On the Effect of Forced-Oscillation Amplitude upon the Flow in a Cubic Cavity Heated Below(Fluids Engineering)

Tanigawa, Hirochika; Nakamura, Noriyuki; Fujita, Satoshi; Funaki, Jiro; Hirata, Katsuya

doi:10.1299/kikaib.75.759_2106

Cited by 3 publications

(15 citation statements)

References 9 publications

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“…Because, we have confirmed in advance that they are strictly periodic. We have already confirmed the numerical accuracies in both non-forced-oscillation and forced-oscillation cases in the terrestrial-gravity environment (Hirata et al, 2006;Tanigawa et al, 2009;Hirata et al, 2013). On the other hand, there might exist unknown factors concerning the numerical accuracy in forced-oscillation cases in low gravity environments.…”

Section: Numerical Proceduressupporting

confidence: 64%

“…The governing equations (1) -(3) are solved by a finite difference method based on the MAC scheme for velocity-pressure coupling using a staggered computational grid, as well as Hirata et al (2006), Tanigawa et al (2009) and Hirata et al (2013). Concerning the mesh size, we adopt 81 3 for the main computations.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…According to our previous studies (Miyanishi et al, 1999;Tanigawa et al, 2000;Hirata et al, 2006;Tanigawa et al, 2009), K is more useful than other global indicators like the Bejan number, the Nusselt number, spatially-averaged internal energy (or spatially-averaged temperature), spatially-averaged vorticity and so on. More specifically, the dominant spectral peaks of K tend to be clearer than those of the other global indicators.…”

Section: Global Indicatormentioning

confidence: 99%

“…Because, during each forcing cycle in the Types (3) - (8), there exists the time interval during which fluid is stationary everywhere and during which temperature is steady conductive. Even if about the start-up is from conductive state, the S4 is tend to be first induced in the terrestrial environment, (Tanigawa et al, 2009). The start-up with the S4 is consistent with the fact that we cannot observe the S4 in the Type (2), where there exists no conductive state at any time during one forcing cycle.…”

Section: Frequency and Amplitude Responsesmentioning

confidence: 99%

“…The full Navier-Stokes equations in three-dimensional Cartesian coordinates are simplified by introducing the Boussinesq approximation. Then, these simplified equations are solved by using the finite difference method (Hirata et al, 2006;Tanigawa et al, 2009;Hirata et al, 2013). We especially focus upon the influences of both Ra η and ω.…”

Section: Introductionmentioning

confidence: 99%

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On <i>g</i>-jitter effects on three-dimensional laminar thermal convection in low gravity

Hirata

Tatsumoto

Nobuhara

et al. 2015

Mechanical Engineering Journal

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We numerically study the forced-oscillation-frequency responses on the three-dimensional thermal convection in a cubic cavity heated from one wall and chilled from its opposite wall in the non-gravitational field at vibrational Rayleigh number (the Rayleigh number based on the cavity's acceleration amplitude instead of the gravitational acceleration) Ra η = 5.0×10 3 -1.1×10 5 , Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillation frequency ω = 1.0×10 0 -1.0×10 3 . The direction of the forced sinusoidal oscillation is parallel to the temperature gradient inside the cubic cavity. We especially focus upon the influences of both Ra η and ω. As a result, five kinds of structures S2 (with a single roll), S4 (with a toroidal roll), S5 (with four roll), S6 (with four roll) and S (with six roll) appear in the tested ranges of Ra η and ω. The S consists of a pair of trident currents, namely, three ascending streams and three matching descending streams in the cubic cavity. And, such flow structures are revealed in detail. Whenever it is not conductive but convective for ω < 5.0×10 2 , convective motion always starts with the S4 from the rest at each forcing cycle. We find out the optimum frequency where the amplitude of a spatially-averaged kinetic energy K , which is defined by the difference between the maximum K and the minimum K over one forcing cycle, attains the maximum at each Ra η . At ω = , the flow structure is characterised by the S4. So, this fact suggests that the optimum frequency can be related with the S4. In addition, we show the occurrence condition for convection as a function of Ra η and ω, and the boundary for the quasi-steady approximation which is permissible at ω ≲ 10 0 from a quantitative viewpoint.

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Section: Numerical Proceduressupporting

confidence: 64%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Global Indicatormentioning

confidence: 99%

Section: Frequency and Amplitude Responsesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On <i>g</i>-jitter effects on three-dimensional laminar thermal convection in low gravity

Hirata

Tatsumoto

Nobuhara

et al. 2015

Mechanical Engineering Journal

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Thermal Convection in an Oscillating Cube at Various Frequencies and Amplitudes

Hirata

Fujita

Okaji

et al. 2013

JTST

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In this study, the authors numerically investigate the frequency response on the three-dimensional thermal convection in a cubic cavity heated below in the gravitational field, concerning flow characteristics such as flow structure and a global quantity the spatially-averaged kinetic energy . The authors assume incompressible fluid with a Prandtl number Pr = 7.1 (water) and with a Rayleigh number Ra = 1.0×10 4 or 4. can observe the optimum frequency where the amplitude of attains the maximum, each η. And, for both Ra's, becomes the minimum at η = 1.5 -2.0. Especially for Ra = 4.0×10 4 , is affected by the initial conditions. For both Ra's, the maximum of the amplitude uniquely exists at each η, when η < 1.5. On the other hand, we can observe not single but plural peak frequencies with locally-maximum 's each η, when η ≥ 1.5. It is confirmed that such plural frequencies are related with the appearances of various flow structures such as S1, S2, S4, S5, S6 and S8. Especially for Ra = 4.0×10 4 , this relation is also affected by the initial conditions. In addition, the details of a new flow structure S8 is reported.

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Thermal convection inside an oscillating cube analysed with proper orthogonal decomposition

Tatsumoto

Nobuhara

Tanigawa

et al. 2015

Mechanical Engineering Journal

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We reveal the fundamental and dominant flow structures of thermal convection in a cubic cavity under forced oscillation heated differentially by analysing the flow field with the proper orthogonal decomposition (referred to as POD). The database is made of consequtive series of three-dimensional results obtained by the direct numerical simulation based on the Boussinesq approximation for a forcedly-oscillating cube under the zero-gravity environment, at vibrational Rayleigh number (the Rayleigh number based on the cavity's acceleration amplitude instead of the gravitational acceleration) Ra η = 5.0×10 4 -1.1×10 5 , Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillating frequency ω = 1.0×10 0 -2.0×10 2 . The direction of the forced sinusoidal oscillation is parallel to the temperature gradient. It appears that the most energetic POD modes, or the first POD eigenfunctions with large eigenvalues, account for the transient process on flow structures during one forcing cycle. The first eigenfunctions correspond to the steady and laminar flow structures which appear inside a non-oscillating cube in the terrestrial environments. The POD expansion coefficient is found to be useful for predicting a consecutive series of the dominant flow structures. structures, the data can often be represented satisfactorily using only a few of the first modes. We expect that the most important modes could reflect the dominating flow structures. It is usually not possible to have sufficiently high time resolution to get several snapshots of the concerning flow. Furthermore, a snapshot of a given flow may contain random fluctuations due to turbulence and may be a superposition of several coherent flow structures. Hence, it is necessary for us to use some kind of statistical analysis of the data to extract flow structures effectively. In contrast to methods like conditional sampling, the POD does not need any assumptions about flow. Thus, the analyses using the POD have previously been applied to various experimental and computational outputs (Mayer et al., 2007).In the present study, we numerically investigate the influence of the forced oscillation upon the three-dimensional thermal convection in a cubic cavity heated from one wall and chilled from its opposite wall in the non-gravitational field with a vibrational Rayleigh number Ra η = 5.0×10 4 -1.1×10 5 , a Plandtl number Pr = 7.1 (water) and non-dimensional forced-oscillation frequency ω = 1.0×10 0 -2.0×10 2 . The direction of a forced sinusoidal oscillation is parallel to the temperature gradient. The full Navier-Stokes equations in three-dimensional Cartesian coordinates are simplified by introducing the Boussinesq approximation. These simplified equations are solved by using the finite difference method (Hirata et al., 2006, Tanigawa et al., 2009, Hirata et al., 2013. We especially focus upon the identification of the periodically-fluctuating flow during one forcing cycle by means of the use of POD, in order to educe fundamental and dominant flow structures in tran...

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On the Effect of Forced-Oscillation Amplitude upon the Flow in a Cubic Cavity Heated Below(Fluids Engineering)

Cited by 3 publications

References 9 publications

On <i>g</i>-jitter effects on three-dimensional laminar thermal convection in low gravity

On <i>g</i>-jitter effects on three-dimensional laminar thermal convection in low gravity

Thermal Convection in an Oscillating Cube at Various Frequencies and Amplitudes

Thermal convection inside an oscillating cube analysed with proper orthogonal decomposition

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