Meshing strategy for hybrid tet-hex PHES layered bed heat storage

Article describes a meshing strategy for efficient computation of generic layered heat storage device for pumped heat energy storage (PHES). Mesh for structural solid body and fluid boundary layer is with unstructured flow field is presented. A rationale for geometry choice, mesh topology and different types of mesh topologies considered in this study. The effect of coarse and fine mesh on computational time and accuracy of results for transient analysis of coupled fluid and heat flow is described.


Background
Rapid growth of global electrical power demand next to the climate change issue [1] is influenced by introduction of new environmental regulations concerning emission reductions of carbon dioxide [2]. This goal is realized by fast increase of renewable energy (RE) technologies share to energy mix of many countries, mostly solar and wind power. Utilization of these sources depends on weather conditions and potential of power generation is highly variable. Unproductive periods without wind and sunless days are interlaced with the peaks of electricity production exceeding the current demand. This surplus should be stored or otherwise is wasted, what causes rise of production costs as well as premature network wear.
Literature analysis has indicated that TES offers relatively high energy density and much lower price per kWh of built storage comparing to very high energy density batteries. Classical TES approach allows to obtain efficiencies up to 60%. However such high value is very difficult to achieve and in case of low short term and long term energy prices fluctuations this value does not provide sufficient cost effectiveness. Therefore development of this technology is focused on investigations of round-trip efficiency (the ratio of energy put in to energy retrieved from storage) increasing concepts. Pumped heat energy storage is one of the most promising TES derived approach which has the potential to meet this demand [3]. PHES concept is based on heat pump principle of operation during loading and turbomachinery devices during discharging of hot side storage tank.
Small number of papers describe existing prototypes of PHES in the context of heat transfer and storage components of the system [4]. This paper concerns the mesh preparation for conjugate heat transfer CFD calculations of fluid and heat flow in fixed bed heat storage reservoir.

Preparation of the geometry
The study is performed on a segment of generic layered thermal storage as presented in  The CAD geometry is composed of two solid body (in context of CAD modelling) regions representing layers of storage and fluid region respectively.
Individual holes in the discussed geometry are arranged in a triangular/hexagonal pattern and are shifted in relation to upper and lower level. Hole diameter is 40mm, distance between hole centrelines is 100mm, layer thickness is 50mm and distance between layers is 25mm. Geometry does not represent any particular storage design (Fig. 2). It was found that the flow phenomena occurring in such entity are mostly in the direction of flow with minimal activity in radial, with regard to hole centrelines, direction. Therefore presented generic geometry was then sliced to obtain smallest possible volume that represents a single "cell" of the storage (Fig  3.). Side walls will be marked as symmetry boundary condition.

Meshing approach and topology
Mesh was created in Pointwise V18.0R4 meshing software.
Based on previous experiences of the research team, a structural, hexahedral mesh was intended for this study. Although not very complex, the geometry does not mesh with fully hexagonal meshes without interfaces, therefore a following approach was made.
A topology for solid body (dark grey in Fig. 2) was created on the face of the solid body perpendicular to the flow direction (Fig 4). As the software used allows for "patch independent" meshing, that is: mesh information can be independent from the geometry, both solid and fluid regions were meshed during this operation. Remaining fluid volume was then filled with unstructured, isotropic tetrahedra with pyramid transitioning layer (Fig 5). Such basic geometry was then copied to form 32 solid domain layers (or 16 pairs with shifted hole patten) with one fluid domain around them.
One of the early approaches for meshing was to create an o-grid topology in the fluid boundary.
Although the mesh quality in the fluid boundary was more than acceptable, the rounded section of the o-grid made it impossible to create a high quality pyramid transition layer and transition to tetrahedra.
Final mesh consists a 4 meter long cut from layered bed heat storage device, including 30cm inlet and outlet regions. Such geometry represents the discussed device in 1:1 scale. Results on heat flux, heat capacity and mass flow are easily scalable for a real device with given area of thermal storage cross-section.

Mesh sizing and quality
Initial meshes considered for this study were created for high resolution fluid boundary layer with y+ parameter calculated to value of 5, based on reference velocity and hydraulic diameter of the bed holes. Real value of y+ based on flow-field values is in order of magnitude of 2, ranging up to 4 where velocity magnitude increases locally. Full 32 layers of fine mesh result in around 14.2 million elements. Estimated physical flow time for completing a single charge/discharge cycle was 6 hours. Completing this physical flow on a 120 core HPC cluster was estimated to be completed in 32 years for a single charge/discharge cycle. Although the quality of the results was superior to the coarse grid, the computational wall-time made the calculation inherently impractical.
For coarse mesh element count was reduced by half in each direction of the mesh for both structured and unstructured domains. This resulted in a mesh with y+ parameter in order of magnitude of 50. Cell count is also drastically reduced to 2 million cells. Real y+ values calculated from flow data range from 13 to 23 where local velocity magnitude is increased. Using a coarsened mesh resulted in achieving relatively practical wall-time with three charge/discharge cycles completed in 21 days.
Mesh quality is comparable for both meshes. Quality figures for full 32 layer mesh are presented in figures 7 thru 9.

Conclusions
It is concluded, that for best quality results, mesh sizing must retain y+ sizing in order of magnitude of 1 for best conjugate heat transfer resolution. However for large scale computations, even implementing a section of the storage requires very large computational resources.
It is suggested that for large scale computations, one should perform a detailed analysis of a single heat storage cell (such as the basic geometry, fig. 3) in order to obtain values of heat capacity of such cell per unit volume and unit area, followed by the implementation of these values in properties of porous material. Further work is described in [6] This research was supported in part by PLGrid Infrastructure.