domain: spi phys

text:
Fatih Uncu
email: fatih.uncu@onera.fr

Benjamin Franc

Nicolas Buffaz

Ébastien Le Guyader

ASSESSMENT OF RANS TURBULENCE MODELS ON SIMPLIFIED GEOMETRIES REPRESENTATIVE OF TURBINE BLADE TIP SHROUD FLOW

Keywords:

RANS turbulence models are assessed here in simulations of simplified configurations representative of geometries and flows found in tip shrouds of low-pressure turbines rotor blades. The complex flow inside a tip shroud is highly turbulent, its boundary layer separates at the sharp angled tangential fins and reattaches in the inter-fin cavity after a recirculation. The flow in the tip seal of the rotor blade, and the jet mixing flow at the exit of the shroud cause pressure losses and influence substantially the aerodynamic performance of the turbine. Such flows are quite challenging for the RANS models. The main aim of this paper is to assess the capability of the used turbulence models to predict tip shroud representative physics of detached, reattached and jet mixing flows. The simplified geometries consist of a backward facing step, a rib roughened channel and a jet in crossflow. The Reynolds numbers of these configurations are close to those estimated in real tip shrouds. Experimental data are available in each case to evaluate the accuracy of the simulations and understand the behavior of the models. The evaluated turbulence models include several widely used eddy-viscosity models based on Boussinesq's hypothesis and a differential Reynolds stress model. Comparisons with measured components of the Reynolds stress tensor, turbulent kinetic energy and velocity profiles are presented. The velocity profiles are in good agreement with the measurements except in the recirculation regions, and eddy-viscosity models overpredict the level of experimental turbulent kinetic energy. Analysis of the strengths and weaknesses

D

Jet-pipe's diameter ER

Step expansion ratio H Backward facing step height h Ribs height r Velocity ratio in jet flow k

Turbulent kinetic energy P k

Turbulent kinetic energy production term R i j = -ρu ′ i u ′ j ij-component of the Reynolds stress tensor S i j

Mean strain tensor µ t Eddy viscosity U i i th component of the mean velocity

INTRODUCTION

Reducing aerodynamic losses in multistage turbine is a constant focus for aircraft and helicopter engines manufacturers.

Cavity flows and tip shroud flows have both a significant contribution in the overall loss. Numerical simulation has become a major tool in turbomachinery design. Increased accuracy of the simulation method is required to estimate slight differences of losses between two geometries. On the other hand, a small computational time is essential for engineers during a design cycle. The RANS is still considered a good compromise between those two aspects. However, in regions of complex geometry presenting multiple separations, recirculations and reattachments, RANS models can fail to predict accurate results. The high turbulence level and important turbulence anisotropy in such non-equilibrium regions is still challenging for the classical eddy-viscosity models. Blade tip leakage and cavity flows belong to these problematic categories and turbulence modeling has to be wisely chosen.

Main studies on the cavity and labyrinth flows have used the kω SST turbulence model with a Kato-Launder limiter [START_REF] Horwood | Flow Instabilities in Gas Turbine Chute Seals[END_REF][START_REF] Jones | An Advanced Single-Stage Turbine Facility for Investigating Non-Axisymmetric Contoured Endwalls in the Presence of Purge Flow[END_REF][START_REF] Wang | Rim Seal Ingestion in a Turbine Stage From 360 Degree Time-Dependent Numeri-cal Simulations[END_REF]. Perez et al. [START_REF] Perez | Detailed Experimental Measurement and RANS Simulation of a Low Pressure Turbine With High Lift Blading[END_REF] have preferred a simpler oneequation Spalart-Allmaras model to simulate a single stage turbine with purge flow emanating from an upstream hub cavity. The authors noted that the simulation overpredicts the pressure losses between 20% and 40% in channel height, which corresponds approximately to the position of the passage vortex. Horwood et al. [START_REF] Horwood | Flow Instabilities in Gas Turbine Chute Seals[END_REF] find that the flow coming from the purge feeds this vortex. Spalart-Allmaras fails to reproduce accurately the interactions between the jet flow coming from the cavity and the main flow. Horwood et al. use the kω SST model and obtain results which are in good agreement with the experiment, except the overprediction of the purge flow egress which increases artificially the passage vortex and by consequence the pressure losses. The eddy-viscosity models are insensitive to curvatures [START_REF] Arolla | Modeling Rotation and Curvature Effects within Scalar Eddy Viscosity Model Framework[END_REF] which could explain the lack of representativeness in cavity and tip shroud flows.

Gier et al. [START_REF] Gier | Interaction of Shroud Leakage Flow and Main Flow in a Three-Stage LP Turbine[END_REF] used the kω Wilcox 1988 model to simulate a three-stage turbine with hub cavities and tip shrouds, as well as an ideal flow path case where the cavities are not modelled. The comparison to the experiment shows the importance of taking into account the cavities for the prediction of losses and isentropic efficiency. The cavity modelled simulation retrieves the experimental static pressure around blades but over-predicts locally the isentropic efficiency in the upper part of the channel (near tip shrouds), which is explained by the authors as a probable issue in the turbulence modelling leading to a lower radial mixing of the flow.

The off channel components, like tip shrouds, have complex geometries generating highly turbulent and anisotropic flows. The Boussinesq approach underestimates this anisotropy. Schmitt [START_REF] Schmitt | About Boussinesq's Turbulent Viscosity Hypothesis: Historical Remarks and a Direct Evaluation of its Validity[END_REF] introduces an indicator measuring the validity of the Boussinesq hypothesis. This indicator is an inner product of the Reynolds and the mean strain tensors. Gao et al. [START_REF] Gao | Advanced Numerical Simulation of Turbine Rim Seal Flows and Consideration for RANS Turbulence Modelling[END_REF] have shown that for a linear eddy-viscosity model the indicator is close to The present work proposes to assess several turbulence models used in the aeronautical industry in very simple geometries that are representative of a tip shroud flow in turbine blade (Fig. 1). That will give us the possibility to understand how different models predict the detachment, reattachment and mixing flows in configurations that have a rich experimental database including Reynolds stresses. Such measurements are generally not possible in turbomachinery due to the complexity of setting up the appropriate experimental instrumentation. The conclusions are intended to be applicable to a tip shroud. In order to discuss the prediction capability of each model for the flow physics inside the clearance region, three configurations that isolate a detached, reattached and a mixing flow are studied. The detached flow, which appears after the entry in the tip shroud and at the tangential fins inside, is represented by the backward facing step of Driver and Seegmiller [START_REF] Driver | Features of a Reattaching Turbulent Shear Layer in Divergent Channelflow[END_REF] and the rib roughened channel of Coletti et al. [START_REF] Coletti | Flow Field Investigation in Rotating Rib-roughened Channel by Means of Particle Image Velocimetry[END_REF]. The behaviour of the models in the recirculation region before the reattachment is studied in these two configurations. The mixing process of the reduced velocity flow exiting the clearance area and the main flow, is represented by the jet in crossflow configuration of Andreopoulos and Rodi [START_REF] Andreopoulos | Experimental Investigation of Jets in a Crossflow[END_REF].

Often, turbulence models strengths and weaknesses are not well identified when applied to complex configurations with tip shroud and cavity flows. The originality of this work lays in the parallel comparison of the selected models on these three simple configurations enabling to extend the conclusions on a turbomachinery case.

First, the paper introduces the methodology. Then, the configurations and meshes are presented. Finally, velocity, turbulent kinetic energy and Reynolds stresses profiles are compared to the experiment and the results are discussed.

METHODOLOGY 1.RANS

Turbulence is modelled in RANS approach through the Reynolds stress tensor which appears in the Reynolds averaged momentum equation. This equation and the Reynolds averaged conservation of the mass equation for an incompressible flow (as it is the case for the three studied configurations) read:

∂U i ∂ x i = 0 (1)
ρ ∂U i ∂t + ρU j ∂U i ∂ x j = - ∂ P ∂ x i + ∂ ∂ x j (2µS i j + R i j ) (2)
with U, ρ, P, S i j , and R i j the Reynolds averaged values of the velocity, density, pressure, rate of strain tensor, and Reynolds stress tensor:

S i j = 1 2 ∂U i ∂ x j + ∂U j ∂ x i R i j = -ρu ′ i u ′ j (3)
To close the equation system, additional equations are needed to solve the double correlations of the velocity fluctuations, i.e. the components of the Reynolds stress. The transport equation of the Reynolds stress components on which all RANS turbulence models are based reads:

ρ ∂ u ′ i u ′ j ∂t + ρU k ∂ u ′ i u ′ j ∂ x k = P i j -ρε i j + φ i j + D i j + D ν i j (4)
where:

P i j = R ik ∂U j ∂ x k + R jk ∂U i ∂ x k
, is the production term

ρε i j = 2µ ∂ u ′ i ∂ x k ∂ u ′ j ∂ x k
, is the dissipation term

φ i j = p ′ ∂ u ′ i ∂ x j + ∂ u ′ j ∂ x i , is the redistribution term D i j = -∂ ∂ x k ρu ′ i u ′ j u ′ k + p ′ u ′ i δ jk + u ′ j δ ik , is the turbulent diffusion term D ν i j = ∂ ∂ x k µ ∂ u ′ i u ′ j ∂ x k

, is the viscous diffusion term

Turbulence models Boussinesq's turbulent viscosity hypothesis on which main two-equation models are based, links linearly R i j to the turbulent kinetic energy k and the gradients of the mean flow S i j :

R i j = 2µ t S i j - 2 3 ρkδ i j (5)
The three two-equation models that are utilized in the present work, kl Smith [START_REF] Smith | A Near Wall Model for the k-l Twoequation Turbulence Model[END_REF], kω Menter SST [START_REF] Menter | Two-equation Eddy-viscosity Turbulence Models for Engineering Applications[END_REF] and kω Wilcox 2006 [START_REF] Wilcox | Turbulence Modeling for CFD[END_REF], have a first equation on k which is half of the trace of the Eq. 4 and a second on the scale determining equation. The trace operator vanishes the redistribution term, φ i j , for an incompressible flow leaving the production P k , dissipation ε and diffusion D (pressure, molecular and turbulent transport) terms:

ρ Dk Dt = P k R i j ∂U i ∂ x j - ρε ρν ∂ u ′ i ∂ x j ∂ u ′ i ∂ x j + D ν k +D k ∂ ∂ x j µ ∂ k ∂ x j -ρ u ′ i u ′ i u ′ j 2 -p ′ u ′ j (6)
The contribution of the redistribution term, φ i j , is significant as it redistributes the Reynolds stresses among the different directions. The absence of such term in two-equation models is not helping the non-isotropic nature.

Non-linear models such as the kω Hellsten EARSM model [START_REF] Hellsten | New advanced k-w Turbulence Model for High-Lift Aerodynamics[END_REF], reduce also the six-unknowns problem (components of R i j ) into two equations but add a non-linear term in Eq. 5. This non-linearity adds anisotropy in the turbulence. A similar attempt has been made with a simpler non-linear term in the Quadratic Constitutive Relation (QCR) correction for the Spalart-Allmaras model [START_REF] Spalart | Strategies for Turbulence Modelling and Simulations[END_REF] and it has been extended to all the Boussinesq-based models:

R i j,QCR = R i j -C cr1 O ik R jk + O jk R ik (7) with O ik = 2Ω ik / ∂U m ∂ x n ∂U m ∂ x n , Ω ik = 1 2 ∂U i ∂ x k - ∂U k ∂ x i (8)
Reynolds stress transport models (RSM) are more complex as they have an equation per Reynolds stress tensor component and an equation for the dissipation scale. Just few (but nonetheless important) terms in the Eq. 4 necessitates modelling. Those are the dissipation, redistribution and turbulent diffusion terms. An additional transport equation is needed for the dissipation scale. The RSM model used in this study is the SSG/LRRω [START_REF] Cécora | Differential Reynolds-Stress Modeling for Aeronautics[END_REF] and it uses the same dissipation scale equation as the one of Menter's.

Flow solver and Numerical parameters

Finite volume elsA solver [START_REF] Cambier | The Onera elsA CFD Software: Input from Research and Feedback from Industry[END_REF] has been used in this study. The numerical scheme used for the simulations is the Roe upwind scheme [START_REF] Roe | Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes[END_REF] with a second order van Albada flux limiter [START_REF] Van Albada | A Comparative Study of Computational Methods in Cosmic Gas Dynamics[END_REF]. The time integration scheme is the implicit Euler method.

The assessed turbulence models are the kl Smith, the SST Menter, the Wilcox 2006 and the RSM SSG/LRR-ω.

CONFIGURATIONS

Figure 2 shows the dimensions and boundary conditions of the three configurations. More details can be found in [START_REF] Driver | Features of a Reattaching Turbulent Shear Layer in Divergent Channelflow[END_REF][START_REF] Coletti | Flow Field Investigation in Rotating Rib-roughened Channel by Means of Particle Image Velocimetry[END_REF][START_REF] Andreopoulos | Experimental Investigation of Jets in a Crossflow[END_REF]. The rib roughened channel is composed of 8 ribs of height h which are confined in a channel of height 10h. The ribs are transverse to the flow direction and are spaced of 10h. The inlet velocity, turbulent kinetic energy and turbulent dissipation scale are prescribed according to the profiles given by the measurements of Coletti et al. [START_REF] Coletti | Flow Field Investigation in Rotating Rib-roughened Channel by Means of Particle Image Velocimetry[END_REF]. Similarly to the backward facing step, the flow at the symmetry plane of the channel is not influenced by the lateral walls (verified by a simulation) which allowed us to reduce the problem into a 2D flow. All the PIV measurements have been effectuated on the domain between the 6 th and 7 th rib, where the flow has reached a somewhat periodicity.

The jet in crossflow configuration is constituted of a pipe of diameter D which is 12D long and perpendicular to a flat plate. The velocity of the flow coming from the pipe is half of the crossflow: r = V jet /V cross f low = 0.5. The velocity and turbulent quantities profiles are prescribed at the main inlet. A flow rate condition is imposed in the jet inlet in order to respect r = 0.5 while on the outlet boundary condition the static pressure is equal to 1 atm. The flow regimes and the geometrical characteristics are presented and compared to a tip shroud flow in the Tab. 1.

Tip shroud [START_REF]Effects of Tip Shroud Geometries on Low-Pressure Turbine Performance[END_REF] Step Ribbed channel Jet

MESHES

For all of the three configurations, the first wall cell size verifies y + < 1 and the number of points in the boundary layer is at least equal to 20, with an expansion ratio of 1.13. The first two configurations that have been simplified into 2D cases have been meshed with a structured grid. An unstructured grid has been used for the jet in crossflow. Indeed, the unstructured approach is intended to be used in a tip shroud configuration. In the unstructured mesh, layers of pentahedral prisms are used on the walls of the flat plate and hexahedral prims on the walls of the pipe. The interior of the pipe is also composed of prisms and the main region of the crossflow area is made of tetrahedrons. Sectional views of the meshes are given in Fig. 3. The mesh size are respectively 120 000, 320 000 and 6 700 000 cells for the back step, rib roughened channel and jet in crossflow.

Backward facing step

Figure 4 shows the comparisons of streamwise velocity U, turbulent kinetic energy k, and Reynolds shear stresses u ′ v ′ between experimental measurements [START_REF] Driver | Features of a Reattaching Turbulent Shear Layer in Divergent Channelflow[END_REF] and simulation results.

The first profile is 4H upstream of the step (at x = -4H), the two following are in the recirculation region (1H and 4H), the station at 6H is located just upstream of the reattachment point (which is measured experimentally at 6.26H) and finally, the last station is downstream of the recirculation (10H).

Firstly, all the models predict a boundary layer thickness at the upstream of the step (x = -4H) that is coherent with the experimental data: all the models predict a flow that reaches the step with an accurate U and k profiles. The following mean flow profiles are in quite good agreement with experimental data except for a slight overprediction of the shear stress level u ′ v ′ . Notice however, that all ω-based models fail to predict the expected k-peak near the wall at x = -4H, unlike the kl model. Fur- thermore the LRR near-wall RSM closure is known to fail in correctly predicting the near wall anisotropy [START_REF] Jones | Anisotropic, Isothermal, Turbulent Swirling Flow in a Complex Combustor Geometry[END_REF].

The kl model based on a transport equation of a length scale stands out by over-predicting the backflow at x=1H just after the step. In this region a secondary recirculation is present. This recirculation is smaller and contrarotative compared to the main one. The analysis of the size of the corner recirculation shows that this model finds a smaller volume and length of recirculation compared to the others. The negative velocity at the station 1H is a result of this. Despite this default, it succeeds in catching up the experimental profiles in the following stations. It also predicts quite well turbulent quantities in the initial part of the mixing layer just downstream of the corner.

Another important point concerns the low velocity in the recirculation region of the models with a transport equation on specific dissipation rate, ω. It is particularly visible near the reattachment point (x = 6H). kω models present slower recovery in the vicinity of the reattachment point which mitigates downstream of the recirculation. This latency is accompanied with a bulge in the velocity profile between y = 0H and y = 1H.

For the same kω models, the turbulent kinetic energy is too low near the wall at the first post-detachment station (x = 1H). Whereas the experimental data shows two peaks of energy at y = 0.2H and 1H, the simulations are not able to reproduce this behaviour (Fig. 4c). The measurements show that the near-wall peak increases at the center of the recirculation region (high turbulence intensity) and that the peak coming from the upstream boundary layer merges: the location of the peak's maximum lowers in the y direction. The same evolution is also visible in the Reynolds shear stress profiles (Fig. 4d).

The RSM SSG/LRRω model behaves like SST Menter and Wilcox 2006: low velocity at the end of the recirculation bulb and a near-wall bulge in the velocity profile. In addition, there is no velocity gradient in the near wall region in all the post-step stations. The experimental data close to the wall does not show this behaviour. The direct numerical simulation of Le et al. [START_REF] Le | Direct Numerical Simulation of Turbulent Flow over a Backward-facing Step[END_REF] on a backward facing step with an expansion ratio of 1.2, does not also show a zero U-gradient in the near wall region. The LRR model which is active in the near wall region is defective. Eisfeld and Rumsey [START_REF] Eisfeld | Length-scale Correction for Reynolds-stress Modeling[END_REF] proposed a correction based on Yap's work on the transport equation for the dissipation scale, which improves the behaviour of the model near the reattachment point but has no impact on the global flow prediction.

Menter [START_REF] Menter | A Comparison of Some Recent Eddy-Viscosity Turbulence Models[END_REF] compared different eddy-viscosity models on this configuration and showed that the Spalart model predicts too much backflow in the recirculation region like what we found for the kl Smith. He also found that none of the evaluated models (Spalart, Menter SST, k -ε 2-L and RNG 2-L) accelerate enough near the wall to correctly predict the relaxation processes. The simulated flow is slower than the measured one: the recovery is too slow and so the reattachment is longer. He noticed that this behaviour is not only present in the backstep flow but in all sepa-rated flows for the assessed models. This behaviour is generally observed in RANS models [START_REF] Gerolymos | Term-by-term Analysis of Near-wall Second-moment Closures[END_REF] which generally do not include lag-mechanisms to account for the detachment-reattachment hysteretic behaviour of turbulence. This strengthens our conclusions on the difficulties of capturing the correct streamwise velocity near the wall in the separated region.

Shih et al. [START_REF] Shih | A New Reynolds Stress Algebraic Equation Model[END_REF] find also the bulge in the streamwise profiles with an EARSM model.

Rib roughened channel

Fransen et al. [START_REF] Fransen | Steady and Unsteady Modeling for Heat Transfer Predictions of High Pressure Turbine Blade Internal Cooling[END_REF] have studied the rib roughened channel using the kl Smith model and showed that RANS simulation misses locally the fluid acceleration and recirculation at the top of ribs. Some wall-resolved LES simulations have been carried out on this configuration and they show very good agreement with the experiment reproducing very well all the velocity and turbulence profiles [START_REF] Grosnickel | Large Eddy Simulations of Static and Rotating Ribbed Channels in Adiabatic and Isothermal Conditions[END_REF][START_REF] Fransen | Large Eddy Simulation of Rotating Ribbed Channel[END_REF][START_REF] Grosnickel | Simulations des grandes échelles pour la prédiction des écoulements de refroidissement des pales de turbines[END_REF].

The flow with the presence of a rib is very close to what is seen in the precedent case (Fig. 5). The two contrarotative recirculations in the downstream of the rib are the same as in the backward facing step. The following ascending step is an obstacle for the flow and a third recirculation is created at the left bottom corner of the 7 th rib. A last recirculation region is visible at the top of the rib where there is not enough space to recreate an attached boundary layer.

Figure 5 shows that the main recirculations are reproduced by all the models except in the downstream corner and above the rib (recirculations 1 and 4). Indeed the flow over the rib has an attached boundary layer and the downstream corner recirculation is too small to be visible. Only the RSM model predicts a small bulb at the top of the rib but it is very marginal compared to The main recirculation is longer for the kω Menter and Wilcox models. That was also observed in the backward facing step but is amplified in this configuration due to the error accumulation of the reattachment length's misprediction. These two models have an SST limiter modifying the definition of the eddy viscosity: µ t = k/ω e f f with ω e f f greater or equal to ω. Reducing the eddy viscosity leads to less Reynolds stress and so to a longer recirculation bulb. This result is also found by Wilcox [START_REF] Wilcox | Formulation of the k-w Turbulence Model Revisited[END_REF], where the increase of the coefficient C lim in the SST formulation of the Wilcox 2006 model extends the reattachment length.

The velocity profiles are presented in the Fig. 6. No significant differences are observed between the kω and SSG/LRRω models. Like in the backward facing step case, a delay in the recirculation region between the two ribs appears for these models. All the calculations underpredict the streamwise velocity between y = 0h and y = 2h. The Smith model marks a difference by its capacity to well predict the near-wall mean flow. The downstream recirculation (number 2 in Fig. 5) is well reproduced. Finally, at x = 9.5h, the experiments show a separated boundary layer, while a new boundary layer starts to develop in the upper part of the ribs in the simulations. The error on the velocity between the two ribs is also due to the absence of this separation. Beyond that, all of the turbulence models are able to predict a mean flow dynamics which is in agreement with the measurements. In our simulations the high Tu x area is not reproduced at the top of the obstacle. Assuming that it is the footprint of the recirculation in this location, it is normal that the simulations do not predict it knowing that the separated boundary layer is not captured. A second default is the anomaly on the overproduction of the v ′ v ′ stress at the upstream top corner. This behaviour is present in all the three eddy-viscosity models. The exact production term of the turbulent kinetic energy is

Turbulence fields

P k = R i j ∂U i ∂ x j .
For an incompressible flow and with the Boussinesq hypothesis, this term simplifies into P k = µ t S 2 with S = 2S i j S i j and S i j = 1 /2 ( ∂U i/∂ x j + ∂U j/∂ x i ). The production term field, P k , computed with the Menter SST model is presented in the Fig. 8. The maximum of this production is reached at the same location as the anomaly of Tu y . It is therefore a defect of the Boussinesq hypothesis which is the well-known stagnation point anomaly [START_REF] Durbin | On the k-3 Stagnation Point Anomaly[END_REF] which is characterized by a turbulence overproduction in high acceleration and deceleration regions. The RSM model (Fig. 7) does not reproduce this anomaly: the production term is exempt from modeling. One way to solve this anomaly is to change the production term with the Kato-Launder modification [START_REF] Kato | The Modelling of Turbulent Flow Around Stationary and Vibrating Square Cylinders[END_REF]:

P k = µ t SΩ with Ω = 2Ω i j Ω i j and Ω i j = 1 /2 ( ∂U i/∂ x j -∂U j/∂ x i ),
or to use the vorticity source term [START_REF] Menter | Improved Two-equation k-omega Turbulence Models for Aerodynamic Flows[END_REF]: P k = µ t Ω 2 . As it can be seen in the Fig. 8, these two other formulations of the production terms help indeed to reduce the anomaly. In this zone, a high ∂U /∂x gradient contributes to S which leads to a turbulence overproduction. This gradient disappears in the vorticity term. In our The Reynolds shear stress which is the dominant Reynolds stress component in the momentum equations of a turbulent boundary layer, must be well-modeled. Figure 7 shows that all the models predict a lower u ′ v ′ than the measurements. The RSM simulation gives the most accurate distribution of u ′ v ′ . The four other models show a filet of negative stress just after the leading edge. A zone of positive stress in the upstream of the leading edge is visible for the Smith and Menter models. It is the main difference between the Menter and Wilcox models. This difference could be explained by the SST limiter which is a function of Ω i j Ω i j for the former and of S i j S i j for the latter. Given that S is greater in the leading edge area, the SST limiter will further decrease µ t and consequently u ′ v ′ in the case of the Wilcox model. The same argument explains why the Tu x pocket at the same area is not present for the Wilcox model and that the Tu y pocket is lower than the Menter SST simulation. The upstream anomaly is less visible with the Wilcox 2006, the difference being in the level of eddy viscosity. For this configuration, the SST limiter used by [START_REF] Wilcox | Turbulence Modeling for CFD[END_REF] is preferable to the one presented in Menter's model [START_REF] Menter | Two-equation Eddy-viscosity Turbulence Models for Engineering Applications[END_REF].

SSG/LRR -ω SST Pk ∝ S 2 SST Pk ∝ Ω 2 SST Pk ∝ ΩS
In addition, three-dimensional RANS simulations have been carried out to understand the importance of turbulence anisotropy in the creation of "lateral" secondary structures. The LES simulation of Grosnickel [START_REF] Grosnickel | Simulations des grandes échelles pour la prédiction des écoulements de refroidissement des pales de turbines[END_REF] shows that along the channel, parietal structures are created. These are Taylor-Görtler type vortices. These structures of very low speed are shown in the Fig. 9 in the plane between the 6 th and 7 th ribs at a constant x/h = 4.5. The non-linear EARSM Hellsten model was also evaluated here to see how it behaves compared to a linear model. The RSM and EARSM models are able to create those structures while an eddy-viscosity model like Menter cannot. The two other Boussinesq models that are not shown here behaves the same way as the kω Menter SST. The main difference is the anisotropy being naturally present in the former models while a classical Boussinesq model is based on a linear constitutive relation. The addition of a non-linear term through the QCR correction in this relation is here helping to reproduce similar structures. The LES [START_REF] Grosnickel | Simulations des grandes échelles pour la prédiction des écoulements de refroidissement des pales de turbines[END_REF] EARSM Hellsten SSG/LRR-ω anisotropy of turbulence, measured here by the ratio v ′ v ′ /w ′ w ′ , is primordial in the generation of such streamlines. The nonlinearity of the QCR correction seems to create an anisotropy closer to the RSM simulation (Fig. 10) and is therefore recommended in simulations where parietal structures and turbulence anisotropy are important. The simulation without QCR shows Reynolds stresses that are quasi equivalent in the directions y and z, while there is a ratio of more than 5 for the RSM model. The anisotropy of the EARSM model (which is not presented) does not reach this ratio, but near the left and right walls v ′ v ′ >> w ′ w ′ which causes the apparition of the recirculations. The same underprediction of anisotropy applies also to the QCR.

k -ω Menter k -ω Menter QCR

Simulation of mixing flow

At very low velocity ratios, which is the case here, the flow inside the pipe starts to bend before the exit plane [START_REF] Andreopoulos | Measurements in a Jet-Pipe Flow Issuing Perpendicularly Into a Cross Stream[END_REF]. At the pipe outlet, the streamlines are totally aligned with the crossflow: the momentum being half of the main flow, the jet cannot resist and is dragged by the orthogonal flow. The main flow bends to get around the flow coming from the pipe. A complex is created: the main flow is deviated partly above and at each sides of the "obstacle". A horseshoe vortex and a CVP (Counter-rotating Vortex Pair) are the main secondary structures that develop (view Fig. 11). These vortices contribute to the mixing process and cause pressure losses. In film-cooling jet flows, they amplify the thermal exchanges.

Flow dynamics of the mean flow Streamwise velocity U

A deceleration above the pipe exit (which is located between x/D = -0.5 and x/D = 0.5) in the symmetry plane z/D = 0 (first 5 stations) is visible before an acceleration due to the dragging of the main flow (Fig. 12a). High velocity gradients are present at x/D = 1 and x/D = 2. These gradients connect the low nearwall velocities and the external U e flow. It is shown that the ∂U /∂y gradient is the main term contributing to the production of turbulence in the wake area of the jet.

At z/D = 0.5, the velocities are greater than on the symmetry plane where the wake acts like an obstacle which slows down the flow. The velocity is increasing near the wall. The explanation is the deviation and acceleration of the main flow around the wake region [START_REF] Andreopoulos | Experimental Investigation of Jets in a Crossflow[END_REF].

The simulations are able to reproduce the streamwise velocity profiles on the first stations (until x/D = 0.5). Indeed, the bended jet flow does not influence the crossflow in that region. Downstream the behaviour of the Smith model which fits nearly all the experimental dots at x/D = 0.5 and x/D = 1 (z/D = 0.5) is remarkable. The same is visible on the symmetry plane, where the other two models underestimate U, the k-l Smith model captures the experimental profile downstream of the jet exit and in the wake region.

On the other hand, the same model predicts velocity profiles that seem to be smoothed and the gradients erased especially in the inflection points at x/D = 2. This behaviour can be associated to the level of eddy viscosity produced by this model.

The similarity of the flow dynamics predicted by the Menter SST and SSG/LRR-ω should be noted. They both show discrepancies in the plane z/D = 0.5 from x/D = 0.25 to x/D = 2. A recirculation, which is not proven by the experiment, is predicted u ′ w ′ stress The u ′ w ′ stresses pilot the lateral spread of the jet wake. The RANS momentum equation projected on the x and z axis show that the derivatives of u ′ w ′ in the spreading directions (∂ /∂ x and ∂ /∂ z) modify to the first order the dynamics of the flow in these two directions.

The main gradients contributing to the production of u ′ w ′ are ∂U /∂z and ∂W /∂y according to the decomposition of the production term:

P xz = -ρu ′ u ′ ∂W ∂ x -ρu ′ v ′ ∂W ∂ y -ρu ′ w ′ ∂W ∂ z -ρw ′ u ′ ∂U ∂ x -ρw ′ v ′ ∂U ∂ y -ρw ′ w ′ ∂U ∂ z (9)
Among these terms, u ′ w ′ , w ′ v ′ and the gradient ∂W /∂x are very small and negligible. The measured stresses are quasi zero in the first stations because the main gradients in Eq. 9, i.e. ∂U /∂z and ∂W /∂y are also very small at the location of the jet exit. Once these gradients start growing, the production and the level of u ′ w ′ increase.

Both eddy-viscosity models and the evaluated RSM model are not able to give a realistic simulation of u ′ w ′ evolution. Indeed, from x/D = 0.5 to x/D = 2 the simulations predict a positive peak where the experiment shows negative stresses. Andreopoulos and Rodi [START_REF] Andreopoulos | Experimental Investigation of Jets in a Crossflow[END_REF] explain it for the eddy-viscosity models by the fact that Boussinesq's constitutive relation links this stress to ∂U /∂z and ∂W /∂x but not ∂W /∂y. However in our case, the RSM model which has its own transport equation for u ′ w ′ also does not perform well.

CONCLUSIONS

The present study focuses on the assessment of turbulence models in turbine tip shroud flow representative configurations.

For detached and reattached flows, all the evaluated models show good agreement with the experimental mean profiles. However, it is seen that kω models as well as the SSG/LRRω model have a latency in the velocity profiles in the recirculation region. The prediction of the flow recovery at the end of the recirculation is not accurate in the near wall region. The k -ω models find a recirculation length which is longer than expected. It can be solved by preferring a model without an SST limiter like the Menter BSL model. The RSM model has a zero-gradient streamwise velocity profile in the near wall region of the recirculation. This behaviour can be locally improved by a Yap correction but has no impact on the global flow prediction. And finally, the turbulence length transporting model underpredicts the secondary recirculation in the downstream corner of the step and overpredicts the backflow.

The RSM SSG/LRR-ω is the model that fits the best the experimental mean turbulence profiles. Boussinesq models overpredict the turbulent kinetic production due to the stagnation point anomaly. This can be overcome by a modification of the production term with a vorticity source term that reduces the anomaly just upstream of the rib.

The anisotropy of turbulence has shown to be important in the prediction of lateral-wall related secondary structures. This anisotropy being naturally present in the RSM and EARSM models, they are able to create those structures while an eddyviscosity model cannot do it without a QCR correction. However, this better prediction of the RSM is at a higher cost of calculation. The computational time per iteration per cell is ∼ 20% longer than a classical 2-equation model.

For the jet in crossflow, the model that fits the best the mean profiles is the kl Smith while for turbulence profiles it is still the RSM. The Smith model predicts a correct mean velocity thanks to a good prediction of the turbulence locally at the jet exit, but everywhere else, it largely overpredicts the turbulence level inside the mixing region. Finally the Menter SST and SSG/LRRω, which share a nearly common dissipation transport equation and blending functions, show a very similar flow dynamics solution.

It would be now interesting to see if these conclusions are retrieved and if the RSM, which shows the best agreement with turbulence measurements and predicts an accurate mean flow dynamics, performs also well in a turbomachinery configuration. This is the subject of ongoing research.

FIGURE 1 :

 1 FIGURE 1: Tip shroud flow on a low-pressure turbine

FIGURE 2 :

 2 FIGURE 2: Dimensions and BCs of the (a) backward facing step, (b) rib roughened channel and (c) jet in crossflow

FIGURE 3 :

 3 FIGURE 3: Sectional views of the meshes : (a) backward facing step, (b) rib roughened channel, and (c-d) jet in crossflow

FIGURE 4 :

 4 FIGURE 4: (a) Position of stations and profiles of normalized (b) streamwise velocity, (c) k and (d) u ′ v ′

k

  ω Menter SST kω Wilcox 2006

FIGURE 5 :FIGURE 6 :

 56 FIGURE 5: Normalized velocity fields between 6 th and 7 th ribs

Figure 7

 7 presents the normalized shear stress, Tu x and Tu y with Tu i = u ′ i 2 /U 0 . The measurements show a plume of u ′ u ′ in the upper part of the ribs which is the signature of the separated boundary layer. The maximum u ′ u ′ is reached at the downstream top corner of the rib, where a shear layer starts to develop. The PIV measurements [10] SSG/LRR-ω kl Smith kω Menter SST kω Wilcox 2006

FIGURE 7 :

 7 FIGURE 7: Tu x , Tu y and normalized Reynolds shear stress fields

FIGURE 8 :

 8 FIGURE 8: Normalized k production term fields, P k

FIGURE 9 :

 9 FIGURE 9: Streamlines and U on a plane at constant x/h = 4.5

FIGURE 10 :

 10 FIGURE 10: v ′ v ′ /w ′ w ′ , on a plane at constant x/h = 4.5

FIGURE 11 :

 11 FIGURE 11: Streamlines and total pressure in the jet in crossflow

FIGURE 12 :

 12 FIGURE 12: Normalized streamwise velocity U at (a) z/D = 0, (b) z/D = 0.5, and (c) transverse velocity W at z/D = 0.5

FIGURE 13 :

 13 FIGURE 13: Normalized k at (a) z/D = 0 and (b) z/D = 0.5, u ′ v ′ at (c) z/D = 0 and (d) z/D = 0.5, and (e) u ′ w ′ at z/D = 0.5

TABLE 1 :

 1 Flow regimes of the three configurations

ACKNOWLEDGMENT

The authors wish to thank Georges Gerolymos (Sorbonne University), Raphael Barrier (ONERA) and Jacques Demolis (Safran Helicopter Engines) for the fruitful discussions on turbulence modeling and on the results analysis.

Transverse velocity W

The transverse component of the velocity is negative on the first stations. The main flow moves away from the symmetry plane from either sides of the jet. Downstream W becomes positive: the low pressure region generated by the wake attracts the flow towards the symmetry plane.

All the simulations overestimate the distancing from the symmetry plane at the jet exit area. On the plane of the downstream outlet corner (x/D = 0.5) and on the following profile, the k-ω and SSG/LRR-ω models capture the good transverse velocity profiles while the Smith model predicts too much lateral spread between y/D = 0.1 and y/D = 0.3.

Turbulence fields Turbulent kinetic energy

The main term contributing to the production of turbulence, P k , is -ρu ′ v ′ ∂U /∂y. The velocity gradient ∂U /∂y pilots the turbulence production in the mixing region. This is easily verified by checking the correlation of the peaks positions of this gradient and k profiles. Another gradient participating to the production is ∂W /∂z. Downstream, the gradients and the turbulent kinetic energy dissipate. The peaks of k are convected to the near-wall region.

On the symmetry plane, the two eddy-viscosity models overpredict the turbulent kinetic energy in the wake region of the jet (Fig. 13a). This over-evaluation is all the more important with the k-l Smith model as k is almost three times greater than what is measured at x/D = 1 and x/D = 2. The RSM model retrieves the experimental level of k and the position of the peak is also well-predicted. However, none of the models reproduce the convection of k towards the flat plate in the last stations (x/D = 4 and x/D = 6).

At z/D = 0.5, again the Smith model overestimates k as early as x/D = 0. The double peak of k (also present in the gradient ∂U /∂y) is retrieved for the k-ω and RSM models but with much lower levels of energy. A third peak is also observed for these two models (x/D = 0.25 and x/D = 1) near the wall. Andreopoulos [START_REF] Andreopoulos | Experimental Investigation of Jets in a Crossflow[END_REF] notes also the presence of this peak out of the measurement probe area.

The Smith model, which produces too much turbulence in the mixing region, predicts a level of k which is equivalent to the measurements at x/D = 0.25 and x/D = 0.5 in the z/D = 0.5 plane (Fig. 13b). It corresponds to the region where the mean flow dynamics is remarkably well predicted by the same model. The Smith model differentiates itself in the downstream corner of the jet exit. One conclusion is that even if the turbulence kinetic energy is overevaluated in the mixing region (jet wake), the flow dynamics will be mainly impacted by the prediction of k just after the jet exit plane.

The evolution of u ′ v ′ is very similar to that of k. Indeed the prevailing production term in P k includes u ′ v ′ . The gradient ∂U /∂y is also the main production mechanism of the Reynolds shear stress through the term: -ρv ′ v ′ ∂U /∂y. We can notice on the measurements that the maximum of u ′ v ′ is reached further downstream than k's. That could be explained by the fact that the production does not depend only on the precedently cited gradient but also on v ′ v ′ which is convected from upstream.

Just like the turbulent kinetic energy, the Reynolds shear stresses u ′ v ′ are also overestimated by the Menter SST and k-l Smith models from x/D = -0.2 to x/D = 2. Mengler et al. [START_REF] Mengler | Numerical Prediction of Momentum and Scalar Fields in a Jet in Cross Flow: Comparison of LES and Second Order Turbulence Closure Calculations[END_REF] finds that even LES simulations show discrepancies and overpredict the level of u ′ v ′ stresses. In contrast, the RSM SSG/LRR-ω simulation performs very well in retrieving the


Aitor Hernández

Hannes A Houck

Fermin Elizalde

Marc Guerre
email: guerre@chimie.ups-tlse.fr

Haritz Sardon
email: haritz.sardon@ehu.eus

Filip E Du Prez
email: filip.duprez@ugent.be

Internal catalysis on the opposite side of the fence in non-isocyanate polyurethane covalent adaptable networks

Keywords: Covalent adaptable network, non-isocyanate polyurethane, polyhydroxyurethane, transcarbamoylation, internal catalysis

Within the context of covalent adaptable networks (CANs), we developed in this study a novel methodology to provide non-isocyanate polyurethane-based CANs with embedded tertiary amines that serve as internal catalytic moieties for the dynamic bond exchange processes. For the CAN design, we made use of multifunctional N-substituted 8-membered cyclic carbonates that are ringopened by macromolecular amines. Several model reactions were conducted to investigate transcarbamoylation bond exchange reactions at elevated temperatures and assess the influence of catalytic moieties within the urethane structure. This led us to design a non-isocyanate polyurethane CAN wherein the position of the internal catalyst was changed with respect to previous reported polyhydroxyurethane CANs, while maintaining close proximity to the dynamic carbamate linkages. It is shown that this positioning change of the tertiary amines still resulted in an internal catalytic effect on the dynamic exchange reactions, hence providing a better understanding of the role of tertiary amines as internal catalysts during the reprocessing of polyurethane networks. Moreover, the model experiments and thermomechanical investigations of the (re)processed networks allowed to identify the occurrence of competing reactions, involving a dissociative mechanism giving rise to urea formation, which significantly impacts the materials' reprocessability and properties.

Introduction

The discovery of thermoplastics marked a scientific revolution in the field of material sciences because of their low viscosity when heated beyond their glass transition or melting temperature when compared to metal based materials, enabling processing operations such as extrusion and injection moulding. [START_REF] Shenoy | Thermoplastic Melt Rheology and Processing[END_REF] However, thermoset materials proved to possess far superior mechanical properties [START_REF] Flory | Network Structure and the Elastic Properties of Vulcanized Rubber[END_REF] because of their crosslinked structure, making them attractive as high performance materials such as engineering-grade composites. [START_REF] Toozandehjani | Conventional and Advanced Composites in Aerospace Industry: Technologies Revisited[END_REF] Yet, thermosetting materials lack thermo-mechanically induced reprocessability because of their permanent covalent network structure. Being the main drawback of conventional thermoset materials, Bowman and co-workers [START_REF] Kloxin | Covalent Adaptable Networks (CANs): A Unique Paradigm in Cross-Linked Polymers[END_REF][START_REF] Bowman | Covalent Adaptable Networks: Reversible Bond Structures Incorporated in Polymer Networks[END_REF][START_REF] Kloxin | Covalent adaptable networks: smart, reconfigurable and responsive network systems[END_REF] broke new ground by introducing reversible covalent bonds within the network structure, thereby creating a new class of polymeric materials known as covalent adaptable networks (CANs).

Unlike previously known non-covalent networks relying on supramolecular interactions, [START_REF] Cordier | Self-healing and thermoreversible rubber from supramolecular assembly[END_REF][START_REF] Fox | High-Strength, Healable, Supramolecular Polymer Nanocomposites[END_REF][START_REF] Bossion | Synthesis of self-healable waterborne isocyanate-free poly(hydroxyurethane)based supramolecular networks by ionic interactions[END_REF] CANs consist of chemically crosslinked polymers that display healing and original viscosity dependence when subjected to specific stimuli such as light, [START_REF] Houck | Light-Stabilized Dynamic Materials[END_REF] pH change [START_REF] García | Multi-responsive coordination polymers utilising metal-stabilised, dynamic covalent imine bonds[END_REF] or heat [START_REF] Gandini | The furan/maleimide Diels-Alder reaction: A versatile click-unclick tool in macromolecular synthesis[END_REF] as a result of dissociative and/or associative covalent bond exchange mechanisms. [START_REF] Winne | Dynamic covalent chemistry in polymer networks: a mechanistic perspective[END_REF] A specific subclass of associative CAN materials known as 'vitrimers', introduced by Leibler et al., [START_REF] Montarnal | Silica-Like Malleable Materials from Permanent Organic Networks[END_REF][START_REF] Capelot | Metal-Catalyzed Transesterification for Healing and Assembling of Thermosets[END_REF] exhibits a linear viscosity dependence that follows an Arrhenian behaviour. This means that the rheological profile is controlled by the thermally initiated associative exchange reactions, resulting in a steady change in viscosity while keeping their crosslink density unaltered. [START_REF] Denissen | Vitrimers: permanent organic networks with glass-like fluidity[END_REF] This rheological behaviour allows for a specific viscosity control different than to thermo-responsive dissociative CANs that follow a Williams-Landen-Ferry model and typically lose their network connectivity as the temperature rises [START_REF] Denissen | Vitrimers: permanent organic networks with glass-like fluidity[END_REF][START_REF] Jourdain | Rheological Properties of Covalent Adaptable Networks with 1,2,3-Triazolium Cross-Links: The Missing Link between Vitrimers and Dissociative Networks[END_REF]. In addition to the original polyester-based vitrimers, [START_REF] Montarnal | Silica-Like Malleable Materials from Permanent Organic Networks[END_REF][START_REF] Capelot | Metal-Catalyzed Transesterification for Healing and Assembling of Thermosets[END_REF] numerous other chemical platforms have been widely developed to yield new types of vitrimer materials. [START_REF] Winne | Dynamic covalent chemistry in polymer networks: a mechanistic perspective[END_REF][START_REF] Denissen | Vitrimers: permanent organic networks with glass-like fluidity[END_REF][START_REF] Scheutz | Adaptable Crosslinks in Polymeric Materials: Resolving the Intersection of Thermoplastics and Thermosets[END_REF]. However, dissociative processes which do not induce a considerable loss in crosslink density, may have a negligible effect on the viscoelastic properties, allowing the network to still follow the aforementioned Arrhenian behaviour within a specific temperature interval. [START_REF] Jourdain | Rheological Properties of Covalent Adaptable Networks with 1,2,3-Triazolium Cross-Links: The Missing Link between Vitrimers and Dissociative Networks[END_REF][START_REF] Shi | Cross-linked polyurethane with dynamic phenol-carbamate bonds: properties affected by the chemical structure of isocyanate[END_REF][START_REF] Elling | Reprocessable Cross-Linked Polymer Networks: Are Associative Exchange Mechanisms Desirable?[END_REF] Additionally, despite the clear distinction between associative and dissociative mechanisms, CANs in which both kinds of mechanisms coexist have been identified (e.g. those based on polyhydroxyurethane backbones). [START_REF] Shi | Cross-linked polyurethane with dynamic phenol-carbamate bonds: properties affected by the chemical structure of isocyanate[END_REF][START_REF] Fortman | Structural effects on the reprocessability and stress relaxation of crosslinked polyhydroxyurethanes: ARTICLE[END_REF] Often, different types of CANs have proven to be effective only when subjected to the presence of external catalysts, [START_REF] Capelot | Metal-Catalyzed Transesterification for Healing and Assembling of Thermosets[END_REF][START_REF] Self | Brønsted-Acid-Catalyzed Exchange in Polyester Dynamic Covalent Networks[END_REF] which could be problematic in case the catalyst becomes deactivated, degrades upon reprocessing, or leaches out during the material's live cycle. [START_REF] Denissen | Vitrimers: permanent organic networks with glass-like fluidity[END_REF] Additionally, the catalyst could influence the associative/dissociative nature of the involved chemical exchange reactions, e.g. organotin catalysts in carbamate exchanges. [START_REF] Elizalde | Dynamic polyurethane thermosets: tuning associative/dissociative behavior by catalyst selection[END_REF][START_REF] Yan | Multifunctional polyurethane-vitrimers completely based on transcarbamoylation of carbamates: thermally-induced dual-shape memory effect and self-welding[END_REF][START_REF] Fortman | Reprocessing Cross-Linked Polyurethanes by Catalyzing Carbamate Exchange[END_REF] Hence, dynamic systems which are free of external catalysts, [START_REF] Denissen | Vinylogous Urethane Vitrimers[END_REF][START_REF] Zheng | Catalyst-Free Thermoset Polyurethane with Permanent Shape Reconfigurability and Highly Tunable Triple-Shape Memory Performance[END_REF][START_REF] Debnath | Catalyst-Free Partially Bio-Based Polyester Vitrimers[END_REF] do not require any catalysts at all, or entail an internal catalyst that remains covalently attached within the material, have attracted considerable attention. In particular the latter is an interesting design principle. Indeed, the chemical environment is a key factor in understanding chemical reactivity as bond exchange processes are often influenced by the stereoelectronic effects in the vicinity of the reactive sites. [START_REF] Sustmann | A simple model for substituent effects in cycloaddition reactions. II. The diels-alder reaction[END_REF] In this context, internally catalysed networks [START_REF] Van Lijsebetten | Internal catalysis for dynamic covalent chemistry applications and polymer science[END_REF] should be highlighted where strong hydrogen bonding or covalent interactions have been proven to highly impact several chemistry platforms, allowing some dynamic materials to display faster exchange rates. [START_REF] Cromwell | Malleable and Self-Healing Covalent Polymer Networks through Tunable Dynamic Boronic Ester Bonds[END_REF][START_REF] Hao | Triethanolamine-Mediated Covalent Adaptable Epoxy Network: Excellent Mechanical Properties, Fast Repairing, and Easy Recycling[END_REF][START_REF] Delahaye | Internal Catalysis in Covalent Adaptable Networks: Phthalate Monoester Transesterification As a Versatile Dynamic Cross-Linking Chemistry[END_REF][START_REF] Taplan | Covalent Adaptable Networks Using β-Amino Esters as Thermally Reversible Building Blocks[END_REF] This has been proven to be a tuneable characteristic by altering the entropy of activation through displacement of the functionality that induces the internal catalytic effect (e.g. neighbouring group participation in the phthalate monoester transesterification) [START_REF] Zhang | Intramolecularly Catalyzed Dynamic Polyester Networks Using Neighboring Carboxylic and Sulfonic Acid Groups[END_REF][START_REF] Podgórski | Thiol-Anhydride Dynamic Reversible Networks[END_REF] or by adding even more accumulative effects within the proximity of the dynamic bond (e.g. double neighbouring group participation). [START_REF] Delahaye | Double neighbouring group participation for ultrafast exchange in phthalate monoester networks[END_REF] Polyurethane-based CANs are an interesting type of materials with regard to catalysed bond exchange processes [START_REF] Yan | Multifunctional polyurethane-vitrimers completely based on transcarbamoylation of carbamates: thermally-induced dual-shape memory effect and self-welding[END_REF][START_REF] Fortman | Reprocessing Cross-Linked Polyurethanes by Catalyzing Carbamate Exchange[END_REF]. In particular, so-called non-isocyanate polyurethanes (NIPUs) [START_REF] Ecochard | Hybrid polyhydroxyurethanes: How to overcome limitations and reach cutting edge properties?[END_REF][START_REF] Bossion | Unexpected Synthesis of Segmented Poly(hydroxyurea-urethane)s from Dicyclic Carbonates and Diamines by Organocatalysis[END_REF] are an emerging class of more sustainable dynamic PU-based networks, since NIPU building blocks can be potentially derived from renewable feedstock such as cyclic carbonates from CO 2 whereby toxic isocyanates can be avoided. [START_REF] Fanjul-Mosteirín | Rational Study of DBU Salts for the CO 2 Insertion into Epoxides for the Synthesis of Cyclic Carbonates[END_REF][START_REF] Mcguire | Synthesis of 5-to 8membered cyclic carbonates from diols and CO2: A one-step, atmospheric pressure and ambient temperature procedure[END_REF] Whereas for many decades, polyurethanes (PUs) have been industrially relevant because of their versatility and wide range of properties -making them ideal for an array of applications ranging from foams to coatings [START_REF] Engels | Polyurethanes: Versatile Materials and Sustainable Problem Solvers for Today's Challenges[END_REF] -, PUs gain increasing attention as they are often used in (self-)healable dynamic networks. [START_REF] Aguirresarobe | Healable and self-healing polyurethanes using dynamic chemistry[END_REF] Indeed, many polyurethane materials exhibit dynamic properties owed to transcarbamoylation reactions that are externally catalysed by, e.g. organotin, organic acid or Lewis acid compounds, which are commonly used in their preparation. [START_REF] Elizalde | Dynamic polyurethane thermosets: tuning associative/dissociative behavior by catalyst selection[END_REF][START_REF] Jousseaume | Efficient bismuth catalysts for transcarbamoylation[END_REF] Yet, metal-free dynamic polyurethane and polyhydroxyurethane (PHU) networks having tertiary amine moieties in the beta-position to the carbamate nitrogens (denoted as R 3 N β -N in Fig. 1.A, left) have also been reported. [START_REF] Fortman | Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers[END_REF][START_REF] Chen | Reprocessable polyhydroxyurethane networks exhibiting full property recovery and concurrent associative and dissociative dynamic chemistry via transcarbamoylation and reversible cyclic carbonate aminolysis[END_REF][START_REF] Chen | Recyclable polymer networks containing hydroxyurethane dynamic cross-links: Tuning morphology, cross-link density, and associated properties with chain extenders[END_REF][START_REF] Chen | Reprocessable Polymer Networks Designed with Hydroxyurethane Dynamic Cross-links: Effect of Backbone Structure on Network Morphology, Phase Segregation, and Property Recovery[END_REF][START_REF] Chen | Reprocessable Polyhydroxyurethane Network Composites: Effect of Filler Surface Functionality on Cross-link Density Recovery and Stress Relaxation[END_REF][START_REF] Hu | Biobased Reprocessable Polyhydroxyurethane Networks: Full Recovery of Crosslink Density with Three Concurrent Dynamic Chemistries[END_REF] Given that tertiary amine-based external organocatalysts have been used as an alternative to tin catalysts in the design and depolymerisation process of PUs, [START_REF] Sardon | Synthesis of Polyurethanes Using Organocatalysis: A Perspective[END_REF][START_REF] Jehanno | Organocatalysis for depolymerisation[END_REF] we hypothesized that the embedded amines might have an internal catalytic effect on the transcarbamoylation reaction. Since the spatial proximity of the amine would be a key factor as internal catalysis is governed by bond distance rather than at which side of the urethane linkage it is attached to, having tertiary amine moieties in the beta-position to the carbamate oxygen (R 3 N β -O, see Fig. 1.A, right) instead of the carbamate nitrogen R 3 N β -N should still result in transcarbamoylation exchange reactions.

To investigate our hypothesis, a series of small molecule experiments were performed to monitor both associative and dissociative bond exchanges of different carbamates, with and without the presence of a tertiary amine in the beta-position, at elevated temperatures. Further, we synthesised a new internally catalysed non-isocyanate polyurethane (IC-NIPU, Fig. 1.B) using Nsubstituted 8-membered cyclic carbonates, which in the presence of amines give rise to polyhydroxyurethanes wherein the tertiary amine moieties are not positioned in the beta-position relative to the carbamate nitrogen but are incorporated on the opposite, carbamate oxygen side (R 3 N β -O). The thermal and mechanical properties of the resulting networks were evaluated in terms of their reprocessability, which resulted in the identification of urea bond formation that competes with the dynamic transcarbamoylation reactions. β α β α Fig. 1. A) Dynamic polyhydroxyurethane linkage based on tertiary amine moieties in beta position to the carbamate nitrogen (R 3 N β -N), as reported by Dichtel and co-workers (left), [START_REF] Fortman | Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers[END_REF] and where the tertiary amine position is displaced towards the carbamate oxygen (R 3 N β -O) as investigated in this work. B) Synthesis of internally catalysed non-isocyanate polyurethane (IC-NIPU) covalent adaptable network.

Experimental Section

Reagents and Solvents

Bis(pentafluorophenyl)carbonate 97 % (Fluorochem CAS: 59483-84-0), butyl isocyanate 98 % (Sigma-Aldrich, CAS: 111-36-4), chloroform ≥99.8 % (Sigma-Aldrich, CAS: 67-66-3), chloroform-D 3 99.80 % D (Eurisotop, CAS:865-49-6), 2-cyclohexylethanol 99 % (Alfa Aesar, CAS: 4442-79-9), dibutyltin dilaurate >95.0 % (TCI Europe, CAS: 77-58-7), dichloromethane ≥99.8 % (Sigma-Aldrich, CAS: 75-09-2), 2-(diethylamino)-ethanol >99 % (Alfa Aesar, CAS: 100-37-8), diglycerol (mixture of isomers) >80.0 % (TCI Europe, CAS: 627-82-7), dimethyl carbonate 99 % (Sigma-Aldrich, CAS: 616-38-6), 2-(dimethylamino)-ethanol >99 % (Alfa Aesar, CAS: 108-01-0), dimethylsufoxide-d 6 99.80 % D (Eurisotop, CAS:2206-27-1), diphenyl ether 99 % (Avocado Research Chemicals Ltd, CAS: 101-84-8), hexyl isocyanate >98.0 % (TCI Europe, CAS: 2525-62-4), JEFFAMINE® T-403 polyetheramine (Huntsman), methanol >99 % (Chem-Lab CAS: 67-56-1), 3-methyl-1-butanol >99.0 % (TCI Europe, CAS: 123-51-3), 2-phen lethanol ≥99 % ( one well l ka S --8 roton-S onge (Sigmal rich S -8-), sodium methoxide 25 % wt in methanol (Sigma-Aldrich, CAS: 124-41-4), tetrah rof ran ≥99.8 % ( ischer Scientific S 9-99-9 N N N′ N′-tetrakis(2hydroxyethyl)ethylenediamine (Sigma-Aldrich, CAS: 140-07-8) and trib t lamine ≥99. % (Sigma-Aldrich, CAS: 102-82-9). All reagents and solvents were used as received from their supplier. 13 C Nuclear Magnetic Resonance (NMR) spectroscopy. NMR spectra were recorded using a Bruker Avance 300 (300 MHz) or Bruker Ascend 400 (400 MHz). The NMR chemical shifts were reported as δ in parts per million (ppm) relative to the traces of non-deuterated solvent (δ = 7.26 for CDCl 3 an δ = 2.50 for DMSO). Data were reported as follows: chemical shift, multiplicity (s = singlet, d = doublet, t = triplet, q '= quadruplet, p = quintuplet, h = hextuplet, hept = heptuplet, m = multiplet, br = broad), coupling constants (J) given in Hertz (Hz), and integration values. Standard applied parameters (number of scans, pulse delay, acquisition time, tilt angle, pulse time): 1 H spectra ( M z ns = D = . s Q = . s ° = . μs; M z ns = D = . s Q = . s ° = . μs); 13 C spectra (300 MHz: ns = 3072, D1 = 2.0 s, AQ = .8 s ° = . μs; M z ns = D = . s Q = . s ° = . μs).

Instrumentation and Characterisation Methods

H and

Attenuated Total Reflectance -Fourier-Transform Infrared Spectroscopy (ATR-FTIR).

ATR-FTIR measurements were performed on a PerkinElmer Spectrum 1000 FTIR spectrometer equipped with Pike ATR module. Spectra were recorded between 4000-600 cm -1 with a spectrum resolution of 4 cm -1 . All spectra were averaged over 10 scans. Data were reported as follows: wavenumber (cm -1 ), for defined shapes (br = broad, sh = sharp) and intensity (s = strong, m = medium, w = weak).

Differential Scanning Calorimetry (DSC). DSC measurements were performed on a Mettler

Toledo 1/700 calorimeter equipped with a Full Range Sensor (FRS5) sensor containing 56 thermocouples, liquid nitrogen cooling system enabling a temperature range of -150 °C to 700 °C and automatic sample robot. All measurements were carried out under a nitrogen atmosphere in perforated stan ar μL aluminium crucibles containing 5 -15 mg of the polymeric material. A consecutive heating-cooling-heating run was performed in a temperature range of -100 °C to 150 °C at a heating/cooling rate of 10 °C min -1. The obtained thermograms were analysed with the STARe Excellence Software and the reported glass transition temperature (T g ) was determined as the midpoint from the second heating run, which is defined as the intercept of the DSC curves and the bisector of the angle formed by the extrapolation of the baselines before and after the transition.

Gas Chromatography-Mass Spectrometry (GC/MS

). GC/MS measurements were carried out on an Agilent 6890 GC connected to an Agilent 5973 mass spectrometer, equipped with electrospray ionisation (EI) source and a 2 min splitless injection system. The equipped column was a non-polar Agilent DB-5ms composed of 5% phenyl-dimethyloxane, operated under a 1.3 mL/min constant flow of Helium as a carrier gas at an inlet temperature of 250 °C heated to 320 °C in a heating ramp of 17.5 °C/min after 3 initial min at 70 °C.

High-Resolution Mass Spectrometry (HRMS).

High-resolution mass spectrometry (HRMS) has been measured (by direct injection) in a Waters SYNAPTTM G2 HDMSTM, using a Q-TOF detector and (positive) electrospray ionisation ESI+. The experiments were performed in parallel plate geometry using 8 mm sample disks, using a normal force of 1 N, an oscillating frequency of 1 Hz, a strain of 0.8 % and the applied stress was always comprised in the linear viscoelastic region at the measured temperatures. For time sweep experiments, the storage modulus (G') was followed over time at a constant temperature. For stress relaxation experiments, the relaxation modulus (G'(t)) was followed over time at a constant temperature. The series of stress relaxation experiments at different temperatures were performed successively on the same sample.

Thermal Gravimetric Analysis (TGA). Thermal gravimetric measurements were performed on a Mettler Toledo TGA/SDTA851e equipped with a Julabo FP50 circulator with HP control unit which is calibrated using three indium pills and approximately 6 mg aluminium. Samples were placed in ceramic pans and heated from 25 °C up to 500 °C at 10 °C min -1 under a nitrogen atmosphere. The obtained thermograms were analysed with the STARe Excellence Software and the onset temperature of degradation was defined at 2 % and 5 % weight loss.

Uniaxial tensile tests.

Uniaxial tensile testing was performed on a Tinius-Olsen H10KT tensile tester equipped with a 100 N load cell using ASTM standard type IV dog bones (ISO 527-2-2B). The dog bone-shaped samples had an effective gauge length of 12 mm, a width of 2 mm, and a thickness of ±2 mm, and they were cut using a Ray-Ran hand operated cutting press. The tensile measurements were performed using a preload of 0.05 N and a pulling speed of 10 mm min -1 until sample failure. The stress σ was recorded as a function of strain ε. Reported values: elongation (%), stress at break (Pa), and Young's modulus (Pa) are the average and standard deviations of at least seven samples. Exhibited tensile curves were selected to be representative of the average values.

Experimental procedures

Model Compound Studies. Three model study tests were performed to assess the exchange reactions in the presence of an excess of alcohol groups (Fig. 2.A-C). The experiments were performed by mixing the chosen model compounds (0.90 mmol, 1 eq.) with 2-phenylethanol (4.50 mmol, 5 eq.) and stirring for 72 h at 130 °C in a sealed vial. Then, all reaction mixtures were analysed through 1 H-NMR and GC-MS and compared with the initial batches. Two additional model study tests were carried out to evaluate the carbamate exchange reactions in the absence of alcohols (Fig. 3.A,D). The experiments were performed under the same conditions used in the previous tests with a mixture of two of the selected model compounds (2.30 mmol, 1 eq.). For subsequential analyses, the mixtures were subjected to GC-MS and FT-IR.

Network Processing and Reprocessability Tests. Samples were processed by compression moulding at 130 °C for 30 min under 1.5 -2 Mt in a steel mould. In order to release the applied load gradually during the decompression step, the heating system was disconnected at a slow overnight decompression rate and cooling effect in a steel rectangular mould (A: 70 mm x 40 mm x 2 mm; B: 30 mm x 15 mm x 2 mm). Reprocessability tests, performed complementarily to the uniaxial tensile measurements, consisted in cutting and compressing small fragments from broken dog bones and the excess of material from the previous processing cycle. The resulting samples were then folded in half and pressed again to give a fully healed material.

Network Solubility Tests. Solubility tests were carried out using two pairs of discs of 6 mm diameter and 2 mm thickness, cut from networks that were processed one time and reprocessed five times. The samples were immersed in 5 mL of diphenyl ether, [START_REF] Fortman | Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers[END_REF] placed in sealed vials kept at room temperature and 100 °C for 24 h respectively (Fig. S9). The discs were then dried under vacuum overnight at 65 °C. The swelling ratios and soluble fractions were calculated using equations ( 1) and (2), respectively, where m 0 , m s , m d are the initial, swollen and dry masses of the respective samples.

(1) [START_REF] Flory | Network Structure and the Elastic Properties of Vulcanized Rubber[END_REF] Additionally, solubility experiments were performed at 25 °C and 130 °C using diethylethanolamine and 2-phenylethanol to evaluate the effect of different hydroxylated solvents and temperatures. This test was conceived to evaluate if the material would undergo exchange reactions without any applied mechanical stress. (Fig. S10).

Results and Discussion

Model Studies

Both dissociative and associative exchange mechanisms have been previously reported to take place in polyhydroxyurethane-based dynamic materials. [START_REF] Fortman | Structural effects on the reprocessability and stress relaxation of crosslinked polyhydroxyurethanes: ARTICLE[END_REF] Associative transcarbamoylation reactions mainly compete with reverse urethane dissociation and reverse cyclic carbonate formation. In order to investigate whether the tertiary amine groups also have a proximity-induced internal catalytic effect [START_REF] Van Lijsebetten | Internal catalysis for dynamic covalent chemistry applications and polymer science[END_REF] when introduced at the oxygen side of the carbamate (but keeping the bond distance to the carbonyl unit unaltered), nine low molecular weight compounds [MC1 to MC9, (Table S1)] with an R 3 N β -O motif were synthesized and subjected to transcarbamoylation model studies (Figs. 2,3). In a first transcarbamoylation test reaction (reaction A, Fig. 2.A), model carbamate MC1 was heated at 130 °C in the presence of 5 equivalents 2-phenylethanol to assess the exchange dynamics in the absence of a tertiary amine catalyst. Analysis of the obtained reaction mixture through gas chromatography -mass spectrometry (GC-MS) (Fig. 2.C) indicated that no exchange product MC2 formed after 72 hours at 130 °C. Repeating the model reaction in the presence of one equivalent of tributylamine, acting as an external catalyst, also yielded no exchange product being detected through GC-MS and 1 H-NMR (Fig. 2.A and Fig. S5). In contrast, reaction B with model compound MC3 (containing the R 3 N β -O), (Fig. 2.B), did yield the expected exchange product since MC2 could be detected via GC-MS analysis (Fig. 2.D). The exchange conversion of this last reaction was calculated using 1 H-NMR by comparing the integrals of the signals of the methylenes in alfaposition of the oxygen of the carbamate bonds of MC2 with their counterpart in MC3. This method gave a conversion of about 58%. However, this could be only interpreted as an approximation due to the presence of small overlapping impurities (Fig. S6). A second approximation of this value was obtained based on the decrease of the integration of the relative area of the starting compounds observed by GC (Fig. 2D), which gave a similar value of 60 %. A second range of model experiments was conducted utilizing only a mixture of two different carbamates to examine whether carbamate exchange can proceed also in the absence of alcohols (reaction C (Fig. 3.A). Heating an equimolar mixture of the amine-free carbamates MC1 and MC4, exchange products peaks were observed by GC-MS (Fig. 3.B) (MC5 and MC6), despite the absence of tertiary amines or hydroxyl groups in the system. Nonetheless, in the results observed for reaction D (Fig. 3.D), in which an equimolar mixture of R 3 N β -O carbamates was used, the CG chromatogram (Fig. 3.E) showed more relatively intense exchange product peaks (MC8 and MC9) when compared to the signals of the remaining MC3 and MC7 and even when compared to the alcohol and isocyanate signals formed during the GC-MS analyses. It should be noted that reactions C and D could only be analysed qualitatively since their conversions could not be followed through 1 H-NMR due to the signal similarity between the original and the exchange products. Because of this, the obtention of the reaction yields though GC relative peak area integrations could not be cross checked and verified.

It should be noted that the presence of tertiary amines also resulted in additional side reactions. This was evidenced by the higher amount of undetermined side products that could be detected in the gas chromatogram of the crude mixture of reaction D (Fig. 3.D) compared to reaction C (Fig. 3.A). Furthermore, FT-IR analyses confirmed the formation of urea products with their characteristic C=O stretching signal at 1650 cm -1 in the outcome of reaction D (Fig. 3.F). Presence of ureas was further confirmed by High Resolution Mass Spectrometry (HRMS) analyses of the obtained product mixture from reaction D, in which of N,N'-dibutylurea and N,N'-dihexylurea were detected (Fig. S7). Considering the absence of the unequivocal isocyanate stretching signal usually found between 2270 -2240 cm -1 in all FT-IR analyses performed (Figs. [START_REF] Toozandehjani | Conventional and Advanced Composites in Aerospace Industry: Technologies Revisited[END_REF].C,F), it could not be concluded if the carbamate exchanges occurred as a result of a urethane dissociation mechanism with the formation of isocyanates and alcohols. Some authors have suggested that PHU-based networks are able to dissociate to cyclic carbonates and amine groups, under specific conditions. [START_REF] Fortman | Structural effects on the reprocessability and stress relaxation of crosslinked polyhydroxyurethanes: ARTICLE[END_REF] Moreover, in the presence of strong bases such as 1,5,7-triazabicyclo(4.4.0)dec-5-ene (TBD), it has been shown that the newly formed amines are able to react with carbamate groups to form linear ureas. [START_REF] Bossion | Unexpected Synthesis of Segmented Poly(hydroxyurea-urethane)s from Dicyclic Carbonates and Diamines by Organocatalysis[END_REF] Then, thermally-induced urea exchange reactions would start to take place between ureas and free amines. [START_REF] Erice | Reprocessable and recyclable crosslinked poly(urea-urethane)s based on dynamic amine/urea exchange[END_REF] Yet, the reaction between tertiary amine-free carbamates indicates the possibility of an exchange mechanism where isocyanates are not involved, since the absence of the formation of MC1 in reaction A (Fig. 2.A) and the absence of isocyanates in the FT-IR spectra (Fig. 3.C) lead to the conclusion that no isocyanates got released during model reaction A (with and without one equivalent of tributylamine). Based on these results, we could conclude that there is evidence for an internal basic or nucleophilic catalytic effect of beta tertiary amines on associative/dissociative mechanisms involving carbamate linkages, similar to the ones observed in the presence of strong bases. In (Fig. 4), two possible reaction schemes are proposed on how an internal catalyst could trigger the exchange reaction known for polyhydroxyurethanes [START_REF] Fortman | Structural effects on the reprocessability and stress relaxation of crosslinked polyhydroxyurethanes: ARTICLE[END_REF] as well as the linear urea formation in IC-NIPU networks, i.e. thorugh associative transcarbamoylation (Fig. 4.A) (also applicable to R 3 N β -N carbamates), and urethane dissociation followed by base catalysed linear urea formation (Fig. 4.B) (only applicable to R 3 N β -O carbamates).

Synthesis of R 3 N β -O-based Network

As the beta-amino groups along the carbamate-oxygen side proved to promote exchange product formation, the following step in our investigation was the preparation of a covalently crosslinked material containing the embedded R 3 N β -O groups. Thus, an IC-NIPU was synthesized from the dicyclic 8-membered ring carbonate monomer (BN8C), previously reported by Sardon and co-workers, [START_REF] Yuen | Room temperature synthesis of non-isocyanate polyurethanes (NIPUs) using highly reactive N-substituted 8-membered cyclic carbonates[END_REF] and JEFFAMINE® T-403 as a multifunctional amine crosslinker (Fig. 5). In order to obtain 6.00 g of the BN8C-JAT403-Network (Fig. 5), BN8C (3.00 g, 10.32 mmol, 3.00 eq.) and JEFFAMINE® T-403 Polyetheramine (3.12 mL, 6.84 mmol, 2.00 eq.) were mixed in a 60 mL polypropylene cup. To disperse the solid BN8C into the viscous amine crosslinker to obtain a homogeneous dispersion a DAC 150.1 FVZ speed mixer was used at 2500 rpm for 2 min. Then, the mixed sample was kept 24 h at room temperature. The curing process was performed without any solvent or external catalyst by keeping the neat samples at 100 °C for 3 h. The result was an opaque white soft elastomer polyhydroxyurethane (Fig. 8. A1), which turned to a transparent yellow and more amber in colour material upon reprocessing by hot pressing (Fig. 8A). The material was subsequently characterized through Fourier-Transform Infrared Spectroscopy (FT-IR), solubility tests, Thermogravimetric Analysis (TGA), Differential Scanning Calorimetry (DSC) and uniaxial tensile tests in order to determine the structure and thermomechanical properties of the targeted network.

The obtained FT-IR spectrum of the as synthesized IC-NIPU network showed the characteristic signals of the polyether prepolymer segments and was shown to contain polyhydroxyurethanes, identified by the broad O-H stretches of the hydroxyl groups around 3400 cm -1 and H-bonded carbamate C=O stretching bands at 1726 cm -1 (Fig. 8.B). Calculated gel fractions of a one-time processed network obtained through swelling tests in diphenyl ether [START_REF] Fortman | Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers[END_REF] at 25 °C and 100 °C were 99.6 % and 89.4 %, respectively (Table S4). When using an excess of 2-diethylethanolamine and 2phenylethanol as reactive solvents, full solubility of the crosslinked materials was obtained at 130 °C, proving that they undergo dynamic exchange reactions without any applied mechanical stress at elevated temperatures (Fig. S10). TGA analyses showed the degradation temperatures corresponding to a 2 % and 5 % weight loss to be 148 °C and 175 °C, respectively (Fig. S12). Additionally, glass transition temperatures (T g ) derived from the second heating run of DSC experiments on samples processed from one to four times were detected within the temperature interval of -20 °C to -16 °C (Fig. S13), as can be expected for a soft rubbery material with slight crosslink density fluctuations originated from the contribution of a dissociative bond exchange process. One-time processed sam les ha an average Yo ng's mo l s of . ± . M a a total elongation of ± % an ultimate stress of 0.40 ± 0.05 MPa in uniaxial tensile tests (Table 1). Overall, the obtained FT-IR, TGA, solubility and reprocessing results are within those expected for a crosslinked dynamic elastomeric material.

Fig. 5. Reaction scheme for the synthesis of IC-NIPU materials.

Rheological analysis

Following the insights into the internal catalytic effect of the tertiary amine on the small molecule transcarbamoylation reaction, a material level study was conducted to evaluate the dynamic bond exchange properties within the synthesized R 3 N β -O-based IC-NIPU network. Viscoelastic properties can be studied through stress-relaxation experiments upon applying a constant deformation at a certain temperature. The relaxation times (τ*) were calculated in a defined temperature interval when (G/G 0 ) equalled to 1/e, where (G) is the relaxation modulus, (G 0 ) the relaxation modulus at t = 0. [START_REF] Montarnal | Silica-Like Malleable Materials from Permanent Organic Networks[END_REF][START_REF] Capelot | Metal-Catalyzed Transesterification for Healing and Assembling of Thermosets[END_REF] The obtained results from the measurements performed by subjecting the material to 0.8 % deformation from high (i. The studied network seemed to fit a single Maxwell decay model, as the system displayed a linear correlation of relaxation times within the described temperature range (Fig. 6.B). This result could indicate a pure associative nature or that the expected dissociative mechanisms still allowed for the material to maintain efficiently crosslinked states at the studied temperature interval. Additionally, the observed activation energy (E a = 118 ± 2 kJmol -1 ) had a similar value in comparison to the catalyst-free polyhydroxyurethane-vitrimers reported by Hillmyer and co-workers [START_REF] Fortman | Structural effects on the reprocessability and stress relaxation of crosslinked polyhydroxyurethanes: ARTICLE[END_REF][START_REF] Fortman | Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers[END_REF], which included a R 3 N β -N amines at the same distance yet opposite side to the carbonyl groups as the network studied herein. Both results seem to indicate that the internal catalytic effect of tertiary amines on the transcarbamoylation rather relies on the proximity between the tertiary amino group and the carbonyl of the urethane group, rather than on the position in relation to the carbamate functionality.

Although the here synthesized IC-NIPU network displays stress relaxation properties that are consistent to structurally related CAN materials, the relaxation modulus at t = 0 (G 0 ) showed a significant drop after the first stress relaxation measurement at 150 °C and its value increased as the temperature was lowered before each successive measurement (Fig. 7.A). This observation hinted toward a dissociative contribution that was not detected during the initial measurement, most likely because the material was only briefly exposed to high temperatures. To further investigate this phenomenon, the storage modulus values were obtained via time sweep experiments at different temperatures starting from 150 °C down to 100 °C (Fig. 7.B) following an initial annealing step at 150 °C for 10 minutes to allow for the system to equilibrate. According to lor 's molec lar theor of elasticity, [START_REF] Flory | Network Structure and the Elastic Properties of Vulcanized Rubber[END_REF][START_REF] Flory | Molecular Theory of Rubber Elasticity[END_REF] a partial reduction of the crosslink density in a polymeric network is described to result in a reduction of the storage modulus of the material. This can be easily understood through a reformulation of lor 's eq ation ma e b Kloxin and Bowman, [START_REF] Kloxin | Covalent adaptable networks: smart, reconfigurable and responsive network systems[END_REF] which describes a linear effect of the crosslink density on the elastic modulus of a material through equation ( 3) where only the storage modulus (E), crosslink density (ρ x ), temperature (T) and the universal gas constant (R) have to be considered. As expected, the storage moduli obtained from the time sweep experiments (Fig. 7.B) thus indicated that the network was less densely crosslinked during the first stress relaxation measurement at 150 °C. As the temperature was lowered for every consecutive measurement, the system experienced progressive crosslink density recovery with increasing storage modulus as a result of the re-establishment of the dissociative exchange equilibrium, favouring an increasing extent of bond connectivity until the temperature was low enough to suppress the dissociative exchange.

(3) Fig. 7. A) Relaxation modulus values at t = 0 at temperatures ranging from 150 °C to 80 °C. B) Average storage mo l s val es at the tem erat res at which the material's relaxation times could be determined (Fig. 6.A).

Network Recyclability

Finally, the mechanical properties of reprocessed IC-NIPU networks were studied to evaluate the recyclability potential of the material by compression moulding at 130 °C for 30 min under 1.5 -2 Mt in a steel mould. In order to release the applied load gradually during the decompression step, the hot press was switched off at a slow overnight decompression and cooling rate to allow for the dissociative bond exchange mechanism to regenerate the lost crosslinking density. Next, dog bones cut from a sample processed once and five consecutive times at 130 °C were subjected to uniaxial tensile measurements (Fig. 8.C). The stress (σ) was recorded as a function of strain (ε) and the obtained elongation (%), ultimate stress, and Young's modulus are given as the average of seven samples (Table 1). The measurements revealed a decrease in the Young's modulus, most likely attributed to degradation of the samples, which also turned the material more amber in colour after each cycle (Fig. 8.A). The occurrence of side reactions was confirmed by ATR-FTIR of the reprocessed network, with urea C=O stretching formation detected at 1650 cm -1 that became more intense after each reprocessing cycle (Fig. 8.B). These side reactions were able to turn the IC-NIPU into a poly(hydroxyurea-urethane) network, which has been shown in previous research to lead to a significant enhancement in the phase separation behaviour of NIPUs. [START_REF] Erice | Reprocessable and recyclable crosslinked poly(urea-urethane)s based on dynamic amine/urea exchange[END_REF] Additionally, in order to further establish the effect of temperature on the urea formation, an additional recycling test was performed at 160 °C to test the effect of higher temperatures on degradation and faster urea formation upon reprocessing. For this, a freshly synthesized network was recycled four times by compression moulding at 160 °C using the same conditions as detailed above (i.e. 30 minutes) with a significantly more rapid degradation and urea formation being detected, since the material turned brown already after the first processing. During the following cycles, coloration became more pronounced and the network showed a progressive loss of its dimensional stability, resulting in a viscous paste after the 4 th reprocessing (Fig. S14.1). ATR-FTIR analyses taken after each cycle confirmed the faster urea signal intensity increase (Fig. S14.2). Nonetheless, the data obtained from the tensile tests confirmed that the synthesized material can be successfully reprocessed at 130 °C while partially retaining its mechanical properties and keeping its thermal behaviour, with only slight changes etecte in the network's T g that remained within the interval comprised between -20 °C and -16 °C (Fig. S13).

Rheology.

  Rheology experiments were carried out with a Modular Compact Rheometer (MCR) 302 from Anton Paar containing an air-bearing-supported synchronous Electrically Commutated (EC) motor, integrated normal force sensor, TruRate TM sample adaptive controller, TruStrain TM real-time position control and a Convection Temperature Device 180 (CTD 180) heating unit. Measurements were designed and analysed by making use of the RheoCompass TM software.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Overview of transcarbamoylation model studies. A) Exchange reaction A of tertiary amine-free MC1 with an excess of 2-phenylethanol (5 eq.) both in the absence and presence of nBu 3 N (1 eq.) as an external catalyst (no exchange product detected). B) Internally catalysed exchange reaction of MC3 with 2-phenylethanol (5 eq.) resulting in the formation of exchange product MC2. C) GC chromatogram of the crude resulting from reaction A without (after 72 h, top) and with external catalyst (after 72 h, bottom). D) GC chromatogram of the crude resulting from reaction B before (t = 0 h, top) and after heating (t = 72 h, bottom). *Note that the trace signal detected at 10.26 min does not correspond to the tributylamine signal, but to a small amount of a degradation product barely visible in the chromatogram below.◊ The explanation for the presence of alcohol and isocyanate signals on the GC-MS chromatograms can be found in the SI.

Fig. 4 .

 4 Fig. 4.Proposed reaction mechanisms of the basic internal catalysis for the A) associative transcarbamoylation and B) base catalysed linear urea formation.[START_REF] Bossion | Unexpected Synthesis of Segmented Poly(hydroxyurea-urethane)s from Dicyclic Carbonates and Diamines by Organocatalysis[END_REF]

  e. 150 °C) to low temperatures confirmed the dynamic behaviour of the R 3 N β -O IC-NIPU network with a decrease of the relaxation modulus G(t) over time. Relaxation times (τ*) were determined as the measurement time at which G/G 0 equals 1/e throughout a temperature interval of 150 -100 °C (Fig. 6.A).

Fig. 6 .

 6 Fig. 6. A) IC-NIPU network stress-relaxation curves obtained at different temperatures ranging from 150 °C down to 80 °C. B) Arrhenius plot of R 3 N β -O IC-NIPU relaxation times between 100 and 150 °C with a linear correlation.

Fig. 8 .

 8 Fig. 8. A) Pictures of the IC-NIPU samples (1) As synthesized, (2) shredded and prepared for compressionmoulding, (3) after one-time processing (130 °C for 30 min under 1.5 -2 Mt), (4) after (top to bottom) one, three and five-times (re)processing. B) ATR-FTIR spectra of as synthesized (A.S., black), one (red), three (blue) and five (green) times (re)processed IC-NIPU network at 130°C. C) Representative uniaxial tensile stress measurements of IC-NIPU samples after a 1 st (red) and 5 th (green) (re)processing step.

Table 1 .

 1 Ultimate stress, elongation an Yo ng's mo l s erive from uniaxial tensile tests performed on the (re)processed IC-NIPU samples.

Acknowledgements

This roject has receive f n ing from the E ro ean Union's orizon research an innovation rogramme n er the Marie Skło owska-Curie Grant agreement No 860911. The authors thank Bernhard De Meyer and Jan Goeman for technical support and Dr. Yann Spiesschaert and Filip van Lijsebetten for their fruitful discussions.

Conclusions

In this work, we demonstrated the importance of internal catalysis in the dynamic behaviour of non-isocyanate polyurethanes based on N-substituted 8-membered cyclic carbonates and macromolecular amines. The exchange reactions between carbamates were qualitatively proven to be more effective on internally catalysed samples, although urea formation was also detected. Due to the formation of these urea groups, the IC-NIPU material experienced a crosslink density decrease upon reprocessing as shown by stress relaxation experiments. [START_REF] Fortman | Structural effects on the reprocessability and stress relaxation of crosslinked polyhydroxyurethanes: ARTICLE[END_REF] Nonetheless, the materials maintained a sufficiently crosslinked state during the measurements to fit a single Maxwell decay Arrhenian model, likely attributed to the contribution of an associative transcarbamoylation exchange mechanism. In spite of the similarity of the observed activation energy of the herein synthesized R 3 N β -O-based IC-NIPU network with the system reported by Hillmyer and coworkers [START_REF] Fortman | Mechanically Activated, Catalyst-Free Polyhydroxyurethane Vitrimers[END_REF], the presence of urea groups indicates a more complicated dynamic exchange pathway.

While the internal catalytic effect of the tertiary amine within the system seems to rely only on the proximity between the amino group and the carbonyl moieties, rather than on the location of the amino group, the presence of the R 3 N β -O functionality proved to catalyse side reactions that involve urea formation. In general, this study emphasized the role and helped for the understanding of internal catalysis in the research area of CANs. Particularly in polyurethane-based systems, the ability to control urea formation without significantly affecting the crosslinking density stands as an appealing feature to be further investigated to enhance the potential of these internally catalysed non-isocyanate CANs [START_REF] Erice | Reprocessable and recyclable crosslinked poly(urea-urethane)s based on dynamic amine/urea exchange[END_REF].

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Disclaimer

This article reflects only the authors' view. The European Union is not liable for any use that may be made of the information contained herein.

Appendix A. Supplementary material

Supplementary data to this article can be found online at (to be provided)

The raw data required to reproduce these findings are available upon request to the corresponding author. The processed data required to reproduce these findings are available upon request to the corresponding author.