## 1 Introduction
[PERSON] and [PERSON] [8] conducted a study on a moving packed-bed shell-and-tube heat exchanger to be used for power tower CSP plants with a particle-based storage. The authors studied two designs for the heat exchanger, differing from each other by the tube bundle arrangement. In the first design (called the reference design), the tube bundle is arranged with a horizontal tube pitch ratio of 2.5 in a 60\({}^{\circ}\) staggered formation, while in the adapted design is 1.5 in a 72\({}^{\circ}\) staggered formation. The particles used were sintered bauxite and quartz sand with a mean particle size of 0.5 mm and 0.8 mm. The particles flow inside the shell with superficial inlet velocities up to 5.0 mm/s and a maximum temperature of ~500 \({}^{\circ}\)C; and thermal oil flows through the tubes as heat sink. The authors found that the stagnant zones for the adapted design are thinner, but somewhat higher than those of the reference design. The velocity profile shape and the dimensions of the stagnant and void zone are not affected by the superficial velocity of the bulk. Additionally, the authors found that the effectiveness of the adapted design improved substantially due to the higher integral particle velocity (lower tube pitch and lower flow area) and the shorter contact time between the particles and the tube walls. [PERSON] et al. [9] studied the heat transfer characteristics of sand bulk flow in a sand-air heat exchanger. The tested heat exchanger was made of a transparent polymer box which included a tube bank consisting of eight tubes arranged in three rows in a staggered formation. The tubes, either bare or finned, were made out of carbon steel and electrically heated by heater cartridges. Experiments were conducted on silica sand and olivine sand with two parameters being changed, namely, the power input (100 W to 350 W) and sand velocities (1 and 3 mm/s). The authors found that heat transfer coefficient was slightly affected by the sand type, with olivine a little higher than silica. The sand velocity was found to have a positive and significant effect on the heat transfer coefficient, and the reported values for bare and finned tubes were found in the range of 80-160 W/m\({}^{2}\)-K, with bare tubes higher than finned tubes. [PERSON] et al. [10] continued the previous work by testing five particulate materials: fracking sand, Atlanta industrial sand, Riyadh white sand, and small and large proppants. The authors investigated the effect of higher particles velocities on the heat transfer coefficient; the velocities used were 3, 5, and 10 mm/s. The results showed that the particles velocity had a great effect on enhancing the heat transfer coefficient. The reduced contact area (induced by stagnant zones on top of the tubes and void zones on the tubes' bottom) between particles and tubes' walls was one of the main obstacles towards a highly-effective thermal performance. By looking closely at the stagnant/void zones around circular tubes, an approximate diamond shape can be noticed. This might suggest that a sharp-edge tube profile (following the particles streamline) could eliminate/reduce the extent of such zones and promote the heat transfer. Therefore, the KSU-CSP team collaborated with Grenzbach company to fabricate a heat exchanger with a design that replaced circular tubes by diamond-shaped tubes; in this way, the extent of the stagnant zones and void zones are to be minimized, which will improve the contact between particles and tubes' walls. The Grenzbach heat exchanger was incorporated in the KSU PBCSP facility; it linked the particle thermal system to the recuperated microturbine [11]. The thermal capacity of the heat exchanger is about 100 kW, and it has six passes of diamond-shaped tubes (894 tubes) with a heat transfer area of approximately 90 m\({}^{2}\). The heat exchanger was tested using Riyadh red sand; the recuperated air of the microturbine, flowing inside the tubes, was used to heat the red sand.