Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock
Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geom...
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E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1970 |
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| Reproduktion: |
Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 |
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| Übergeordnetes Werk: |
in: Journal of Quantitative Spectroscopy and Radiative Transfer - Amsterdam : Elsevier, 10(1970), 7, Seite 775-787 |
| Übergeordnetes Werk: |
volume:10 ; year:1970 ; number:7 ; pages:775-787 |
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NLEJ177306424 |
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| 245 | 1 | 0 | |a Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock |
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| 520 | |a Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. | ||
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(DE-627)NLEJ177306424 (DE-599)GBVNLZ177306424 DE-627 ger DE-627 rakwb eng Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock 1970 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 Pirri, A.N. oth Clarke, J.H. oth in Journal of Quantitative Spectroscopy and Radiative Transfer Amsterdam : Elsevier 10(1970), 7, Seite 775-787 (DE-627)NLEJ177070757 (DE-600)1491916-3 0022-4073 nnns volume:10 year:1970 number:7 pages:775-787 http://linkinghub.elsevier.com/retrieve/pii/0022-4073(70)90020-8 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 10 1970 7 775-787 |
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(DE-627)NLEJ177306424 (DE-599)GBVNLZ177306424 DE-627 ger DE-627 rakwb eng Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock 1970 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 Pirri, A.N. oth Clarke, J.H. oth in Journal of Quantitative Spectroscopy and Radiative Transfer Amsterdam : Elsevier 10(1970), 7, Seite 775-787 (DE-627)NLEJ177070757 (DE-600)1491916-3 0022-4073 nnns volume:10 year:1970 number:7 pages:775-787 http://linkinghub.elsevier.com/retrieve/pii/0022-4073(70)90020-8 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 10 1970 7 775-787 |
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(DE-627)NLEJ177306424 (DE-599)GBVNLZ177306424 DE-627 ger DE-627 rakwb eng Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock 1970 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 Pirri, A.N. oth Clarke, J.H. oth in Journal of Quantitative Spectroscopy and Radiative Transfer Amsterdam : Elsevier 10(1970), 7, Seite 775-787 (DE-627)NLEJ177070757 (DE-600)1491916-3 0022-4073 nnns volume:10 year:1970 number:7 pages:775-787 http://linkinghub.elsevier.com/retrieve/pii/0022-4073(70)90020-8 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 10 1970 7 775-787 |
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(DE-627)NLEJ177306424 (DE-599)GBVNLZ177306424 DE-627 ger DE-627 rakwb eng Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock 1970 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 Pirri, A.N. oth Clarke, J.H. oth in Journal of Quantitative Spectroscopy and Radiative Transfer Amsterdam : Elsevier 10(1970), 7, Seite 775-787 (DE-627)NLEJ177070757 (DE-600)1491916-3 0022-4073 nnns volume:10 year:1970 number:7 pages:775-787 http://linkinghub.elsevier.com/retrieve/pii/0022-4073(70)90020-8 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 10 1970 7 775-787 |
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(DE-627)NLEJ177306424 (DE-599)GBVNLZ177306424 DE-627 ger DE-627 rakwb eng Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock 1970 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. Elsevier Journal Backfiles on ScienceDirect 1907 - 2002 Pirri, A.N. oth Clarke, J.H. oth in Journal of Quantitative Spectroscopy and Radiative Transfer Amsterdam : Elsevier 10(1970), 7, Seite 775-787 (DE-627)NLEJ177070757 (DE-600)1491916-3 0022-4073 nnns volume:10 year:1970 number:7 pages:775-787 http://linkinghub.elsevier.com/retrieve/pii/0022-4073(70)90020-8 GBV_USEFLAG_H ZDB-1-SDJ GBV_NL_ARTICLE AR 10 1970 7 775-787 |
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accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock |
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Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock |
| abstract |
Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. |
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Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. |
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Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ177306424</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20210706044402.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">070505s1970 xx |||||o 00| ||eng c</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ177306424</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVNLZ177306424</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Accuracy of differential approximation for radiative ionization in cold precursor of axisymmetric detached shock</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">1970</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">z</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zu</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Radiative ionization in the cold precursor of the shock preceding a blunt body immersed in a hypersonic monatomic gas flow is studied using the Milne-Eddington type differential approximation. In order to assess the accuracy of the differential approximation for a multidimensional, axisymmetric geometry, the results are compared with earlier work that presents an exact formulation. The precursor gas is non-emitting with a prescribed frequency dependent absorption coefficient, and the governing differential equation describing the radiation in the precursor is the (elliptic) Helmholtz equation; specification of the boundary conditions pose an interesting dilemma. An integral formulation is proposed and the resulting integral equation is solved to yield the spectral radiant energy density. Calculations of the volumetric photon absorption and the degree of ionization for argon in the near precursor are presented for a downstream degree of ionization on the stagnation streamline of 0.8, an upstream temperature of 300^oK, and an upstream pressure of 10^-^3 atm. The results are found to be sufficiently accurate for many purposes when the influenced point is only a few photon mean free paths from the surface and is close to the shock axis.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Elsevier Journal Backfiles on ScienceDirect 1907 - 2002</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pirri, A.N.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Clarke, J.H.</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">in</subfield><subfield code="t">Journal of Quantitative Spectroscopy and Radiative Transfer</subfield><subfield code="d">Amsterdam : Elsevier</subfield><subfield code="g">10(1970), 7, Seite 775-787</subfield><subfield code="w">(DE-627)NLEJ177070757</subfield><subfield code="w">(DE-600)1491916-3</subfield><subfield code="x">0022-4073</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:10</subfield><subfield code="g">year:1970</subfield><subfield code="g">number:7</subfield><subfield code="g">pages:775-787</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://linkinghub.elsevier.com/retrieve/pii/0022-4073(70)90020-8</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_H</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-SDJ</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">10</subfield><subfield code="j">1970</subfield><subfield code="e">7</subfield><subfield code="h">775-787</subfield></datafield></record></collection>
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