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Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

Übertragungsverhalten beim Wärmeentzug aus einem zylindrischen Wärmespeicher mit Kugelschüttung

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Abstract

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Red = 10.3–2200, porosityɛ=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu d=f [modified Prandtl numberPr * (d/D), Red) and Fourier numberFo = f(d/D, L/D, Pr*, Red).

Zusammenfassung

Das Übertragungsverhalten beim Wärmeentzug aus einem zylindrischen Wärmespeicher mit Kugelschüttung wurde experimentell untersucht. Dabei wurden verschiedene Einflußgrößen berücksichtigt, wie beispielsweise der Volumenstrom, der Kugeldurchmessser der Schüttungsteilchen im Speicherbehälter, die Temperaturdifferenz zwischen der strömenden kalten Luft und der Schüttung sowie die physikalischen Eigenschaften des Speichermaterials.

Die Experimente wurden in folgenden Bereichen durchgeführt:

  • Reynoldszahl, bezogen auf den Kugeldurchmesser des Schüttguts im SpeicherRe d = 10.3–2200.

  • Porosität der Kugelschüttungɛ=0.310–0.475.

  • Verhältnis von Kugeldurchmesser der Schüttung und Zylinderdurchmesser des Speichersd/D=0.0075–0.177 und

  • Verhältnis von Zylinderlänge und Zylinderdurchmesser des SpeichersL/D=2.5–10.0.

Es wurde festgestellt, daß insbesondere der Volumenstrom und die Abmessungen der kugelförmigen Teilchen der Schüttung von großer Bedeutung bei der Bewertung des Übertragungsverhaltens beim Wärmeentzug, speziell im Bereich der Speicherwand, sind. Wenn der Volumenstrom und der Kugeldurchmesser des Schüttguts erhöht wird, bei einem vorgegebenen Durchmesser des Speicherbehälters, steigt der mittlere Wärmetransportkoeffizient zwischen zuströmender kalter Luft und der heißen Schüttung; der Zeitraum der Entladung verkürzt sich.

Die experimentell ermittelte Abhängigkeit des mittleren Wärmetransportkoeffizienten zwischen der strömenden Luft und der Kugelschüttung von der Entladungszeit des Wärmespeichers ermöglicht die Bestimmung der Abhängigkeit dieses Entladevorgangs von der NusseltzahlNu d f (modifizierte PrandtlzahlPr *, d/D, Red) und der FourierzahlFo =f(d/D, L/D, Pr*, Red).

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Abbreviations

A :

sectional area of cylindrical bed

α :

thermal diffusivity

α * :

modified thermal diffusivity,λ*/(ϱ cp)*

Cp :

specific heat at constant pressure

D :

diameter of cylindrical porous layer

d :

diameter of spherical particle

d * :

effective diameter of spherical particle, 6/S υ

Fo :

Fourier number,λ*τc/d2

Fo * :

Modified Fourier number, Fo/[(d/D)−1.09(L/D)0.322Pr*1/3]

g :

gravitational acceleration

h :

heat transfer coefficient between flowing fluid and the particles

L :

length of cylindrical porous layer

Nu d :

Nusselt number,h m d/λ

Pr * :

Prandtl number, ν/α*

Δp :

pressure drop

Q :

heat

R :

distance in the radial direction

Re d :

Reynolds number,Ud/ν

Re *d :

modified Reynolds number,U* d/ν

S t :

total surface area if spherical solid particles packed in porous bed

S υ :

specific surface, surface of the particles per unit volume of porous bed,S t[AL(1−ɛ)]

T :

temperature

ΔT :

temperature difference between inlet fluid and initial porous bed, Tout−Tin

U :

superficial fluid velocity based on empty cylinder

U * :

actual velocity of fluid in the bed,U/ɛ

X :

distance in the axial direction

ɛ :

porosity

γ :

specific weight

λ :

thermal conductivity

λ * :

effective thermal conductivity of porous medium

μ :

viscosity

ν :

kinematic viscosity

ϱ :

density

τ :

time

τ c :

time period to finish the heat release porous layer

f, s :

fluid (air) and solid (spherical particle) phases, respectively

in:

inlet to porous layer

m :

mean value

out:

outlet from porous layer

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Authors and Affiliations

  1. Department of Mechanical Engineering, Kitami Institute of Technology, Koen-Chol 65 Kitami, 090, Hokkaido, Japan

    H. Inaba (Associate Professor) & T. Fukuda (Research Assistant)

  2. Department of Mechanical Engineering, Muroran Institute of Technology, Mizomoto-Cho Muroran, 050, Hokkaido, Japan

    H. Saito (Professor)

  3. Lehrstuhl A für Thermodynamik, Technische Universität München, Arisstraße 21, D-8000, München 2, FRG

    F. Mayinger (Professor)

Authors
  1. H. Inaba
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  2. T. Fukuda
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  3. H. Saito
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  4. F. Mayinger
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Inaba, H., Fukuda, T., Saito, H. et al. Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles. Wärme- und Stoffübertragung 22, 325–333 (1988). https://doi.org/10.1007/BF01387888

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  • DOI: https://doi.org/10.1007/BF01387888

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