^{1}

^{1}

^{1}

This paper presents a numerical case study of heat transfer mechanisms during the charging process of a stratified thermal storage tank applied in a specific adsorption heat pump cycle. The effective thermal conductivity of the heat transfer fluid during the charging process is analyzed through CFD simulations using Unsteady Reynolds-averaged Navier-Stokes equations (URANS). The aim of the study is to provide an equivalent thermal conductivity for a one-dimensional storage tank model to be used in a system simulation of the complete adsorption heat pump cycle. The influence of the turbulent mixing and also the advection effect due to fluid bulk motion are investigated. The results show that in the case considered here, the turbulence effect on the effective thermal conductivity is more considerable than the advection effect.

The achievable coefficient of performance (COP) of adsorption heat pump systems can be increased by coupling the adsorber in a specific way to a stratified thermal storage tank [

tank. Such models are commonly employed in system simulations of solar thermal heating and cooling systems, see e.g. [

In order to be able to describe the thermal behavior of the storage tank in a system model, the influences of turbulent mixing and advection on the effective thermal conductivity have been investigated by means of a CFD model of thermal storage tank. Effective thermal conductivity is the determining parameter for the description of stratification and mixing in the thermal storage tank. Regarding operation of the thermal storage, the main aim is to maintain thermal stratification by minimizing any mixing effects that may be caused by inertial effects of fluid insertion, turbulence effects or buoyancy effects in case of a temperature mismatch of inserted fluid. For this reason, the convection heat transfer plays an important role in the thermal storage tank. Convection heat transfer includes both diffusion (individual motion of fluid particle in small scale) and advection (bulk fluid motion in large scale). Thermal analysis of the storage tank has been widely studied both experimentally and numerically by a number of researchers. Zurigat et al. [

1) Plume entrainment

Near the inlet region, momentum effects of the fluid entering the storage are commonly more important than buoyancy effects. In such situations, fluid plume can be defined as fluid jet. Because of the velocity gradient and shear effect, the surrounding fluid will be entrained, resulting in an increased mixing effect [

2) Inlet jet mixing

Because of the high momentum of the entering fluid, turbulent mixing in the near of the inlet leads to a locally increased mixing. One of the advantages of the stratification pipe for the charging process is that turbulent kinetic energy can be partly bounded inside of the stratification pipe. Therefore, the mixing effect influences have been more restricted.

3) Conduction heat transfer within the storage medium and storage tank wall

Conductive heat transfer tends to reduce the temperature gradient and consequently more destratification. In the current study the storage tank for application in the adsorption heat pump cycle has been simulated and its charging process has been investigated. The charging of the storage tank has been carried out through a rigid inlet stratification pipe with a similar structure to the stratification pipe marketed by Sailer GmbH [

・ Height: 1.9 m;

・ Diameter: 19 cm;

・ Width of the heater and cooler ports: 0.41 cm (as ring around tank perimeter);

・ Heater outlet position: 57% of the storage height from the bottom (1.08 m);

・ Heater inlet position: at the top of the storage tank;

・ Cooler outlet position: 25% of the storage height from the bottom (0.47 m);

・ Cooler inlet position: at the bottom of the storage tank.

The development potential of this adsorption heat pump cycle bases upon the internal heat recovery between adsorption and desorption processes [

The function of the heater cycle is to provide that part of the desorption heat, which is not covered from the released heat during the adsorption half cycle. The heat transfer fluid is extracted at the level of the heater position (heater outlet in CFD model) and after heating up, will be inserted at the top of the tank. The function of cooler cycle in this application is to provide a heat sink. The cooler cycle absorbs that part of the released heat during the adsorption that will not be used for the desorption half cycle.

The storage tank is considered here for a high-temperature adsorption cycle utilizing zeolite 13X/water as the

adsorption pair [

Commercial CFD code Ansys Fluent 14.0 based on the finite volume method has been used for the simulation. The fluid cylindrical domain in the storage tank has been simulated as a 2-D axisymmetric CFD model. The pressure-based coupled algorithm has been applied in order to solve the flow governing equations. Second order upwind discretization scheme for momentum, turbulent kinetic energy and dissipation rate has been employed in the computation. The fluid domain has been discretized with about 400,000 cells, which is a combination of block-structured and unstructured grid. Second order implicit time discretization has been applied for the transient formulation of the charging process with a time step of 0.2 second.

Since there is no single state of the storage that could be considered as representative of the whole adsorption/ desorption cycle, an arbitrary state that might occur during the adsorption half cycle has been selected for this case study. The fluid inside of the storage tank has been initialized with linear function of temperature with 38˚C at the bottom of the tank to 200˚C at the top of the tank (as shown in

The modified version of

where

In transport equations of turbulent kinetic energy and turbulent energy dissipation rate,

In the

The value of

The effective thermal conductivity due to turbulent mixing in the fluid domain is calculated from the Equation (4),

In Equation (4)

Due to the temperature difference and, therefore, density difference, the natural buoyancy results in a buoyancy- driven flow in thermal energy storage.

In simulation of TES, the buoyancy term has been modeled by means of a body-force term in momentum equation (Boussinesq Model). This body-force term has been shown in Equation (5) [

where

Heat advection caused by the bulk fluid motion contributes to effective thermal conductivity with an additional part. This part of effective thermal conductivity has been calculated for the current selected case of charging process in adsorption heat pump cycle. The equations used for the calculation of advection part in effective thermal conductivity have been represented in Equation (6).

where

tion pipe and storage tank wall.

The main mechanisms influencing the transient development of the temperature profile in a Thermal Energy Storage are heat transport process, mixing of the charging fluid with stored fluid, and local turbulence because of stratification [

In the 1-D plug flow model of thermal storage tank in adsorption heat pump system simulation, the effect of all heat transfer processes can only be taken into account as an effective heat conduction between adjacent fluid

layers. In the current numerical investigation of the charging process, advection due to the bulk fluid flow has been considered as another heat transfer mechanism, which leads to stronger mixing in the tank. In order to calculate the advection part of the effective thermal conductivity according to Equation (6), a User Defined Function (UDF) has been applied to the CFD model. The UDF has been interpreted and executed to calculate the desired variables in Equation (6). The advective heat transfer part has been integrated over horizontal surfaces at different heights of the tank. In addition, the production of horizontal surface and average value of temperature gradient in axial direction has been exported over different horizontal surfaces at different heights of the tank. By means of these parameters, the effective thermal conductivity due to advection has been calculated at different charging times.

Turbulent diffusion in fluid flow in TES enhances the mixing due to increasing the transport rate of momentum, which leads to homogenization. On the other hand, enhanced energy transport rate due to turbulence causes an intensified heat transfer process. This enhancement can be considered on the basis of additional thermal conductivity called effective thermal conductivity due to turbulent motions.

In transient simulation, effective thermal conductivity in the storage with the realizable

The effective thermal conductivity due to turbulence and advection in the thermal storage tank is an important parameter influencing the performance of the whole adsorption heat pump system under consideration. It accounts for convection effect and turbulent mixing in the storage tank. Therefore, it can only be determined for a specific geometry of tank, inlet and outlet ports, initial and boundary conditions. For any given geometry, it depends on the fluid charging volume flow rate, heat transfer fluid, and the temperature profile in the storage tank. The results reveal that in this CFD model and under the conditions chosen here, the influence of the turbulence part on the effective thermal conductivity is much more important compared to the advection part. Turbulent mixing leads to more intense mixing effect and destratification and shows stronger influence on the effective thermal conductivity. Under these circumstances, the results can also be expected to strongly depend on the details of the turbulence model used, and therefore should be treated with caution. A reassessment of these results with more fine-grained turbulent flow computation methods such as Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS) would be welcome.

Application of an inlet stratification pipe restricts the impact of the turbulent mixing partly to the inner region of that pipe and therefore would be advantageous in order to avoid higher level of turbulent mixing and effective thermal conductivity inside of the storage tank. One of the demonstrative disadvantage of the applied geometry for the stratification pipe is the entrainment effect which leads to suction of the fluid from storage to the stratification pipe.

H. Taheri would like to sincerely thank Karlsruhe Institute of Technology for providing a scholarship (Rektorstipendium), and also Balazs Pritz for his constructive comments. F. P. Schmidt gratefully acknowledges project funding by the state of Baden-Württemberg (ZO-III Initiative) through the Project Management Agency Karlsruhe (PTKA-BWP).

cs Cross section

conv Convection

eff Effective

hor Horizontal

ref Reference

COP Coefficient of Performance

CFD Computational Fluid Dynamics

RANS Reynolds Averaged Navier-Stokes Equation

UDF User defined function

1-D One Dimensional

2-D Two Dimensional