colaitis2021thesis,
    author   = {Cola\"{i}tis, Y.},
    title    = {{Stratégie numérique pour l’analyse qualitative des interactions aube/carter}},
    year     = {2021},
    note     = {\href{https://tel.archives-ouvertes.fr/tel-03318777}{oai: tel-03318777}},
    abstract = {This thesis introduces a frequency-domain numerical methodology based on the harmonic balance method coupled to a predictor-corrector continuation algorithm for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. In order to enhance the robustness of the methodology, attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed alternating frequency/time scheme features a Lanczos filtering so that spurious oscillations of the computed nonlinear contact forces become negligible. The proposed methodology is shown to be fully compatible with the numerical models used for existing industrial time integration strategies. The proposed numerical methodology is combined with a model reduction technique on several industrial blades (compressor and fan) as well as on a full 21-blades bladed disk. In order to assess the influence of both contact law regularization and Lanczos filtering, obtained results are thoroughly compared to an existing, state-of-the-art, time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment that was previously confronted to experimental results. The presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. A local stability analysis of the computed solutions is also performed thanks to Floquet theory by means of both monodromy matrix computation and Hill's determinant solution. These results thus complement existing time integration-based results on blade-tip/casing contact, providing a much needed qualitative understanding of the interaction and an accurate estimation of the nonlinear resonance frequency. }}
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Cette page contient diverses informations associées à l'un des modèles de l'aube NASA rotor 67 utilisé dans les publications du LAVA.

<btn type="warning" size="md" modal="modal_fr">Fichiers téléchargeables</btn>
<modal id="modal_fr" title="Libre accès">
**[[https://gitlab.lava.polymtl.ca/depots_publics/modeles/nasa/rotor67|lien vers le projet Git]]**
</modal>

===== Modèle original =====

  * Rapport technique original [(cite:urasek1979design>Reid. «Performance of two-stage fan having low-aspect-ratio first-stage rotor blading » 1979.  {{ https://ntrs.nasa.gov/citations/19780025165|pdf}})]: <code>@TechReport{urasek1979design,
author      = {Urasek, D. C. and Gorrell, W. T. and Cunnan, W. S.},
title       = {Performance of two-stage fan having low-aspect-ratio first-stage rotor blading},
institution = {NASA Lewis Research Center Cleveland, OH, United States},
note        = {NASA-TP-1493, url~: \url{https://ntrs.nasa.gov/citations/19790018972}, 1979 (accessed 2021-09-09)}} 
</code>
  * Photographies : <grid>
<col md="6"> 
{{ ..:rotor_67:r67_1.png?nolink&750 |}}
<caption>Fig 1. https://catalog.archives.gov/id/17500553 </caption>
</col>
<col md="6"> 
{{ ..:rotor_67:r67_2.jpeg?nolink&300 |}}
<caption>Fig 2. https://catalog.archives.gov/id/17500556 </caption>
</col>
</grid><code>@Misc{huebler1977records,
author   = {Laity, D.},
title    = {Stage 67 rotor and stage 67 casing half stators mounted. {R}ecords of the {N}ational {A}eronautics and {S}pace {A}dministration, 1903 - 2006. {P}hotographs relating to agency activities, facilities and personnel, 1973 - 2013},
note     = {\href{https://catalog.archives.gov/id/17500553}{https://catalog.archives.gov/id/17500553}, 1980 (accessed 2021-09-09)}, % Fig. 1
note     = {\href{https://catalog.archives.gov/id/17500556}{https://catalog.archives.gov/id/17500556}, 1980 (accessed 2021-09-09)}, % Fig. 2
}
</code>
  
===== Maillage éléments finis =====
<grid>
<col md="6"> 
  * Nombre de noeuds : 20393
  * Nombre total d'éléments : 6232
  * Nombre de degrés de liberté : 59964
  * Type d'élément : pentaèdre quadratique 

{{ ..:rotor_67:r67_mesh_pz.png?nolink&250 }}
<caption> aperçu du maillage éléments finis (maillage grossier) - {{ :public:modeles:rotor_67:r67_coarse.zip |sources LaTeX}}</caption>
</col>
<col md="6"> 
  * Nombre de noeuds : 83393
  * Nombre total d'éléments : 28560
  * Nombre de degrés de liberté : 246960
  * Type d'élément : quadratic pentahedron

{{ ..:rotor_67:r67_mesh_pz_fine.png?nolink&285 }}
<caption> aperçu du maillage éléments finis (maillage fin) - {{ :public:modeles:rotor_67:r67_fine.zip |sources LaTeX}}</caption>
</col>
</grid>

===== Propriétés matériau =====
  * Le matériau original du rotor 67 n'est pas défini dans le rapport de la NASA 
  * Propriétés considérées : alliage de titane Ti-6Al-4v : 
     - Module d'Young  E = 108 GPa 
     - masse volumique $\rho$ = 4400 kg/m3 
     - coefficient de Poisson $\nu$ = 0,34
     - limite élastique $\sigma_Y$ = 0,824 GPa
  * Trois premiers modes prévus (noeuds de la base encastrés) pour le maillage grossier :
     - 1F : 2040,7 rad/s / 324,8 Hz
     - 2F : 6345,9 rad/s / 1010,0 Hz
     - 1T : 10734,6 rad/s / 1708,5 Hz
  * Trois premiers modes prévus (noeuds de la base encastrés) pour le maillage fin :
     - 1B: 2039,7 rad/s  / 324,6 Hz
     - 2B: 6340,6 rad/s / 1009,1 Hz
     - 1T: 10735,0 rad/s / 1708,5 Hz
===== Références du laboratoire =====
  * //Stratégie numérique pour l’analyse qualitative des interactions aube/carter// [(cite:colaitis2021thesis>Colaïtis. « Stratégie numérique pour l’analyse qualitative des interactions aube/carter » 2021.  {{ https://tel.archives-ouvertes.fr/tel-03318777|oai}})] <btn type="primary" modal="art01fr" size="xs"> BibTex</btn><modal id="art01fr">
    @Article{colaitis2021thesis,
    author   = {Cola\"{i}tis, Y.},
    title    = {{Stratégie numérique pour l’analyse qualitative des interactions aube/carter}},
    year     = {2021},
    note     = {\href{https://tel.archives-ouvertes.fr/tel-03318777}{oai: tel-03318777}},
    abstract = {This thesis introduces a frequency-domain numerical methodology based on the harmonic balance method coupled to a predictor-corrector continuation algorithm for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. In order to enhance the robustness of the methodology, attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed alternating frequency/time scheme features a Lanczos filtering so that spurious oscillations of the computed nonlinear contact forces become negligible. The proposed methodology is shown to be fully compatible with the numerical models used for existing industrial time integration strategies. The proposed numerical methodology is combined with a model reduction technique on several industrial blades (compressor and fan) as well as on a full 21-blades bladed disk. In order to assess the influence of both contact law regularization and Lanczos filtering, obtained results are thoroughly compared to an existing, state-of-the-art, time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment that was previously confronted to experimental results. The presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. A local stability analysis of the computed solutions is also performed thanks to Floquet theory by means of both monodromy matrix computation and Hill's determinant solution. These results thus complement existing time integration-based results on blade-tip/casing contact, providing a much needed qualitative understanding of the interaction and an accurate estimation of the nonlinear resonance frequency. }}
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