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Thermo-mechanical analysis of packed beds for large-scale storage of high temperature heat

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Abstract

Thermal storage systems are central elements of various types of power plants operated using renewable and conventional energy sources. Where gaseous heat transfer media are used, a regenerator-type heat storage with a packed bed inventory is a particularly cost-effective solution. However, suitable design tools to analyse the thermo-mechanical aspects of large-scale storage of high temperature heat are currently still missing. As a basis for such a tool, this contribution presents a novel approach for the prediction of the thermo-mechanical behaviour of such storage under thermo-cyclic operation. The relevant relations are formulated on the basis of the discrete element method (DEM). Here, the forces interacting between spherical particles are calculated by spring, dashpot and friction models and the resulting translations and rotations are determined solving Newton’s equations of motion. Coupling these equations with a simplified thermal model that considers the heat resistance within the particles allows for investigation of the thermo-mechanical behaviours of a packed bed. For adequate implementation of this new approach and for reduced computational effort, a time-step control has been implemented and validated. Initial simulation results include the temporal and spatial displacements as well as the forces acting on the individual bodies for a thermo-cyclic operation.

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Abbreviations

c :

Specific heat capacities (J/kg K)

C :

Damping coefficient (kg/s)

e :

Coefficient of restitution

F :

Contact force (N)

g :

Gravitational acceleration (m/s2)

h :

Heat transfer coefficient (W/m2 K)

J :

Moment of inertia (kg m2)

k :

Regenerator heat transfer coefficient (W/m2 K)

K :

Spring constant (N/m)

m :

Mass (kg)

\( \dot{m} \) :

Mass flow rate (kg/s)

\( \vec{n} \) :

Normal directed vector

O :

Total heat transfer surface (m2)

r :

Particle radius (m)

t :

Time (s)

\( \vec{t} \) :

Tangential directed vector

Δt :

Time-step size (s)

T :

Temperature (K)

ν:

Relative velocity (m/s)

V :

Volume (m3)

x :

Particle coordinates (m)

α:

Linear expansion coefficient (K−1)

γ:

Damping parameter

δ:

Penetration depth (m)

ζ:

Normalisation of time

η:

Normalisation of space

λ:

Thermal conductivity (W/m K)

Λ:

Reduced regenerator length

μ:

Coulomb friction coefficient

Π:

Reduced period duration

ρ:

Density (kg/m3)

σ:

Mean stress tensor (Pa)

τ:

Charge/discharge duration (s)

Φ:

Equilibrium criterion (m)

ψ:

Hausen parameter

\( \vec{\omega } \) :

Rotational speed (s−1)

f :

Fluid medium

i :

Particle i

j :

Particle j

n :

Normal direction

s :

Solid medium

t :

Tangential direction

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Authors and Affiliations

  1. Institute of Technical Thermodynamics, German Aerospace Centre (DLR), Pfaffenwaldring 38-40, 70569, Stuttgart, Germany

    Volker Dreißigacker, Hans Müller-Steinhagen & Stefan Zunft

Authors
  1. Volker Dreißigacker
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  2. Hans Müller-Steinhagen
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  3. Stefan Zunft
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Correspondence to Volker Dreißigacker.

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Dedicated to Professor Dr.-Ing. Dr.h.c. mult. Karl Stephan on the occasion of his 80th birthday.

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Dreißigacker, V., Müller-Steinhagen, H. & Zunft, S. Thermo-mechanical analysis of packed beds for large-scale storage of high temperature heat. Heat Mass Transfer 46, 1199–1207 (2010). https://doi.org/10.1007/s00231-010-0684-5

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