One Dimensional Turbulent Transfer Using Random Square Waves – Scalar/Velocity and Velocity/Velocity Interactions

Schulz, Harry Edmar; Júnior, Guilherme Barbosa Lopes; Simões, André Luiz Andrade; Lobosco, Raquel Jahara

doi:10.5772/23563

Cited by 7 publications

(28 citation statements)

References 12 publications

(12 reference statements)

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“…1, adapted from Schulz et al [26] shows the trend to linear profiles for lower values of z* obtained with eqn (1), and also the mentioned straight line covering the whole domain. [26]. Fig.…”

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 74%

“…Schulz et al [26] proposed eqn (1) for the mean concentration of a scalar, n, at interfacial regions. n was taken as the gas concentration in water.…”

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 99%

“…Schulz et al [26,27] used E defined for 0≤n≤1, but here it is defined for 0.01≤n≤1.  is a nondimensional transfer coefficient.…”

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 99%

“…Numerical solutions for transient cases are found in Schulz et al [26,27], Lopes Jr. and Schulz [28], Gonçalves and Schulz [29] and Gonçalves [30]. Eqn (2) is an equivalent integrated second order equation obtained for eqn (1), described by Souza et al [31].…”

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 99%

“…For turbulent scalar transport, Schulz and Janzen [8] and Schulz et al [26,27] used a "random square waves" (RSW) methodology, applied to one-dimensional (1D) mass transport. For this 1D case, four functions were defined to "adjust" a square random signal to the original turbulent record.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Solutions of scalar mean profiles close to gas–liquid interfaces under turbulent free slip motion

Schulz¹,

Gonçalves²

2015

Computational Methods in Multiphase Flow VIII

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Mean profiles of scalar properties close to moving gas-liquid interfaces subjected to turbulence are quantified using Random Square Waves (RSW). The condition of stationary turbulent transfer allows reducing the third order nonlinear governing equation successively to a second order and to a first order equation, which admits theoretical integration, furnishing the set of solutions analyzed in the present study. It is shown that different solutions may apply to different parts of the calculation domain (physical domain). It is also shown that the stationary problem admits a linear profile close to the gas-liquid interface, while a nonlinear function describes the mean properties apart from the interface.

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Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 74%

“…Schulz et al [26] proposed eqn (1) for the mean concentration of a scalar, n, at interfacial regions. n was taken as the gas concentration in water.…”

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 99%

“…Schulz et al [26,27] used E defined for 0≤n≤1, but here it is defined for 0.01≤n≤1.  is a nondimensional transfer coefficient.…”

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 99%

Section: Rsw Equations For 1d Turbulent Transfer At Interfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solutions of scalar mean profiles close to gas–liquid interfaces under turbulent free slip motion

Schulz¹,

Gonçalves²

2015

Computational Methods in Multiphase Flow VIII

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Organização de equações estatísticas para transferência de massa em processos turbulentos

Júnior¹,

Barbosa²

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Cada página aqui escrita está dedicada à família. Não posso jamais esquecer o apoio incondicional e, sem dúvida, imprescindível dado pelos meus pais, Guilherme e Margarida, cujo apoio, paciência e incentivo, foram a força motriz para o sucesso durante o desenvolvimento deste. Aos avôs e avós, cujos ensinamentos diretos e indiretos foram essenciais na minha formação como pessoa, cujas lições valiosas me fazem discernir sobre os caminhos a tomar e sem cujo passado, não haveria o meu presente. Agradeço também aos irmãos. Não só os de sangue: Renata, Roberta, e Rodrigo, que deram todo apoio possível, mas também os de coração que estiveram presentes de coração ao longo desses anos. Não vale citar nomes, que possam gerar ressentimento a outros, mas para quem aqui dedicar um pouco de tempo a esta leitura saberá que estou falando dos AMIGÕES, primos, primas e cunhado que me foram leais do começo ao fim e serviram de impulso nas minhas conquistas. Também não me esqueço dos padrinhos de coração. Meus tios Fábio e Alexandre e as minhas tias Malba e Elza, que foram como pais para mim, dando apoio em tudo que me foi necessário ao longo da minha vida. Aos tio Ivo e Graça, de cujo amor e carinho se deve uma grande parcela do meu equilíbrio na distância de casa, tendo sido excelentes representantes da família tão amada. Aos meus pais, Guilherme e Margarida. Aos meus avôs (in memorian) e minhas avós. Aos meus irmãos de sangue e de coração. Aos padrinhos e madrinhas.

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Turbulence aspects of mass transfer in the thin interfacial region of the concentration boundary layer in gas–liquid systems

Schulz¹,

Lavin²,

Gonçalves³

2017

Int. J. CMEM

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The quantification of overall mass transfers in gas-liquid systems depends on the spatial evolution of the relevant variables close to the interface of the two phases. When turbulence is present (in the present study the turbulence is considered in the liquid phase), the methods of treating the problem consider the differential form of the momentum and mass conservation equations. The continuous hypothesis that underlies these equations in principle allows verifying the limiting trends very close to the interface. Because the theoretical concepts of turbulence are defined using statistical tools, the mentioned verification depends on the intrinsic definitions used in the statistical approach. In this study the turbulent mass transfer parameters are calculated for the thin region close to the interface based on the tool of random square waves (RSW). Theoretical results are obtained and analyzed in the context of existing experimental data and conceptual discussions of the literature, using a constant 'reduction function', a parameter defined in this methodology. The results of the present analysis show that the RSW method allows obtaining functional trends, as well as indicate the adequacy of using a variable reduction function to better represent reality.

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One Dimensional Turbulent Transfer Using Random Square Waves – Scalar/Velocity and Velocity/Velocity Interactions

Cited by 7 publications

References 12 publications

Solutions of scalar mean profiles close to gas–liquid interfaces under turbulent free slip motion

Solutions of scalar mean profiles close to gas–liquid interfaces under turbulent free slip motion

Organização de equações estatísticas para transferência de massa em processos turbulentos

Turbulence aspects of mass transfer in the thin interfacial region of the concentration boundary layer in gas–liquid systems

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