Karunesh Kant

Pascal Henry Biwole

A Shukla

Atul Sharma

Shiva Gorjian

Heat Transfer and Energy Storage Performances of Phase Change Materials Encapsulated in Honeycomb Cells

Keywords: Phase change materials, Thermal energy storage, Numerical simulation, Heat transfer, Melt fraction

Solar energy is an abundantly available, clean, and sustainable energy source therefore it is accepted as one of the most favorable alternative energy sources for sustainable development [START_REF] Qiao | Performance and optimization of a novel active solar heating wall coupled with phase change material[END_REF][START_REF] Kong | Experimental study on a novel hybrid system of active composite PCM wall and solar thermal system for clean heating supply in winter[END_REF][START_REF] Gorjian | A review on opportunities for implementation of solar energy technologies in agricultural greenhouses[END_REF][START_REF] Kant | Thermal energy storage based solar drying systems: A review[END_REF][START_REF] Shukla | Solar greenhouse with thermal energy storage: A review[END_REF]. Due to the intermittency by its nature, unreliability is the major impeding factor for the massive use of solar energy in agriculture and food processing. The unreliability of solar energy utilization can be diminished by stowing solar energy when it is excess compared to the demand and consuming the stowed energy whenever required. The energy storage system is, consequently, important to any system that is based largely on solar energy. Solar energy can be stored in the form of thermal energy in thermal energy storage (TES) devices. During the past few decades, the latent heat TES devices using PCM have gained larger attention due to their favorable thermophysical properties. However, these materials show poor thermal conductivity, which restricts the thermal transport in the storage medium and alleviates the melting/solidification process. To evade this shortcoming and enhance thermal transport throughout the solid-liquid phase transition, multitudinous approaches have been recommended in past studies. These approaches are the addition of highly thermal conductive nanoparticles [START_REF] Dutil | A review on phasechange materials: Mathematical modeling and simulations[END_REF][START_REF] Kant | Heat transfer study of phase change materials with graphene nano particle for thermal energy storage[END_REF][START_REF] Kant | Heat transfer study of building integrated photovoltaic (BIPV) with nano-enhanced phase change materials[END_REF], incorporation of metal matrix [START_REF] Tong | Enhancement of heat transfer by inserting a metal matrix into a phase change material[END_REF], addition porous matrices [START_REF] Marín | Improvement of a thermal energy storage using plates with paraffin-graphite composite[END_REF], and use of multiple PCMs [START_REF] Adine | Numerical analysis of the thermal behaviour of a shell-andtube heat storage unit using phase change materials[END_REF][START_REF] Tian | Thermal and exergetic analysis of Metal Foam-enhanced Cascaded Thermal Energy Storage (MF-CTES)[END_REF]. Amid these approaches, the incorporation of the metal matrix in PCM is the focus of the present study because it is cheap and easy to integrate with the system.

In recent years, several studies have been executed to assess the heat transfer behavior of metal matrices integrated PCMs. In this regard, Biwole et al. [START_REF] Biwole | Influence of fin size and distribution on solid-liquid phase change in a rectangular enclosure[END_REF] conducted a numerical simulation of RT-25 PCM filled in a rectangular enclosure to assess the effect of fin size and distribution. The effective fin configuration was investigated and it was perceived that the fin surface area is an important factor that guides the melting of PCM and the rate of heat transfer between the PCM and the front hot surface, while the fin structures advance greater natural convection, leading to an advanced heat flux. Groulx et al. [START_REF] Groulx | Phase change heat transfer in a rectangular enclosure as a function of inclination and fin placement[END_REF] conducted a numerical simulation to assess the influence of fin placement and angle of inclination on the melting of RT25 PCM in a rectangular enclosure. Based on the study it was concluded that the convection heat transfer causes a significant acceleration in the melting process of the PCM. Also, a negligible effect for the computational domain's inclination angle smaller than 75° from vertical on the heat transfer behavior of all considered configurations was reported.

Darzi et al. [START_REF] Rabienataj Darzi | Melting and solidification of PCM enhanced by radial conductive fins and nanoparticles in cylindrical annulus[END_REF] studied the melting and solidification behavior of PCM considering radial fins and thermally conductive nanoparticles to enhanced thermal transport. The phase change process was accelerated by increasing the nanoparticle concentration and the elliptical tube decreases the melting time as compared to the circular tube. Further, increment the fin number show system deficient due to the suppression of natural convection. A numerical study of PCM solidification was conducted by Abidi et al [START_REF] Mat | Enhance heat transfer for PCM melting in triplex tube with internal-external fins[END_REF] to investigate the best configuration that minimizes the melting and solidification time of PCM in a triplex tube heat exchanger with both external and internal fins. In continuation with the thermal transport enhancement using fin structure, a novel snowflake crystal fin structure was investigated by Sheikholeslami et al. [START_REF] Sheikholeslami | Numerical analysis of discharging process acceleration in LHTESS by immersing innovative fin configuration using finite element method[END_REF] to enhance the thermal efficiency of the latent heat thermal energy storage (LHTES) device during the heat discharging process. The obtained results were indicated that the discharging process of the LHTES is improved by applying Snowflake shaped fin structure, in comparison with the nanoparticle diffusion, while it does not considerably reduce the maximum thermal energy storage capacity. Wu et al. [START_REF] Wu | Numerical analysis and improvement of the thermal performance in a latent heat thermal energy storage device with spiderweb-like fins[END_REF] performed numerical analysis and improved the thermal transport behavior of the LHTES device with spiderweb-like fins. From the obtained results it is observed that the spiderweb-like fins decrease melting and solidification time by reducing the heat transfer hysteresis region.

In the recent past, several investigators have made substantial efforts to improve the thermal performance of LHTES devices by using different thermally conductive fin structures. The researchers had paid their most attention toward modified rectangular and annular fin structures. Conversely, several studies have shown that proposed conventional fins have a simple structure with a small specific surface area which makes it tough to realize reasonable thermal transport performance of LHTES devices. Consequently, some fins with mixed structures and a high specific surface have been found to enhance the thermal transport effectiveness of LHTES devices. Recently, bionics are advanced in the field of fluid flow and heat transfer applications including chemical reactor [START_REF] Chen | Hydrodynamics of a droplet passing through a microfluidic Tjunction[END_REF], biomedical equipment [START_REF] Zhang | Gravity-capillary evaporation regimes in microgrooves[END_REF][START_REF] Liu | Investigation of spherical and concentric mechanism of compound droplets[END_REF], and electronic cooling [START_REF] Chen | Thermal and hydrodynamic characteristics of constructal tree-shaped minichannel heat sink[END_REF][START_REF] Zhang | Flow boiling in constructal tree-shaped minichannel network[END_REF][START_REF] Daguenet-Frick | Constructal microchannel network for flow boiling in a disc-shaped body[END_REF][START_REF] Wu | Flow boiling characteristics in constructal treeshaped minichannel[END_REF][START_REF] Sciacovelli | Maximization of performance of a PCM latent heat storage system with innovative fins[END_REF]. The fin structures made by natural assortment encourages the improvement of the LHTES device. By realizing natural structures, the fins with bionic structures for instance tree-shaped fins [START_REF] Sciacovelli | Maximization of performance of a PCM latent heat storage system with innovative fins[END_REF][START_REF] Zhang | Improving the energy discharging performance of a latent heat storage (LHS) unit using fractal-tree-shaped fins[END_REF], Koch fractal fins [START_REF] Li | Numerical study on the solidification performance of a latent heat storage unit with Koch-fractal fin[END_REF], and snowflake-shaped fins [START_REF] Sheikholeslami | Numerical analysis of discharging process acceleration in LHTESS by immersing innovative fin configuration using finite element method[END_REF][START_REF] Sheikholeslami | Response surface method optimization of innovative fin structure for expediting discharging process in latent heat thermal energy storage system containing nano-enhanced phase change material[END_REF] have been recently proposed by researchers to the enhanced thermal performance of PCM thermal energy storage devices.

The bionic fins provide an effective means for thermal transport, therefore increasing the thermal transport effectiveness of LHTES devices. Though the hysteresis exists during melting and solidification of PCM with various ranges depends on the gaps between fins. The presence of hysteresis impedes the additional enhancement of the thermal efficiency of such devices. The extensive existence of honeycomb meshed structure in nature offers an idea to solve the hysteresis problem. As shown in Figure 1, the honeycomb has a compact and uniformly distributed structure over the entire structure. Based on this quality, the use of honeycomb-like fin introduces a high interest for improved efficiency of charging and discharging processes of LHTES devices.

Figure 1 Honey bee honeycomb

Through a comprehensive literature assessment, it can be chronicled that not much investigation has been dedicated to investigating the charging efficiency of LHTES devices with honeycomb meshed fins. The melting behavior of PCM and interstitial thermal energy absorption process between honeycomb meshed fin structures and PCM is still imprecise.

Further, the effect of the honeycomb meshed fin structure on the charging efficiency of LHTES devices has not been exposed so far. The effect of natural convection on the melting progression has been highlighted by numerous researchers; however, no known study has been found in the literature on the melting and energy storage behavior of PCM in the honeycomb structure and limited works have focused on the effect of the container's tilt angle on the melting behavior of the PCM process. Consequently, the current analysis provides an advanced insight into how the thorough nature of honeycomb meshed fins influence the heat absorption behavior of LHTES devices while can be considered as an important work to enhance the thermal storage and discharge effectiveness.

The article is structured as follows: In the introduction section, the overall background and the goal of the current study are presented. After the introduction, the computational model with all the simulation details including the dimensions and constants used in the study are described. Next to the computational model, the mathematical formulation, boundary conditions, and computational technique with model validation are presented. Further, detailed discussions on the results of the present study are presented, trailed by a summary of the key conclusions.

COMPUTATIONAL MODEL

The geometry of the computational domain considered in the present work has been presented in Figure 2. The computational domain is poised of two vertical metallic plates connected with hexagonal honeycomb cells; the fin thickness of each hexagonal cell, as well as the vertical plate, is . The height (H) and width (W) of the container are fixed, with values 0.077942 m and 0.045 m respectively and the inclination angle of the computational domain from horizontal is o as shown in Figure 2. Each cell in the container has the same length ( ) and uniform thickness. Internal fins are also made of the same material as front and back vertical plates. The cell length , the inclination angle of the container from horizontal and the fin thickness are given in Table 2. The thermo-physical properties of metallic fins and PCM considered in the present study are shown in Table 1. The computational domain is primarily set at a temperature = 23. In the present study, n-octadecane is considered as PCM and its thermo-physical properties are given in Table 1. Four different angles of inclination and fin thicknesses are studied for four different honeycomb cell sizes. The study has also been conducted without honeycomb cells in the rectangular plane of the container considered. The studied combinations of the fin thickness and inclinational angles are given in Table 2, where is the honeycomb cell length, is the fin thickness of the honeycomb cells and θ is the angle of inclination of the computational domain from horizontal as shown in

MATHEMATICAL FORMULATIONS

Numerical simulation model description

The following equations ( 1) and ( 2) with the boundary conditions are applied on the heated front and back external surface correspondingly:

-,

-.

-

/ 0 /1 = + ℎ ( -) (1)
-,

-.

-/ 0 /15 678 9:

95 678 = ℎ ( -) (2)
Further, the equation of heat transfer diffusion realized within the fins and PCM domain is:

-.

-

; + ∇(-,∇ ) + = >? • ∇ = 0 (3)
where ρ, and k represents density, specific heat, and thermal conductivity respectively. For the PCM, the value of ρ, k and varies with temperature as given by eq. ( 7), ( 8) and ( 9)

respectively. The fluid velocity = >? is always zero in the metallic fins as well as on the surface of metallic fins, and is given in the PCM domain by numerically solving the Navier-Stokes and continuity equation; the equation of modified momentum conservation for the PCM domain can be given [START_REF] Groulx | Phase change heat transfer in a rectangular enclosure as a function of inclination and fin placement[END_REF]:

-A > >? -; + (= >? • ∇)u >? = -∇ + C1 -D( -E )FG ? + H • ∇ = >? - (IJK(.)) L K M (.)9N = >? (4)
where and H are respectively the density and dynamic viscosity is of melted PCM, β is the thermal expansion coefficient of PCM and G ? is the acceleration because of gravity constant.

The value of constant C (Kozeny-Carman permeability) can be determined by the inherent characteristics of the PCM material. Increasing its value causes a decrease in the melted PCM's flow in the transition zone, and consequently to a smoother nature of the liquidus melting front while decreasing its value will have the contrary influence. The value of constant C in the present study is 10 5 kg/ (m 3 •s). Here, ɛ is constant with a given value of 10 -3 as in [START_REF] Kant | Heat transfer studies of photovoltaic[END_REF] to evade dividing by zero. The melted fraction function P( ) of PCM is defined as:

P( ) = Q R S R T 0, < W E - ∆. Y .J. Z 9∆./ ∆. , W E - ∆. Y < < W E + ∆. Y 1, > W E + ∆. Y (5)
Here ∆ is transition temperature and its value is taken 2 o C in the present study. The varying thermo-physical properties of PCM are modeled as a function of temperature through Eqs. ( 6)- [START_REF] Marín | Improvement of a thermal energy storage using plates with paraffin-graphite composite[END_REF]. The viscosity μ of PCM is adjusted to ensure a very high value when the PCM is in the solid-state [START_REF] Biwole | Influence of fin size and distribution on solid-liquid phase change in a rectangular enclosure[END_REF].

H( ) = H W1 + (IJK(.)) L \ (K M (.)9N) Y (6)
( ) = ] + ( -] ) • P( ) (7)
,( ) = , ] + (, -, ] ) • P( )

where the value of is taken 1 kg/(m 3 .s) to make sure unit consistency, ] and are the density of the solid and liquid phases of PCM, respectively. Similarly, the , ] and , are the PCM's thermal conductivity for solid and liquid phases respectively. The specific heat of PCM which is temperature-dependent modeled including an extra term which accounts for the latent heat of fusion stored or released in the melting or solidification process, consequential in an adjusted heat capacity of PCM can be given by [START_REF] Biwole | Influence of fin size and distribution on solid-liquid phase change in a rectangular enclosure[END_REF]:

( ) = ] + W -] Y • P( ) + ^( ) (9)
where

^( ) = _ `(a`a Z ) L (∆a/b) L cd(∆./e) L (10)
The reason for considering the Gaussian function D(T) in eq. ( 9) is conserve the latent heat of PCM all over the transition period, because the integral of function D(T) over the whole range of transition temperature ΔT is always 1 [START_REF] Biwole | Phase-change materials to improve solar panel's performance[END_REF]. The consideration of ΔT produces a numerical mushy region. The mushy region thickness grows with the growth in the value of ΔT. The value of ΔT depends on the nature of the materials and can be fixed empirically if one has previous information on the melting behavior of PCM. The deformation of geometry owing to the PCM's thermal expansion is not considered in the present study.

Computational method, meshing and validation of the model

The above-mentioned equations are implemented in a fluid and laminar flow module of COMSOL Multiphysics 5.5. The present study used fixed-grid approaches similar to the one labeled in this section that consents to evade the necessity to solve the Stefan problem at the varying melting front. Furthermore, the melting front tracing method necessitates an already existed liquid layer, which is not the situation for the present study. Through fixed-grid approaches, the standard method for the liquid flow and energy for instance the finite element numerical resolution of N-S equations can be applied with partial modifications.

To solve the problem, an extremely fine mesh is chosen with a maximum and minimum size of the element of value 5.98 ×10 -4 m and 6.9×10 -6 m respectively, which results in the total number of 62716, 72050, 80806, and 95166 linear free triangular mesh elements for LC = 0.015 m, LC = 0.01 m, LC = 0.0075 m and LC = 0.0075 m respectively. The maximum mesh size is defined using a condition on the mass mesh Peclet number [START_REF] Biwole | Phase-change materials to improve solar panel's performance[END_REF]:

= A > >?∆/ f < 2 ( 11
)
where Δx is the maximum length of mesh cell in a unit 2D surface. From numerical simulations, the maximum velocity in the honeycomb cell is taken as 5×10 -3 m/s. Therefore, Eq. [START_REF] Adine | Numerical analysis of the thermal behaviour of a shell-andtube heat storage unit using phase change materials[END_REF] gives Δx ≈ 2×10 -3 m. In the present study, Pe is kept lower than 1 to increase numerical stability. Consequently, the maximum mesh size is 1×10 -3 m. The mesh is refined at the borders of the PCM domain (see Figure 3). The first layer thickness of the boundary layer is 5.22×10 -5 m. Mesh sensitivity tests were also conducted at three increasing mesh element sizes and the transient average temperature of the container's front surface was observed at 38202, 50836, and 62716 mesh elements, as presented in Figure 4 for LC = 0.015 m. For the other LC, the maximum and minimum mesh sizes are the same, therefore the change in the mesh size will not affect the output results from the model. From this figure, it is observed that there is a negligible change in the variation of the front surface temperature when increasing the number of mesh elements. Therefore, for the sake of accuracy, maximum numbers of mesh elements were selected for the present study.

The numerical model presented above has been experimentally validated with our previous experimental study by Biwole et al. [31] and a comparison of the temperature variation is presented in Figure 5. For more details about the experimental setup and PCM properties, etc. please refer to Biwole et al. [START_REF] Biwole | Phase-change materials to improve solar panel's performance[END_REF]. The model explained above has also been validated with the experimental results reported by Shokouhmand and Kamkari [START_REF] Shokouhmand | Experimental investigation on melting heat transfer characteristics of lauric acid in a rectangular thermal storage unit[END_REF] on the Lauric

RESULTS AND DISCUSSION

The findings of this study are described in four different subsections. In the first one, the temperature variation in each cell and the whole computational domain, as well as the observed evolution of the melt fraction are discussed, for a single honeycomb cell size and container's angle of inclination. In the next subsections, the effect of honeycomb cell size, container tilt angle, and honeycomb fin thickness are discussed. In the present study three factors are used to evaluate the efficiency of charging and discharging of PCM: (i) the average temperature of the front surface, which must keep on the lowest possible value for the longest possible time, (ii) the melt fraction of the PCM with time, (iii) the time-dependent energy storage content with a 1,000 W/m 2 constant heat flux on the front surface of the computational domain.

The melt fraction of the PCM in the computational domain is defined as:

g = hi AE_ i ;j_ E_ ;_k l m C.n(. Z 9∆./ )F .i;o pi AE_ i l m (11)
The energy stored in the PCM is calculated based on the temperature of the PCM.

for

< E : r = ( - ) (12)
for

= E : r = s ( E - ) + t (13)
for

> E : r = s ( E - ) + + ( -E )t ( 14
)
Hear E is energy storage content and m is the mass of the PCM filled in the computational domain. The amount of energy stored in the melted PCM is computed as the energy stowed in entire numerical elements plus the computational domain.

Melting of PCM in honeycomb cells

The PCM's melting in honeycomb cells is presented in Figure 6, at different time intervals with 0.015 m cell length and 0.0005 m honeycomb fin thickness. The color contours represent the variation of temperature, arrows show the velocity field, and the white line denotes the melting front of the PCM. The heat flux applied to the front (left) surface of the computational domain heats the PCM filled in the cells near the front surface. The PCM starts melting and melted PCM moves upward due to the buoyancy force and collects at the top of each cell. It can also be noted that the thermal behavior on each cell is related to that of its vertical neighbors. Despite the fact that they receive the same normal heat flux from the left, the cells situated at the top of the container heat up faster than the cells situated at the bottom.

The warmer liquid PCM collected at the top of each cell, thus warming the cell directly above, also explains this. For all these reasons, a double temperature gradient is observed from top to bottom both in each cell and in the PCM container. As expected, a horizontal temperature gradient in the container is also noted as the heat propagates from the heated plate.

Figure 6 Temperature field, melting front (white contours) and moving direction (black arrows) of n-octadecane in honeycomb cells at different times

The average temperature variation of the front and back surfaces, as well as the variation of melt fraction (ϕ) with time, are presented in Figure 7. The two inflexion points noted on the curves of each surface average temperature are explained by the start and end of the PCM melting in the container, as obvious when comparing with the melt fraction curve. At first, the average front surface temperature increases sharply up to the melting temperature of the PCM. Then, it increases more gradually until the melt fraction of the PCM reaches its maximum value (i.e. 1). It resumes increasing sharply again as the heat storage is done in the form of sensible heat.

From t = 60 min to t = 90 min, a sudden increase in the front surface temperature of the computational domain is observed because of the complete melting of the cell near the front surface, which affects the melting of the PCM in the other cells of the container. At the same time, it was observed that there is a gradual increment in the melt fraction of the PCM compared to the initial stage of melting. The average back surface temperature gradually increases from the start of melting until the complete melting of PCM. Except at the start and end of PCM melting, there is no sudden increment or decrement in its temperature variation.

Effect of honeycomb cell size

Effect of honeycomb cell size on the melt fraction

The variation of melt fraction in the computational domain for different cell sizes and various inclination angles is shown in Figure 10. Four disparate inclination angles (i.e. 0 o , 30 o , 60 o, and 90 o ) are considered in the present study. The melt fraction without honeycomb cells is advanced as compared to that with honeycomb cells up to 140 min, regardless of the cell sizes. This behavior is observed because of two reasons. Firstly, the presence of honeycomb cells transfers heat to the entire computational domain, not only to the PCM available near the front heating surface. Due to the absorption of heat as sensible heat by the computational domain, the melt fraction of the PCM without cells is higher for a certain time and melting starts later for the smallest cell size as compared to larger cell size. Secondly, in the beginning, the convection heat transfer is accentuated in the configuration without cells, since the melt PCM has more room for movement. After a certain amount of time (140 min here), the latter convection process fails to achieve fast melting of the solid PCM situated as the bottom left of the container and becomes less efficient than that of celled configurations where heat is transported everywhere, as shown in Figure 8.

The latter reasoning holds when comparing meshed configurations. One can observe that for cases with higher cell sizes, melting starts earlier but ends later than for smaller cell sizes. As the heat which is transferred from the heated surface to the entire computational domain is reduced with larger cells, their initially higher melting rate decreases, and they finally take a longer time to achieve complete melting. For all the inclination angles it is observed that the melting starts at around 60 min, 35 min, 20 min, and 10 min for u = 0.005 m, u = 0.0075 m, u = 0.01 m, and u = 0.015 m respectively, meaning that the finer the mesh, the later the melting start.

There are several inflection points observed in the melt fraction variation for all the cell sizes and inclination angles. The first inflection point for u = 0.005 m, u = 0.0075 m, u = 0.01 m, and u = 0.015 m is observed when melt fraction reaches around 0.1, 0.15, 0.2 and 0.3 respectively. The second inflection point in the melt fraction is not observed when u = 0.015, however for u = 0.005 m, u = 0.0075 m, u = 0.01 m the inflection point is observed when the melt fraction reaches 0.225, 0.45, and 0.55 respectively. The number of inflection points in the melt fraction variation depends on the number of cells in the direction of the heat flux application. The inflections in the melt fraction are because of the uneven heat transfer that happened simultaneously by the additional contact resistance at the surface of each cell and to convection in the melted PCM within the cells. Regarding the latter cause, the heat transfer to the honeycomb cell is faster when the PCM filled in the previous cell is completely melted. If the PCM filled in the previous cell is not completely melted, the heat is absorbed by the solid PCM and a reduced amount of energy is transferred to the next cell which reduces the melting rate in that cell, resulting in a reduced melt fraction.

Effect of honeycomb cell size on the energy stored

The energy stored is calculated for different cell sizes and tilt angles, as presented in Figs.

Figure 11(a)-(d). The maximum energy is stored for the computational domains that have no hexagonal cells because, without honeycomb cells, the temperature of the computational domain is higher as compared to other configurations, which results in additional energy stored in as sensible heat. The honeycomb cells facilitate the heat transfer to the backplate and the environment beyond, thus reducing the thermal energy remaining in the container.

The decrease in the cell size causes an increased number of cells in the computational domain, which reduces the actual volume of the PCM in the container. Therefore, finer mesh configurations exhibit a lower heat storage capacity. For meshed configurations, it is also observed that the inclination angle does not significantly affect the energy content in the PCM.

Effect of the inclination angle

The melting of PCM in a rectangular container also depends on the inclination angle due to the convection effect. The effect of the tilt angle of the computational domain from horizontal on the average temperature of the front surface, melt fraction, energy stored in the container is presented for two different cell sizes, = 0.015 and = 0.0075 . For both cell sizes, the minimum average front surface temperature is obtained with θ = 90 o because of higher convective heat transfer in the computational domain. The impact of the angle of inclination on the average front surface temperature is negligible with smaller cell sizes because of the enhanced thermal transport due to the existence of the fin structure. The presence of the fin structure reduces the velocity field; however, it enhances thermal transport via the metallic structure.

Influence of inclination angle on the average front surface temperature

Influence of inclination angle on the melt fraction

The Influence of the tilt angle of the computational domain on the melt fraction for two different cell sizes is presented in Figures 12(b) and (e). For a certain time duration, the melt fraction is advanced when the computational domain is completely horizontal (θ = 0 o ) for both cell sizes. Further, there are inflection points in the melting curve of both cell sizes. As previously mentioned, this is due to the uneven heat transfer that happened because of the additional contact resistance at the surface of each cell and to convection in the melted PCM within the cells. The number of inflection points in the melt fraction depends on the number of hexagonal cells present in the computational domain.

Influence of inclination angle on the energy stored

The energy storage content in the PCM with time at different inclination angles is presented in Figure 12(c) and (f) for = 0.015 m and = 0.0075 m, respectively. There is a small variation are observed for the different angle of inclination during energy storage with = 0.015 m, however, there is no variation with = 0.0075 m. for given cell size and fin thickness the overall rate of energy storage is the same, regardless of the angle of inclination. This is due to the hypothesis of normal heat flux on the front surface in all configurations.

The results might be different in real applications where the amount of solar radiation received depends on the container's tilt angle. ). Four different cell sizes are also considered. Figure 13 (a) represents the average temperature variation for = 0.005 m. At first, the minimum temperature is obtained with a thicker fin because of higher heat transmission to the backplate. But due to enhanced heat transfer to the PCM and reduced volume of PCM in the container, the thicker fin configuration is also the one with a shorter melting time and its average front surface temperature becomes highest after the complete melting of PCM. The same behavior is observed for all fin thicknesses, with the inversion depending on the fin thickness, except before the end of melting where there is a very small temperature difference for = 0.5 , 1 xyz 1.5 . As

shown in Figure 13 (b)-(d) the cell size does not significantly change the above-described pattern. However larger cell sizes reduce thermal transport to the PCM and therefore, the average front surface temperature is higher for the higher cell size.

.2. Effect of the honeycomb cell fin thickness on the melt fraction

The effect of honeycomb cell fin thickness on melt fraction for different cell sizes is shown in Figure 14(a)-(d). Figure 14(a) represents the melt fraction at = 0.005 m for different fin thicknesses. The melting of PCM starts later for higher fin thicknesses as compared to lower ones, because of the higher fin thickness transport to the backplate and higher storage of sensible heat in the fins. Due to sensible heating below the melting temperature, the melting of PCM starts later which can be visible in Figure 14(a). Similar to the previous subsection, after fin sensible heating, the heat transfer is enhanced with higher fin thickness, with less volume of PCM, which explains the end of melting, earlier than that of lower fin thicknesses. Results have shown that natural convection plays an important role in maintaining the average temperature of the front surface to a constant value and for continuous thermal transport in PCM. Further, optimized honeycomb cell length and fin thickness choices would be vital for a rapid heat transfer to the rear end of the computational domain. It was also found that a tilt angle of the honeycomb cells has a minor influence on the heat transfer behavior of all studied patterns when the cell size is small. The total melting time is minimum for lower cell sizes and higher fin thickness regardless of the orientation of the computational domain. With such a configuration, it is possible to keep the front surface temperatures at 32 o C, which is around 90 o C lower compared to the horizontal case (pure conduction, θ = 0 o ).

The energy storage behavior of the PCM with varying time is also investigated for the range of parameters selected in the present study and it is found that the total energy content is higher without honeycomb mesh because of the higher amount of PCM, while the tilt angle has a marginal effect on the energy storage rate in cases where the heat flux remains normal to the heated surface. Finally, it is concluded that this type of fin structure leads to enhanced thermal transport in the PCM to maintain the front surface temperature constant. Besides, the charging and discharging time of PCM is reduced as compared to without meshed configuration. Overall, such studies for PCM encapsulated in honeycomb cells may be utilized for appropriate thermal management and to optimize heat transfer and energy storage.

  Nomenclature specific heat [J/(kgK)] ℎ heat transfer coefficient on the front and back surface [W/(m 2 K)] H height of computational domain [m] k thermal conductivity [W/(mK)] Lc cell length [m] latent heat of PCM [J/kg] P pressure [Pa] peclet number [1] incident heat flux on the front surface [W/m 2 ] melted PCM[m/s] W width of the computational domain [m] fin thickness [m] θ tilt angle from horizontal [ o ] ρ density [kg/m 3 ] density of liquid PCM [kg/m 3 ] density of solid PCM [kg/m 3 ] β thermal expansion coefficient of PCM [1/K] μ viscosity of melted PCM [Pa.s]

  2 o C and the front metallic plate is subjected to a continuous heat flux of = 1000 ⁄ perpendicular to the front surface for the period of the numerical simulation. As the present study is only focused on the influence of honeycomb structure on the heat transfer behavior in PCM, the convective heat transfer coefficient on the front and back surface is fixed. The front and back surface of the container is opened to convection cooling with an ambient temperature of = 23.2 o C as well as the convection heat transfer coefficient ℎ = 2 / . The top and bottom of the computational domain are subjected to symmetry boundaries (adiabatic). The acceleration due to gravity is always working in the downward direction for the entire tilt angle range. To conduct numerical simulation the following assumptions has been considered in the present study: (i) the liquated PCM is incompressible and Newtonian, (ii) the melted PCM's flow is laminar, radiation and three-dimensional convection are neglected, (iii) volume expansion due to the melting of PCM is neglected.

Figure 2 .

 2 The numerical simulation was conducted at 4 different angles of inclination θ without honeycomb cells as well as at 4 different LC (i.e. = 0.005 m, = 0.0075 m, = 0.010 m and = 0.015 m) considering = 0.0005 m to investigate the effect of inclination angle as well as honeycomb cell length on front surface temperature, melt fraction, and energy storage content. Further, to investigate the effect of the honeycomb fin thickness, the studies are conducted at 4 different honeycomb fin thickness with 4 honeycomb cell length while the angle of inclination of the computational domain is fixed at 60 o . Through the change in honeycomb cell size, fin thickness, tilt angle from horizontal, initial, and boundary conditions to the mathematical model are described in the next section and thermal energy storage behavior of computational domain is described arrangements are described.

Figure 2

 2 Figure 2 Geometry and boundary conditions of the system considered for the numerical simulation

  acid's melting in another previous study conducted byBiwole et al. [13]. The verification of the model with previous experimental results provides the confidence for the detailed systematic parametric studies of honeycomb geometry for enhanced thermal transport in PCM.

Figure 3 2 ,Figure 4 Figure 5

 3245 Figure 3 Meshing of the computational domain

Figure 7

 7 Figure 7 Variation of melt fraction (g) and average front and back surface temperature of the container

Figure 8

 8 Figure 8 represents the temperature field, the melting front and shows the moving direction of the molten PCM in the computational domain for four different honeycomb cell sizes, at t = 150 min for = 0.0005 m and θ = 60 o . For the smallest honeycomb cell size ( u = 0.005 m), the PCM is completely melted, whereas for u = 0.0075 m, 0.01 m and 0.015 m, some un-melted PCM remains. For the smaller cell sizes, the temperature gradient in the computational domain is reduced as compared to the larger cell sizes.

Figure 8

 8 Figure 8 Temperature field, melting front (white contours) and moving direction (black arrows) of n-octadecane in honeycomb container for different cell size at 150 min ( = 0.0005 m and θ = 60 o )

Figure 9

 9 Figure 9 Average front surface temperature variation with time for different honeycomb cell sizes: (a) at θ = 0 o , (b) θ = 30 o (c) θ = 60 o and (d) θ = 90 o

Figure 10

 10 Figure 10 Melt fraction variation with time for different honeycomb cell sizes: (a) at θ = 0 o , (b) θ = 30 o (c) θ = 60 o and (d) θ = 90 o

Figure 11

 11 Figure 11 Energy stored in PCM with time for different honeycomb cell sizes: (a) at θ = 0o, (b) θ = 30o (c) θ = 60o and (d) θ = 90o

Figure 12 (

 12 Figure 12(a) and (d) show the average front surface temperature variation at different angles of inclination for two different cell sizes = 0.015 and = 0.0075 , respectively.

Figure 12

 12 Figure 12 Effect of tilt angle on average front surface temperature, melt faction and energy stored in the PCM: (a)-(c) LC = 0.015 m, (d)-(f) LC = 0.0075 m

Figure 13

 13 Figure 13 Average front surface temperature variation with time at different honeycomb fin thickness: (a) at LC = 0.005 m, (b) LC = 0.0075 m (c) LC = 0.010 m and (d) LC = 0.015 m

Figure 14

 14 Figure 14 Melt fraction variation with time at different honeycomb fin thickness: (a) at LC = 0.005 m, (b) LC = 0.0075 m (c) LC = 0.010 m and (d) LC = 0.015 m

Figure 15

 15 Figure 15 Energy stored in PCM with time at different honeycomb fin thickness: (a) at LC = 0.005 m, (b) LC = 0.0075 m (c) LC = 0.010 m and (d) LC = 0.015 m

Table 1

 1 Thermophysical properties of PCM and metallic fin

	Properties /Material				PCM		Metallic fin
	Melting temperature ( o C)			28.2		NA
	Specific heat (J/kg.K)				1934 (s), 2196 (l)	900
	Latent heat of fusion (kJ/kg)			245		NA
	Density (kg/m 3 )				814 (s), 775 (l)		2700
	Thermal conductivity (W/m.K)		0.350 (s), 0.149 (l)	238
	Thermal expansion coefficient (1/ o C)		9.1×10 -4		NA
	Kinematic viscosity (m 2 /s)			5×10 -6		NA
	Table 2 Parameters considered in the present study
		θ o (at !"# = 0.0005 m)	!"# [m] (at θ = 60 o )
	Without cells	0	30	60	90	NA	NA	NA	NA
	$ % = &. &&' (	0	30	60	90	0.00025	0.0005	0.001	0.0015
	$ % = &. &&)' (	0	30	60	90	0.00025	0.0005	0.001	0.0015

Acknowledgment

The authors want to acknowledge the Université Clermont Auvergne postdoctoral grant 2020-2021.

Declaration of competing interest

The authors have no conflict of interest regarding this work.


Michaela Polanská
email: m.polanskámichaelapolanska@yahoo.fr

Gravettian backed points from Unit K11 of Dolní Věstonice II (South Moravia, Czech Republic)

Introduction

Hunting points and microliths have always attracted interest from specialists in Prehistory. Consequently, these artifacts have been regarded (often mistakenly) as sufficiently typical for use as guide fossils to enable the identification and characterization of complex technologies or "cultures". Their classification via traditional morphological typologies facilitated their ranking according to different typological lists, such as that established by D. de Sonneville-Bordes (Sonneville- Bordes and Perott, 1956) and that proposed by G. Laplace [START_REF] Laplace | Essai de typologie systématique[END_REF]. The lists that gained prominence and were translated in various languages (e.g., [START_REF] Klíma | Statistická metoda -pomůcka při hodnocení paleolitických kamenných industrií. Návrh české terminologie mladopaleolitických kamenných industrií[END_REF]) are still regarded in many countries as references for studying lithics. However, since their publication, those lists have evolved, and during the last two decades, studies of materials from Western Europe of the Upper Paleolithic period have highlighted new types of armatures (e.g., [START_REF] Klaric | L'unité technique des industries à burins du Raysse dans leur contexte diachronique. Réflexion sur la variabilité culturelle au Gravettien à partir des exemples de la Picardie, d'Arcy sur Cure, de Brassempouy et du[END_REF][START_REF] Klaric | Un nouveau type d'armature en contexte gravettien et son mode de production sur les burins du Raysse (la Picardie, commune de Preuilly-sur-Claise)[END_REF][START_REF] Pesesse | La pointe à dos alternes", un nouveau fossile directeur du Gravettien?[END_REF] and have facilitated the reassessment of old definitions [START_REF] Pesesse | La pointe de Font-Yves et les productions lithiques des derniers aurignaciens[END_REF](Pesesse, -2010;;[START_REF] Simonet | Les gravettiens des Pyrénées[END_REF]. These changes are not easy to follow (due to difficulties in terms of language, circulation, and publishing); hence, many years are necessary for their integration. Terms such as Gravette point, microgravette and Vachons point group often heterogeneous artifacts across Europe (e.g., [START_REF] Hays | Réflexions sur la fonction des microgravettes et la question de l'utilisation de l'arc au Gravettien ancien[END_REF][START_REF] Klaric | Des armatures variées, des modes de production variables: réflexions à partir de quelques exemples du Gravettien d'Europe occidentale (France, Portugal, Allemagne)[END_REF][START_REF] Moreau | Le Gravettien ancien d'Europe centrale revisité: mis au point et perspectives[END_REF][START_REF] Pesesse | Le Gravettien existe-t-il? Le prisme du système technique lithique[END_REF][START_REF] Soriano | Les microgravettes du Périgordien de Rabier à Lanquais (Dordogne): analyse technologique fonctionnelle[END_REF]. In Central Europe, the typological list of D. de Sonneville-Bordes is widely used, but it has not been adapted to the types that are present in this area. The armatures often remain unknown, despite various original types [START_REF] Polanská | Questionnement sur la diversité du Pavlovien morave par l'étude technologique des gisements de Milovice I, Pavlov I, Pavlov VI, Dolní Věstonice II-WS, Předmostí Ib[END_REF].

Therefore, the main objective of this paper is to report the presence and describe the microlithic points from Unit K11 of Dolní Věstonice II (Dolní Věstonice-Pavlov-Milovice settlement area, Southern Moravia, Czech Republic; Fig. 1). This limited collection is not directly dated, but the typological aspect enables an association with Gravettian sensu lato. Nevertheless, the first analysis leads us to underline the originality of these artifacts compared to the Pavlovian or Middle Gravettian backed tools and microliths of Dolní Věstonice-Pavlov-Milovice settlement area, which are dated between 27,500 -25,500 uncal BP (geometric microliths, microgravettes of sub-type Dolní Věstonice and sub-type Milovice, and Milovice points).

The main advantages of this limited collection are its homogeneity, the sieving of the sediment and the closed context from which the material originates [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF]. This enables a more detailed study of the armatures, and it highlights the particularities compared to other assemblages in the settlement area This study does not ground on a typo-technological and functional approach, due to the points and other stone materials being linked to the phase of the production of the bladelets blanks and the manufacture of armatures on site.

Archaeological context

Moravia, particularly the region below the Pavlov Hills (Dolní Věstonice-Pavlov-Milovice settlement area), contains dense concentrations of Gravettian sites (Fig. 1; e.g., [START_REF] Klíma | Dolní Věstonice. Výzkum tábořiště lovců mamutů v letech 1947-1952[END_REF]Oliva, 2009b;[START_REF] Svoboda | Dolní Věstonice II-Western slope[END_REF][START_REF] Svoboda | K analýze velkých loveckých sídlišť: Prostorová struktura a chronologie lokality Dolní Věstonice II-IIa[END_REF][START_REF] Svoboda | Paleolithic Hunting in a Southern Moravian Landscape.The Case of Milovice IV, Czech Republic[END_REF]. It seems that Gravettian hunters had a preference for higher-ground settlements, which enabled visual monitoring of the animal herds that were moving through the valleys [START_REF] Svoboda | Palaeolithic landscapes of Moravia: A mosaic of occupation strategies[END_REF].

One of this microregion's complexes of sites is Dolní Věstonice II, which is comprised of several localities and sections that differ in terms of chrono-cultural occupation [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF][START_REF] Polanská | Dolní Věstonice II: a complex of sites with different chrono-cultural occupations. Preliminary results of the study of lithic assemblage[END_REF][START_REF] Svoboda | Dolní Věstonice II-Western slope[END_REF][START_REF] Svoboda | K analýze velkých loveckých sídlišť: Prostorová struktura a chronologie lokality Dolní Věstonice II-IIa[END_REF][START_REF] Svoboda | Dolní Věstonice II. Chronostratigraphy, Paleoethnology, Paleoanthropology[END_REF]. This site complex is divided into several sections: the brickyard, the northern slope, the western slope, the top, the mammoth bone accumulations, and Dolní Věstonice IIa and IIb. Most of the occupations (Units S1-S5; S7; K1, K5-K9) belong to the Pavlovian sensu stricto (27,500 uncal BP), namely, to the group with microsaws [START_REF] Polanská | Chapter XIV. L'industrie lithique de Dolní Věstonice II découverte avant[END_REF][START_REF] Polanská | Questionnement sur la diversité du Pavlovien morave par l'étude technologique des gisements de Milovice I, Pavlov I, Pavlov VI, Dolní Věstonice II-WS, Předmostí Ib[END_REF]. Some assemblages, such as the three units in the lower part of the northern slope (S6, K10-11), have been attributed to the Gravettian sensu lato, Early Gravettian or the Late/Final Gravettian [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF][START_REF] Svoboda | K analýze velkých loveckých sídlišť: Prostorová struktura a chronologie lokality Dolní Věstonice II-IIa[END_REF].

Dolní Věstonice II (Northern slope -lower part)

The three units of the lower part of the northern slope were first discovered in 1985 (rescue excavations) during the development works that were conducted in the area when loess was extracted for use in the construction of the Nové Mlýny dam (Fig. 1; [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF]. The loess, which was of considerable thickness and approximately 2 100 meters long, revealed a cultural horizon at a variable depth of between 2 and 4 m, which was characterized by a grayish color with charcoal remains. The charcoal remains were uniformly spread across the horizon and sometimes occurred in higher concentrations, and they were rarely found alongside faunal remains (mammoth, horse, and reindeer) and lithic artifacts. The lithics was composed of three concentrations (K10-11, S6). One of the units (K11) was associated with very small bone fragments and was located within a shallow basin (1x1 m) with a hollow hearth [START_REF] Klíma | Zachraňovací výskum nad cihelnou v Dolných Věstonicích[END_REF]. The lithic artifacts from these three concentrations were made on local raw material (Krumlovský les chert type), the source of which is found approximately 30 km from the site as the crow flies. The three lithic concentrations, which differ by approximately 20 m from each other, each present unique typological features while also showing similaritie s; because of this, it is not yet possible to determine their relationship. The characterization of these three assemblages must also be conducted on similar kinds of collections, which remain to be identified. The symbolic artifacts and tools in hard animal materials are absent.

Unit S6

Unit S6 (formerly Unit B) mainly produced pieces that were derived from blade production activities [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF][START_REF] Svoboda | K analýze velkých loveckých sídlišť: Prostorová struktura a chronologie lokality Dolní Věstonice II-IIa[END_REF]. Among the original types, there are burins on which the blow is projected onto an often concave direct truncation that is twisted along/on the lower face (non-sieved sediment, lacking of small fraction of industry). Unit S6 is dated to 27,660±80 uncal BP (GrN-13962), which corresponds to its stratigraphic position in the subsoil of interpleniglacial soil (Svoboda, 2001, p. 85).

Unit K10

The lithic industry of Unit K10 (formerly Unit A, which is dated to 23,540±180 uncal BP; GrN-19498) appears to be less homogeneous and lacks characteristic tool types. The artifacts, which are mostly formed on radiolarite, Krumlovský les chert type, spongolite or exceptionally silicites of erratic origin, seem to be less homogeneous [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF]. This assemblage, which is often described as containing "Aurignacian types", is difficult to interpret. Indeed, the bladelet cores where the striking platform is formed by the lower face of a blade or flake are often present in Moravian Gravettian collections and do not allow for direct cultural attributions. In addition, the value of this single bladelet core, namely, "carinated end-scraper like", in the collection remains to be determined as it is formed on silicite of erratic origin, which is a raw material that is rare in this assemblage.

Armature fragments are produced on radiolarite as the various bladelet cores.

Unit K11

The sediment from Unit K11, unlike those of the two other assemblages, was sieved. Hence, it was possible to find the very small backed pieces manufactured on-site. Most of the material is burnt because it was recovered from a shallow basin with a hollow hearth. This assemblage shares limited similarities with the previous two: it presents similar backed points (Unit K10, five pieces) and an artifact à épine (Unit S6).

Methodological approach

The elements that are used to characterize the production of the materials and the description of the formal tools from Unit K11 are highly limited due to a very poor quantitative sample. However, the discovery conditions, the homogeneity and the sample are favorable for a more detailed study of the modalities of transformations of the blanks for the production of this type of armature.

The typological and technological approaches to the lithics are often presented as complementary methods, which differ in terms of their objectives (e. g., [START_REF] Valentin | Typologie vs typologie (sic!). Comment la technologie contribue à raffiner la typologie des armatures lithiques[END_REF][START_REF] Tixier | Technologie et typologie dérives et scléroses[END_REF]. However, these methodologies are linked by the objective of understanding a type of artifacts. These approaches originate from different levels of understanding and are used for the study of tools.

The common methodology involves the identification of the following (influenced by the work of J. Pelegrin; e. g., [START_REF] Pelegrin | Productions lamellaires attribuées à l'Aurignacien : chaînes opératoires et perspectives technoculturelles[END_REF]:

-the blank production methods, -the shape of the blank that was used for the production of the tool, -the modifications that are needed for realizing the "ideal" shape of the object, namely, the description of the steps for reaching a specified shape (such as modes and techniques of retouch, modification to obtain the cutting edge or hafting of the piece), -the final shape to define the typical pieces and the atypical variations and, eventually, to describe the "deviant" pieces.

Few studies are devoted to obtaining a new understanding of the typology, where the final shape of the tool is perceived not as the "desired shape" but as the result of several parameters that lead to that shape (e.g., the "state of the pieces" and the used raw materials). In this case, the evaluation of the knapping constraints and the identification of the retouch techniques and of the knowledge that is necessary for the production are suitable for describing the "ideal type" and the atypical or deviant versions of it (e. g., [START_REF] Duches | Success of a flexible behavior. Considerations on the manufacture of Late Epigravettian lithic projectile implements according to experimental tests[END_REF][START_REF] Marder | Reconstructing microlith shaping: archaeological and experimental observations of Early and Final Natoufian lunates at Eynan (Aïn Mallaha), Israël[END_REF][START_REF] Valentin | Typologie vs typologie (sic!). Comment la technologie contribue à raffiner la typologie des armatures lithiques[END_REF]. Consequently, according to B. Valentin, the typologies of tools are fed by technology.

Therefore, it is impossible to separate the technological and typological approaches.

We wish to conduct our study of the K11 armatures using "a typological approach", consists of attempting to construct and describe the types of tools from the perspectives of the prehistoric artisans who made them, before referring to any established type-lists" (Pelegrin and O'Farrell, 2005, pp.109).

The stone hunting points from Central European assemblages are poorly understood. This knowledge is often limited to the types that are classified according to the Sonneville-Bordes type list and, at best, to tables of drawings (e.g., [START_REF] Klíma | Zur Frage der Mikroindustrie aus Pavlov[END_REF]Hromada and Kozlowski, 1995). Discussion of types of Central Europe industries and attempts to define and describe the production systems are rare (e.g., Oliva, 2009a;Polanská et al., in presse;[START_REF] Polanská | Réflexion autour des industries gravettiennes « post-pavloviennes » de Slovaquie occidentale et de Moravie[END_REF][START_REF] Vlačiky | The hunters from Trenčianske Bohuslavice-Pod Tureckom site, one of the most important Gravettian open air sites in Western Slovakia[END_REF][START_REF] Wilczyński | Loess, flints and bones: Multidisciplinary research at Jaksice II Gravettian site (southern Poland)[END_REF]. Hence, the detailed description and characterization of the types from this geographical area are important.

Material: The backed points from Unit K11

The stone industry of the Unit K11 assemblage consists of 1,196 pieces [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF], 51 of which are formal tools, and 2 are possible tools (artifacts with use retouch). They are dominated by 33 backed points fragments and 9 roughouts/unfinished backed microliths (Fig. 45678). Other artifacts correspond to the "basic tool kit" containing two burins, three retouched blades, one fragment of tools, one pointed artifact, and one composite tool, which does not allow us to refine the cultural attribution. Most of the assemblage consists of unretouched thermic fragments and fragments of burned flakes. More than 600 artifacts are smaller than one cm (the result of the sieving of sediment).

Study sample of backed points and bladelet production

The collection includes 4 bladelet cores on flakes with a narrow flaking platform (Fig. 2345678). The bladelet production is unipolar on the side of the flake or blade. One of the sides of core is often composed of the ventral face of the flake blank, and the striking platforms are plain and oblique (Fig. 2: 8). This knapping sequence matches various unretouched bladelets with straight or slightly curved profiles (Fig. 2: 1-5). The collection does not include the waste of bladelet production but it includes a few products broken during the backing process (Fig. 7: 1-4).

To better understand the modalities of edge treatment management, we classified this group of armatures and roughouts using 6 categories (Tab. 1; Fig. 3): -bladelets with two retouched edges (one backed; This classification enables the outlining of the production objectives with a simplified quantification. From this perspective, the objective is clear: to create a straight backed piece (at least 19 backed pieces out of 33), which is obtained, in most cases, on the thicker part of the blank (total backing).

The assemblage does not include entire pieces. The most complete artifact is one piece (subentire), where the butt/flaking platform is present in the proximal part (Fig. 6: 2), of which the distal part is broken but was probably asymmetrically retouched.

Morphometrical data of the backed points

Within the 33 point fragments and 9 roughouts of backed pieces, 28 enable the exploration of at least two dimensions (width and thickness; Fig. 8). The other 14 are too fragmented.

Based on the analysis of the available sample, a standardized width of within 3 and 4,5 mm was sought (Fig. 89).

Most of the backed pieces (including the unfinished ones) are 1,5 to 3 mm in thickness (Fig. 8, 10); this thickness corresponds to the thickness of the unretouched bladelets that were likely produced on the spot.

Because it is a highly restricted sample, data on the bladelet production are scarce.

Nevertheless, it seems that some roughouts of backed pieces are produced on small blades (Fig. 7: 4). From this perspective, the only backed piece that was obtained with inverse retouching shows a total backing that enables the narrowing of the initial width of 3 mm. This piece poses questions regarding a larger dimensional variability of the backed armatures from Unit K11 and the likely presence of two distinct types. The most complete piece of the series is 3,1 mm long.

Main characteristics of the backed points

As discussed previously, it seems that the objective of the K11 group was to create narrow and light armatures.

We have limited indices for describing the armatures of these units since the sample is small (33 pieces, excluding the roughouts) and its conservation is fragmentary. It seems that these pieces are narrow with standardized width where the backing of edges is asymmetrical; indeed, one of the edges presents a more invasive or total backing than the other (or it has been unretouched). In summary, the recurrent features are as follows (Fig. 11):

-straightness of the profile and of the back delineation, -standardized width, -asymmetrical backing of the edges, -asymmetrical shape.

Edges (Fig. 11) One edge is modified by direct or crossed, abrupt, steep backing, mostly in the widest part of the blank. It seems that a straight opposite edge is sought, and this can be unretouched or retouched via direct retouching with various degrees and extension of backing (generally, continuous retouching is used).

Ends (Fig. 11) Since no entire piece is available, we cannot describe the possible ends. However, it seems that two asymmetrical ends are sought and that these are in continuity with the back. They can be obtained from the opposite edge via direct retouching (with different degrees of backing) to produce pointed ends. The shape of the end is linked to the initial blank morphology (the section) and to the technical options to obtain the desired shape (Fig. 12). For example, if the blank is thin and has a regular triangular section, it is useful to approach the main ridge via the backing of the two edges to obtain a pointed end along the axis of the blank (Fig. 4: 4, 6; 6: 4). In contrast, if the blank has a quadrangular or irregular triangular section, it is easy to retouch a straight back and, subsequently, add an oblique retouch to join the back; in this case, the end has an asymmetrical shape (Fig. 4: 2, 7; 5: 4, 6-7; 6: 2, 6).

It is possible that the ends have undergone inverse retouching, but the only two pieces are not highly significant: one is too fragmentary (Fig. 6: 15), and the other has been classified as 'deviant' (Fig. 4: 7; the production is clumsy, which corresponds to the blank curve).

In summary, an uncertainty persists regarding the management of the ends. No less than 22 fragments out of 33 have pointed ends, but this could be a solution for joining the back and not an intentional creation.

Preferential orientation of the backed points?

It is possible to determine the modifications of the ends on 11 pieces. Among those fragments, 8 pieces have a right backing, 2 have a left backing and one has double backing. Within the industries with backed pieces, the upper and lower faces were distinguished by prehistoric makers, and the back was preferentially produced on the right edge (with a technological orientation of the piece); consequently, the basis and the apex were distinguished (e.g., [START_REF] Klaric | Des armatures variées, des modes de production variables: réflexions à partir de quelques exemples du Gravettien d'Europe occidentale (France, Portugal, Allemagne)[END_REF]Pelegrin and O'Farell 2005;[START_REF] Simonet | Les gravettiens des Pyrénées[END_REF].

The questions regarding the preferential orientation and the distinction between the basis and the apex are unanswered for Unit K11 from Dolní Věstonice II due to the fragmentation and the small number of pieces.

However, since 8 pieces out of 11 have a right backing, the makers of those armatures made this distinction, which is similar to that of most of the Upper Palaeolithic backed points.

Fractures

Overall, the armatures are part of a complex system, which is comprised of various elements. This cannot be discussed here since the points came from the manufacturing phase.

Among the fractures, V. Borgia observed a very high percentage (60%) of total plan fractures, namely, snaps, which do not supply any information regarding the functions of the tools (pers. comm.). Only four fractures are bending/cone fractures (Fig. 4: 9-6 and 5: 8-7), but none of them was a diagnostic impact scar (for types of fractures, see Borgia, 2006 and2008;[START_REF] Fischer | Macro and Micro Wear Traces on Lithic Projectile Points[END_REF][START_REF] O'farrell | Approche technologique et fonctionnelle des pointes de la Gravette: une analyse archéologique et expérimentale appliquée à la collection de Corbiac[END_REF][START_REF] O'farrell | Les pointes de La Gravette de Corbiac (Dordogne) et considérations sur la chasse au Paléolithique supérieur ancien[END_REF][START_REF] Perpère | Les pointes de la Gravette de la couche 5 de l'abri Pataud. Réflexions sur les armes de pierre dans les outillages périgordiens[END_REF]. This scenario is the result of a post-depositional or debitage fragmentation. These observations demonstrate the characteristics of lithics, which prove the production of blanks and their transformation in armature on-site.

Discussion

The shape of the points from Unit K11 is not clear due to the poor conservation of the ends. If we consider that these armatures are backed points with modified ends (one or both) that have been shaped by inverse retouch, the similar asymmetric pieces are identified from several phases of the Gravettian (e.g., [START_REF] Bodu | Le gisement des Bossats a Ormesson, région de Nemours (Seine-et-Marne): un site gravettien à faune dans le Bassin parisien[END_REF][START_REF] Pesesse | La pointe à dos alternes", un nouveau fossile directeur du Gravettien?[END_REF]Fig. 13-14). They have been reported in the Late/Final Gravettian of Western, Central and Eastern Europe [START_REF] Klaric | Des armatures variées, des modes de production variables: réflexions à partir de quelques exemples du Gravettien d'Europe occidentale (France, Portugal, Allemagne)[END_REF][START_REF] Reynolds | The mid Upper Palaeolithic of European Russia: chronology, culture history and context: a study of five Gravettian backed lithic assemblages[END_REF][START_REF] Sinitsyn | Variabilité du Gravettien de Kostienki (Bassin moyen du Don) et des territoires associés[END_REF][START_REF] Terberger | [END_REF]. Other analogous points have been reported for the Middle Gravettian in Moravia, France, Italy, Ukraine or Russia [START_REF] Bodu | Le gisement des Bossats a Ormesson, région de Nemours (Seine-et-Marne): un site gravettien à faune dans le Bassin parisien[END_REF][START_REF] Borgia | Le punte a dorso degli strati alla base della serie gravettiana di Grotta della Cala (Marina di Camerota, Salerno)[END_REF]Oliva, 2009a;[START_REF] Polanská | Questionnement sur la diversité du Pavlovien morave par l'étude technologique des gisements de Milovice I, Pavlov I, Pavlov VI, Dolní Věstonice II-WS, Předmostí Ib[END_REF], for the Early Gravettian in Lower Austria and Germany [START_REF] Moreau | Le Gravettien ancien d'Europe centrale revisité: mis au point et perspectives[END_REF] or Western Europe [START_REF] Pesesse | Le Gravettien existe-t-il? Le prisme du système technique lithique[END_REF]. Those points are called sometimes microgravettes [START_REF] Klaric | Des armatures variées, des modes de production variables: réflexions à partir de quelques exemples du Gravettien d'Europe occidentale (France, Portugal, Allemagne)[END_REF][START_REF] Pesesse | Le Gravettien existe-t-il? Le prisme du système technique lithique[END_REF] or Vachons points [START_REF] De | Lexique typologique du Paléolithique Supérieur[END_REF], but usually, they are larger than those from Unit K11 in Dolní Věstonice II (Fig. 1314).

At the first sight, it is possible to find similar points across Europe. Nevertheless, the attribution to a more precise stage of Gravettian remains difficult without taking into account other features of the associated industry (diagnostic formal tools, technical systems of productions, raw material used) and without direct study of the material. But Unit K11, which contains a poor sample and non-diagnostic industry, does not support such comparisons. That is why our reflection focuses mainly on Dolní Věstonice-Pavlov-Milovice area and the territories surrounding Moravia.

5.1 Other Units from the Dolní Věstonice-Pavlov-Milovice settlement rea A more detailed study is being prepared to be published for the units of northern slope -(lower part) of Dolní Věstonice II. Currently, it can be established that the Unit K10 (located 40 m from K11) includes highly fragmentary five backed points, which are mostly in radiolarite [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF]Fig. 13: 7-9). They are backed pieces with asymmetrical outline and asymmetrical backing of the edges. However, they seem more massive and thicker than the K11 pieces. This unit is not without problems (possibly nonhomogeneous, small sample size, and the absence of sieving). Consequently, the direct link between the direct date of de 14C 23,540±180 uncal BP (GrN-19498) and the lithics remain uncertain.

Unit S6 (dated 27,660±80 uncal BP; GrN-13962) does not include the backed armatures and in general small fraction of industry (non-sieved material; [START_REF] Klíma | Dolní Věstonice II. Ein Mammutjägerplatz und seine Bestattungen[END_REF][START_REF] Svoboda | K analýze velkých loveckých sídlišť: Prostorová struktura a chronologie lokality Dolní Věstonice II-IIa[END_REF]. The lithic industry is laminar with prevalence of the burins on truncation.

In general, the three lithic collections of northern slope (lower part) of Dolní Věstonice II appear to be too different (poor samples, non-diagnostics tool types, non-comparable productions and stratigraphy) to make the relevant comparison.

The G and H sectors from Milovice I include more than 100 microgravettes of Milovice sub-type (Oliva, 2009a;[START_REF] Polanská | Questionnement sur la diversité du Pavlovien morave par l'étude technologique des gisements de Milovice I, Pavlov I, Pavlov VI, Dolní Věstonice II-WS, Předmostí Ib[END_REF]Fig. 13-14). As in the previous examples, the points show an asymmetrical backing of the edges; one has a rectilinear delineation, while the other is either unretouched or retouched. At least one of the ends has an inverse low-angle or semi-abrupt retouch. However, those pieces are wider and more massive than the Unit K11 pieces.

Several assemblages of the group with micro-saws include microgravettes of Dolní Věstonice sub-type [START_REF] Polanská | Questionnement sur la diversité du Pavlovien morave par l'étude technologique des gisements de Milovice I, Pavlov I, Pavlov VI, Dolní Věstonice II-WS, Předmostí Ib[END_REF]Fig. 13-14). These points present an asymmetrical backing of the edges; one has a rectilinear delineation (direct or crossed backing) while the other is partly unretouched. One or both ends (systematically the base) are modified via inverse semi-abrupt short retouching. Nevertheless, those points show the dimensional variability and they are wider than the Unit K11 pieces.

In general, Unit K11 modifications of the points ends, their dimensions are different than the other Middle Gravettian collections from Dolní Věstonice-Pavlov-Milovice settlement area. Other characteristic tools are absent or are also different.

Sites from Bohemia (Czech Republic)

Many sites of the Bohemian Gravettian have backed points, which are classified as microgravettes [START_REF] Otte | Le Gravettien en Europe central[END_REF]Šída, 2009;Fig. 14).

The Lubná village (Northwestern Bohemia) includes several sites of the Late/Final Gravettian. After the published drawings, Lubná I-IV include narrow backed points, and some of the ends have undergone inverse retouching. This cultural attribution is supported by the data [START_REF] Verpoorte | Absolute dates for the Bohemian Middle Upper Palaeolithic[END_REF]Lubná I dated 21,760 ± 270;GrA-20006 uncal BP and 21,400 ± 260 uncal BP;GrA-20008).

The lithic industry from Jenerálka, which is dated 22,480 ± 290 BP and 21,910 ± 270 uncal BP, also includes microgravettes fragments (Šída, 2009).

Sites from Lower Austria

The collection of Willendorf II (level 5; dated 30,500+900/-800 uncal BP (GrN-11193) included a small microgravettes which have been associated to Early Gravettian (e. g. [START_REF] Haesaerts | Revised stratigraphy and chronology of the Willendorf II sequence, Lower Austria[END_REF]Fig. 13-14). Their dimensions seem to be comparable to those of the Unit K11 (1 to 2 mm thickness, 3 to 5 mm in width, approximately until 3 cm length; Moreau, 2012, fig. 6). However, these microgravettes were accompanied by flechettes, which is not the case with the Unit K11. The analogies require further investigation with their direct study.

Sites from the Rhineland (Germany)

The microgravettes are reported in many sites from the Rhineland, especially in Sprendlingen and Mainz-Linsenberg (30 km from each other). Due to the presence of those small points, the sites from this microregion have been associated with the Late/Final Gravettian from Central Europe [START_REF] Cziesla | Die mittlere Steinzeit im Landkreis Pirmasens[END_REF].

The very narrow backed points from Sprendlingen (Late Gravettian) are similar to those from Unit K11/Dolní Věstonice . According to the drawings, the artifacts are highly fragmented [START_REF] Bosinski | Sprendlingen: ein Fundplatz des mittleren Jungpalaolithikums in Rheinhessen[END_REF].

It is not easy to determine whether the basis and/or apex of those points have been inversely retouched systematically. However, they are thin, and the opposite edge to the backing is unretouched or has been directly retouched.

The Mainz-Linsenberg site (dated 22,460±100 uncal BP; Terberger, 2013) hosted a lithic industry, which included small backed points, the extremities of which have been modified via inverse retouching [START_REF] Klaric | Des armatures variées, des modes de production variables: réflexions à partir de quelques exemples du Gravettien d'Europe occidentale (France, Portugal, Allemagne)[END_REF][START_REF] Terberger | [END_REF]. The blanks of those microgravettes come from the production of polyhedric burins, as in various industries from the Late Gravettian in France [START_REF] Klaric | Des armatures variées, des modes de production variables: réflexions à partir de quelques exemples du Gravettien d'Europe occidentale (France, Portugal, Allemagne)[END_REF].

Conclusions

In the assemblage of Unit K11 of Dolní Věstonice II, 33 backed bladelets have been found. They have been manufactured on-site and attributable to Gravettian sensu lato. Despite the limited sample, it has been possible to identify the principal typo technological features of this material. The backed bladelets have a controlled width and an asymmetric rectilinear retouch of the edges; the ends (one or both) possibly present an inverse retouch (which may not have been systematic?).

The raw material that was used to manufacture the armatures is a chert type Krumlovský les, which is not easy to work (more difficult for knapping, with many impurities). This material was rarely used in the Palaeolithic of Moravia and the Dolní Věstonice-Pavlov-Milovice area [START_REF] Přichystal | Kamenné suroviny v pravěku východní části střední Evropy[END_REF]. The question remains for future research and experimentations whether there is a link between the small size of the points and the hardness and inhomogeneity of the material. Only lithics of Unit S6 (neighbour unit) of Dolní Věstonice II are made from this raw material, however, the artifacts assemblage does not allow direct comparisons (see 2.1.1 part).

The armatures of Unit K11 differ from other pieces with asymmetric edges that have been found in the Central European Gravettian (at the sites of Lubná, Milovice I and Dolní Věstonice II -Units S1 to S4) due to their smaller thickness. They have certain similarities with small microgravettes identified in layer 5 of Willendorf II [START_REF] Moreau | Le Gravettien ancien d'Europe centrale revisité: mis au point et perspectives[END_REF]. To the best of our knowledge, these tools remain unique in the micro-region and are entirely absent from the Pavlovian sensu stricto industries, which dominate the Gravettian settlements that are localized under the Pavlov Hills.

This study adds to the research on the "gravettoid" collections of Dolní Věstonice-Pavlov-Milovice settlement area (Milovice I site, Pavlov I, other units of Dolní Věstonice II) to improve understanding regarding the significance of the various regional facies. -2, 6-9, and 19-20, 27-29 by M. Polanská;drawings 3-5 from Škrdla, 2005;drawings 10-18 from Bosinski et al., 1995;drawings 21-26, 30-32 Moreau, 2012. Fig. 14. Gravettian sites and microregions with backed points that are similar to Unit K11 of Dolní Věstonice II (CAD by M. Polanská).

Captions of figures and table

Tab. 1. Classification of the backed points from Unit K11 of Dolní Věstonice II according to the degree/depth of the backing (total, invasive, or marginal), which is based on the study of [START_REF] Christensen | Armatures de projectiles et outils: de la production à l'abandon[END_REF] Tab. 1. Classification of the backed points from Unit K11 of Dolní Věstonice II according to the degree/depth of the backing (total, invasive, or marginal), which is based on the study of [START_REF] Christensen | Armatures de projectiles et outils: de la production à l'abandon[END_REF].

  Fig. 4: 2, 4-7; 5: 3-5, 7; 6: 2, 4), -bladelets with one retouched edge (backed; Fig. 4: 1, 9; 6: 5, 11-12), -bladelets with two retouched edges (without backing, marginal retouching; Fig. 6: 6, 9), -pieces that are too fragmentary (undefined; Fig. 4: 3; 5: 1-2,8; 6:1, 3, 6-8, 10, 13-15), -and roughouts of backed bladelets (total or invasive backing; Fig. 8).

Fig. 1 .

 1 Fig. 1. Geographical localization of Unit 11 from Dolní Věstonice II (CAD by M. Polanská).

Fig. 2 .

 2 Fig. 2. Unretouched bladelets (1-5) and bladelet cores of Unit K11 (drawings by B. Klíma, photos M. Polanská).

Fig. 3 .

 3 Fig. 3. Classification of the backed points from Unit K 11 of Dolní Věstonice II according to the degree/depth of the backing (total, invasive, or marginal).

Fig. 4 .

 4 Fig. 4. Backed points of Unit K11 (drawings and photos by M. Polanská).

Fig. 5 .

 5 Fig. 5. Backed points of Unit K11 (drawings and photos by M. Polanská).

Fig. 6 .

 6 Fig. 6. Backed points of Unit K11 (drawings 1-10 and 13-14 by M. Polanská; drawings 11-12 by B. Klíma).

Fig. 7

 7 Fig. 7. 1-4 -Unfinished backed pieces (drawings 1-3 by B. Klíma, drawing 4 by M. Polanská).

Fig. 8 .

 8 Fig. 8. Relation between the width and the thickness of the backed points in Unit K11.

Fig. 9 .

 9 Fig. 9. Width distributions of Unit K11 backed points.

Fig. 10 .

 10 Fig. 10. Thickness distributions of Unit K11 backed points.

Fig. 11 .

 11 Fig. 11. Main characteristics of the Unit K11 backed points.

Fig. 12 .

 12 Fig. 12. Modalities of edge treatment/Arrangement modalities of the shaped end relative to the morphology of the support (CAD by M. Polanská).

Fig. 13 .

 13 Fig. 13. Various types of backed points and microgravettes of the Middle and Late/Final Gravettian periods in Austria, Moravia and Germany. Drawing 1-2, 6-9, and 19-20, 27-29 by M. Polanská; drawings 3-5 from Škrdla,

  .

		Bladelets with	Bladelets	Bladelets with	Undefined Roughouts of	Roughouts of	Total
		2 retouched	with 1	2 retouched		backed	backed
		edges (one	retouched	edges		bladelets (total	bladelets
		backed)	edge	(marginal		backing)	(invasive
			(backed)	retouch)			backing)
	Median		3		3	2		8
	fragments
	One end	12	2	2	9	2	4	31
	conserved
	Sub-entire	1	1				1	3
	Total	13	6	2	12	4	5	42

Acknowledgements

The author wish to thank Professor J. Svoboda for the materials and for his useful contributions and J. Pelegrin (CNRS; UMR 7055 PreTech) for an important discussion on armatures and proofreading. For constructive comments and attention to this paper we would like to thank V. Borgia, K. Jaworski, and K. Matulová. The work was supported by the Czech Academy of Sciences (PPLZ program) and partially conducted during the PhD research (Pantheon-Sorbonne University; UMR 7041-ArScAn).