domain: spi phys

text:
Matteo Gelain
email: matteo.gelain@safrangroup.com

Alexandre Couilleaux
email: alexandre.couilleaux@safrangroup.com

Marc Errera
email: marc.errera@onera.fr

Ronan Vicquelin
email: ronan.vicquelin@centralesupelec.fr

Olivier Gicquel
email: olivier.gicquel@centralesupelec.fr

Conjugate heat transfer analysis of a surface air-cooled oil cooler (SACOC) installed in a

teaching and research institutions in France or abroad, or from public or private research centers.

Surface air-cooled oil coolers (SACOC) are one of the reference technologies adopted in modern turbofan engines to meet the lubricant-cooling requirements. Installed in the by-pass duct, the SACOC are usually composed of a series of staggered fins dissipating the heat load of the engine oil through forced convection with the by-pass flow. Due to the pressure drop generated by the SACOC, which reduces the propulsive thrust of the engine, the performances of the heat exchanger need to be carefully analyzed. Experimentally, several studies have been carried out in wind tunnel test rigs, yet real engine flow conditions, which have a strong influence on the behavior of the SACOC, are arduous to reproduce. The objective of this work is to identify the most relevant integration effects on a finned surface heat exchanger as well as to understand how these effects should be properly replicated in experiments. To do so, conjugate heat transfer simulations are performed in two different configurations. In the former, the SACOC is installed on the outer fixed structure of a turbofan by-pass duct. In the latter configuration, the heat exchanger is mounted on a simple square wind tunnel and the inlet boundary conditions are extracted from the first simulation with different degrees of representativeness. Results obtained with the two configurations are compared, allowing us to assess the most significant sensitivities of the SACOC to engine integration effects.

I. Nomenclature

II. Introduction

The increasing architectural complexity of modern high by-pass ratio turbofan engines poses severe technological challenges with regard to the lubricant cooling as the demand of heat removal capacity keeps growing [START_REF] Jafari | Thermal management systems for civil aircraft engines: Review, challenges and exploring the future[END_REF]. Several common oil-cooling strategies are based on the engine air stream as a cold heat sink with a heat exchanger (usually referred to as Air/Oil Heat Exchanger, AOHE) directly installed in the by-pass duct. An optimized design of such exchangers is of fundamental importance not only due to the heat exchange requirements but also because the pressure loss generated by the aerodynamic blockage of the AOHE has a direct impact on the propulsive thrust of the engine. While traditional plate or tube types of AOHE, as shown, for instance, in [START_REF] Griffin | Lubrication cooling system for aircraft engine accessory[END_REF] and [START_REF] Schwarz | Air-oil heat exchanger[END_REF], are still commonly used in aircraft engines, in recent years attention has been drawn to Surface Air-Cooled Oil Coolers (SACOC), a type of AOHE which has the potential to introduce lower flow disturbances, thereby reducing the overall impact on the performance of the engine. A typical SACOC (see, for instance, [START_REF] Bajusz | Air-oil heat exchanger placed at the location of the air separator nose of a turbojet, and a turbojet including such an air-oil heat exchanger[END_REF] and [START_REF] Elder | Gas turbine engine heat exchanger with tapered fins[END_REF]) is composed of a series of staggered fins aligned with the direction of the main flow. The heat, transferred to the fins through a complex oil circuit located beneath the heat exchanger, is thus dissipated by the by-pass flow through forced convection.

The aerothermal performance of finned heat exchangers has been extensively studied analytically (Kadle and Sparrow [START_REF] Kadle | Numerical and experimental study of turbulent heat transfer and fluid flow in longitudinal fin arrays[END_REF]), numerically (Jonsson et al. [START_REF] Jonsson | Influence of fin spacing, fin thickness and inlet velocity on the performance of plate fin heat sinks under varying bypass conditions using CFD[END_REF], S. Kim et al. [START_REF] Kim | Investigation of high-speed bypass effect on the performance of the surface air-oil heat exchanger for an aero engine[END_REF], M. Kim et al. [START_REF] Kim | A numerical study on various pin-fin shaped surface air-oil heat exchangers for an aero gas-turbine engine[END_REF]) and experimentally (Sparrow et al. [START_REF] Sparrow | Forced convection heat transfer from a shrouded fin array with and without tip clearance[END_REF], Lau and Mahajan [START_REF] Lau | Effects of tip clearance and fin density on the performance of heat sinks for VLSI packages[END_REF], Wirtz et al. [START_REF] Wirtz | Effect of flow bypass on the performance of longitudinal fin heat sinks[END_REF]), yet only a few works have investigated the behavior of surface heat exchangers while taking into account the specificity of turbofan by-pass flows. Kim et al. [START_REF] Kim | Investigation of high-speed bypass effect on the performance of the surface air-oil heat exchanger for an aero engine[END_REF] performed a numerical and experimental analysis of the influence of a surface AOHE on the engine performance depending on the location and orientation of the fins while Sousa et al. [START_REF] Sousa | Thermal analysis and modeling of surface heat exchangers operating in the transonic regime[END_REF] and Villafane and Paniagua [START_REF] Villafañe | Aerodynamic impact of finned heat exchangers on transonic flows[END_REF] carried out experimental studies of a SACOC integrated on the splitter of a turbofan engine reproducing the transonic and high-swirl conditions of by-pass flows downstream of the fan.

In this work, the numerical conjugate heat transfer (CHT) analysis of a finned SACOC is performed. In CHT, the thermal conduction of a solid domain and the aerodynamics of the flow in which the solid is immersed are solved simultaneously, allowing the examination of the fluid-structure thermal interactions. The aim of the study is to assess the sensitivity of the performance of a SACOC, in terms of heat exchange and pressure drop, to integration effects and to understand how these effects should be reproduced in low-scale experiments. To achieve this goal, two configurations are explored. In the former, the SACOC is directly installed in the by-pass duct (BPD) of a turbofan on the outer fixed structure (OFS) slightly downstream of the outlet guide vane (OGV): the flow making contact with the heat exchanger is thus characterized by a non-equilibrium boundary layer with residual swirl coming from the fan. In the latter, the SACOC is installed in a square wind tunnel, which is the most common testing configuration: boundary conditions at the inlet are extracted from the engine configuration with different degrees of fidelity. Results obtained with the two configurations are compared, the most relevant installation effects are identified and guidelines are given about the level of representativeness required in surface heat exchanger test rigs to reproduce realistic engine conditions.

The work is organized as follows. In section §III, the numerical setup of the CHT computations is described and details about the boundary conditions applied to the fluid-solid interface are given; in section §IV, the surface heat exchanger adopted in this work is introduced and the two studied configurations are presented; finally, results are shown in section §V, followed by the conclusions in §VI.

III. Numerical method A. Conjugate heat transfer approach and algorithm

In the present work, CHT is realized via a partitioned approach and a steady-state solution is sought. The fluid and solid domains are treated by two independent codes which exchange the boundary conditions at a common interface until convergence of temperature and heat flux is attained. For the fluid domain, the compressible Reynolds-averaged Navier-Stokes (RANS) equations are solved by the multi-purpose CFD software package elsA [START_REF] Cambier | elsA-An efficient object-oriented solution to CFD complexity[END_REF] using a time-marching cell-centered finite-volume scheme. For the solid domain, the steady heat equation is solved by the software package Zset [START_REF]Zset : Non-linear material & structure analysis suite[END_REF] with a finite-element method. Finally, the exchange and interpolation of data between the two solvers is performed by the CWIPI coupling library [START_REF]CWIPI: coupling with interpolation parallel interface[END_REF].

In order to obtain a fast steady solution to the aerothermal problem, the CHT is carried out through the basic four-step conventional serial staggered (CSS) algorithm, which is schematically shown in Figure 1. First, the solid solver transfers the boundary conditions computed on the solid side of the interface ∂Ω s to the fluid side ∂Ω f ; after receiving these boundary conditions, the fluid solver's time-marching scheme advances over a pre-determined number of iterations (usually referred to as coupling period); then, the new boundary conditions computed on the fluid interface ∂Ω f are sent to the solid interface ∂Ω s ; finally, the solid code solves the steady heat equation in its domain and the algorithm is repeated from the first step until convergence.

B. Interface treatment

When a partitioned approach is chosen in aerothermal coupling, stability issues can arise at the fluid-solid interface due to the exchange of boundary conditions even in the case where both solvers are intrinsically stable. Consequently, particular attention needs to be paid to the interface treatment in such numerical simulations. The most natural approach is that of imposing the Dirichlet-Neumann boundary conditions at the fluid-solid interface, that is:

qs = -q f Tf = T s , (1)
where T s/ f and q s/ f are respectively the temperature and the normal heat flux at the solid and fluid interface; q is computed as q = -λ∂T/∂ν, where λ is the thermal conductivity and ν is the inward-pointing unit normal; finally, the super-imposed hat symbol (•) denotes the sought value. These boundary conditions guarantee the continuity of temperature and heat flux between the two domains throughout the simulation. Yet, as shown in [START_REF] Giles | Stability analysis of numerical interface conditions in fluid-structure thermal analysis[END_REF] with a normal mode stability analysis and an assumption of one-dimensional diffusive fluid-solid transfer, this approach is not unconditionally stable. A straightforward way of improving stability is to add a relaxation coefficient to the first condition in (1), leading to the following Dirichlet-Robin boundary conditions:

qs + α f Ts = -q f + α f T f Tf = T s . (2)
On the one hand, the relaxation coefficient α f plays a positive role on the stability of the coupling and, as shown in [START_REF] Errera | Comparative study of coupling coefficients in Dirichlet-Robin procedure for fluid-structure aerothermal simulations[END_REF] and [START_REF] Moretti | Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction[END_REF] through a one-dimensional Godunov-Ryabenkii stability analysis, a lower stability bound α min f can be identified, which depends on fluid and solid physical properties as well as on several numerical parameters. On the other hand, α f can negatively affect the convergence rate if its value is too high. As shown in [START_REF] Errera | Optimal solutions of numerical interface conditions in fluid-structure thermal analysis[END_REF], [START_REF] Errera | Comparative study of coupling coefficients in Dirichlet-Robin procedure for fluid-structure aerothermal simulations[END_REF] and [START_REF] Moretti | Stability, convergence and optimization of interface treatments in weak and strong thermal fluid-structure interaction[END_REF] through the same Godunov-Ryabenkii stability analysis, a relaxation coefficient α opt f of compromise between the fast but prone-to-instability coefficients (α f ∈ [α min f , α opt f ]) and the stable but over-relaxing coefficients (α f α opt f ) can be expressed as:

α opt f = K f 1 + 1 + 2D f , (3)
where K f = 2λ f /∆y, with λ f the fluid thermal conductivity and ∆y the size of the fluid cell adjacent to the wall, and D f = a f ∆t c /∆y 2 , with a f the fluid thermal diffusivity and ∆t c the coupling period. Interestingly, α opt f

does not depend on any solid physical or numerical properties; furthermore, it is a locally computed coefficient which can assume different values according to the stability requirements of each fluid wall-adjacent cell.

In the present work Dirichlet-Robin conditions (2) are imposed on the fluid-solid interface and the relaxation coefficient (3) is employed. The convergence criterion is based on the infinite norm of the interface temperature with a tolerance equal to 10 e-03 . Since, as mentioned in section §III.A, the fluid code solves the RANS equations to steady-state with a time-marching scheme, α opt f is computed taking into account the local time step of the fluid near-wall cells.

IV. Problem description

The study aims at analyzing and comparing the aerothermal behavior of a surface air-oil heat exchanger in two fluid environments, that is the by-pass duct of a turbofan engine and the square tunnel of a typical test bench. The section is organized as follows: in section §IV.A the surface air-cooled oil cooler (SACOC) is introduced and details about geometry, physical properties and boundary conditions are given; section §IV.B is dedicated to the fluid domain and the turbofan by-pass duct ( §IV.B.2) and test bench ( §IV.B.3) configurations are described in detail.

A. Solid domain: surface air-cooled oil cooler (SACOC)

Figure 2 shows a schematic representation of the geometry of the surface heat exchanger while its characteristic dimensions, normalized with respect to the fin height H, are specified in Table 1. The SACOC consists of a series of staggered fins oriented along the direction of the main flow (i.e. the X-axis in Figure 1). The cold sink of the heat exchanger, as mentioned above, is the airstream flowing through the fins; the surface in contact with the air is the CHT fluid-solid interface ∂Ω s introduced in section §III.A and its boundary conditions have been extensively described in section §III.B. In practical applications (see [START_REF] Bajusz | Air-oil heat exchanger placed at the location of the air separator nose of a turbojet, and a turbojet including such an air-oil heat exchanger[END_REF], for instance), the hot source of the exchanger consists of a complex system of channels and winglets placed beneath the air-fins in which the oil of the engine circuit flows. In this work, in order to simplify the numerical simulations, the oil circuit is not taken into account and the hot source is simply represented by a temperature-imposed surface (with T p = 400 K) situated at the base of a platform of thickness e (see Figure 2).

The inner part of the domain is discretized with an unstructured mesh of around 300,000 nodes per fin; the material is considered to be an isotropic aluminum alloy of constant thermal conductivity λ s = 150 W/(m K). The steady-state energy equation is thus reduced to:

∇ 2 T = 0 , (4)
which is solved by the solid solver at every coupling instant.

B. Fluid domain

Physical model

For both fluid configurations, the full compressible RANS equations are solved to steady state through an implicit cell-centered second-order time-marching scheme on a structured mesh. The local time step is calculated in every fluid cell with a Courant-Friedrichs-Lewy number CFL = 10 and the fluid-solid coupling takes place every 50 fluid iterations. The fluid is considered to be a calorically perfect gas with heat capacity ratio γ = 1.4 and specific gas constant R = 287 J/(kg K); its dynamic viscosity depends on temperature through the Sutherland law and thermal conductivity is computed with the Prandtl number Pr = 0.72. The contribution of turbulence to the mean flow is taken into account with the two-equation kmodel of Smith [START_REF] Smith | A near wall model for the k-l two equation turbulence model[END_REF] with a constant turbulent Prandtl number Pr t = 0.9.

Turbofan by-pass duct configuration

The aim of the turbofan configuration is to reproduce the real engine conditions at which a surface heat exchanger normally operates as they may have a strong impact on its performance, in terms of both heat exchange and head losses. For this purpose, a series of 50 fins of the SACOC described in section §IV.A is installed on the outer fixed structure (OFS) of a turbofan by-pass duct (BPD). As shown schematically in Figure 3, the SACOC is placed slightly downstream of the outlet guide vane (OGV).

Fig. 3 Schematic cross section of a turbofan by-pass duct with SACOC.

The fluid domain, of which a three-dimensional view is given in Fig. 4, represents an angular sector of the BPD (with azimuthal periodic conditions imposed at the lateral boundaries), wide enough to include one fan/OGV blade. The coordinate system, as shown in Fig. 4, is cylindrical with X representing the engine's axis, R the radial direction (pointing downward so that R = 0 on the OFS) and Θ the azimuth. The domain, discretized with a structured mesh of around 60 million nodes, extends from the inlet, situated downstream of the air-intake (which is consequently not simulated) to the outlet, placed at the throat of the nozzle, and can be conceptually divided into three sub-domains:

• Fan sub-domain: in the axial direction it extends from the inlet to the interface with the OGV sub-domain while the azimuth ranges between Θ ∈ [-10 • , 10 • ]; at the inlet, uniform stagnation pressure and stagnation temperature are imposed, thus neglecting the thickness of the boundary layer originating at the air-intake; the fan blade is completely immersed in the fluid at the center of the domain and an adiabatic no-slip boundary condition is applied at its wall; finally, in order to simulate the rotation of the blade, the steady-state Navier-Stokes equations are solved in a non-inertial frame of reference rotating at the speed of the fan. The fan operates at take-off in standard conditions (i.e., at standard pressure P st d = 101325 Pa and temperature T st d = 288.15 K). • OGV sub-domain: in the axial direction it extends from the rotor-stator interface to the entry of the BPD while Θ ∈ [-4.5 • , 4.5 • ]; the OGV blade is considered to be an adiabatic no-slip wall; since the blade does not rotate, the frame of reference is Galilean and a simple way of ensuring the communication between the rotor and the stator is that of interposing a mixing-plane [START_REF] Dawes | Towards improved throughflow capability: The use of 3D viscous flow solvers in a multistage environment[END_REF][START_REF] Dawes | Multi-blade row Navier-Stokes simulations of fan-bypass configurations[END_REF] which applies a circumferential average of the flow properties. As a consequence, a certain degree of homogenization is introduced into the flow but radial gradients are nevertheless preserved. • BPD sub-domain: extending from the interface with the OGV sub-domain to the outlet and between Θ ∈ [-4.5 • , 4.5 • ], it includes the SACOC, placed on the OFS. Since the mesh requirements of this domain, especially because of the presence of the SACOC fins, are different from those of the OGV domain, the two fluid zones are independently meshed and a non-matching interface, through which flow properties are adequately interpolated, is inserted in between; the SACOC surface is thermally coupled with the solid domain described in §IV.A and the Robin-Dirichlet boundary conditions detailed in §III.B are prescribed; an adiabatic no-slip condition is applied to the remaining surfaces of the by-pass duct; finally, at the outlet, a pressure imposed boundary condition is prescribed (P s = P st d ). Due to the presence of the fan and OGV, several aspects of the functioning of a realistic turbofan can be taken into account, such as: the aerodynamic interaction which may occur between the SACOC and the OGV; the impact of the heat exchange and of the pressure drop generated by the heat exchanger on the engine's thrust; the real conditions of the flow making contact with the SACOC fins, i.e., a non-equilibrium boundary layer with residual swirl coming from the fan. In this work, we will be focusing on the latter.

Test bench configuration

Ideally, the performances of a SACOC would always be assessed in its operating environment, in this case a turbofan; however, such full-scale tests are extremely expensive and time-consuming, especially when a great number of heat exchanger designs need to be tested. Consequently, the most common testing configuration still remains the wind tunnel and it is important to understand to which extent such an experimental environment can be representative of the real engine conditions.

The aim of the second configuration studied in this work is, therefore, to analyze the performance of a SACOC in a typical test rig and to compare the results with those obtained with the engine configuration described in section §IV.B.2. The geometry of the test bench, shown in Figure 5, is that of a square wind tunnel of side H WT so that H/H WT = 0.15, where H is the SACOC fin height (see §IV.A). The domain is discretized with a structured mesh of around 30 million nodes and includes 16 fins of the SACOC described in section §IV.A which are placed on the lower wall of the wind tunnel at the same distance from the inlet as the one separating the SACOC and the OGV/BPD interface described in §IV.B.2. At the side walls, as well as at the upper and lower ones, adiabatic no-slip boundary conditions are applied; the SACOC surface is thermally coupled with the solid domain described in §IV.A and the Dirichlet-Robin boundary conditions detailed in §III.B are prescribed; at the inlet, flow properties computed in the engine configuration §IV.B.2 are extracted from the OGV/BPD interface and applied as boundary conditions. This is done with various levels of complexity, as follows:

• Uniform profiles: at the OGV/BPD interface, the fluid properties (stagnation pressure, stagnation temperature, turbulent kinetic energy and length-scale) are averaged between R ∈ [0, H WT ] and Θ ∈ [-4.5 • , 4.5 • ] and imposed at the inlet of the square wind-tunnel. Both radial and azimuthal gradients thus disappear and the flow reaching the SACOC is homogeneous. • One-dimensional profiles: the fluid properties extracted from the engine configuration are averaged along Θ ∈ [-4.5 • , 4.5 • ] for each value of R. While azimuthal gradients vanish, radial gradients are preserved and the SACOC is reached by an average boundary layer. • Two-dimensional profiles: the boundary conditions are extracted from the OGV/BPD interface and simply interpolated on the wind tunnel's grid without any azimuthal or radial average so that all gradients are preserved. These boundary conditions are meant to reproduce the engine conditions at the highest degree of fidelity. At the outlet, a pressure imposed boundary condition is prescribed and the pressure is calibrated so that the bulk velocity coincides between the two configurations.

V. Results

A. Engine configuration

In this section the results obtained with the engine configuration described in §IV.B.2 are presented. In the following, the cylindrical coordinate system of Fig. 4 is used. Therefore, the radial direction points towards the axis of the engine and R = 0 on the OFS; besides, the azimuth Θ ranges between [-4.5 • , 4. Figure 6 shows the distribution of some flow properties at the OGV/BPD interface. As can be seen, the flow is highly heterogeneous downstream of the OGV, with the distribution of the Mach number (6a) revealing the presence of a strong wake originating at the trailing edge of the OGV blade. Figure 6b, instead, shows the pitch angle α of the velocity vector; it can be seen that two counter-rotating vortexes are generated at the hub and at the tip of the OGV, the latter being particularly significant as a consequence of the ongoing effect of the fan blade slack. Finally, Fig. 6c shows the distribution of the yaw angle β of the velocity vector which, except in proximity of the OGV hub and tip, is essentially negative, showing the presence of residual swirl coming from the fan.

The SACOC fins are therefore reached by a complex, three-dimensional, non-equilibrium flow. The temperature field resulting from the forced convection with this flow, is shown in Fig. 7, with θ = T -T r e f / T p -T r e f , where T p the temperature at the base of the SACOC fins (see §IV.A). The temperature distribution is remarkably heterogeneous, with the fins situated on the pressure side of the OGV being significantly colder than those located on the suction side and, especially, in the wake, indicating that certain fins exchange more heat than others. Figure 8a shows the average Nusselt number, computed as Nu = Φ w H/ λ r e f T p -T r e f , fin per fin from the pressure side to the suction side; Φ w is the wall heat flux averaged over the surface of the fin and H is the fin height. As can be seen, the two central fins, placed behind the trailing edge of the OGV blade, exchange approximately 30% less heat than the best performing fins. It is interesting to compare the distribution of the Nusselt number with that of the drag coefficient C D = T w / 1 2 ρ r e f u 2 r e f , where T w is the wall shear stress averaged over the surface of the fin, which is shown in Fig. 8b. The more heat is exchanged by a fin, the more important is the total viscous drag contributing to the pressure drop. This analogy can be explained by analyzing the distribution of the mass flow rate passing through every channel separating two consecutive fins. In Figure 8c both the entering (by the leading edge) and leaving (by the trailing edge) mass flow rates of every fin are shown, non-dimensionalized with respect to P t r e f and T t r e f , with P t and T t the stagnation pressure and temperature, respectively. The distribution of the entering mass flow rate qualitatively resembles those of the Nusselt number and of the drag coefficient, which is intuitive: the more mass flows between two fins, the higher the average speed of the flow is and both the heat exchange and the head losses increase.

It is also interesting to investigate the distribution of the leaving mass flow rate, which actually resembles that of Nu and C D even more than the entering one. For every fin, it can be observed that there is a loss of mass flow between the leading and trailing edges. This can be explained by the fact that the SACOC, because of both its shape and the heat it provides, constitutes an aerodynamic obstacle that the flow prefers to avoid. Therefore, a significant portion of the mass flow escapes from the upper part of the SACOC without crossing its whole length, thereby reducing the thermal efficiency of the fins. On the pressure side of the OGV (left-hand side of Fig. 8c), around 50% of the mass flow rate is lost through the upper side of the fins, yet this phenomenon is exacerbated on the suction side, where, for some fins, less than 30% of the entering mass flow rate attains the trailing edge. Not surprisingly, these fins have among the lowest average Nusselt number and drag coefficient.

A possible explanation for the stronger loss of mass flow on the suction side might be the interaction between the heat exchanger and the vortex generated at the trailing edge of the OGV blade, the sense of rotation of which might help drive the flow away from the SACOC fins. Visualizations of the flow are given in Figure 9. Figure 9a shows the temperature iso-surface θ = 0.4 colored by the Mach number; Figure 9b shows the velocity streamlines on two azimuthal planes Θ = 2.25 • (i.e., on the pressure side of the OGV) and Θ = -2.25 • (i.e., on the suction side of the OGV). As can be seen, on the pressure side the flow remains well attached to the OFS downstream of the SACOC and, while the velocity streamlines do deviate from the fins causing the aforementioned loss of mass flow, the temperature iso-surface adheres to the wall; on the other hand, the suction side is characterized by a stronger deviation of the velocity streamlines with an important flow separation (approximately as high as the SACOC fins and at least twice as long) taking place downstream of the heat exchanger. global Nusselt number and drag coefficient are simply computed by averaging the values of the fins located on each side; the head losses, instead, are calculated between the OGV/BPD interface and a plane located two fin lengths downstream of the SACOC by computing the average stagnation pressure between Θ ∈ [0 • , 4.5 • ] for the pressure side and Θ ∈ [-4.5 • , 0 • ] for the suction side. As can be seen, despite the drag coefficient being higher for the pressure side fins, the global pressure drop is more important on the suction side. Indeed, the dissipation caused by the skin friction between the fins is only one of the contributions to the head losses and, in this case, the separation bubble shown in Fig. 9 seems to play a much more important role. Therefore, it is possible to conclude that the pressure side of the SACOC is significantly better performing than the suction side since not only is the global heat exchange approximately 15% higher but the global pressure drop is around 70% lower.

B. Test bench configuration

The objective of this section is to investigate to which extent the performances of a SACOC installed in a turbofan by-pass duct are reproducible in a common test rig configuration like the one introduced in §IV.B.3. In the following, the frame of reference is the one of Fig. 5; therefore, X represents the axial direction, Y the wall-normal direction (with the SACOC installed on the Y = 0 wall) and Z the spanwise direction; as shown in §IV.B.3, 16 fins are installed in the wind tunnel; furthermore, as already mentioned, the boundary conditions imposed at the inlet of the test channel are extracted from the OGV/BPD interface of the engine configuration with different levels of complexity. In the next paragraphs, the results obtained with uniform ( §V.B.1), one-dimensional ( §V.B.2) and two-dimensional ( §V.B.3) boundary conditions are presented.

Uniform boundary conditions

At the inlet, constant values for the stagnation pressure, stagnation temperature and turbulence are imposed; furthermore, the flow is supposed to be completely axial (i.e., oriented along the X direction, see Fig. 5). Such homogeneous inlet flow conditions are typical of test rigs where the flow reaches the test section after crossing a settling chamber without any further manipulation (see, for instance, [START_REF] Lau | Effects of tip clearance and fin density on the performance of heat sinks for VLSI packages[END_REF]). In order for this flow to be somewhat representative, the inlet conditions are extracted from the OGV/BPD interface and averaged between R ∈ [0, H WT ] and Θ ∈ [-4.5 • , 4.5 • ].

Figure 10 shows the comparison between the Mach number profiles at the wind tunnel's inlet (averaged along the spanwise direction Z) and at the OGV/BPD interface (averaged along the azimuth Θ). As can be seen, at the inlet the Mach profile is essentially flat, except for a small inflection near y/H WT = 0 which is due to the deceleration of the flow running into the aerodynamic blockage of the SACOC. In other words, no boundary layer is injected at the inlet and, with respect to the engine profile, the Mach number is significantly overestimated for y < H, where H represents the fin height (see §IV.A). Figure 11 shows the Nusselt number, drag coefficient and entering as well as leaving mass flow rate for each SACOC fin compared to the results presented in §V.A. The same non-dimensionalization used in §V.A is employed here. As could be expected, all the SACOC fins have a similar behavior (except for a small border effect visible on the mass flow rate distribution) as a consequence of the homogeneous injection. As can be seen, the higher Mach number in the lower part of the wind tunnel leads to a strong overestimation of all the performance parameters. The Nusselt number is around 60% higher compared to the average engine SACOC fin while the drag coefficient is more than 100% more elevated. Concerning the mass flow rate, not only is the entering mass flow over-estimated, yet the ejection event described in §V.A is in this case significantly weaker compared to the engine configuration; indeed, around 30% of the mass flow is lost by the upper part of the SACOC compared to more than 50% for the engine fins.

Thanks to these results, it is possible to conclude that uniform boundary conditions, despite being representative of the mean flow at the OGV/BPD interface, do not allow us to predict any performance parameter of interest of the SACOC. There certainly exists a homogeneous flow capable of reproducing, at least on average, the behavior of the complex, anisotropic flow downstream of the OGV, yet the values to be imposed to the stagnation pressure at the inlet cannot be known a priori. In practice, in case where the test rig cannot generate but homogeneous flows, it could be preferable to limit the average of the fluid properties at the OGV/BPD interface to a lower radius, in order for the boundary conditions to be representative of the portion of the flow that the SACOC actually encounters. Figure 12 depicts the Nusselt number obtained while imposing the stagnation pressure averaged over R ∈ [0, 1.5H], where H is the fin height, and Θ ∈ [-4.5

One-dimensional boundary conditions

At the inlet, one-dimensional profiles of stagnation pressure, stagnation temperature and turbulence are imposed; these profiles are obtained through an azimuthal average at the OGV/BPD interface of the engine configuration; in this case, the pitch and yaw angles of the velocity vector are also averaged and imposed as boundary conditions. Therefore, the direction of the velocity vector at the inlet is not fully axial. Similar boundary conditions, in practice, can be obtained through distortion screens of heterogeneous porosity which, thanks to the pressure drop the flow blockage induces, modify the stagnation pressure profile allowing the reproduction a non-uniform flow (see, for instance, [START_REF] Davis | An argument for enhancement of the current inlet distortion ground test practice for aircraft gas turbine engines[END_REF]).

Figure 13 shows the comparison between the Mach number profiles at the inlet and at the OGV/BPD interface (averaged along the azimuth Θ). As illustrated, these boundary conditions allow us to recreate the boundary layer seen by the average engine fin. Figure 14 shows the Nusselt number, drag coefficient and entering as well as leaving mass flow rate for each SACOC fin compared to the results presented in §V.A. All the SACOC fins have a similar behavior (except for some slight differences for the leaving mass flow rate, see Fig. 14d), which, despite the boundary conditions being uniform along the spanwise direction, is not entirely obvious since the entering flow is not axial. The local distribution of the performance parameters of interest is not captured, yet, as can be seen from Fig. 14a, the average Nusselt number is very well predicted with respect to the average engine fin, with an overestimation of around 6%, which is a significant improvement compared to the results obtained with uniform boundary conditions (see §V.B.1). The drag coefficient (see Fig. 14b), on the other hand, is characterised by an over-prediction of around 20%. The overestimation of both the Nusselt number and drag coefficient can be explained by the behavior of the entering and leaving mass flow rate. If the average entering mass flow rate is extremely well predicted (see Fig. 14c), the leaving mass flow is almost 50% higher compared to the average engine fin. Consequently, more flow runs through the length of the SACOC and both the heat exchange and viscous drag are more elevated. These results illustrate the critical role played by the ejection event taking place within the fins and the importance of accurately reproducing it.

The results shown in Fig. 14, as explained at the beginning of the paragraph, are obtained by imposing a one-dimensional profile for all the inlet fluid properties, i.e., the stagnation pressure, stagnation temperature, turbulence and pitch/yaw velocity angles. So as to understand which profiles are actually fundamental to reproduce in a wind tunnel to obtain accurate results, additional simulations are run where a mix of one-dimensional and uniform boundary conditions are imposed at the inlet. Figure 15 shows the results obtained for the average Nusselt number, where the darkest bars represent the case where all the inlet profiles are one-dimensional (and therefore coincide with the results shown in Fig. 14a) and the lightest bars represent the case where all the boundary conditions are uniform (and therefore coincide with the results shown in Fig. 11a). As can be seen, as long as a one-dimensional profile is imposed for the stagnation pressure, the prediction of the heat exchanged by the SACOC fins does not significantly change regardless of whether the other inlet variables are 1D or 0D. Thanks to these results, it is possible to conclude that the complex, anisotropic flow downstream of the OGV described in §V.A can be rather accurately represented by a one-dimensional flow obtained through a circumferential average; the absence of spanwise gradients does not enable to capture the local distribution of the heat exchange observed on the engine fins, yet the behavior of the average SACOC fin is well retrieved. It is also evident how the fluid property that influences the performance parameters the most is the stagnation pressure; indeed, imposing a 1D profile of stagnation pressure at the inlet amounts to injecting a boundary layer; this leads to a good prediction of the mass flow entering the SACOC fins and, therefore, of the global heat exchange; however, the under-prediction of the ejection event taking place within the fins with respect to the engine configuration leads to a slight overestimation. In practice, such boundary conditions are certainly more laborious to recreate compared to a homogeneous flow, yet, as these results show, necessary.

Two-dimensional boundary conditions

The two-dimensional cartography of the stagnation pressure, stagnation temperature, turbulence and direction of the velocity vector is extracted from the OGV/BPD interface of the engine and imposed as boundary conditions at the inlet of the wind-tunnel. These boundary conditions recreate the most faithful representation of the engine flow with the given test bench geometry.

In Figure 16 the main performance parameters of the SACOC are compared to the results obtained in §V.A. As can be seen from Fig. 16c, imposing the exact field of stagnation pressure at the inlet leads to a very good prediction of the entering mass flow rate of every fin. Furthermore, the distribution of the Nusselt number and of the drag coefficient resembles that of the engine configuration, with the fins on the left-hand side (i.e., the pressure side in the engine configuration) exchanging more heat and being characterized by a higher viscous drag than the fins on the right-hand side (i.e., the suction side in the engine configuration); on the other hand, a certain level of overestimation can be observed, particularly accentuated for the drag coefficient on the right-hand side fins. This can be explained once again by the distribution of the leaving mass flow rate, which is significantly higher for every SACOC fin compared to the engine configuration; this indicates that despite the representativeness of the boundary conditions, it is extremely arduous to finely reproduce the ejection event observed in the SACOC of the engine configuration.

So as to further investigate the behavior of the flow in the wind tunnel, visualizations of the θ = 0.4 iso-surface and velocity streamlines on the left-and right-hand side of the wind tunnel are given in Fig. 17. The analogous flow visualizations given in Fig. 9 showed how the suction side in the engine configuration is affected by a strong flow separation which explains the higher overall pressure drop and higher mass flow loss of the suction-side fins. As can be seen, the wind tunnel flow has a completely different behavior since no flow separation is observed on the right-hand side of the channel and the only difference between the two sides is the stronger deflection of the velocity streamlines on the right-hand side (Fig. 17b,bottom). Given the precision with which the inflow conditions are prescribed, the difficulties encountered in reproducing the engine flow reveal the limited representativeness of the wind tunnel configuration. Its small size in both the wall-normal and spanwise directions might, for instance, confine the inlet vortex in a much narrower space and thus lead to a weaker interaction with the SACOC; or its limited length in the streamwise direction, at the end of which a uniform static pressure is imposed, might force a premature homogenization of the flow.

Table 3 summarizes the global performance parameters of the SACOC on the left-and right-hand side of the wind tunnel, computed as was done in §V.A for building Table 2. The values of the Nusselt number and drag coefficient for both the left-and right-hand side are higher compared to the engine configuration; this is partly due to the aforementioned over-prediction of these quantities and partly due to the fact that fewer fins are installed in the wind tunnel with respect to the engine. On the other hand, the relative difference between the two sides is close to the one observed between the pressure and suction sides (see Table 2). The same cannot be said about the head losses which, due to the absence of flow separation on the right-hand side, present a significantly lower difference between the two sides with respect to the engine configuration. Finally, an additional simulation is performed where the flow is considered to be fully oriented along the streamwise direction X while all the other boundary conditions remain identical. The purpose of the simulation is to assess the impact of the wall-normal and spanwise velocity components on the heat exchange. Figure 18 shows the distribution of the Nusselt number distribution compared to the previous results. As can be seen, the differences with respect to the non-axial flow are very small. These results might corroborate the hypothesis that it is the inflow stagnation pressure which plays the most important role, as seen with the one-dimensional boundary conditions in §V.B.2. On the other hand, given the poor resemblance of the flow downstream of the SACOC with respect to the engine flow even in the case where the exact direction of the velocity vector is imposed at the inlet Figs. 9 and 17), the effect of the inflow gyration on the performance of the heat exchanger remains in fact unclear. In conclusion, imposing the exact same flow conditions of the OGV/BPD interface at the inlet leads to a marked improvement in the prediction of all the quantities of interest and allows us to capture certain local effects, such as the asymmetrical distribution of the heat exchange among the different SACOC fins. However other phenomena, such as the strong recirculation zone observed in the engine configuration, have been impossible to reproduce. In practice, these results confirm, on the one hand, the importance of recreating inlet conditions that are representative of the studied flow; on the other hand, they show how the representativeness of a certain configuration is far from being guaranteed by the mere inlet flow conditions and how other limits of the test bench, such as its geometry, have to be taken into consideration.

VI. Conclusion

The conjugate heat transfer analysis of a state-of-the-art surface air-cooled oil cooler (SACOC) of a turbofan aircraft engine is performed in two distinct configurations. The objective is to both identify the main integration effects influencing the performance of the heat exchanger and understand how these effects should be appropriately reproduced in wind tunnel experiments.

The first configuration, set up to meet the first objective, is the by-pass duct of a turbofan engine, where a series of SACOC fins are installed on the OFS just downstream of the OGV. Results show that the flow reaching the heat exchanger is strongly heterogeneous and characterized by residual swirl coming from the fan, two counter-rotating vortexes at the hub and tip of the OGV and an important wake. As a result, the SACOC fins behave differently depending on their position along the OFS, with the pressure-side (resp. suction-side) fins characterized by a higher (resp. lower) heat exchange and viscous drag on their surface. Furthermore, an important flow separation taking place downstream of the SACOC is observed on the suction side which significantly increases the overall pressure drop generated by the heat exchanger. Finally, the fins are affected by an ejection event, more accentuated on the suction side, which leads to an important mass flow loss through the upper part of the SACOC, which reduces the thermal efficiency of the heat exchanger.

The second configuration, relevant to the second objective, is a typical square wind tunnel test rig, where a reduced number of SACOC fins are installed on the lower wall. At the inlet, three different inflow conditions are considered. First, an axial, homogeneous flow representing the surface average of that reaching the SACOC in the engine configuration; very poor predictions are obtained for all quantities of interest since the lack of a representative boundary layer at the inlet leads to the overestimation of both the heat exchange and viscous drag. Second, a one-dimensional flow obtained through a circumferential average of the engine flow; better results are achieved for all quantities even though only the behavior of the average engine SACOC fin is captured due to the lack of spanwise gradients; besides, further investigations show that as long as a one-dimensional profile of stagnation profile is prescribed at the inlet the prediction of the heat exchange and of the viscous drag remains satisfactory regardless of whether the other inflow conditions are homogeneous or not, confirming the criticality of injecting a representative boundary layer. Third, a two-dimensional flow where every fluid property is directly taken from the engine flow; these boundary conditions lead to a considerable improvement of the predictions of all the quantities of interest and some local effects, such as the distribution of the heat exchange among the fins, are captured; on the other hand, certain features of the engine flow, such as the aforementioned mass loss by the upper part of the heat exchanger and the large flow separation taking place downstream of the SACOC on the suction side, are not observed in the wind tunnel, thus revealing the limited representativeness of this configuration.

The study allows us to draw several conclusions. First of all, the interest in analyzing the performances of the SACOC in its operating environment, i.e., the turbofan by-pass duct, has proven to be unquestionably concrete; the effects of the complex flow leaving the OGV on the heat exchanger are strong and need to be taken into consideration in the SACOC design process; in this work, only the effect of the OGV on the SACOC is studied, although it cannot be excluded that investigating the reciprocal, i.e., the effect of the presence of the SACOC on the performance of the OGV, is equally important. Second, it appears from the study that the thermal performance of the heat exchanger is essentially driven, on the one hand, by the mass flow entering at the leading edge and, on the other hand, by the mass flow leaving the SACOC from the upper part without reaching the trailing edge; the study shows that the former is relatively easy to reproduce since it only depends on the inlet stagnation pressure; the latter, on the contrary, seems to depend on features of the flow, such as the flow separation taking place downstream of the SACOC, which are more challenging to recreate. Moreover, the importance in the present case of the inlet flow conditions in wind tunnel experiments has been assessed; as the study showed, satisfactory average results can a priori be obtained by injecting a representative one-dimensional boundary layer; this, in practice, can be done with distortion screens. Finally, the study shows that in the present case the accuracy of lower scale experiments does not entirely rest on the inflow conditions and that the representativeness of the test rig itself needs to be questioned; in other words, increasing the complexity and the fidelity of the inlet flow without increasing those of the test rig does not necessarily guarantee that considerably better results will be obtained.

  vane R = Specific gas constant, J/(kg K) RANS = Reynolds-averaged Navier-Stokes SACOC = Surface air-cooled oil cooler S f in = Separation between SACOC fins T = Temperature, K W = SACOC thickness α f = Coupling coefficient, W/(m 2 K) γ = Heat capacity ratio ∆t c = Coupling period, s ∆y = Size of first mesh cell, m θ = Non-dimensional temperature Θ = Azimuth angle λ = Thermal conductivity, W/(m K) ν = Inward pointing unit normal Ω s/ f = Solid/Fluid domain ∂Ω s/ f = Interface of fluid/solid domain

Fig. 1

 1 Fig. 1 CSS (Conventional serial staggered) algorithm.

Fig. 2

 2 Fig. 2 Schematic representation of two fins of SACOC with dimensions.

Fig. 4

 4 Fig. 4 Three-dimensional view of the turbofan fluid domain.

Fig. 5

 5 Fig. 5 SACOC implemented in square wind tunnel.

  5 • ]; the subscript (•) r e f indicates a fluid property averaged over the surface of the OGV/BPD interface between R ∈ [0, H WT ] and Θ ∈ [-4.5 • , 4.5 • ]; finally, (•) denotes Reynolds average.

Fig. 6

 6 Fig. 6 Characteristics of the flow at the OGV/BPD interface: Mach number (a), pitch (b) and yaw (c) angles of the velocity vector.

Fig. 7

 7 Fig. 7 Non-dimensional temperature field θ on the SACOC fins.

Fig. 8 Fig. 9

 89 Fig. 8 Distribution of average Nusselt number (a), drag coefficient (b) and mass flow rate (c) on the 50 SACOC fins, from the pressure side to the suction side of the OGV. For Fig. (c) the blue and red bars represent the entering and leaving mass flow rates, respectively.

Fig. 10

 10 Fig. 10 Uniform boundary conditions. Comparison of Mach number profiles: --wind-tunnel's inlet with uniform boundary conditions; OGV/BPD interface of the engine configuration.

Fig. 11

 11 Fig. 11 Uniform boundary conditions. Distribution of average Nusselt number (a), drag coefficient (b), entering (c) and leaving (d) mass flow rate on the SACOC fins: results from engine configuration of §V.A, blue bars; average over SACOC fins of the engine configuration, green bars; results from test bench configuration with uniform boundary conditions, red bars.

Fig. 12

 12 Fig. 12 Uniform boundary conditions, average of boundary conditions limited to R ∈ [0, 1.5H]. Distribution of average Nusselt number. See Fig. 11 for a reference to colors.

Fig. 13

 13 Fig. 13 One-dimensional boundary conditions. Comparison of Mach number profiles: --wind-tunnel's inlet with one-dimensional boundary conditions; OGV/BPD interface of the engine configuration.

Fig. 14

 14 Fig. 14 One-dimensional boundary conditions. Distribution of average Nusselt number (a), drag coefficient (b), entering (c) and leaving (d) mass flow rate on the SACOC fins: blue bars, results from engine configuration of §V.A; green bars, average over SACOC fins of the engine configuration; red bars, results from test bench configuration with one-dimensional boundary conditions.

Fig. 15

 15 Fig. 15 Mix of uniform and one-dimensional boundary conditions. Distribution of average Nusselt number. From light to dark gray: 1D profiles for all boundary conditions and non-axial flow; same as previous bars but turbulence 0D; same as previous bars but axial flow; same as previous bars but stagnation temperature 0D; 0D profiles for all boundary conditions and axial flow.

Fig. 16

 16 Fig. 16 boundary conditions. Distribution of average Nusselt number (a), drag coefficient (b), entering (c) and leaving (d) mass flow rate on the SACOC fins: blue bars, results from engine configuration of §V.A; red bars, results from test bench configuration with two-dimensional boundary conditions.

Fig. 17

 17 Fig. 17 Two-dimensional boundary conditions. Temperature iso-surface θ = 0.4 colored by the Mach number (a) and velocity streamlines (b) on the left-hand side (top) and right-hand side (bottom).

Fig. 18

 18 Fig. 18 Two-dimensional boundary conditions. Distribution of average Nusselt number. Blue bars, results from engine configuration of §V.A; red bars, results from test bench configuration with two-dimensional boundary conditions; light blue bars, same as red bars but axial flow.

Table 1 SACOC's dimensions (normalized with respect to the fin height H).

 1

	L base	L p	H	W	S f in	e
	6.67 7.33 1 0.0533 0.133 0.1

Table 2

 2

										Average Nusselt number
	140
	120
	100
	80
	60
	40
	20
	0	2	3	4	5	6	7	8	9	49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
										(a)

summarizes the global performance parameters of the SACOC on both the pressure and suction side. The

Table 2 SACOC's performances in terms of average Nusselt number, drag coefficient and global head losses on the pressure and the suction side of the OGV.

 2

		Pressure side Suction side Comparison
	Nu	140.1	123.12	+13.7%
	C D	0.0022	0.0016	+37.5%
	Head losses	0.7%	2.2%	-68%

  • , 4.5 • ]. Despite the Nusselt number still being not only above the average but also above the best exchanging engine fin, the overestimation is limited to around 20%.

											Average Nusselt number										Drag coefficient
	200
	175											0.004
	150
	125											0.003
	100
												0.002
	75
	50
												0.001
	25
	0	2	3	4	5	6	7	8	9	48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10	0.000	2	3	4	5	6	7	8	9	49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
											(a)										(b)
	0.30										Entering mass flow rate	0.30									Leaving mass flow rate
	0.25											0.25
	0.20											0.20
	0.15											0.15
	0.10											0.10
	0.05											0.05
	0.00	2	3	4	5	6	7	8	9	49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10	0.00	2	3	4	5	6	7	8	9	49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
											(c)

Table 3 SACOC's performances in terms of average Nusselt number, drag coefficient and global head losses on the left-and right-hand side of the wind tunnel.

 3

		Left-hand side Right-hand side Comparison
	Nu	152.32	134.43	+13.3%
	C D	0.0028	0.0021	+38.4%
	Head losses	1.05%	1.2%	-12%

Acknowledgments

We thank J. Bertucchi of Safran Aircraft Engines for the generation of the meshes used in this work, T. Chantrait of Safran Tech for his help in implementing the aerothermal coupling and T. Hainaut of Safran Aircraft Engines for the fruitful discussions which led to the realization of the engine simulation.


MD Milton Packer
email: milton.packer@baylorhealth.edu

MD Stefan D Anker

PhD Javed Butler

MD, MPH Gerasimos Filippatos

Pedro Ferreira

PhD Stuart J Pocock

PhD Peter Carson

MD Inder Anand

MD Wolfram Doehner

MD Markus Haass

MD João Pedro Ferreira

MD Michel Komajda

MD Alan Miller

MD Steen Pehrson

MD John R Teerlink

MD Martina Brueckmann

MD Waheed Jamal

MD Cordula Zeller

Dipl Math

MSc Sven Schnaidt

MD Faiez Zannad

Effect of Empagliflozin on the Clinical Stability of Patients With Heart Failure and a Reduced Ejection Fraction

Keywords:

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

S

odium-glucose cotransporter 2 (SGLT2) inhibitors have been shown to reduce the risk of hospitalizations for heart failure in 8 large-scale trials, including those that focused on type 2 diabetes, heart failure with a reduced ejection fraction, and chronic kidney disease. [START_REF] Fitchett | Heart failure outcomes with empagliflozin in patients with type 2 diabetes at high cardiovascular risk: results of the EMPA-REG OUTCOME® trial[END_REF][START_REF] Rådholm | Canagliflozin and heart failure in type 2 diabetes mellitus: results from the CANVAS program[END_REF][START_REF] Kato | Effect of dapagliflozin on heart failure and mortality in type 2 diabetes mellitus[END_REF][START_REF] Perkovic | Canagliflozin and renal outcomes in type 2 diabetes and nephropathy[END_REF][START_REF] Cannon | Cardiovascular outcomes with ertugliflozin in type 2 diabetes[END_REF][START_REF] Mcmurray | Trial Committees and Investigators. Dapagliflozin in patients with heart failure and reduced ejection fraction[END_REF][START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF][START_REF] Heerspink | Dapagliflozin in patients with chronic kidney disease[END_REF] Although hospitalization for heart failure has been regarded as a reliable surrogate of disease progression in heart failure, [START_REF] Rosano | Clinical trial design, endpoints, and regulatory requirements[END_REF][START_REF] Bello | Influence of previous heart failure hospitalization on cardiovascular events in patients with reduced and preserved ejection fraction[END_REF] efforts to standardize the identification of events by the process of adjudication typically exclude many events that are regarded as clinically meaningful by the treating physician. [START_REF] Hicks | Standardized Data Collection for Cardiovascular Trials Initiative (SCTI). 2017 cardiovascular and stroke endpoint definitions for clinical trials[END_REF][START_REF] Tyl | Comparison of outcome adjudication by investigators and by a central end point committee in heart failure trials: experience of the SHIFT heart failure study[END_REF][START_REF] Carson | Determination of hospitalization type by investigator case report form or adjudication committee in a large heart failure clinical trial (β-Blocker Evaluation of Survival Trial [BEST])[END_REF][START_REF] Cohn | Valsartan Heart Failure Trial Investigators. A randomized trial of the angiotensin-receptor blocker valsartan in chronic heart failure[END_REF] Furthermore, any benefit on hospitalizations for heart failure should not be counterbalanced by an increase in other causes of hospitalizations, leading to little overall benefit when the effect on hospitalizations for any reason are analyzed.

Importantly, hospitalization for heart failure represents only a small fraction of a patient's total life experiences. [START_REF] Cleland | How to assess new treatments for the management of heart failure: composite scoring systems to assess the patients' clinical journey[END_REF][START_REF] Cleland | A comparison of the effects of carvedilol and metoprolol on well-being, morbidity, and mortality (the "patient journey") in patients with heart failure: a report from the Carvedilol Or Metoprolol European Trial (COMET)[END_REF] If the goal of treatment is to maintain clinical stability, an intervention should have a favorable impact on other manifestations of worsening heart failure, particularly those that occur in an outpatient setting. [START_REF] Greene | Outpatient worsening heart failure as a target for therapy: a review[END_REF] These include worsening functional capacity, worsening of symptoms that require intensification of background therapy (especially diuretics), and the need for treatment in an emergent or urgent care setting. These outpatient events carry an adverse prognostic import comparable to that of a heart failure hospitalization. [START_REF] Mallick | The importance of worsening heart failure in ambulatory patients: definition, characteristics, and effects of amino-terminal pro-B-type natriuretic peptide guided therapy[END_REF][START_REF] Okumura | Importance of clinical worsening of heart failure treated in the cutpatient setting: evidence from the Prospective Comparison of ARNI With ACEI to Determine Impact on Global Mortality and Morbidity in Heart Failure trial (PARADIGM-HF)[END_REF][START_REF] Skali | Prognosis and response to therapy of first inpatient and outpatient heart failure event in a heart failure clinical trial: MADIT-CRT[END_REF][START_REF] Packer | Carvedilol Prospective Randomized Cumulative Survival (COPERNICUS) Study Group. Effect of carvedilol on the morbidity of patients with severe chronic heart failure: results of the carvedilol prospective randomized cumulative survival (COPERNICUS) study[END_REF] Several treatments that reduce the risk of hospitalizations for heart failure in patients with heart failure and a reduced ejection fraction also favorably impact outpatient metrics of clinical instability. [START_REF] Packer | Carvedilol Prospective Randomized Cumulative Survival (COPERNICUS) Study Group. Effect of carvedilol on the morbidity of patients with severe chronic heart failure: results of the carvedilol prospective randomized cumulative survival (COPERNICUS) study[END_REF][START_REF] Packer | Angiotensin receptor neprilysin inhibition compared with enalapril on the risk of clinical progression in surviving patients with heart failure[END_REF][START_REF] Docherty | Effect of Dapagliflozin on Outpatient Worsening of Patients With Heart Failure and Reduced Ejection Fraction: a prespecified analysis of DAPA-HF[END_REF] Little is known about the effect of SGLT2 inhibitors on the broad spectrum of both inpatient and outpatient worsening heart failure events, because these were not documented in trials with these drugs in type 2 diabetes. [START_REF] Fitchett | Heart failure outcomes with empagliflozin in patients with type 2 diabetes at high cardiovascular risk: results of the EMPA-REG OUTCOME® trial[END_REF][START_REF] Rådholm | Canagliflozin and heart failure in type 2 diabetes mellitus: results from the CANVAS program[END_REF][START_REF] Kato | Effect of dapagliflozin on heart failure and mortality in type 2 diabetes mellitus[END_REF][START_REF] Perkovic | Canagliflozin and renal outcomes in type 2 diabetes and nephropathy[END_REF][START_REF] Cannon | Cardiovascular outcomes with ertugliflozin in type 2 diabetes[END_REF] The EMPEROR-Reduced (Empagliflozin Outcome Trial in Patients With Chronic Heart Failure With Reduced Ejection Fraction) trial demonstrated a benefit of SGLT2 inhibition with empagliflozin to reduce both the risk and rate of heart failure hospitalizations. [START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF] The current report expands the findings of the effects on the drug on both inpatient and outpatient worsening heart failure events.

METHODS

The design and methodology used in the EMPEROR-Reduced trial have been described in detail in previous publications. [START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF][START_REF] Packer | Evaluation of the effect of sodium-glucose co-transporter 2 inhibition with empagliflozin on morbidity and mortality of patients with chronic heart failure and a reduced ejection fraction: rationale for and design of the EMPEROR-Reduced trial[END_REF] The trial was a randomized, double-blind, parallel-group, placebo-controlled, and event-driven study. Ethics approval was obtained at each study site, and all patients provided informed consent to participate in the study; the registration identifier at ClinicalTrials.gov is NCT03057977. Data will be made available on request in adherence with transparency conventions in medical research and through requests to the corresponding author. The executive committee of EMPEROR has developed a comprehensive analysis plan and numerous prespecified analyses, which will be presented in future scientific meetings and publications. At a later point in time, the full database will be made available in adherence with the transparency policy of the sponsor (available at https://trials. boehringer-ingelheim.com/transparency_policy.html).

Study Patients

We enrolled men or women with chronic heart failure (New York Heart Association [NYHA] functional class II, III, or IV) with a left ventricular ejection fraction ≤40%, who were all receiving appropriate treatments for heart failure, including diuretics, inhibitors of the renin-angiotensin system and neprilysin, β-blockers, mineralocorticoid receptor antagonists, and when indicated, cardiac devices.

We designed the trial to preferentially enroll patients with a left ventricular ejection fraction of ≤30%. To do so, we limited the number of patients with an ejection fraction >30% by requiring them to have a hospitalization for heart failure within 12 months or high levels of NT-proBNP (N-terminal prohormone B-type natriuretic peptide; ie, ≥1000 pg/ml or ≥2500 pg/ml in those with an ejection fraction of 31% to 35% or 36% to 40%, respectively) as compared with ≥600 pg/ml in those with an ejection fraction of ≤30%. These NT-proBNP thresholds were doubled in patients with atrial fibrillation. [START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF][START_REF] Packer | Evaluation of the effect of sodium-glucose co-transporter 2 inhibition with empagliflozin on morbidity and mortality of patients with chronic heart failure and a reduced ejection fraction: rationale for and design of the EMPEROR-Reduced trial[END_REF]

Clinical Perspective

What Is New?

• Empagliflozin reduced the total number of hospitalizations for heart failure, including those that required intensive care and those that required a vasopressor or positive inotropic drug or mechanical or surgical intervention. • Patients treated with empagliflozin were less likely to require intensification of diuretics and were more likely to experience improvement (and less likely to show deterioration) in New York Heart Association functional class in the outpatient setting. • The effect of empagliflozin to reduce the combined risk of death, hospitalization for heart failure, or an emergent or urgent heart failure visit was statistically significant at 12 days after randomization.

What Are the Clinical Implications?

• The effect of empagliflozin to reduce worsening heart failure events in both the outpatient and inpatient setting reinforces its previously reported benefits to reduce the combined risk of cardiovascular death and hospitalization for heart failure and to decrease the risk of serious adverse renal events. • The combined results of EMPEROR-Reduced and the DAPA-HF trials support the use of SGLT2 inhibitors as part of standard of care for patients with heart failure and a reduced ejection fraction, with or without diabetes.

ORIGINAL RESEARCH ARTICLE

Study Assessments

Patients who fulfilled prespecified inclusion and exclusion criteria were randomized, double-blind (in a 1:1 ratio) to receive placebo or empagliflozin 10 mg daily, in addition to their usual therapy for heart failure. After randomization, all appropriate treatments for heart failure or other medical conditions could be initiated or altered at the clinical discretion of the investigator in response to changes in each patient's clinical status. Patients were assessed at study visits for major outcomes, symptoms and functional capacity related to heart failure, changes in medications used for heart failure, vital signs, biomarkers reflecting changes in the course of heart failure or the action of SGLT2 inhibitors, and adverse events; these assessments took place every 2 to 6 months, depending on the metric and the duration of follow-up. All randomized patients were followed for the occurrence of prespecified outcomes for the entire duration of the trial, regardless of whether the study participants were taking their study medications or were compliant with study procedures.

Trial End Points

We specified 3 measures as major outcomes to be evaluated in a hierarchical manner. The primary end point was the composite of adjudicated cardiovascular death or hospitalization for heart failure, analyzed as time-to-first-event. The first secondary end point was the occurrence of all adjudicated hospitalizations for heart failure (including first and recurrent events). The second secondary end point was the analysis of the slope of the change in estimated glomerular filtration rate during double-blind treatment, which was supported by an analysis of a composite of end-stage renal events. We planned to enroll ≈3600 patients who were expected to experience a target of 841 adjudicated primary end point events during a follow-up period of 6 to 36 months.

To ascertain these major outcomes, we prospectively collected information on all deaths, all hospitalizations for any reason, and all emergent and urgent outpatient events that may reflect worsening heart failure. Hospitalizations were classified as cardiovascular or noncardiovascular based on the judgment of the investigator. In contrast, a heart failure hospitalization was prospectively identified by a clinical-event committee in a blinded manner using prespecified criteria. To qualify as an adjudicated heart failure hospitalization, patients were required to have meaningful worsening of their clinical status and intensification of treatment for heart failure. The duration of the in-hospital stay was at least 12 hours; if the patient had not received intravenous medications for heart failure, the minimum stay of an adjudicated heart failure hospitalization was 24 hours. Investigators documented the clinical course of each hospital admission on a dedicated form, including the prescribing of medications and devices used to treat episodes of clinical decompensation. The committee also adjudicated the occurrence of myocardial infarction, stroke, and transient ischemic attack.

In addition to the adjudication and characterization of hospitalizations for heart failure, at each scheduled study visit, patients were prospectively asked about interval events and changes in the use of diuretics that reflected the occurrence of worsening heart failure since the last visit. Events that were considered to reflect clinical deterioration included: (1) worsening heart failure that required the use of an intravenous drug for heart failure in an emergency department; (2) worsening heart failure that required the use of an intravenous drug for heart failure in an outpatient urgent care setting; (3) intensification of daily doses of diuretics for worsening symptoms; and (4) worsening NYHA functional class. Events treated in an emergency department, urgent care setting, or during a hospital stay shorter than that required for an adjudicated event were grouped together. Physicians were not provided any specific guidance as to the degree or duration of diuretic intensification that would qualify as representing a clinically meaningful change. Ascertainment of these events and measures were prospectively collected in the case report form, and their inclusion in analyses of individual and composite end points was prespecified before the blind of the trial was broken.

Statistical Analysis

For time-to-first-event analyses, differences between the placebo and empagliflozin groups were assessed for statistical significance using a Cox proportional hazards model, with prespecified covariates of age, sex, geographical region, diabetes status at baseline, left ventricular ejection fraction, and estimated glomerular filtration rate at baseline. For these analyses, the assumption of proportional hazards was investigated, and no violations were observed. For the analysis of total (first and repeated) events, between-group differences were assessed using a joint frailty model, with cardiovascular death (for end points including heart failure events) or allcause mortality (for end points including all-cause hospitalization) as competing risks, and using covariates that were used for time-to-first-event analyses. For the analysis of changes in vital signs and laboratory measurements, treatment effects were assessed based on changes from baseline using a mixed model for repeated measures that included age and baseline estimated glomerular filtration rate as linear covariates and baseline score by visit, visit by treatment, sex, region, baseline left ventricular ejection fraction, individual last projected visit based on dates of randomization and trial closure, and baseline diabetes status as fixed effects. The analysis of changes in NT-proBNP was performed on log-transformed data. All P values reported are 2-sided, and P values less than 0.05 were considered statistically significant.

RESULTS

A total of 3730 patients at 520 centers in 20 countries were randomly assigned to placebo (n=1867) or to empagliflozin (n=1863). As previously reported, [START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF] the 2 groups comprised patients with mild, moderate, and severe heart failure, as reflected by left ventricular ejection fraction and circulating levels of NT-proBNP, and were well-balanced with respect to baseline characteristics.

Effect on Combined Risk of Death or Hospitalization

There were 512 patients who died for any reason or were hospitalized for heart failure in the placebo group and 407 such patients in the empagliflozin group,

Effect of Empagliflozin on Hospitalizations

As The effect of empagliflozin on total hospitalizations for heart failure is further described in Table I in the Data Supplement. As compared with placebo, fewer patients in the empagliflozin group were hospitalized for heart failure once (160 versus 231), hospitalized for heart failure twice (50 versus 61), and hospitalized for heart failure ≥3 times (36 versus 50). The effect of empagliflozin on first and recurrent hospitalizations for heart failure was consistent in 12 prespecified subgroups, except for a nominally significant treatment-by-race interaction (Figure II in the Data Supplement).

Empagliflozin also reduced the severity of heart failure admissions and the frequency of utilization of a broad range of interventions used for the management of decompensated heart failure. Empagliflozin decreased the time to the first heart failure hospitalization that required intensive care (HR, 0.65; 95% CI, 0.50-0.85; P=0.002) and also decreased the total number of such heart failure admissions (HR, 0.67; 95% CI, 0.50-0.90; P=0.008; Table ; Figure 1). When compared with the placebo group, the empagliflozin group experienced fewer total hospitalizations for heart failure that required only oral or intravenous diuretics (219 versus 293), fewer hospitalizations for heart failure that required intravenous vasodilators but no vasopressor or positive inotropic agents or mechanical support (36 versus 54), fewer admissions for heart failure that required a vasopressor or positive inotropic agent but no mechanical support (92 versus 152), and fewer hospitalizations for heart failure that required mechanical or surgical intervention (24 versus 34; Table I in the Data Supplement).

For hospitalizations that required a vasopressor or positive inotropic support or mechanical or surgical interventions, empagliflozin not only reduced the timeto-first-event (HR, 0.75; 95% CI, 0.57-0.98; P=0.03), but also decreased the risk of a first or recurrent event (HR, 0.64; 95% CI, 0.47-0.87; P=0.005; 2). When considering all hospitalizations for heart failure, the 2 groups were similar with respect to the median duration of each admission for heart failure (9.0 [interquartile range, 6-15] for placebo versus 8.0 days [interquartile range, 5-15] for empagliflozin).

Effect of Empagliflozin on Worsening Heart Failure Events Other Than Hospitalizations

Patients in the empagliflozin group experienced fewer emergency department or urgent care visits for worsening heart failure (Table I in the Data Supplement). Empagliflozin reduced the time to a first emergent/ urgent care for heart failure (HR, 0.66; 95% CI, 0.53-0.83; P=0.0004) and decreased the risk of total (first or recurrent) emergent/urgent care visits for heart failure (HR, 0.63; 95% CI, 0.49-0.831; P=0.0004); Table ). Many of the emergent and urgent heart failure events were soon followed by admission to a hospital on the same day, but among those that represented standalone events, there were fewer events in the empagliflozin group than in the placebo group (43 and 56 events, respectively).

When a worsening heart failure event is defined as death, hospitalization for heart failure or an emergent or urgent heart failure visit requiring intravenous treatment, empagliflozin reduced the risk of a worsening heart failure event (HR, 0.76. 95% CI, 0.67-0.87; P<0.0001; Figure 3). The benefit of empagliflozin on this end point first reached statistical significance at 12 days after randomization, and statistical significance was sustained from day 34 onwards (Figure III in the Data Supplement).

As compared with placebo, fewer patients in the empagliflozin group reported intensification of diuretics since the previous study visit (297 versus 414), and there were fewer total study visits that reported interval Additionally, at prespecified study visits, patients in the empagliflozin group had a 20% to 40% higher odds of experiencing an improvement in NYHA functional class and had a 20% to 40% lower odds of experience worsening of NYHA functional class. The effect of empagliflozin for shifts in NYHA class were apparent at every scheduled assessment throughout the first year of follow-up; the pattern of benefit was similar whether or not worst score imputations were used for patients who died or had missing data attributable to being lost to follow-up or withdrawal of consent (Figure 4). Statistical significance for both improvement and deterioration in NYHA class was apparent as early as 28 days after randomization and was sustained for 52 weeks.

When a worsening heart failure event is defined as death, hospitalization for heart failure, an emergent or urgent heart failure visit requiring intravenous treatment, diuretic intensification or deterioration in NYHA functional class, a worsening heart failure event occurred in 802 patients in the placebo group, but in only 609 patients in the empagliflozin group, corresponding to annualized rates of 48.1% and 33.8%, respectively (HR, 0.70; 95% CI, 0.63-0.78; P<0.0001) (Table ). The effect of empagliflozin on this composite of inpatient and outpatient worsening heart failure events first reached statistical significance at 12 days after randomization, and statistical significance was sustained from day 12 onwards.

Serial changes in laboratory tests and vital signs are shown in Figures V to IX in the Data Supplement.

Empagliflozin produced significant increases in hematocrit and decreases in uric acid, which were apparent as early as 4 weeks after randomization and were maintained for the first 100 weeks. Patients treated with empagliflozin experienced an early and sustained decrease in body weight, which averaged <1.0 kg. Treatment with empagliflozin was accompanied by small decreases in NT-proBNP after 4 weeks, and the effect increased in magnitude over time (Figure VIII in the Data Supplement). In contrast, the effects of empagliflozin on blood pressure seen after 4 weeks (of approximately 1-2 mm Hg) waned during prolonged treatment (Figure IX in the Data Supplement).

DISCUSSION

In the EMPEROR-Reduced trial, empagliflozin reduced the risk of cardiovascular death or hospitalization for heart failure, a benefit that was driven primarily by an effect of the drug to reduce first and recurrent admissions for worsening heart failure. [START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF] Herein we show that this benefit on disease progression is not dependent on the definition of this end point or on the identification and adjudication of events. The effect of empagliflozin was similar whether the analysis focused on cardiovascular death or all-cause mortality, and the benefit of the drug was not offset by an increase in events unrelated to heart failure. Even when the analysis includes all deaths and all hospitalizations regardless of cause, empagliflozin's effect on morbidity and mortality remained ORIGINAL RESEARCH ARTICLE clinically meaningful and highly significant. As expected, the magnitude of the benefit on hospitalization declined when the focus of the analysis broadened beyond heart failure events, decreasing from 30% for total heart failure hospitalizations to 22% for total cardiovascular hospitalizations to 15% for total hospitalizations for any reason. This decline is expected whenever hospitalizations that are not favorably influenced by a treatment are progressively added to the analysis of events in a clinical setting where only half of the hospital admissions in patients with a meaningfully reduced ejection fraction are related to worsening heart failure. The effect of empagliflozin to reduce hospitalizations for heart failure was apparent across a broad spectrum of event severity. The drug reduced admissions that were treated only with oral or intravenous diuretics as well as hospitalizations that required therapy with intravenous vasopressors or positive inotropic agents, and treatment also decreased the risk of hospitalizations for heart failure that required intensive care. The risk of the latter types of admission was reduced by 35% by treatment with the SGLT2 inhibitor. At the same time, empagliflozin also led to a 34% decrease in the risk of patients seeking emergent or urgent treatment for worsening heart failure that were treated with intravenous diuretics. A similar risk reduction in urgent outpatient worsening heart failure events was also seen with dapagliflozin in a large-scale trial in patients with heart failure and a reduced ejection fraction (DAPA-HF [Dapagliflozin on Worsening Heart Failure or Cardiovascular Death in Patients With Chronic Heart Failure]). [START_REF] Docherty | Effect of Dapagliflozin on Outpatient Worsening of Patients With Heart Failure and Reduced Ejection Fraction: a prespecified analysis of DAPA-HF[END_REF] Importantly, the lower risk of hospital admissions was not counterbalanced by a longer length of stay when patients in the empagliflozin group were hospitalized for heart failure.

In addition to these events requiring an acute intervention, treatment with empagliflozin had a meaningful effect on the risk of worsening heart failure events in the nonurgent outpatient setting. Patients in the empagliflozin group had a 20% to 40% higher odds of experiencing an improvement in NYHA functional class and had a 20% to 40% lower odds of suffering worsening of NYHA functional class. Importantly, these benefits were statistically significant at the first visit at which NYHA functional class was assessed (ie, after only 28 days after randomization). When we identified a worsening heart failure event in a manner similar to the primary end point of the DAPA-HF trial (eg, death, hospitalization for heart failure, or an emergent or urgent heart failure visit requiring intravenous treatment), a benefit of empagliflozin on this end point first reached statistical significance at 12 days after randomization.

The effect of empagliflozin to prevent a meaningful deterioration in functional capacity was paralleled by an effect of the drug to reduce the need for intensification of diuretic therapy, a benefit that was particularly apparent during prolonged treatment. Interestingly, the effect of empagliflozin to prevent intensification of diuretics was twice as great as the effect of the drug to promote decreases in the dose of diuretics. These observations are similar to those reported with dapagliflozin in heart failure and a reduced ejection fraction, where the SGLT2 inhibitor also reduced the need for intensification of diuretic therapy, but had minimal effects on the average dose of prescribed diuretics over the course of double-blind treatment. [START_REF] Jackson | Dapagliflozin and diuretic use in patients with heart failure and reduced ejection fraction in DAPA-HF[END_REF] Importantly, Shown are the odds ratios for empagliflozin vs placebo for improvement in NYHA functional class (top, shown in blue) and for deterioration in NYHA functional class (bottom, shown in red). An odds ratio of 1.3 indicates 30% higher odds of improvement, whereas an odds ratio of 0.7 indicates 30% lower odds of deterioration. Patients who died, were lost to follow-up, or declined consent were assigned worst rank, but very similar results were seen when the analysis was repeated without these worst rank assignments. P values represent the significance of the differences between the 2 treatment groups. NYHA indicates New York Heart Association. Downloaded from http://ahajournals.org by on June 29, 2022 when all outpatient and inpatient worsening events are considered together, the risk of a worsening heart failure event per 100 patient-years of follow-up was nearly 50, indicating that only half of our patients with chronic heart failure maintained clinical stability when followed for 1 year, even though our cohort comprised patients with primarily class II symptoms at the start of followup (Table ).

We observed consistent effects of empagliflozin on a comprehensive series of measures of clinical stability in 12 predefined subgroups. Importantly, concomitant treatment with mineralocorticoid receptor antagonists and neprilysin inhibitors did not attenuate the response to SGLT2 inhibition. In our original publication and in a meta-analysis of the DAPA-HF and EMPEROR-Reduced trials, we noted a somewhat lesser benefit in patients with ejection fraction of 31% to 40% and in patients with class III symptoms. [START_REF] Packer | Cardiovascular and renal outcomes with empagliflozin in heart failure[END_REF][START_REF] Zannad | SGLT2 inhibitors in patients with heart failure with reduced ejection fraction: a meta-analysis of the EMPEROR-Reduced and DAPA-HF trials[END_REF] However, it should be noted that our patients with an ejection fraction of 31% to 40% were not representative of a clinical practice cohort, in that they could be enrolled in our trial only if they had markedly increased levels of natriuretic peptides, and moreover, patients with class III symptoms represented only a quarter of the patients in the trial. Therefore, it is reassuring that when we repeated our subgroup analyses in the current paper, with a focus on total heart failure hospitalizations, the treatment-bysubgroup interaction effects for both ejection fraction and NYHA functional class were no longer apparent.

The mechanisms by which empagliflozin exerts these broad-based effects to maintain clinical stability remain to be defined. Although the early benefits of empagliflozin to prevent clinical deterioration may suggest the possibility of a hemodynamic or natriuretic effect, the magnitude of such an action appears to be modest and is typically short-lived. [START_REF] Yasui | Empagliflozin induces transient diuresis without changing long-term overall fluid balance in Japanese patients with type 2 diabetes[END_REF][START_REF] Sha | Effect of the sodium glucose co-transporter 2 inhibitor canagliflozin on plasma volume in patients with type 2 diabetes mellitus[END_REF][START_REF] Ohara | Effects of the sodium-glucose cotransporter 2 inhibitor dapagliflozin on fluid distribution: A comparison study with furosemide and tolvaptan[END_REF] Conventional diuretics typically produce immediate declines in natriuretic peptides as well as meaningful and durable changes in systolic blood pressure, generally without a change in hematocrit. In contrast, the early effect of empagliflozin on natriuretic peptides was very small in our trial, although the magnitude increased after months of therapy; in contrast, the initial decline in blood pressure waned considerably during the course of doubleblind therapy. This time-dependent pattern suggests that changes in natriuretic peptides may have been the result of (rather than the determinant) of favorable long-term effects of SGLT2 inhibitors on cardiac structure and function. Similar modest changes in natriuretic peptides and systolic blood pressure were reported with dapagliflozin in patients with heart failure and a reduced ejection fraction in 2 trials. [START_REF] Inzucchi | Dapagliflozin effects on biomarkers, symptoms, and functional status in patients with heart failure with reduced ejection fraction: the DEFINE-HF trial[END_REF][START_REF] Serenelli | Effect of dapagliflozin according to baseline systolic blood pressure in the Dapagliflozin and Prevention of Adverse Outcomes in Heart Failure trial (DAPA-HF)[END_REF] Finally, empagliflozin produced meaningful and sustained increases in hematocrit and decreases in uric acid in our study; both have been identified as important determinants of the heart failure benefits of these drugs in trials of patients with type 2 diabetes. [START_REF] Inzucchi | How does empagliflozin reduce cardiovascular mortality? Insights from a mediation analysis of the EMPA-REG OUTCOME trial[END_REF][START_REF] Li | Mediators of the effects of canagliflozin on heart failure in patients with type 2 diabetes[END_REF] Both erythrocytosis and uric acid lowering may represent biomarkers for the effect of SGLT2 inhibitors to promote energy deprivation signaling and reduce oxidative stress. [START_REF] Packer | Critical examination of mechanisms underlying the reduction in heart failure events with SGLT2 inhibitors: identification of a molecular link between their actions to stimulate erythrocytosis and to alleviate cellular stress[END_REF][START_REF] Packer | Uric acid is a biomarker of oxidative stress in the failing heart: lessons learned from trials with allopurinol and SGLT2 inhibitors[END_REF] Our findings should be considered in light of certain limitations. The median duration of follow-up was 16 months, which was shorter than many trials of neurohormonal antagonists in heart failure. Although the effects of SGLT2 inhibitors to reduce heart failure events beyond the trial duration has not been established, there was no indication that the effects of empagliflozin on worsening heart failure events waned during the course of the current trial. We prospectively assessed changes in the Kansas City Cardiomyopathy Questionnaire in our trial, but we did not include changes in this measure as a worsening heart failure event, because these are not typically recognized as such in clinical practice; furthermore, the effect of empagliflozin on this metric are being reported in a separate manuscript. Finally, outpatient events were defined by the investigator and were not reviewed or adjudicated. However, it is noteworthy that, in the current study, the process of adjudication in the current trial did not modify the size of the benefit of empagliflozin on heart failure hospitalizations (Table ).

In conclusion, in patients with heart failure and a reduced ejection fraction, empagliflozin reduced the risk of inpatient and outpatient worsening heart failure events, benefits that were seen within 12 to 28 days of initiation of treatment and were sustained for the duration of double-blind therapy. The effect of SGLT2 inhibitors to maintain clinical stability is akin to that which has been reported with β-blockers, mineralocorticoid receptor antagonists, and angiotensin receptor neprilysin inhibitors, but are seen in patients already receiving treatment with these drugs.

Figure 1 .

 1 Figure 1. Total (first and recurrent) adjudicated heart failure hospitalizations requiring admission to cardiac care unit or intensive care unit in in the placebo and empagliflozin groups. Shown are mean cumulative function curves for placebo (shown in red) and for empagliflozin (shown in blue). HR indicates hazard ratio.

Figure 2 .

 2 Figure 2. Total (first and recurrent) adjudicated hospitalization for heart failure requiring intravenous vasopressor or positive inotropic drug or mechanical or surgical intervention in the placebo and empagliflozin groups. Shown are mean cumulative function curves for placebo (shown in red) and for empagliflozin (shown in blue). HR indicates hazard ratio.

Figure 3 .

 3 Figure 3. Time-to-first-event analysis of all-cause mortality, heart failure hospitalization, or emergent/urgent care visit for worsening heart failure in the placebo and empagliflozin groups. Shown are Kaplan-Meier curves for placebo (shown in red) and for empagliflozin (shown in blue). Only emergent and urgent care visits requiring intravenous therapy are included. HR indicates hazard ratio.

Figure 4 .

 4 Figure 4. Odds of improvement or deterioration in NYHA functional class during first 52 weeks as a result of treatment with empagliflozin.Shown are the odds ratios for empagliflozin vs placebo for improvement in NYHA functional class (top, shown in blue) and for deterioration in NYHA functional class (bottom, shown in red). An odds ratio of 1.3 indicates 30% higher odds of improvement, whereas an odds ratio of 0.7 indicates 30% lower odds of deterioration. Patients who died, were lost to follow-up, or declined consent were assigned worst rank, but very similar results were seen when the analysis was repeated without these worst rank assignments. P values represent the significance of the differences between the 2 treatment groups. NYHA indicates New York Heart Association.

Table ;

 ; Fig- ure

Table . Major Outcomes and Inpatient and Outpatient Worsening Heart Failure Events

 . Downloaded from http://ahajournals.org by onJune 29, 2022

	Packer et al				Empagliflozin on Worsening Heart Failure Events
		Placebo, % (n=1867)	Empagliflozin, % (n=1863)
			Events per		Events per
			100 patient-		100 patient-	Hazard ratio
	Variable		years		years	(95% CI)	P value
	Major outcomes
	Time to all-cause mortality or cardiovascular	674 (36.1)	33.4	556 (29.8)	26.1	0.78 (0.70-0.87)	<0.0001
	hospitalization
	Time to all-cause mortality or hospitalization for any	860 (46.1)	47.3	743 (39.9)	38.4	0.81 (0.74-0.90)	<0.0001
	reason
	Time to first hospitalization for cardiovascular reason	570 (30.5)	28.3	452 (24.3)	21.2	0.75 (0.67-0.85)	<0.0001
	Time to first hospitalization for any reason	796 (42.6)	43.8	688 (36.9)	35.6	0.82 (0.74-0.90)	<0.0001
	Total (first and recurrent) number of cardiovascular	999	-	819	-	0.78 (0.67-0.91)	0.001
	hospitalizations
	Total (first and recurrent) number of hospitalizations	1570	-	1364	-	0.85 (0.75-0.95)	0.007
	for any reason
	Total hospitalizations requiring intravenous	239	-	155	-	0.67 (0.50-0.88)	0.005
	vasopressors or positive inotropic drugs
	Worsening heart failure events
	All-cause mortality or adjudicated hospitalization for	512 (27.4)	23.3	407 (21.8)	17.8	0.76 (0.67-0.87)	<0.0001
	heart failure
	Time to first adjudicated hospitalization for heart	342 (18.3)	15.5	246 (13.2)	10.7	0.69 (0.59-0.81)	<0.0001
	failure
	Time to first adjudicated hospitalizations for heart	120 (6.4)	5.0	91 (4.9)	3.8	0.75 (0.57-0.98)	0.03
	failure requiring IV vasopressor or positive inotropic
	drugs or mechanical or surgical intervention
	Time to first adjudicated hospitalization for heart	139 (7.3)	5.7	89 (4.8)	3.7	0.65 (0.50-0.85)	0.002
	failure requiring CCU/ICU care
	Total (first and recurrent) number of adjudicated	553	-	388	-	0.70 (0.58-0.85)	0.0003
	hospitalizations for heart failure
	Total adjudicated hospitalizations for heart failure	186	-	116	-	0.64 (0.47-0.87)	0.005
	requiring IV vasopressor or positive inotropic drugs or
	mechanical intervention
	Total adjudicated hospitalizations for heart failure	171	-	118	-	0.67 (0.50-0.90	0.008
	requiring CCU/ICU care
	Time to first investigator-identified hospitalization for	429 (23.0)	20.1	317 (17.0)	14.2	0.71 (0.61-0.82)	<0.0001
	heart failure
	Time to first emergency or urgent care visit for	185 (9.9)	7.9	126 (6.8)	5.3	0.66 (0.53-0.83)	0.0004
	worsening heart failure requiring IV therapy
	Total (first and recurrent) emergency or urgent care	261	-	184	-	0.63 (0.49-0.81)	0.0004
	visits for worsening heart failure requiring IV therapy
	Time to first study visit that reported interval	414 (22.2)	19.4	297 (15.9)	13.2	0.67 (0.58-0.78)	<0.0001
	intensification of diuretics
	Total (first and recurrent) study visits that reported	564	-	380	-	0.67 (0.57-0.78)	<0.0001
	interval intensification of diuretics
	Time to all-cause mortality, hospitalization for heart	519 (27.8)	23.7	415 (22.3)	18.2	0.76 (0.67-0.87)	<0.0001
	failure or emergent or urgent care for heart failure
	requiring IV therapy
	Time to all-cause mortality, hospitalization for heart	727 (38.9)	36.7	555 (29.8)	25.9	0.70 (0.63-0.78)	<0.0001
	failure, emergent or urgent care for heart failure
	requiring IV therapy, or diuretic intensification
	Time to all-cause mortality, hospitalization for heart	802 (43.0)	48.1	609 (32.7)	33.8	0.70 (0.63-0.78)	<0.0001
	failure, emergent or urgent care for heart failure
	requiring IV therapy, diuretic intensification, or
	deterioration of NYHA functional class
	January 26, 2021

Circulation. 2021;143:326-336. DOI: 10.1161/CIRCULATIONAHA.120.051783 330 ORIGINAL RESEARCH ARTICLE End points that include diuretic intensification were post hoc. CCU indicates cardiac care unit; ICU, intensive care unit; IV, intravenous; and NYHA, New York Heart Association. Circulation. 2021;143:326-336. DOI: 10.1161/CIRCULATIONAHA.120.051783 January 26, 2021 331 ORIGINAL RESEARCH ARTICLE diuretic intensification in the empagliflozin group (380 versus 564) (Table; Table I in the Data Supplement). Conversely, the empagliflozin group had somewhat more patients (281 versus 246) and more study visits (334 versus 291) where the dose of diuretics was reported to have been reduced. Empagliflozin decreased the time to the first study visit that reported diuretic intensification (HR, 0.67; 95% CI, 0.58-0.78; P<0.0001) as well as the total number of study visits that reported intensification of diuretics since the previous visit (HR, 0.67; 95% CI, 0.57-0.78; P<0.0001; Table; Figure IV in the Data Supplement).

Downloaded from http://ahajournals.org by onJune 29, 2022

January 26, 2021 Circulation. 2021;143:326-336. DOI: 10.1161/CIRCULATIONAHA.120.051783

Sources of Funding

Supplemental Materials

Data Supplement Figures I-IX Data Supplement Table I