Nathanaël Guillaud

Guillaume Balarac

Eric Goncalves Da Silva

Jeronimo Zanette

E Goncalvès

Large Eddy Simulations on Vertical Axis Hydrokinetic Turbines -Power coefficient analysis for various solidities

Keywords: Vertical Axis Hydrokinetic Turbines, Tip Speed Ratio, Solidity, Large Eddy Simulations

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Tidal currents represent a large renewable energy resource concentrated in a few dozen sites in the world [START_REF] Bryden | Me1-marine energy extraction: tidal resource analysis[END_REF]. Vertical Axis Hydrokinetic Turbines (VAHT) are less expensive than traditional hydropower facilities. They are also faster to install and allow the exploitation of more sites due to the possibility to create taylor-made arrays of turbine within regions such as rivers, man-made channels or tidal straits where the local bathymetry focuses the flow [START_REF] Dominguez | Fast power output prediction for a single row of ducted cross-flow water turbines using a bem-rans approach[END_REF]. Given the promise of VAHT technology, the investigation of their performance is of increasing interest to researchers and companies.

A key parameter of VAHT is the turbine solidity, which allows to characterize the blockage of the flow due to the presence of the turbine. In this work, the turbine solidity is defined as the ratio between the cumulated blade chord length and the turbine diameter, = 2 , with the number of blades, the blade chord and the turbine radius. Note that slight difference can appear about the definition of this quantity, in literature. For example, Gosselin et al. [START_REF] Gosselin | Parametric study of h-darrieus vertical-axis turbines using cfd simulations[END_REF] define the turbine solidity as ∕ , whereas Shiono et al. [START_REF] Shiono | An experimental study of the characteristics of a darrieus turbine for tidal power generation[END_REF] define the turbine solidity as ∕ [START_REF] Dominguez | Fast power output prediction for a single row of ducted cross-flow water turbines using a bem-rans approach[END_REF]. The turbine solidity has a major impact on the turbine efficiency and on the turbine capacity to support hydrodynamic loads. The influence of the turbine solidity on the turbine power coefficient has been studied experimentally by Shiono et al. [START_REF] Shiono | An experimental study of the characteristics of a darrieus turbine for tidal power generation[END_REF] and Blackwell et al. [START_REF] Blackwell | Wind tunnel performance data for the darrieus wind turbine with naca 0012 blades[END_REF]. These studies show that for a given geometry, it exists an optimal solidity which maximizes the power coefficient of the turbine. This optimal solidity strongly depends on the turbine geometry. Shiono et al. [START_REF] Shiono | An experimental study of the characteristics of a darrieus turbine for tidal power generation[END_REF] found an optimal solidity equals to 0.56, whereas Blackwell et al. [START_REF] Blackwell | Wind tunnel performance data for the darrieus wind turbine with naca 0012 blades[END_REF] found a lower optimal solidity varying between to 0.2 and 0.25. An analyze of the causes of the obtained optimal solidity is not given in these studies. A first motivation of this present work is to deeper understand the influence of the turbine geometry details on the VAHT performances.

As observed by Shiono et al. [START_REF] Shiono | An experimental study of the characteristics of a darrieus turbine for tidal power generation[END_REF] and Blackwell et al. [START_REF] Blackwell | Wind tunnel performance data for the darrieus wind turbine with naca 0012 blades[END_REF], the turbine solidity influences the optimal Tip Speed Ratio (TSR).

A higher solidity leads to a lower optimal TSR. The TSR is equal to 0 , where is the turbine rotation speed magnitude and 0 is the free-stream velocity. As described by Zanette [START_REF] Zanette | Hydroliennes à flux transverse: contribution à l'analyse de l'interaction fluide-structure[END_REF], the TSR defines the relative flow incidence on a VAHT blade. Considering a constant free-stream velocity accross the turbine, it can be shown that:

= arctan sin ( ) cos ( ) + (1)
where is the angular position of the VAHT defined in Figure 1. The blade incidence is thus time dependent and periodic.

As described by Paraschivoiu [START_REF] Paraschivoiu | Wind turbine design: with emphasis on Darrieus concept[END_REF], at small TSRs, the static stall angle of incidence of the blade is exceeded and the dynamic stall phenomenon [START_REF] Mccroskey | The phenomenon of dynamic stall[END_REF] occurs. As the optimal TSR of high solidity turbines is low, high solidity turbines operates with dynamic stall phenomenon at their optimal TSR. The dynamic stall phenomenon in VAHT has been observed in various experimental studies [START_REF] Mccroskey | The phenomenon of dynamic stall[END_REF][START_REF] Fraunie | Water channel experiments of dynamic stall on darrieus wind turbine blades[END_REF][START_REF] Fujisawa | Observations of dynamic stall on darrieus wind turbine blades[END_REF][START_REF] Ferreira | Visualization by piv of dynamic stall on a vertical axis wind turbine[END_REF][START_REF] Mccroskey | Dynamic stall on advanced airfoil sections[END_REF][START_REF] Carr | Analysis of the development of dynamic stall based on oscillating airfoil experiments[END_REF]. This phenomenon is strongly influenced by the maximum angle of incidence and the reduced frequency of the blades [START_REF] Guillaud | Large eddy simulations on a pitching airfoil: Analysis of the reduced frequency influence[END_REF]. A definition of the reduced frequency of the blades of a VAHT has been introduced by Laneville

and Vittecoq [START_REF] Laneville | Dynamic stall: the case of the vertical axis wind turbine[END_REF]:

= ⋅ 1 -1 ⋅ arctan 1 √ 2 -1 -1 (2)
As shown by this equation, the reduced frequency and consequently the dynamic stall phenomenon in a VAHT is influenced by the TSR and the solidity of the VAHT.

Numerous numerical studies have been performed on VAHT. However, the flow in a VAHT and the associated turbine power coefficient are challenging to predict. Unsteady Reynolds Averaged Navier-Stokes (URANS) computations have been of power coefficient as a function of TSR was reproduced with slight difference with experimental data. The flow topology at different TSRs was compared with measurements obtained from Particule Image Velocimetry (PIV) [START_REF] Bossard | Caractérisation expérimentale du décrochage dynamique dans les hydroliennes à flux transverse par la méthode piv (particle image velocimetry). comparaison avec les résultats issus des simulations numériques[END_REF]. Whereas the numerical vorticity fields are coherent the dynamic stall vortex development is delayed in the simulations. The two-dimensional approach does not take into account the losses due to blade tips, arms and shaft. Consequently, the turbine power coefficient is largely overestimated. Three-dimensional URANS simulations were also performed by Pellone et al. [START_REF] Pellone | 3d rans modeling of a cross flow water turbine[END_REF] and Zanette [START_REF] Zanette | Hydroliennes à flux transverse: contribution à l'analyse de l'interaction fluide-structure[END_REF].

The prediction of the turbine power coefficient was improved. However, the turbine power coefficient evolution with angular position still shows discrepancies compared with the experimental results and the dynamic stall vortex development is still delayed. Simulations on a high solidity VAHTs including blade tips, arms and shaft highlighted the high losses generated by blades tips and blade/arm connections at optimal TSR. Yet, the influence of the turbine solidity was not studied. Joo et al. [START_REF] Joo | Aerodynamic characteristics of two-bladed h-darrieus at various solidities and rotating speeds[END_REF] studied the influence of solidity of a VAHT by performing 3D URANS computations. The geometry is simplified and does not contain arms and shaft. The increase of the optimal TSR with a decrease of the solidity is found, as well as a solidity which maximize the power coefficient of the turbine. Authors highlight the impact of solidity on the flow blockage and the flow interaction between the blades and the free stream.

Posa et al. [START_REF] Posa | Wake structure of a single vertical axis wind turbine[END_REF] investigated the wake of an isolated vertical axis wind turbine using large-eddy simulations. A filteredstructure fonction model and immersed boundary method was used. Losses due to blade tips, arms and shaft were not modeled as the studied geometry consists in three blades in rotation, with a periodicity condition applied in the rotation axis direction.

Comparison with experimental data can therefore not be quantitative. However, ensemble averaged velocity profiles in the near wake of the turbine showed a good qualitative agreement with PIV measurements. Besides, the relative size and number of distinct structures in the wake of the turbine obtained by LES is in close agreement with experimental data. A numerical study involving both 2D and 3D URANS simulations and large-eddy simulations was led by Li et al. [START_REF] Li | 2.5 d large eddy simulation of vertical axis wind turbine in consideration of high angle of attack flow[END_REF] on a vertical axis wind turbine. A -SST model and a dynamic Smagorinsky subgrid-scale model was used, respectively. The study case is a simplified geometry composed of three blades and a shaft, with a periodicity condition in the shaft direction. It does not take into account the losses due to blade tips and arms. The authors compared the evolution of the blade tangential force coefficient during a round with experimental results. Both URANS approaches delayed the dynamic stall and consequently overshot the tangential force in the region 0°< < 180°. The LES approach improved the prediction of the dynamic stall phenomenon and consequently improved the blade tangential force prediction. The prediction of turbine power coefficient is therefore improved by LES.

Even though its high computational cost, LES approach has shown its superior accuracy compared with RANS approach in various applications such as aerodynamic studies [START_REF] Breuer | Comparison of des, rans and les for the separated flow around a flat plate at high incidence[END_REF], combustion [START_REF]Large-eddy simulation of turbulent combustion[END_REF], meteorology [START_REF] Santiago | Comparison between large-eddy simulation and reynoldsaveraged navier-stokes computations for the must field experiment. part i: study of the flow for an incident wind directed perpendicularly to the front array of containers[END_REF], flow around hdyrofoil [START_REF] Liu | Cavitation-vortex-turbulence interaction and one-dimensional model prediction of pressure for hydrofoil ale15 by large eddy simulation[END_REF][START_REF] Decaix | Rans and les computations of the tip-leakage vortex for different gap widths[END_REF],

and architectural fluid mechanics [START_REF] Tominaga | CFD modeling of pollution dispersion in a street canyon: Comparison between LES and RANS[END_REF] but also for less standard applications dealing for instance with accurate rain measurements [START_REF] Constantinescu | Simulation of airflow around rain gauges: Comparison of les with rans models[END_REF], electronic system cooling design [START_REF] Liu | Comparison of zonal rans and les for a non-isothermal ribbed channel flow[END_REF], sediment transport [START_REF] Chang | Modeling unsteady turbulent flows over ripples: Reynolds-averaged navier-stokes equations (rans) versus large-eddy simulation (les)[END_REF], or process engineering [START_REF] Rhea | RANS modelling and LES of a single-phase, impinging plane jet[END_REF]. LES is then an attractive approach to capture the flow dynamics and to correctly predict the power coefficient of a vertical axis turbine. One of the main objectives of this work is then to perform the first LES of a complete VAHT geometry in order to deeply investigate the turbine performances and the influence of its solidity. Then, in this work, LES are performed on a complete three-blade VAHT, namely the Achard turbine [START_REF] Achard | Hydraulic turbomachine[END_REF]. A particular emphasis is placed on the impact of solidity on the performances, which is today partially understood. To analyze the turbine performances, the global power coefficient is investigated with the introduction of local quantities. These local quantities are defined as the contribution of various elements of the turbine to the global power coefficient. To evaluate the major losses generated by the real turbine, simulations of an ideal turbine composed with only three infinite blades are also performed.

The paper is organized as follows: the next section 2 details the study cases (sec. 2.1), the analyzed quantities (sec. 2.2)

and the numerical set up (sec. 2.3). Section 3 allows to confirm the reliability of the performed simulations by using classic verification (sec. 3.1) and validation (sec 3.2) procedures. The section 4 gives the results of this work by first analyzing the VAHT at two solidities (sec. 4.1). In this part "real" and "ideal" turbines are considered. Simulations of the ideal turbine are finally performed for various solidities at the optimal TSR to study the evolution of optimal power coefficient as a function of solidity (sec. 4.2). Conclusions are drawn in section 5 with a sum-up of the main mechanisms having an effect on the turbine performances.

Numerical methodology

Configurations studied

The considered geometry is an Achard turbine [START_REF] Achard | Hydraulic turbomachine[END_REF]. The first geometry considered is this work corresponds to the turbine experimentally studied by Dellinger [START_REF] Dellinger | Instrumentation d'un tunnel hydrodynamique pour la caractérisation de turbines à flux transverse[END_REF] and Mentxaka Roa et al. [START_REF] Mentxaka Roa | Numerical and experimental analysis of a darrieus-type cross flow water turbine in bare and shrouded configurations[END_REF]. This turbine is a Darrieus-type turbine composed by three blades, as shown in Figure 2. The blade section is a projected NACA0018 profile without pitch angle and the main characteristics of the turbine are summarized in table 1. This leads to a turbine with a solidity = 0.55, for which the optimal TSR is known from experimental data [START_REF] Dellinger | Instrumentation d'un tunnel hydrodynamique pour la caractérisation de turbines à flux transverse[END_REF][START_REF] Mentxaka Roa | Numerical and experimental analysis of a darrieus-type cross flow water turbine in bare and shrouded configurations[END_REF], = 2. Three TSRs are therefore considered, = 1, 2 and 2.5. To study the effect of solidity, this first geometry is modified to consider a second turbine with = 0.16. This modification is obtained by conserving the blade chord and by varying the turbine radius. For this new solidity, the optimal TSR can be estimated from experimental data compilation, showing that ∝ 1∕ √ [START_REF] Beaudet | Etude expérimentale et numérique du décrochage dynamique sur une éolienne à axe vertical de forte solidité[END_REF]. The estimated optimal TSR for = 0.16 is then equal to 3.4.

The three considered TSRs in this case are therefore 2.9, 3.4 and 3.9.

Shaft diameter 22mm

Table 1: Characteristics of the real turbine geometry.

These turbines are denoted as the real turbines in the following. To evaluate the major losses generated by these real turbines, ideal turbines only composed by three infinite blades are also considered, as shown in Figure 3. Then, the performance of these ideal turbines will not be affected by blade/arm connection, arm, shaft, blade tip, ... The same solidities and the same TSRs as the real turbines are considered. Finally, to investigate the evolution of the optimal turbine power coefficient of this ideal turbine as a function of its solidity, additional solidities 0.11, 0.34 and 1.08 are considered at the estimated optimal TSR, respectively 4.1, 2.3 and 1.3.

For all these turbines the free-stream velocity 0 is set to 2.8 m/s, and the TSR is varied by changing the turbine rotation speed magnitude, . Considering all tested TSRs, this leads to a range of Reynolds number based on the chord length = (where is the water kinematic viscosity) varying between 8.9 × 10 4 and 3.7 × 10 5 . Note that this Reynolds number variation is only due to the variation of , but at a given TSR, the Reynolds number is the same for all considered turbines, similarly to experiments.

Quantities of interest

To compare and study the different VAHTs, we introduce the mean and the instantaneous power coefficient ⟨ ⟩ and defined as:

⟨ ⟩ = ⟨ ⟩ 0.5 3 0 ; = ∬ ⃖⃖⃖⃖⃗ (3)
where ⟨ ⟩ is the mean power generated by the turbine equal to ⟨ ⟩ , where ⟨ ⟩ is the mean torque generated in the rotation axis direction. is the turbine surface and ⃖⃖⃖⃖⃗ is a local power coefficient generated by the point of the turbine surface:

⃖⃖⃖⃖⃗ = ⃖⃖⃖⃖⃗ 0.5 3 0 (4)
⃖⃖⃖⃖⃗ is the axial torque generated by the point of the turbine:

⃖⃖⃖⃖⃗ = ⃖⃖⃖⃖⃗ ∧ -⃖ ⃗ + ⋅ ⃖ ⃗ ⋅ ⃖⃖⃗ (5)
where is the pressure, is the viscous stress tensor, ⃖ ⃗ is the surface normal at the point and ⃖⃖⃗ is the axial unit vector (turbine rotation axis direction).

To study the performances of different zones of the real turbines, the instantaneous power coefficient is integrated on parts of the turbine surface. A power coefficient is then defined for each region: Only the upper symmetry of a blade is considered.

= ∬ ⃖⃖⃖⃖⃗ . ( 6
)
The considered VAHT regions are defined in Figure 4.

In order to compare the performance of the regions involving different heights, a region efficiency is introduced:

= ⋅ ℎ ( 7
)
where ℎ is the height of the considered region.

The different variables presented in this section will be used to perform a detailed analysis of the VAHT performance.

Layouts of ⃖⃖⃖⃖⃗ over the turbine surface will be shown. Isosurfaces of the Q-criterion [START_REF] Hunt | Eddies, streams, and convergence zones in turbulent flows[END_REF] will also be shown to highlight the principal vortices of the flow.

Numerical set-up

To study the performance of these turbines, Large-Eddy Simulations (LES) of the flow configurations are performed.

Conversely to URANS approach, LES allows to explicitly describe the turbulent motion at the largest scales of the flow [START_REF] Sagaut | Large Eddy Simulation for Incompressible Flows: An Introduction[END_REF]. It leads to a more complete physical description of the flow, but with a much higher computational cost than for classic statistical calculations. In this work, LES were performed using the YALES2 flow solver [START_REF] Moureau | Design of a massively parallel cfd code for complex geometries[END_REF]. This code solves the incompressible and low-Mach number Navier-Stokes equations for turbulent flows on unstructured meshes using a projection method for pressurevelocity coupling [START_REF] Chorin | Numerical solution of the navier-stokes equations[END_REF]. It relies on fourth-order central finite-volume schemes and on highly efficient linear solvers [START_REF] Malandain | Optimization of the deflated conjugate gradient algorithm for the solving of elliptic equations on massively parallel machines[END_REF]. The time integration is explicit for convective terms using a fourth-order modified Runge-Kutta scheme [START_REF] Kraushaar | Application of the compressible and low-mach number approaches to large-eddy simulation of turbulent flows in aero-engines[END_REF], with a semi-implicit integration for the diffusive terms. YALES2 solver is able to deal with unstructured grids composed only by tetrahedron elements or by prisms and tetrahedron elements, allowing to perform LES or DNS of complex geometries in the context of massively parallel computations. The solver has been validated for various applications such as combustion [START_REF] Moureau | From large-eddy simulation to direct numerical simulation of a lean premixed swirl flame: Filtered laminar flame-pdf modeling[END_REF][START_REF] Guedot | Design of implicit high-order filters on unstructured grids for the identification of large-scale features in large-eddy simulation and application to a swirl burner[END_REF], biomechanics [START_REF] Chnafa | Image-based large-eddy simulation in a realistic left heart[END_REF], hydro-electricity [START_REF] Wilhelm | Analysis of head losses in a turbine draft tube by means of 3d unsteady simulations[END_REF], wind energy [START_REF] Benard | Large-eddy simulation of wind turbines wakes including geometrical effects[END_REF], or multiphase flows [START_REF] Odier | Numerical analysis of the flapping mechanism for a two-phase coaxial jet[END_REF]. In this work, the equations are solved in a rotating frame and a rotating velocity condition is imposed at the inlet. A constant Courant-Friedrichs-Lewy (CFL) number of 0.9 is set for all cases. The Smagorinsky dynamic subgrid-scale model is used [START_REF] Germano | A dynamic subgrid-scale eddy viscosity model[END_REF].

For both real and ideal turbines, the domain extension is equal to 16 turbine diameters around the VAHT to avoid confinement effect (see next section for a verification of this choice). A no-slip boundary condition is imposed on the turbine surface, with no wall laws. As no turbulence is imposed at the inlet, the flow is laminar upstream from the VAHT. The flow is assumed to be incompressible. Finally, for the real turbines, in the spanwise direction (rotation axis direction) the domain size is 1.43 turbine height as in the experiments [START_REF] Dellinger | Instrumentation d'un tunnel hydrodynamique pour la caractérisation de turbines à flux transverse[END_REF][START_REF] Mentxaka Roa | Numerical and experimental analysis of a darrieus-type cross flow water turbine in bare and shrouded configurations[END_REF], and a slip-wall condition is used on top and bottom. For the ideal turbines, to represent infinite blades, the blades cross the domain and a periodicity condition is applied on top and bottom limits. For these cases, the domain height is set to 5 . Computation domain and boundary conditions are illustrated in Figure 5 for the real turbine case with = 0.55.

Verification and Validation of simulations

Verification: mesh convergence and confinement effect

To confirm the reliability of the performed simulations, a mesh convergence is first performed. The results for the real turbine case with = 0.55 is presented. Four meshes are generated with the same topology. The mesh is generated using 6 prism layers close to the turbines walls, and tetrahedrons elements elsewhere. The prisms layers are defined by the characteristics of the first layer (the closest layer to the turbine wall), i.e. by the length to the prism normal to the wall, Δ , and by its aspect ratio with the triangle base-length of the prism. Here, this ratio does not exceed 20, and the element growth rate from the wall is equal to 1.1. After the prism layers, tetrahedrons elements are used. In a first region defined with a radial extension equal to 6 turbine radius, the element size is limited to Δ 1 . Outer this first region, the element size is limited to Δ 2 . For the overall mesh, the growth rate is set to 1.1. The characteristics of the four meshes are summarized in table 2 and an illustration of the mesh M3 is given in Figure 6. The evolution of the power coefficient for = 2 as a function of the turbine angular position, , is shown for the four meshes in Figure 7. Whereas a strong influence of the mesh is observed for the two coarser meshes (M0 and M1), the finer meshes (M2 and M3) are close. The result shows that the mesh independency is obtained for the finer mesh M3. Only this mesh will be considered in the following. Note that this mesh leads to a most likely value of the first cell size to the wall equals to 3 wall unit (Δ + ≈ 3) along the turbine and is always smaller than 20 wall unit. This result is in agreement with other works [START_REF] Liu | Large eddy simulation of cavitation vortex interaction and pressure fluctuation around hydrofoil ale 15[END_REF].

Mesh

Another verification step is to insure that the domain size is large enough to avoid that confinement effect affects the turbine performance. Then, three domain sizes have been tested: 4 , 8 , and 16 , with the turbine diameter (see Figure 5 for an illustration of the case with a domain extension of 16 ). Figure 8 shows the evolution of the power coefficient for = 2 for the three considered domain size. The case with a domain extension of 4 shows a strong effect of the confinement, with an over-estimation of the turbine performance. For the two other cases, the effect is smaller. A domain extension equals to 16 turbine diameters is therefore chosen.

Finally, to respect the mesh criteria and the ratio between the domain and the turbine diameters, the mesh is adapted for each geometries. The number of elements of each generated mesh is summarized in tables 3 and 4 for real and ideal turbines, respectively. It is then expected that LES approach leads to a more complete physical description of the flow, but with a much higher computational cost than for classic RANS calculations. For the final meshes, the CFL constraint leads to an angle variation in one time step around 5 × 10 -3 degree. Then, for these meshes, a complete revolution of the turbine needs around 27h on 768 cores (Bull B720 Haswell, CPU frequency: 2.6 GHz). 1 ; 2 ; 2.5 2.9 ; 3.4 ; 3.9

0 • 45 • 90 • 135 • 180 • 225 • 270 • 315 • -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Validation: comparison with experimental results

160

For validation, the real turbine with the solidity = 0.55 is now compared with experimental data obtained on a similar configuration for the three TSRs: = 1, 2, and 2.5. In experiments, PIV measurements have been performed to obtain the axial vorticity fields around a blade, and the instantaneous torque is obtained from a synchronous generator connected to the shaft (see [START_REF] Bossard | Caractérisation expérimentale du décrochage dynamique dans les hydroliennes à flux transverse par la méthode piv (particle image velocimetry). comparaison avec les résultats issus des simulations numériques[END_REF][START_REF] Dellinger | Instrumentation d'un tunnel hydrodynamique pour la caractérisation de turbines à flux transverse[END_REF][START_REF] Mentxaka Roa | Numerical and experimental analysis of a darrieus-type cross flow water turbine in bare and shrouded configurations[END_REF] for details of the experimental set-up). It should be noted that the width of the experimental test section is only four times the turbine diameter, leading to confinement effect. As a consequence, the blockage ratio of the experimental configuration is four times higher than the numerical value. According to the work of Mentxaka Roa et al. [START_REF] Mentxaka Roa | Numerical and experimental analysis of a darrieus-type cross flow water turbine in bare and shrouded configurations[END_REF], the turbine power coefficient decreases as the blockage ratio decreases. An estimation of the blockage effect on the mean power coefficient at the optimal TSR has been introduced by Werle [START_REF] Werle | Wind turbine wall-blockage performance corrections[END_REF], by defining the blockage ratio, , as the ratio of the cross-sectional areas between the turbine and the test section. The optimal mean power coefficient of two turbines for which the blockage ratio is 1 and 2 respectively follows the relation:

⟨ ⟩ 1 ≈ ⟨ ⟩ 2 1 -2 2 1 -1 2 (8)
Figure 9 shows the experimental and numerical mean power coefficients ⟨ ⟩ as a function of TSR. Numerical values obtained with and without the blockage correction are presented for the optimal TSR. The classic bell-shaped curve of the mean power coefficient as a function of TSR is well reproduced. At the lower value = 1, the result obtained from LES is close to the experimental result. At this low rotation speed, the flow blockage led by the turbine is low and the influence of the test section area is small. The flow blockage increases with the turbine rotation speed. The influence of the test section area thus increases as the TSR increases. For the values = 2 and = 2.5, the blockage ratio influence is clearly observed. Numerical results using the correction show a very good agreement with the optimal experimental mean power coefficient. Note that the correction is only valid at the maximum power condition and then it can be only used for the optimal TSR [START_REF] Werle | Wind turbine wall-blockage performance corrections[END_REF]. Note that the LES have also been qualitatively compared with experimental data obtained by PIV [START_REF] Guillaud | Large eddy simulations on vertical axis hydrokinetic turbines and flow phenomena analysis[END_REF]. In particular, it has been shown that LES is able to reproduce the deep dynamic stall [START_REF] Lee | Investigation of flow over an oscillating airfoil[END_REF] observed for small TSR. ⬟ : = 0.55, ■ : = 0.16 --: real turbines, ---: ideal turbine.

Results and discussion

4.1. Analysis of the VAHT at solidities = 0.55 and = 0.16

Mean power coefficients analysis

Figure 11 presents the mean power coefficients obtained for the real and ideal turbines at solidities = 0.55 and = 0.16, respectively. The results for the real turbines are depicted in plain lines while the results for the ideal turbines are depicted with dashed lines. As no losses are generated by blade tips, blade/arm connections, arms, arm/shaft connections and shaft, the power coefficients of the ideal turbines are strongly higher than those of the real turbines at the optimal TSRs (around 40% for the high solidity and 70% for the low solidity). The estimation of the optimal TSR for the low solidity turbine is correct for the ideal turbine. In the real turbines, the losses generated at high rotation speed lead to decrease the optimal TSR. As regard to the solidity influence for the ideal turbine, the optimal mean power coefficient is 31% higher for the low solidity configuration. This difference is reduced to 8.1% when considering the real turbines. A low solidity VAHT can therefore produces a better power coefficient compared to a high solidity VAHT. However, low solidity turbines operates at higher TSR, which leads to increase losses and to limit the power coefficient gain. If the considered turbine geometry generates high losses, the power coefficient can be lower for the low solidity turbine.

The real Achard turbine has been designed with only one arm per blade in order to limit the losses. The blade/arm connection is also designed to limit the interactions between these two components. This leads the low solidity real turbine to have an optimal performance slightly higher than the high solidity real turbine.

The next sections are dedicated to the analysis of the differences of performance between the high and the low solidity turbines. We first propose a detailed analysis of the high solidity turbine performance at its optimal TSR. Then, a comparison between the high and the low solidity turbines will be made at their respective optimal TSRs. 4.1.2. Analysis of the high solidity turbine ( = 0.55) at its optimal TSR ( = 2)

The power coefficients and efficiencies as introduced in the section 2.2 for each region is now considered. At this solidity, the obtained regional power coefficients on the arm, arm/shaft connection and shaft are negligible and will not be reported here.

Figure 12 shows a global view of the flow through the real turbines. The main vortices are identified by plotting isosurfaces of the Q-criterion. The blade tip vortices are clearly illustrated. ). The blade generates few power coefficient in the downstream half-disk and can even produce negative torque. Figure 14 shows a contour of absolute velocity magnitude on a plane located at quarter-blade height. The high solidity of the VAHT leads to a high flow blockage and the flow velocities observed in the downstream half-disk ([180°≤ ≤ 360°]) are low. Few energy is then available after the flow goes through the upstream blades. The low velocity leads the angles of incidence on the blades to be close to 0°. It explains that the regional power coefficients can reach negative values in the downstream half-disk. As a consequence, the estimation of the flow incidence on the blades given by equation 1 is no more correct in the downstream half-disk. However, it remains a good approximation in the upstream half-disk. According to equation 1, the maximal angle of incidence on a blade at = 2 is close to 30°. This angle of incidence is strongly higher than the static stall angle of incidence of the blade. According to equation 2, at = 0.55 and = 2 the blade reduced frequency is equal to 0.35. These high reduced frequency and angle of incidence show that the blade operates with a dynamic stall phenomenon in the upstream half-disk.

To better understand the evolution of the power coefficient of the blade region in the upstream half-disk, the axial vorticity field at the vicinity of a blade is shown in Figure 15. At the revolution beginning, the angle of incidence on the blade increases and the flow seems to be entirely attached to the blade even when the static stall angle is exceeded (cf. Figure 15, ≈ 20.5°, = 65°). The power coefficient generated by the blade increases with the incidence. Then, the angle of incidence on the blade continues to increase and the flow starts to detach from the trailing edge toward the leading edge (cf. Figure 15, ≈ 29.0°, = 105°). As seen in Figure 13, the instantaneous power coefficient generated by the blade region starts to decrease whereas the angle of incidence on the blade still increases. The blade hydrodynamic performance thus decreases. At the very beginning of the downstroke phase (cf. Figure 15, = 125°, ≈ 29.9°), the separation of the boundary layer is maximal and has nearly reached the blade leading edge. In the rest of the downstroke phase, the boundary layer reattaches to the blade from the leading edge toward the trailing edge. As seen in Figure 13, the instantaneous power coefficient of the blade region decreases with the angle of incidence on the blade.

The reduced frequency at this TSR and at this solidity leads the blade to operate with a dynamic stall phenomenon, which leads to benefit from the high incidences reached by the blade. A high amount of power is generated in the upstream half-disk, even if the lift-to-drag ratio of the blade is slightly decreased by the dynamic stall phenomenon. Although all regions generate the major part of the power in the upstream half-disk, Figure 13 shows that the contributions of each region are unequal. The blade region generates the major part of the power coefficient. The different heights of the regions partialy explain these discrepancies. However, Figure 16 shows that the efficiency of the blade tip and the blade/arm connection are lower than that of the blade region. As seen in Figure 17, the blade tip vortex directly impacts the ⃖⃖⃖⃖⃗ distribution. The blade tip causes a leak of flow streamlines due to the difference of pressure between the pressure side and the suction side of the blade. A lift loss and consequently a local decrease of ⃖⃖⃖⃖⃗ is observed at the blade tip leading edge (cf. Figure 17a). The generated vortex also generates a brake area on the suction side at the blade tip trailing edge vicinity.

The important lack of efficiency of the blade tip compared to the other regions appears in the upstream half-disk, where the pressure difference between the pressure side and the suction side is high. In the downstream half-disk, the blade tip vortices are weak as it can be seen in Figure 12. Figure 17a shows that the lack of efficiency of the blade/arm connection region seems to be firstly due to a lift loss at the leading edge. The arm deflects the flow streamlines towards up and down directions. The flow streamlines are consequently not perpendicular to the blade and the lift generated by the blade is degraded. Secondly, interferences between boundary layers of the blade and the arm lead to a brake area at the rear part of the blade/arm connection. As the blade/arm connection of the studied geometry has been designed to reduce these interferences, the efficiency of this region is less degraded than the blade tip efficiency. To quantify the disturbance due the blade tip and the blade/arm connection, the efficiency of the real turbine is compared with the ideal turbine configuration in Figure 18. The efficiency of the blade region for both geometries is globally equivalent.

We notice a degradation of the efficiency for the real turbine in the angular ranges 90°≤ ≤ 180°and 270°≤ ≤ 360°. The blade region efficiency is consequently slightly decreased by the blade tip and the blade/arm connection region.

To end up with the analysis of the high solidity turbine ( = 0.55) at optimal TSR ( = 2), This part was dedicated to the analysis of the high solidity turbine at optimal TSR. The next section aims to better understand the mean power coefficient differences observed between the high and the low solidity VAHT at their optimal TSR. maximal power coefficient generated in the downstream half-disk is consequently lower than that generated in the upstream half-disk. However, a non-zero power coefficient is obtained on a larger range of angles in the downstream half-disk.

According to equations 1 and 2, with = 0.16 and = 3.4, the reduced frequency is equal to 0.07 and the maximal angle of incidence on the blade is equal to 17.1°. The low solidity turbine blade operates either in a quasi-steady regime either with a weak dynamic stall phenomenon. As shown in Figure 21, the flow around the blade is less detached during a round.

It is more pronounced in the downstream half-disk where the flow velocity is lower. The lift-to-drag ratio of the blade is consequently better in the low solidity turbine case than in the high solidity turbine case. Figure 22a shows the evolution of the instantaneous power coefficient for both ideal and real configurations at their optimal TSR. For the ideal turbine cases, we notice that the power coefficient of the low solidity turbine is higher for all angular positions. However, this is not observed for the real turbines. Depending on the angular position, the low solidity turbine generates more or less power than the high solidity turbine. Note that the power coefficient varies less during a revolution for the low solidity turbine cases whatever the geometry.

Figure 22b shows the evolution of the efficiency of the blade region as a function of angular position for high and low solidity turbines. The differences of behavior are highlighted. As already explained, for the high turbine solidity cases, the major part of the mean power coefficient is generated into the upstream half-disk. Due to a low TSR, high angles of incidence are reached. The dynamic stall phenomenon leads the blades to generate high instantaneous power coefficient values. For the low solidity turbine cases, the higher optimal TSR leads to lower angles of incidence. Despite a higher rotation speed the power coefficient generated in the upstream half-disk is lower than that of the high solidity turbine case. However, for the low solidity turbine case, the flow velocities observed in the downstream half-disk are high enough to generate a high amount of power coefficient. Consequently, for the ideal turbine cases, the mean power coefficient generated by the low solidity turbine case is strongly higher in comparison with the high solidity case.

However, as seen in Figure 22b, the efficiency of the blade region is degraded for the real turbine case compared to the ideal turbine case in the angular ranges 90°≤ ≤ 180°and 270°≤ ≤ 360°. A higher gap of efficiency between the ideal and the real turbines is observed in the low solidity turbine case. The efficiency of the blade region is thus more degraded by the blade tip and the blade/arm connection in the low solidity case than in the high solidity case. According to Figure 24, it seems that the decrease of efficiency of the blade region in the low solidity real turbine is mainly due to the blade tip. A blade tip vortex is observed in Figure 25. The associated decrease of ⃖⃖⃖⃖⃗ values due to the leakage of streamlines seems to extend over a larger part of the blade compared to the high solidity case as seen in Figure 17a. In the ideal turbine case where there is no blade tip vortex, ⃖⃖⃖⃖⃗ values at the leading edge are higher and its distribution is uniform along the blade.

Figure 23a shows the evolution of as a function of the angular position for the blade/arm connection and the blade tip regions. The impact of the solidity decrease on the blade/arm connection region is similar to that of the blade region. A solidity decrease leads to decrease the power coefficient generated in the upstream half-disk and to increase the power coefficient generated in the downstream half-disk. A decrease of the power coefficient in the upstream half-disk is also observed for the blade tip. However, no significant power coefficient increase is observed in the downstream half-disk. Finally, the arms contribute to decrease the global power coefficient of the low solidity real turbine. Indeed, Figure 23b shows that the arms of the low solidity real turbine generate a high level of losses compared to those of the high solidity real turbine. The higher length of the arms coupled with a higher rotation speed lead to a dramatic increase of the drag of the arms.

Table 6 sums up the differences of mean regional power coefficients and mean regional efficiencies between high and low solidity turbines. In the real turbines, the potential gain of mean power coefficient due to the solidity decrease is affected by the blade tips and their impact on the rest of the blade and by the connection arms. The blade/arm connection region is less affected by the blade tip than the blade region as it is further away from the blade tip. The performance increase of the blade/arm connection region due to the solidity decrease is thus higher than that of the blade region. The efficiency increase of the blade/arm connection region is even higher than that of the blade region of the ideal turbine cases. It can be due to the lower angles of incidence reached by the blade at = 3. As seen in this section, a decrease of the turbine solidity can increase the turbine mean power coefficient, especially for an ideal turbine case. In the next section, additional ideal turbines at various solidities are investigated in order to clarify the • : blade tip, ▴: blade/arm connection, ■: arm.

evolution of the optimal mean power coefficient as a function of turbine solidity.

Evolution of the optimal power coefficient as a function of solidity for ideal turbines

Figure 26 shows the evolution of the optimal mean power coefficient ⟨ ⟩ as a function of the turbine solidity. A maximum value is observed at = 0.16. The turbine of higher solidity operates with a more and more pronounced dynamic stall phenomenon as the solidity increases, since the associated optimal TSR decreases. The increase of the mean power coefficient from high solidities to = 0.16 is gradual. No local maximum value which could appear from a particular dynamic stall regime has been observed.

For solidities lower than the optimal value, the angle of incidence on the blade becomes too low, the lift generated by the blade decreases and the projection of lift and drag on the rotation circle does not favor a positive torque, which leads to decrease the mean power coefficient.

Figure 27a shows that variations of the instantaneous power coefficient during a revolution become lower as the solidity decreases. Figure 27b shows that the power coefficient generation is concentrated in the upstream half-disk for high solidities.

The power coefficient generation decreases in the upstream half-disk and increases in the downstream half disk as the solidity decreases. It becomes balanced between the upstream and the downstream half-disk at the optimal solidity = 0.16. When the solidity decreases more, the gain in the downstream half-disk seems to be lower than the loss in the upstream half-disk and the turbine mean power coefficient globally decreases.

Conclusions

Large Eddy Simulations (LES) have been performed on Vertical Axis Hydrokinetic Turbines (VAHT) in order to deeply analyze the efficiency of turbines, allowing to better understand the influence of the turbine solidity. Real and ideal turbines are considered. Whereas the real turbines correspond to the Achard turbine, the ideal turbines are only composed by infinite blades. This enables to evaluate the effect of major losses due to arm, shaft, blade tip, ... on the turbine performance.

Considering first the ideal turbines, for high solidity turbine cases, most of the power coefficient is generated in the upstream half-disk, 0°≤ ≤ 180°, where a dynamic stall phenomenon delays the flow stall, even if the angles of incidence on the blades exceed the static stall angle. However, there is an important flow blockage with a strong decrease of flow velocity in the downstream half-disk, 180°≤ ≤ 360°. Conversely, in the lower solidity cases, the optimal Tip Speed Ratio (TSR) is higher than in the high solidity turbine cases and lower incidence angles are reached. The lower solidity turbine blade consequently operates with a less pronounced dynamic stall phenomenon. A lower flow blockage is therefore observed, and the power coefficient generated by the blade is balanced between the upstream half-disk and the downstream half-disk. An optimal solidity is then found at ≈ 0.16, leading to the optimal mean power coefficient. For lower solidities than this optimal value, incidence angles on the blade become too low and projection of lift and drag does not favor a positive torque.

Considering now the real turbines, the performance of the turbine is mainly degraded by blade tips, arm and blade/arm connections. Moreover, there is no clear gain to decrease the solidity, as observed for the ideal turbine. Because of the higher optimal TSR for smaller solidity, this is mainly due to two effects: (i) the increase of the drag of the arm, and (ii) the increase of the losses due to the blade tips. Due to these high losses, the difference of mean power coefficients between the real and the ideal turbines increases for lower solidity. The optimal solidity of a Darrieus turbine thus strongly depends on its design.

For example, Shiono et al. [START_REF] Shiono | An experimental study of the characteristics of a darrieus turbine for tidal power generation[END_REF] studied a turbine with two arms per blade and blade tips. This implies a low optimal TSR to limit losses, and they consequently found a high optimal solidity ( = 0.56). Conversely, Blackwell et al. [START_REF] Blackwell | Wind tunnel performance data for the darrieus wind turbine with naca 0012 blades[END_REF] investigate a turbine with a shape close to an ideal troposkien. The losses are limited and a higher optimal TSR can be reached. A lower optimal solidity situated between 0.2 et 0.25 has consequently been found. The optimization of VAHT design to limit the turbine losses is therefore of paramount importance to bring closer real VAHT optimal solidity to ideal VAHT optimal solidity and to increase the optimal mean power coefficient. • : = 0.55, ▴: = 0.34, ■: = 0.16, +: = 0.11.

Figure 1 :

 1 Figure 1: Top view of the VAHT for angular position definition.

Figure 2 :

 2 Figure 2: Illustration of the real turbine with = 0.55.Figure 3: Illustration of the ideal turbine with = 0.55

Figure 3 :

 3 Figure 2: Illustration of the real turbine with = 0.55.Figure 3: Illustration of the ideal turbine with = 0.55

Figure 4 :

 4 Figure 4: VAHT regions used for performance analysis • : blade tip, • : blade, • : blade/arm connection, • : arm, • : arm/shaft connection, • : shaft.

Figure 5 :

 5 Figure 5: Illustration of the computation domain and boundary conditions for the real turbine case with = 0.55: (a) global view, (b) top view, (c) side view.

Figure 6 :

 6 Figure 6: Illustration of the mesh M3 for the real turbine case with = 0.55.

Figure 7 :Figure 8 :

 78 Figure 7: Power coefficient as a function of angular position for the real turbine with = 0.55 and = 2. Comparison of four meshes: M0 (--), M1 (--), M2 (--), and M3 (--).

Figure 10 depicts

 10 Figure10depicts the evolution of the instantaneous VAHT power coefficient as a function of the turbine angular position for the three computed TSRs. At the solidity = 0.55 and ≥ 2, a blade generates most of the power coefficient in the 60-120°zone. As the turbine is composed of three blades, the instantaneous turbine power coefficient shows three periodic zones corresponding to successive blades presence into the 60-120°zone. The evolution of the power coefficients as a function of the angular position is in good agreement with experimental data. The switch of the maximum power coefficient at approximately = 60°for = 1 instead of = 90°for = 2 and 2.5 is well predicted. Due to the difference of blockage ratio between the experimental and numerical configuration, the computed values of are lower than the experimental data, except for the lowest TSR value = 1. Note that the LES have also been qualitatively compared with experimental data obtained by PIV

Figure 9 :

 9 Figure 9: Mean power coefficient as a function of TSR. ⬟ : LES, ■ : LES with blockage ratio correction, -⋅ -: experimental data extracted from [32].

Figure 10 :Figure 11 :

 1011 Figure 10: Power coefficient as a function of angular position.--: = 1, --: = 2, --: = 2.5, --: LES, ---: experimental data extracted from[START_REF] Dellinger | Instrumentation d'un tunnel hydrodynamique pour la caractérisation de turbines à flux transverse[END_REF].

Figure 12 :

 12 Figure 12: Isosurface of the Q-criterion, = 2.25 × 10 5 -2 , colored by vorticity magnitude ( -1 ) for the real turbine at = 0.55 and = 2. The flow goes from right to left.

Figure 13

 13 Figure 13 shows the evolution of for the blade region, the blade tip region and the blade/arm connection region as a function of the angular position . At a solidity = 0.55, a blade generates most of the power coefficient in the upstream halfdisk ([0°≤ ≤ 180°]). The blade generates few power coefficient in the downstream half-disk and can even produce negative

Figure 13 :

 13 Figure 13: as a function of angular position for the real turbine at = 0.55 and = 2. ⧫: blade, • : blade tip, ▴: blade/arm connection.

Figure 14 :

 14 Figure 14: Slice of the computation domain at quarter-blade height colored by absolute velocity magnitude ( . -1 ) for the real turbine at = 0.55 and = 2.

Figure 15 :

 15 Figure 15: Contour of spanwise vorticity ( -1 ) at quarter-blade height for the real turbine at = 0.55 and = 2. Angle of incidence on the blade has been obtained with equation 1.

Figure 16 :Figure 17 :

 1617 Figure 16: as a function of angular position for the real turbine at = 0.55 and = 2. ⧫: blade, • : blade tip, ▴: blade/arm connection.

4. 1 . 3 . 4 Figure 19 Figure 18 :

 1341918 Figure19shows the evolution of for the blade region, the blade tip and the blade/arm connection as a function of the angular position for the low solidity real turbine at = 3.4. Contrarily to the previous observation for the high solidity turbine, the power coefficient is generated in the upstream half-disk and in the downstream half-disk. According to Figure20, the flow blockage is lower in comparison with the high solidity turbine case. The velocities observed in the downstream halfdisk are high enough to generate power. These velocities are however lower to those observed in the upstream half-disk. The

Figure 19 :

 19 Figure 19: as a function of angular position for = 3.4. ⧫: blade, • : blade tip, ▴: blade/arm connection.

Figure 20 :

 20 Figure 20: Slice of the computation domain at quarter-blade height colored by absolute velocity magnitude ( . -1 ).

Figure 21 :

 21 Figure 21: Contour of spanwise vorticity ( -1 ) at quarter-blade height for the real turbine at = 0.16 and = 3.4. Angle of incidence on the blade has been obtained with equation 1.

  Figure 22: (a) and for the blade region (b) of real and ideal turbines. --: = 0.55 and = 2, --: = 0.16 and = 3.4. --: real turbine, ---: ideal turbine.

Figure 23 :

 23 Figure 23: of real turbines for blade tip and blade/arm connection (a) and for arm (b) as a function of angular position. --: = 0.55, --: = 0.16.

Figure 24 :Figure 25 :

 2425 Figure 24: Contour of ⃖⃖⃖⃖⃗ for sreal turbine (a) and ideal turbine (b) at = 335°for = 3.4, = 0.16.

Figure 26 :Figure 27 :

 2627 Figure 26: Optimal mean power coefficient as a function of solidity for ideal turbines.

Table 2 :

 2 Characteristics of the considered meshes for the real turbine case with = 0.55.

		Δ	Δ 1	Δ 2	Number of elements
	M0	0.2 mm	80 mm 800 mm	16 million
	M1	0.1 mm	40 mm 400 mm	29 million
	M2	0.05 mm 20 mm 200 mm	54 million
	M3	0.025 mm 10 mm 100 mm	105 million

Table 3 :

 3 Solidities, corresponding mesh element num-

	1.08	0.55	0.34	0.16	0.11
	Mesh 42 M	44 M	48 M	63 M	85 M
	1.3	1 ; 2 ; 2.5	2.3	2.9 ; 3.4 ; 3.9	4.1
	ber (in million) and computed TSRs for LES of real tur-
	bines.

Table 4 :

 4

Solidities, corresponding mesh element number (in million) and computed TSRs for LES of ideal turbines.

table 5

 5

	sums up the values of

Table 6 :

 6 4 compared to = 2. It possibly leads to reduce the boundary layers interactions and the associated drag. ⟨

			⟨	⟩			⟨	⟩
	Region	1 = 0.55	2 = 0.16	2 -1	= 0.55	= 0.16	2 -1
	Blade (ideal)	0.0615	0.0811		0.0196	0.1231	0.1622	0.0391
	Blade	0.0320	0.0371		0.0051	0.1118	0.1299	0.0181
	Blade tip	0.0068	0.0045		-0.0023 0.0678	0.0450	-0.0228
	Blade/arm connection 0.0079	0.0127		0.0048	0.0688	0.1111	0.0423
	Arm	≈ 0	-0.0078	-0.0078 -	-	-

⟩ and ⟨ ⟩ for = 0.55 at = 2 and = 0.16 at = 3.4.

performed in 2D configurations by Pellone et al.[START_REF] Pellone | 3d rans modeling of a cross flow water turbine[END_REF] and Zanette[START_REF] Zanette | Hydroliennes à flux transverse: contribution à l'analyse de l'interaction fluide-structure[END_REF] on high solidity VAHT ( = 0.55). The classic bell-shape

Acknowledgments

This work has been supported by the Hydrofluv Project, a Research Program piloted by HydroQuest. Vincent Moureau and Ghislain Lartigue from the CORIA lab, and the SUCCESS scientific group are acknowledged for providing the YALES2 code. Computations presented in this paper were performed using HPC resources from GENCI (Grant No. 020611) and CIMENT infrastructure (supported by CPER07 13 CIRA and ANR-10-EQPX-29-01). Jean-Luc Achard and Stéphane Barre are acknowledged for technical discussions. Patrick Bégou is acknowledged for IT support. G.B. is also grateful for the support from Institut Universitaire de France.


Michael Von Cotta

Silvio Enea

; Piccolomini

Sylvius Aeneas

Silvius Aeneas

Kaiser Piccolomini

Friedrich

Michael Von Cotta-Schönberg

In summer 1446, two German missions were dispatched to Pope Eugenius IV in order to obtain the reinstatement of two prince electors, the archbishops of Cologne and Trier, deposed by the pope, as well as other concessions. The missions were part of an ongoing diplomatic process aiming at ending German neutrality between the pope and the rump council in Basel with its antipope, Felix V. One mission was from the emperor, Friedrich III, represented by Enea Silvio Piccolomini, secretary in the imperial chancery. The other embassy was from the German prince electors, represented by Gregor Heimburg, an influential German opponent of the papacy. Heimburg's mission was to present the princes' demands of the pope, and his personality ensured that it would be conducted in an arrogant and haughty manner. Piccolomini's mission was to facilitate negotiations between the papal curia and the princes' embassy and to soften the presumed ill effects of their demands -and of Heimburg's insolence. The two embassies were received by the pope in a consistory on 6 July 1446. As the emperor's representative Piccolomini spoke first, delivering the oration "Et breviter me hodie", in which he, on the emperor's behalf, recommended the petitions of the princes. Afterwards Heimburg presented these petitions.

(Orations of Enea Silvio Piccolomini / Pope Pius II; 10) NOTE TO THE READER

This edition of the oration "Et breviter hodie" is based on the only manuscript presently known to contain that oration. It is owned by the Zaklad Narodowy im. Ossolinskich in Wroclaw. The text in the manuscript is very difficult to read and rather corrupt. On the one hand it may seem premature to publish the oration at the present stage, but it belongs, of course, in an edition of Piccolomini's collected orations, and moreover it documents a crucial event in the development leading from German neutrality between Pope Eugenius IV and the rump council in Basel with its antipope, Felix V. So I have chosen to publish it anyway, hoping that other copies of the text will eventually surface and provide a better manuscript basis for a revised final edition. I do not doubt that if and when such copies become available, a number of the emendations and readings proposed by me will have to be corrected.

Even though the present textual basis is not quite adequate, it is sufficient as basis for a translation which gives, I trust, a reasonably faithful rendition of Piccolomini's original text.

Michael v. Cotta-Schönberg 19 December 2018

Foreword

In 2007, I undertook a project of publishing the Latin texts with English translations of the orations of Enea Silvio Piccolomini / Pope Pius II. Altogether 80 1 orations (including papal responses to ambassadorial addresses) are extant today, though more may still be held, unrecognized, in libraries and archives.

At a later stage the project was expanded to include ambassadors' orations to the pope, of which about 40 are presently known.

I do not, actually, plan to publish further versions of the present volume, but I do reserve the option in case I -during my future studies -come across other manuscripts containing interesting versions of the oration or if important new research data on the subject matter are published, making it appropriate to modify or expand the present text. It will therefore always be useful to check if a later version than the one the reader may have previously found via the Internet is available.

I shall much appreciate to be notified by readers who discover errors and problems in the text and translation or unrecognized quotations.

12 September 2019 MCS 1 81 orations, if the "Cum animadverto" is counted is a Piccolomini-oration, see oration "Quam laetus" [18], Appendix Abbreviations

II. TEXT AND TRANSLATION

1.

Introduction [1] 2.
Nefarious consequences of division in the Church [2] 3.

Papal initiatives to counter threats to the Church [3] 4.

Imperial initiative to restore church unity [4]

5.

Petition of German prince electors [5-6] 6.

Emperor's recommendation [7] I. INTRODUCTION

Context 1

In 1445, Emperor Friedrich III2 had sent Enea Silvio Piccolomini, secretary in the imperial chancery, on a mission to Pope Eugenius IV3 to pursue negotiations aimed at ending German neutrality [START_REF]perditi , postquam fides catholica in subjectis deficere cepit. Asia quondam Christum credebat crucifixum et una cum occidentalibus in arca fidei morabatur. Id quoque 5 Africa fecit. At hodie, proh dolor[END_REF] between the pope and the rump Council of Basel5 with its antipope Felix IV. 6 7 The negotiations developed positively, but then the pope rather inadvisedly decided to remove two German prince electors, the archbishops of Trier and Cologne,8 from their offices. This naturally caused an uproar in Germany, and in March 1446 the German princes met in Frankfurt to formulate their demands of the pope.9 Among them were: The princes sent their demands to the emperor -in secrecy -requesting his adhesion. The emperor temporized, and then two embassies were sent to the pope, one from the emperor, represented by Piccolomini, and the other from the princes, led by Gregor Heimburg. 10 Piccolomini joined up with the papal envoy to the emperor, Bishop Parentucelli of Bologna, returning to Rome, whom he let know the demands of the princes so that he could inform the pope about them.


The princes' embassy reached Rome in the beginning of July, one day before the imperial embassy, but Bishop Parentucelli managed to get access to the pope before his audience with the embassy and explained to him the extreme importance of the princes' demands, as recommended by the emperor. Since the pope was easily moved to anger when his dignity was slighted, it was in the present situation highly important that he did not let himself be provoked by the -calculatedarrogance and haughtiness of the spokesman of the princely embassy, Gregor Heimburg. The pope understood the message and agreed to receive the recommendation of the emperor benevolently.

In When they reached Rome, Eugenius, at Tommaso's suggestion, heard Aeneas before he heard the delegates of the electors; he promised to do everything that the emperor urged. 1 2 In that consistory, Piccolomini spoke first on behalf of the emperor, politely but firmly recommending benevolent acceptance of the princes' demands. Afterwards Gregor Heimburg spoke, with his usual insolence and arrogance, [START_REF]maxime verendum est, ne fides nostra, quae angusta est et admodum parva, et angustissima fiat et minima. Ad quod impediendum non dubitat Caesarea majestas tuam beatitudinem summas operas, summa studia impartiri. Namque enim per tuam diligentiam Graeci, qui jam pluribus saeculis a Latina ecclesia dissidebant, ac nonnulli alii Orientales uniti sunt. Cum 9 saepe auxilia contra Soldanum missa fuerunt, cum adversus Turcos praeparis classem magnosque sumptus feceris, ut et Hungaros, qui murum tenent catholicae fidei, tueris, et Turcos ipsos ab Europa expelleris, et de unguibus eorum infelices Grecos, qui quondam Orientis domini, nunc verum servi videntur, erumperes, quis non videt te multo et ardentius ac efficacius laborare[END_REF] but, forewarned, the pope kept his temper and answered graciously. [START_REF]perditi , postquam fides catholica in subjectis deficere cepit. Asia quondam Christum credebat crucifixum et una cum occidentalibus in arca fidei morabatur. Id quoque 5 Africa fecit. At hodie, proh dolor[END_REF] When the ambassadors returned to Germany, Heimburg made a very negative report of the visit to Rome and the papal reception of the requirements of the princes.5 But the tide was turning, and the imperial and papal negotiators, not the least Piccolomini, managed to create a diplomatic compromise which would lead, in February 1447, to the ending of German Neutrality and the declaration of German obedience to Eugenius IV the following year. 6

Themes

Dangers threatening Christianity

The primary danger to Christianity was the prevailing division in the Latin Church, with the Roman pope, Eugenius IV, and his very large obedience on one side, and the rump Council of Basel with its antipope Felix V and his very limited obedience on the other. Indeed, so few princes and peoples now recognized the council and the antipope, that the return of the German nation to the Roman obedience would surely mean an end to the council and the restoration of church unity. The papacy's relations to Germany and the German embassies to the pope were therefore of critical importance.

In the oration, Piccolomini said:

You

Papal response to the dangers

On behalf of his imperial master, Piccolomini praises the initiatives of the pope to counter the threats to Christian Europe.

Firstly, the pope had successfully held a reunion council with the Greek Church in Ferrara-Florence.

For through your diligent endeavours the Greeks, who had been separated from the Latin Church for several centuries, as well as other Easteners have rejoined Church unity. [Sect. 3] Though the reunion with the Greeks met with serious opposition from the Greek clergy, the results of the council was a major triumph for the papacy:

As a condition for the reunion with the Latin Church, the Greek emperor, Constantine VIII Palaeologus, and his government had posed the condition that the papacy (and the West) should send military and financial aid to his regime in Constantinople, under ever greater military pressure from the Turks. After the reunion, Pope Eugenius actually did his best to organize a European military response to the Turkish war of aggression, but his means were rather limited. 1 Piccolomini tactfully omits to mention the disastrous military campaign against the Turks in 1444, led by King Wladyslaw III of Poland and Hungary and a papal legate, Cardinal Giuliano Cesarini, [START_REF]Posita sunt ante oculos tuos, beatissime pater, quot mala ex hac divisione oriuntur, quae nunc 1 ecclesiae 2 comminantur 3 . Scit tua beatitudo, quomodo frigescit caritas, quomodo fides deperit, quomodo cultus divinus annihilatur, ut non est obedientia in subditis, non justitia in praepositis, non benevolentia inter cives, non pax inter finitimos, non religio inter Christianos[END_REF] which ended in a terrible defeat of the Christians at Varna and the death of both king and cardinal. But he does mention the pope's military aid, including a fleet, as well as financial subsidies to the frontier state, Hungary, directed against the "Sultan". The sultan was presumably the ruler of the Turks, though Piccolomini sometimes uses this term to designate the Mamluk ruler in Cairo3 :

Often help has been sent against the Sultan; you are preparing a fleet against the Turks; and you are spending great sums in order to protect the Hungarians, who are like a wall protecting the Christian faith, and to expel the Turks from Europe and free the pitiable Greeks from their hands, those who were once the masters of the East, but now appear to be slaves.

[Sect. 3]
It should be noted that Piccolomini only speaks about the expulsion of the Turks from Europe, not about reconquering Constantinople (nor the Holy Land, for that matter), since such endeavours were judged to completely exceed papal resources and would be a matter for the secular rulers of Europe, including the emperor.

Restoration of German obedience to the pope

Referring indirecly to the German state of neutrality between pope and council, Piccolomini pledges the emperor's support to end this division:

He [the emperor] now intends to work together with Your Holiness and others to end the schism and he will not cease before he sees that this has been achieved. For as a Christian, as duke, as king, as defender and champion of the Church he will as much as possible use his office to restore peace in the Church. [Sect. 4] As the emperor's ambassador Piccolomini carefully refrains from speaking about the demands of the German princes which would be presented by their own ambassador, Gregor Heimburg. But he emphatically states that the emperor agrees with the proposals of the princes and highly recommends them to the pope:

Since they are decent and appropriate and at this time necessary for the restoration of ecclesiastical peace, His Highness begs that you will receive them kindly and require their implementation, and that you will not show yourself to be severe and difficult who in other important matters have shown yourself to be flexible and lenient. [Sect. 7] Actually, there were important differences between the emperor and the prince electors concerning German policies towards the papacy, but though the pope would have been informed about these in private by the Bishop of Bologna, they could and should not be stated in public. At any rate, the reinstatement of the archbishops of Cologne and Trier was non-negotiable, also for the emperor. If the emperor did not actively and publicly support these two prince electors, it would place him in an extremely difficult, not to say dangerous political position vis-a-vis the German princes.

Date, place, audience and format

The oration was delivered on 6 July 1446. The place was probably the apostolic palace in Rome, and the audience was the pope in a papal consistory and the members of the embassies. The format was a diplomatic address to the pope on behalf of the emperor.

Text 1

It has long been known that Piccolomini delivered an oration at the pope's audience for the German embassies -indeed he himself mentioned in his works (see above) -but apparently the text of the oration was not known. It has recently been discovered as being extant in Wroclaw / Zaklad Narodowy im. Ossolinskich Cod. 601, ff. 24v-26r2

It has not been edited or translated before.

Passages where the Latin text appears to be corrupt or very difficult to read are underlined.

For principles of edition (incl. orthography) and translation, see Collected Orations Pope Pius II, vol. 1, ch. 9-10.

Sources 3

Only one quotation has been identified in the text of the oration, pointing to its being a businesslike diplomatic address, with no room for oratorical exertions. Indeed, Piccolomini was under strong pressure to keep it extremely simple and in no way whatsoever to outshine or take the wind out of the address of Gregor Heimburg, the ambassador of the prince electors.

Introduction

[1] Holy Father, today I am obliged on the one hand to speak briefly and on the other hand to speak at length. Briefly, because I am speaking before Your Holiness who understands my words before I speak them and open my mouth, and who -because of your very long experience, immense prudence, and great wisdom -needs neither rhetorical persuasions nor dialectical syllogisms. At length, because I shall be speaking on behalf of His Most Serene Lord and Emperor, Friedrich, King of the Romans, your most devoted son, about a matter which is very great and very urgent: the ending of the prevailing division in the clergy, the unity of Church, the peace of the faithful, the propagation of the Christian cause, matters about which I do not think that any oration could be [too] long. I really do not know whether to adapt [my oration] to Your Holiness or to the matter at hand. But having been much in doubt, I have now decided [to shape my oration] to suit your ears and to avoid tedious prolixity. So now, Holy Father, I shall put forward the king's wishes, and afterwards these excellent and learned men will go deeper into the matter and explain what is necessary with suitable reasons. [2] You see before your eyes, Holy Father, the many evils caused by the division which is now threatening the Church. Your Holiness knows how charity grows cold, how faith disappears, how divine worship is destroyed, and how there is no obedience among subjects, no justice among leaders, no kindness among citizens, no peace between neighbours, no piety among Christians. Many souls have been lost after the Catholic Faith began to weaken. Formerly, Asia believed in the crucified Christ and stayed, together with the western peoples, in the Ark of Faith. And so did Africa. But today, oh misery, the whole East is separated from us. Libya1 has nothing in common with us. In Europe, too, there are many conflicts: one region is occupied by the gentile Teucrians, another by the Saracens, and yet another by schismatics infected with various heresies. Our Christianity has been reduced and pressed into a corner. [START_REF]Posita sunt ante oculos tuos, beatissime pater, quot mala ex hac divisione oriuntur, quae nunc 1 ecclesiae 2 comminantur 3 . Scit tua beatitudo, quomodo frigescit caritas, quomodo fides deperit, quomodo cultus divinus annihilatur, ut non est obedientia in subditis, non justitia in praepositis, non benevolentia inter cives, non pax inter finitimos, non religio inter Christianos[END_REF] All this is caused by the divisions among churchmen, who seek what is their own and not what is Jesus Christ's. Many would rather deny God than fail in their own endeavours.

Nefarious consequences of division in the Church

Papal initiatives to counter threats to the Church

[3] The evil [of disunity] reigned among priests formerly, and it also prevails today and has spread far and wide. Therefore, it is greatly to be feared that our Faith, already confined and reduced, will become even more so. His Imperial Majesty does not doubt that Your Holiness is doing all in your power to prevent this from happening. For through your diligent endeavours the Greeks, who had been separated from the Latin Church for several centuries, as well as many other Easteners, have rejoined Church unity. Often help has been sent against the Sultan; you are preparing a fleet against the Turks; and you are spending great sums in order to support the Hungarians, a wall protecting the Christian faith, to expel the Turks from Europe, and to free the pitiable Greeks from their claws, those who were once the masters of the East, but now appear to be slaves. 4. Imperial initiative to restore Church unity [4] But it has not yet been possible to restore peace as desired, the schism still prevails, and the labour must be pursued until the end which must be pursued by all means. … Therefore, his Imperial Majesty -who, together with his most reverend and illustrious princes, has been occupied with this whole matter from the very beginning of his rule -has been considering how the desired peace may be gained. He now intends to work together with Your Holiness and others to end the schism, and he will not cease before he sees that this has been achieved. For as a Christian, as duke, as king, as defender and champion of the Church, 1 he will -as much as possible -use his office to restore peace in the Church.

Petition of German prince electors

[5] Therefore, as his aforesaid princes, the most reverend and illustrious electors, have formulated certain articles and means to [restore] peace and union and have communicated them to His Serene Highness, the emperor has decided to send me to Your Holiness in the matter of these articles and to beg you to receive and accept them. For what pleases these princes also pleases him. He considers their articles to have great merit, and he highly commends his princes for being so solicitous for peace and union in the Church: they are all primarily concerned about the state of Universal Church.

[6] Secondly, there are the provisions for the German nation. As Your Holiness knows, His Imperial Majesty has often shown concern and made requests about such.

As a Most Christian King he must consider the peace of the Universal Church and religious unity, for this prince must have care of your office whose protection he undertook together with imperial rule.

Concerning his nation he is moved by affection for the fatherland, for which the best men do not hesitate to give [even] their life. He is also moved by the kingship over the Germans which he took over together with imperial rule. And finally he is moved by justice for he considers that you should assist his nation most of all.

Again the king thanks his prince electors who adopted his views and found means to further them. 1 Piccolomini would reuse this formula in his crusade orations to the German diets folloging the Fall of Constantinople in 1453 [7] 6 Emperor's recommendation [7] What they are, Your Holiness will hear (and thoroughly understand ) through the voice of those present here. Their petitions are honourable, suitable, and at this time necessary for the restoration of ecclesiastical peace. Therefore His Royal Highness begs that Your Clemency will receive them kindly and require their implementation, and that you will not show yourself to be severe and difficult when in other important matters you have shown yourself to be mild and lenient. From the beginning of your pontificate and until now you have been concerned about [ecclesiastical] unity, you have worked for peace, you have diligently promoted the Christian cause, you have loved the common good, and you have been kindly disposed towards the German nation. Act likewise now, and heed the petition of the princes and electors, which is also the petition of the king, and send these ambassadors back with their requirements satisfied. That way is the best one to make the German nation, which is already devoted to you, even more devoted, to uproot the present schism, to restore peace to the Christian people, and to increase the splendor of the Apostolic See. Then the princes and the people will honour your [fairness] and your goodness. You will gain a great reputation among the nobles, you will be admired by those in power, and the princes will honour you and easily obey Your Holiness. May God let you live happily and long, for the salvation of Holy Church. Amen.

  Reinstatement of the two archbishops  Acceptance of the supreme authority of ecumenical councils  Promise to summon a new council in May 1447 in a German city  Alleviation of the papal "taxation" of Germany in the form of annates etc.  Confirmation of those decrees of the Council of Basel which the German princes had accepted on 26 March 1439

Table of volumes in Collected Orations of Pope Pius II. 12 vols. Edited and translated by Michael von Cotta-Schönberg Table of contents

	I.	INTRODUCTION
		1.	Context
		2.	Themes
			2.1. Dangers threatening Christianity
			2.2. Papal response to the dangers
			2.3. Restoration of German obedience to the pope
		3.	Date, place, audience and format
		4.	Text
		5.	Sources
		6.	Bibliography
		7.

  his De rebus Basiliae gestis from 1450, Piccolomini wrote about the mission: 1 Caesarem sibi in omni re auxilio futurum. Is itineri se commisit atque Bononiensi antistiti, qui et ipse Romam ibat, comitem se dedit. Legati principum aliquibus diebus precessere, sed Romam non ante se per diem ingressi sunt. Bononiensis, etsi non poterat omnia scire, que legati principum afferebant, tamen imaginabatur et opinabatur multa. Is Eugenium instruxit, ne legatos ante se audiret, quod factum est.

	no role except presenting petitions, a reply was given that Eugenius would send envoys to the
	meeting at Frankfurt, and there he would answer the princes about their petitions.
	In his Historia Austrialis from 1453-1458, Piccolomini wrote about these events:
	Cesar vocato Enea Senensi secretario suo secreta principum ei aperuit iussitque papam
	accedere ac viam pacis eum suadere, pericula exponere et mentem principum, orare ut
	electores suos restitueret,
	Having heard these thing the king [Friedrich III] said he wished to send envoys to Rome with
	them [the ambassadors of the German princes] and exhort the pope that he grant their
	prayers. If he refused these requests, the king still did not intend to go over to the other
	party, for it would not be fitting to separate from the pope unless he denied those things
	which pertained to the faith. He ordered Aeneas to follow them to Rome and expound the
	matter to Eugenius and exhort that, if he acted as a storm requires, furling his sails a little, he
	would see in what danger affairs stood. The legates of the pope also decided to return to
	Rome by themselves. When Juan de Carvajal fell ill, Tommaso accepted his mission, and
	Aeneas was his companion on the whole journey. Gregor [Heimburg] and his companions
	[envoys of the princes], who had preceded them by four days, arrived only one day ahead,
	but they had not yet been heard. Tommaso was heard first. Taught by Aeneas, at Caesar's
	command, what things they should ask, he informed the pope and persuaded him to hear the
	envoys benignly. But Eugenius doubted whether those who bore letters from the deposed
	electors should be heard. Above all, he wished to know what the electors had written and in
	what terms they had expressed themselves. The electors foresaw this, and, having addressed
	the pope by his title, they subscribed at the end of the letter the word for the dignity shared
	by all electors. Then Aeneas, heard first of that party, declared that Eugenius should grant
	what the electors asked because it would be most pleasing to Caesar and useful to the
	apostolic see in the future. … Gregor had been commissioned to give the weighty oration. …
	Eugenius replied little at the time. … After this Aeneas approached Eugenius separately and
	in the presence of the bishop of Bologna. He opened the mind of the king and obtained a
	pleasing response. … In the negotiations held with the other envoys, however, since they had

1

In his Commentarii from 1462-1464, Pius wrote: At this time

[START_REF]Posita sunt ante oculos tuos, beatissime pater, quot mala ex hac divisione oriuntur, quae nunc 1 ecclesiae 2 comminantur 3 . Scit tua beatitudo, quomodo frigescit caritas, quomodo fides deperit, quomodo cultus divinus annihilatur, ut non est obedientia in subditis, non justitia in praepositis, non benevolentia inter cives, non pax inter finitimos, non religio inter Christianos[END_REF]

the imperial electors met at Frankfurt. Roused by the news that Eugenius had dismissed

[START_REF]maxime verendum est, ne fides nostra, quae angusta est et admodum parva, et angustissima fiat et minima. Ad quod impediendum non dubitat Caesarea majestas tuam beatitudinem summas operas, summa studia impartiri. Namque enim per tuam diligentiam Graeci, qui jam pluribus saeculis a Latina ecclesia dissidebant, ac nonnulli alii Orientales uniti sunt. Cum 9 saepe auxilia contra Soldanum missa fuerunt, cum adversus Turcos praeparis classem magnosque sumptus feceris, ut et Hungaros, qui murum tenent catholicae fidei, tueris, et Turcos ipsos ab Europa expelleris, et de unguibus eorum infelices Grecos, qui quondam Orientis domini, nunc verum servi videntur, erumperes, quis non videt te multo et ardentius ac efficacius laborare[END_REF]

the archbishop of Cologne and Jacob, archbishop of Trier, they made a secret compact: unless Eugenius annulled the dismissals, relieved the nation of its burdens, and recognized the authority granted to their councils at Constance, they would recognize the decrees deposing Eugenius which had been voted at Basel. They sent ambassadors to the emperor to explain these matters privately to him and to six of his sworn counselors, and to beg him to join their compact and send his representative with them to Rome. When the emperor heard of the elector's plan, he said he would send an ambassador to Eugenius and would ask him to grant their petitions; but he would have nothing to do with the compact. It would be an impious outrage, he said, to desert the pope simply because he did not grant what they asked.

Therefore he sent Aeneas to Eugenius to persuade him not to defy the electors, and to beg him instead to restore the deposed archbishops to their former positions, as this would inspire the Germans to abandon their neutrality and return to his side. But if he persisted in his harsh attitude, he risked the scandal of a permanent schism. The emperor, who was not under oath, revealed all the electors' secret decisions to

Aeneas and ordered

him to communicate them to the pope….. Meanwhile the apostolic legates, who had been trying for some time, without success, to learn what the electors had decided at Frankfurt, what they wanted of the emperor and what message they were sending to Rome, decided that one of them should go to Rome as soon as possible. … this duty fell to Bishop Tommaso of Bologna, who accompanied Aeneas on the journey. …

  see before your eyes, Holy Father, the many evils caused by the division prevailing in the Church. Your Holiness knows how charity grows cold, how faith disappears, how divine worship is destroyed, and that there is no obedience among subjects, no justice among leaders, no kindness among citizens, no peace between neighbours, no piety among Christians. Many souls have been lost after the catholic faith began to falter.[Sect. 2] Interestingly, Piccolomini puts the blame for the division squarely on the churchmen:All this is caused by the divisions among churchmen, who seek what is their own and not what is Jesus Christ's. Many would rather deny God than fail in their own endeavours.[Sect. 2]

1

The second danger mentioned is the Turkish expansion into Europe through Greece and the Balkans, following after centuries of Arabic Islamic (Saracen) conquests in the Middle East, Africa and Spain:

But today, oh misery, the whole East is separated from us. Libya 2 has nothing in common with us. In Europe there are many conflicts: one region is occupied by the gentile Teucrians 3 , another by the Saracens …

[Sect. 2]

In this context, Piccolomini for the first time, in an oration, uses the image of Christianity being pressed together in a corner of Europe:

Christianity has been reduced and pressed into a corner of Europe.

[Sect. 2]

This image, Picolomini borrowed from Flavio Biondo's version of Pope Urban IIs oration at the Council in Clermont 1495, included in Biondo's Historiarum ab inclinatione Romanorum Imperii decades.

[START_REF]perditi , postquam fides catholica in subjectis deficere cepit. Asia quondam Christum credebat crucifixum et una cum occidentalibus in arca fidei morabatur. Id quoque 5 Africa fecit. At hodie, proh dolor[END_REF]

  The one quotation is from Flavio Biondo's Historiarum ab inclinatione Romanorum Imperii decades,II, 3 [Im. 75]: per cujus [Europae] omnes provincias et regiones nomen floruit Christianum. Quod nomen nostris temporibus ad parvum orbis angulum coangustari et quotidie de excidio periclitari videmus. 1] {24v} Et breviter me hodie, beatissime pater, et longius orare 1 oportet. Breviter quia coram tua sanctitate verba sum facturus, qui me prius intelliget quam verba [faciam 2 ] quamque os aperiam, et qui pro sua perlonga experientia, ingenti prudentia summaque sapientia nec persuasionibus rhetoricis 3 nec syllogismis indiget dialecticis. Longius 4 videlicet quia ex parte serenissimi domini Caesaris Friderici, Romanorum regis, filii tui devotissimi, verba facturus sum de re maxima et admodum necessaria: de sublatione videlicet divisionis, quae nunc est in clero atque propterea viget, et immo {25r} de unione ecclesiae, de pace fidelium, de augmento nominis Christiani, de quibus rebus nescio, quae oratio longa possit censeri. Nescio igitur, quid agam, ne vestrae beatitudini an rei me coaptem. Inter dubitandum autem potior sententia visa est tuis auribus morem gerere prolixitatisque 5 fastidium evitare. Referam igitur, pater beatissime, regium desiderium. Postea 6 hi clari viri et doctissimi seriosius rem aggredientur, et quod erit necessarium convenientibus rationibus explicabunt.

	Oratio Aeneae facta coram Eugenio papa

[

  Therefore, who does not see that you are working intensely and efficaciously to end the schism in the body [of Christ]. However, in vain do we fight external[enemies] and repel foreigners if we are opposed by those who are inside. Any city wanting to conquer or escape enemies must first have internal concord. But His Serene Highness knows your Holiness' care and labours for church union. He knows the great sums you have spent, the intensive efforts you have made, and the many legates you have sent. In this whole matter, our emperor profusely thanks Your Holiness for not deserting your flock and for not failing to do what you can for the salvation of the people.[4] Verum cum hactenus pax optata reperiri non potuerit, cum adhuc remaneat schisma, cum laborandum est usque ad finem (nullius rei principium tam repperitur quam exitus), nunc Caesarea majestas, quae ab initio sui imperii cum reverendissimis ac illustrissimis principibus suis electoribus de hac re sollicita fuit, propterque quam pax optata reperiri possit, cogitavit, et nunc cum tua sanctitate, communiter cum aliis scilicet ad sublationem schismatis modo intendit, etiam ad id operam dat nec cessare vult, nisi perfectum intueatur. Nam cum sit Christianus, cum sit dux, cum sit rex, cum sit protector et advocatus ecclesiae, ad hoc maxime suum officium interponere vult, ut pacem in ecclesia resarciat.[5] Idcirco cum principes sui praefati, reverendissimi et illustrissimi electores, ad pacem et unionem habendam certa et capitula et media [repperunt 1 ] eaque suae serenitati communicarunt, visum [est 2 ] ipsi Caesari super illis ad tuam sanctitatem me destinare et supplicare, ut ea recipias et amplectaris. Nam quae principibus illis placent et sibi etiam placent illa, quae digna censet, plurimumque suos principes commendavit, qui ad pacem et unionem ecclesiae tam sollertes essent tamque affecti: cunctorum studium in primis universalis ecclesiae statui respicit.[6] Secundario inclytae nationis Germanicae provisiones, ad quas saepe Caesarea majestas affecta fuerat multumque pro illis intercesserat, ut tuae beatitudini constat.[START_REF]maxime verendum est, ne fides nostra, quae angusta est et admodum parva, et angustissima fiat et minima. Ad quod impediendum non dubitat Caesarea majestas tuam beatitudinem summas operas, summa studia impartiri. Namque enim per tuam diligentiam Graeci, qui jam pluribus saeculis a Latina ecclesia dissidebant, ac nonnulli alii Orientales uniti sunt. Cum 9 saepe auxilia contra Soldanum missa fuerunt, cum adversus Turcos praeparis classem magnosque sumptus feceris, ut et Hungaros, qui murum tenent catholicae fidei, tueris, et Turcos ipsos ab Europa expelleris, et de unguibus eorum infelices Grecos, qui quondam Orientis domini, nunc verum servi videntur, erumperes, quis non videt te multo et ardentius ac efficacius laborare[END_REF] Nam de universalis ecclesiae pace cogitare cogitur ipse Christianissimus rex et unione religionis, quoniam in principe esse oportet cura 4 vestri officii, quod cum imperio suscepit, advocationis. De natione vero agit afficiens consequentia quomodolibet vero ad patriam, pro qua et optimus quisque vitam ponere non dubitat 5 . Agit et regalis dignitas, quam super Germanicos cum imperio suscepit. Agit etiam et justitia, quia dignum aestimat super pluribus suae nationi subvenires. Itemque gratias agit principibus electoribus rex ipse, qui suae sententiae se coaptaverunt et media ad eam reperierunt convenientia.

1 em.

[START_REF]Posita sunt ante oculos tuos, beatissime pater, quot mala ex hac divisione oriuntur, quae nunc 1 ecclesiae 2 comminantur 3 . Scit tua beatitudo, quomodo frigescit caritas, quomodo fides deperit, quomodo cultus divinus annihilatur, ut non est obedientia in subditis, non justitia in praepositis, non benevolentia inter cives, non pax inter finitimos, non religio inter Christianos[END_REF]

em.

[START_REF]maxime verendum est, ne fides nostra, quae angusta est et admodum parva, et angustissima fiat et minima. Ad quod impediendum non dubitat Caesarea majestas tuam beatitudinem summas operas, summa studia impartiri. Namque enim per tuam diligentiam Graeci, qui jam pluribus saeculis a Latina ecclesia dissidebant, ac nonnulli alii Orientales uniti sunt. Cum 9 saepe auxilia contra Soldanum missa fuerunt, cum adversus Turcos praeparis classem magnosque sumptus feceris, ut et Hungaros, qui murum tenent catholicae fidei, tueris, et Turcos ipsos ab Europa expelleris, et de unguibus eorum infelices Grecos, qui quondam Orientis domini, nunc verum servi videntur, erumperes, quis non videt te multo et ardentius ac efficacius laborare[END_REF]

Text may be missing

[START_REF]perditi , postquam fides catholica in subjectis deficere cepit. Asia quondam Christum credebat crucifixum et una cum occidentalibus in arca fidei morabatur. Id quoque 5 Africa fecit. At hodie, proh dolor[END_REF]

em.; et Cod.

5

subitat Cod.

  Illa audiat tua beatitudo per organum ipsorum auditorum hic praesentium, et seriosius, quae sunt, intelliget. Quae cum sint honesta et servabilia et hoc tempore ad integrandam pacem ecclesiasticam necessaria, supplicat regia celsitudo, ut ea tua clementia benigne suscipiat et executionem demandet, nec se gravem difficilemque in his praebeat, qui aliquando in majoribus facilem et exorabilem [se 1 ] praebuit. Sed sicut ab initio tui pontificatus usque in haec tempora de unione cogitasti, pacem promovisti, nomen Christianum providus juvasti, commune bonum amasti, nationi Germanicae complacuisti, sic et modo facias, petitionem principum et electorum, quae {26r} et petitio regis est, exaudias, et hos oratores votive expeditos remittas, per quem enim potissimum modum nationem illam Germanicam, quae tibi devota est, devotissimam reddas, schisma, quod nunc viget, extirpabis, pacem in Christiano populo informabis, sedis apostolicae splendorem augebis, et principes ac populum tuum … 2 tuamque bonitatem immensam venerabuntur. Propter hoc claritatem haurebis, … 3 honorem apud primores, in conspectu potentium admirabilis eris, et facies principum admirabuntur te et tuae sanctitati oboedient faciliter, quam Deus feliciter et longaeve tueatur ad salutem 4 ecclesiae sanctae. Amen

CO, I,[START_REF] Koller | Kaiser Friedrich III[END_REF][15] I,; Picolomini: De rebus gestis (WO, II, pp.

[210][211][212][213];Ady, Boulting, Du Fresne de Beaucourt: Histoire, IV,[255][256][257][258][259][260][261] Helmrath: Empire, Koller, Mitchell, Pastor, I, pp. 260; Pückert, Stiebert, Voigt, II,

Friederich III Habsburg (1415-1493): Duke of Austria (as Friedrich V) from 1424. Elected King of Germany and Holy Roman Emperor in 1440, crowned in Rome in 1452

Eugenius IV [Gabriele Condulmer] (1383-1447): Pope from 1431 to his death

At a meeting in Frankfurt in 1438 the German nation declared its neutrality between Pope Eugenius and the Council of Basel which would later depose the pope and elect an antipope, Felix V. In 1443-44 the imperial court began to move towards ending the state on neutrality, which was finally achieved with the Concordat of Vienna in 1447

The Council of Basel was opened in 1431 and finally dissolved by Pope Eugenius as of 1438. The remaining council fathers in Basel refused to accept the pope's decision and continued, a rump council, until 1449 when it finally dissolved itself and recognized the Roman pope, now Nicholas V

Felix V = Amedée VIII (1383-1451) : Count, later Duke of Savoy. In 1439 elected antipope under the name of Felix V by the Council of Basel, after its dissolution by Pope Eugene IV

Cf. Oration "Prius sanctissime praesul"[START_REF]Abbreviations CO = Pius II: Commentarii rerum memorabilium quae suis temporibus contigerunt[END_REF](February 1445, Rome)

Dietrich II von Moers (1385-1463): Archbishop of Cologne from 1414 to his death. Jakob von Sierck (1398-1456) Archbishop of Trier from 1439 to his death

Stiebert,

Heimburg, Gregor (beg. of 15 th c.-1472): German jurist, humanist and statesman. Bitter enemy of Pius II who eventually excommunicated him

Quoted after the translation in Reject, p. 368-370

Piccolomini: Historia Austrialis (Wagendorfer), I,

23-24 2 March 1446 3 By a papal bull of 9 February 1446

CO, I,[START_REF] Koller | Kaiser Friedrich III[END_REF][15] I,

In his biography of Pius, Campano only wrote: Tertiam [sic!] inde obivit legationem ad eundem Eugenium de duobus electoribus Caesarum restituendis, quos ille Faelici assensos et gravia in ipsius dignitatem molitos exautoraverat (Zimolo, p. 15). In Platina's biography, the description of the chain of events is somewhat confused(Zimolo, p. 101)

Pückert, p. 270

Piccolomini: Historia Austrialis (Wagendorfer), I, 23-24: Cum admissi ad conspectum essent, prior Eneas locutus est rogans papam, ut principum legatos et audiret benigne et his sese tractabilem preberet, que res cesari esset future gratissima et Romanae sedi utilis, ex qua pax ecclesie oriretur. See alsoVoigt, I, II,[START_REF]Abbreviations CO = Pius II: Commentarii rerum memorabilium quae suis temporibus contigerunt[END_REF] p. 365

CO, I, 15 (Meserve, I, p.

67)[START_REF]habent gentiles Teucri, partem Saraceni, partem schismatici schismatici diversis haeresibus infecti. Reducta autem et coarctata 7 in angulum quendam est nostra Christianitas. Has divisiones clerici 8 fecerunt, dum quae sua sunt[END_REF] See oration "Non habet me dubium"[11]

Piccolomini had already touched upon the theme of churchmen causing divisions in the Church half a hear before, in his quodlibet disputation at the University of Vienna, the "Aderat nuper" [9] of

November 1445 2 I.e. Africa 3 Note that, here Piccolomini uses the term Teucri (Teucrians) for the Turks, whereas elsewhere in the oration he uses the term Turci. Teucri was used by Virgil to designate the Trojans, and a number of early Renaissance humanists used the term to designate the Turks, in the mistaken belief that the Turks were the descendants of the Trojans themselves or some neighbouring people. Piccolomini himself used the term Teucrians as late as 1447, in the Oration "Tritum est sermone" (January 1447, Rome), but by then he began to reject this usage, his historical studies -corrrectly -showing him that the Turks had migrated to Asia Minor from somewhere in Asia, though he mistakenly identified them as descendants of the Scythians[START_REF]perditi , postquam fides catholica in subjectis deficere cepit. Asia quondam Christum credebat crucifixum et una cum occidentalibus in arca fidei morabatur. Id quoque 5 Africa fecit. At hodie, proh dolor[END_REF] The oration is published in the Appendix to Oration "Quamvis omnibus qui adestis"[21]

On Eugenius' mobilization against the Turks, seeSetton, II,

Giuliano Cesarini (1398-1444): created cardinal by Pope Martin V in 1426. Papal president of the Council of Basel until 1437. Died at the Battle of Varna, 1444. Mentor and friend of Piccolomini

See the Oration Quamvis in hoc senatu of Enea SilvioPiccolomini [17], where Piccolomini speaks of the "Sultan and the Turk" just as he speaks of the "Saracens and the Turks"

Concerning the textual transmission of Pius II´s orations, see Collected orations of PopePius, vol. 1, ch. 5

Helmrath, p.

301, listed it -with a question mark-as: "Rede 'Non Habet me dubium' (?) vor Eugen IV 1447 (f. 24v-26r)"[START_REF]maxime verendum est, ne fides nostra, quae angusta est et admodum parva, et angustissima fiat et minima. Ad quod impediendum non dubitat Caesarea majestas tuam beatitudinem summas operas, summa studia impartiri. Namque enim per tuam diligentiam Graeci, qui jam pluribus saeculis a Latina ecclesia dissidebant, ac nonnulli alii Orientales uniti sunt. Cum 9 saepe auxilia contra Soldanum missa fuerunt, cum adversus Turcos praeparis classem magnosque sumptus feceris, ut et Hungaros, qui murum tenent catholicae fidei, tueris, et Turcos ipsos ab Europa expelleris, et de unguibus eorum infelices Grecos, qui quondam Orientis domini, nunc verum servi videntur, erumperes, quis non videt te multo et ardentius ac efficacius laborare[END_REF] For an analysis of Piccolomini's use of sources, see Collected Orations of Enea SilvioPiccolomini / Pope Pius II, ch. 8

em.; illeg. Cod

em.

rethoricis Cod.

em.; longum Cod.

em.; Simonis matrem add. Cod.

em.; post Cod.

I.e. Africa

Cf. Flavio Biondo: Historiarum ab inclinatione Romanorum Imperii decades, II,

[Im. 75]: per cujus [Europae] omnes provincias et regiones nomen floruit Christianum. Quod nomen nostris temporibus ad parvum orbis angulum coangustari et quotidie de excidio periclitari videmus

em.

illeg. Cod.

illeg. Cod.

em.; statum Cod.

II. TEXT AND TRANSLATION